Citation
Landmine detection by scatter radiation radiography

Material Information

Title:
Landmine detection by scatter radiation radiography
Series Title:
Landmine detection by scatter radiation radiography
Creator:
Campbell, John G.,
Place of Publication:
Gainesville FL
Publisher:
University of Florida
Publication Date:

Subjects

Subjects / Keywords:
Aluminum ( jstor )
Crystals ( jstor )
Energy ( jstor )
Fluence ( jstor )
Image filters ( jstor )
Phosphors ( jstor )
Photons ( jstor )
Soils ( jstor )
Solar X rays ( jstor )
X ray spectrum ( jstor )

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright John G. Campbell. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
021065165 ( alephbibnum )
17886133 ( oclc )

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Full Text














LANDMINE DETECTION BY
SCATTER RADIATION RADIOGRAPHY







by

JOHN G. CAMPBELL


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY




UNIVERSITY OF FLORIDA


1987

















ACKNOWLEDGMENTS


A number of individuals and organizations have played

an important role in my research. First and foremost, I

thank my wife, Becky, for her support, understanding, and

patience.

Dr. Alan Jacobs, who was my research advisor, was

always willing to help, whether the assistance required

discussion of new ideas or manual labor. The basic concept

of the project, using imaging techniques for mine detection,

was his. The generous amount of time he took from a very

busy schedule is greatly appreciated. I thank the other

members of my committee, Dr. Edward Carroll, Dr. Edward

Dugan, Dr. John Staudhammer, and Dr. Mark Yang, for their

time and guidance.

Two graduate students, who worked on other aspects of

the research problem, also contributed to my efforts.

Captain Dale Moss designed the soil box positioning system

and its computer control. Linda Hipp was an equal partner

in the assembly of the positioning system and spent many

long hours performing measurements.

I thank Bill Coughlin of the Radiation Control

Department for the loan of an ionization chamber for the

exposure rate transmission experiments, and Harvey Norton,










of the same organization, for the use of a calibration set

of radionuclide sources. Dr. William Ellis provided the

filter sets used in the measurements.

The electronics skills and untiring efforts of Ken

Fawcett were solely responsible for keeping an old x-ray

machine in operation for the measurements. His expertise

was crucial to this research.

I thank Lois Carroll, who typed this manuscript, for

her professional and always cheerful assistance.

Gary Melocik of Bicron Corporation provided details on

the composition and geometry of the NaI(Tl) detector used in

the experiment. Dr. William Frank, 3M Corporation, provided

information on the composition of the Trimax 12 rare earth

intensifying screens. Without their assistance, the detec-

tor response calculations could not have been performed.

Andrew Lickly of Applied Reasoning Corporation, and

David Hampton of Seattle Telecom and Data, Inc., ran bench-

mark versions of the Monte Carlo code on their accelerator

boards. Two graduate students of the Nuclear Engineering

Sciences Department also helped test the code. Samer Kahook

ran a benchmark on the IBM PC/AT. Kiratadas Kutikkad ran a

mine detection problem on the Cray X-MP/48 using the MCNP

code.

I thank the United States Army for allowing me the op-

portunity to continue my education and for financial support

during the research effort. The measurements portion of

this work was supported by the U.S. Army Belvoir Research


iii










and Development Center under contract, DAAK 70-86-K-0016.

thank those individuals associated with the administration

of the contract for their active interest in the research.

Of those individuals, I particularly thank Edward Ostrosky

for his participation in the early measurements, and Dr.

Robert Moler for his reviews of the progress of the work.
















TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS .. . . . . . . . ii

LIST OF TABLES. .. . . . . . . .. xi

LIST OF FIGURES . . . . . . ... xv

ABSTRACT. . . . . . ... . . . xxxi

CHAPTERS

I INTRODUCTION . . . . . . . 1

II BACKSCATTER MINE DETECTION AND IMAGING . 4

Previous Uses of Scattered Radiation . 5
Backscattered Photon Mine Detection. . 8
Fluorescence Emission . . . .. 8
Rayleigh Scattering . . . . .. 9
Compton Scattering .... .. . 10
Backscatter Radiation Radiography. . . 13
Genesis of Current Research Effort. . 13
Improvements on Previous X-Ray
Backscatter Efforts . . . . .. 17
Research Goals. . . . . . . 17

III EQUIPMENT AND MATERIALS. . . . . 20

Equipment. . . . . . . . . 20
X-Ray Source. . . . . . . 20
Soil Box and Positioning System . . 27
Detector and Related Electronics. . 30
Computer Control System . . . . 36
Materials. . . . . . . . . 38
Soils . . . . . . . . 38
Nonmetallic Antitank Mine Model . . 39
Materials Tests . . . . . . 46

IV RADIATION TRANSPORT. . . . . . 52

Photon Interactions. . . ... . .. 52
Coherent Scattering . . . . . 52
Incoherent Scattering . . . . 59
Photoelectric Effect. . . . . 67
Mass Interaction Coefficients . . 71










TABLE OF CONTENTS continued


CHAPTERS Page

Single Scatter Model . . . . . 73
Computation Scheme. . . . . . 73
Interaction Modeling. . . . . 78
Monte Carlo Model. . .. . . . .. 78
Problem Parameters and Data . . . 80
Random Number Generators. . . . 81
Computation Scheme. . . . . . 83
Modelling Scattering Interactions . 87
Russian Roulette. . . . . . 89
Code Output . . . . . . . 89
Validation of the Monte Carlo Codes. . 90
Number and Energy Albedo Calculations 91
Energy Spectra Comparisons. . . . 91
Comparison with Buried Mine
Calculations. . . . . . . 91
Testing the Scattering Routines . . 99

V X-RAY SOURCE . . . . . . . 105

Kramers' Formula Method. . . . . 105
Kramers' Formula. . . . . . 106
Time Dependent Accelerating Potential 107
Characteristic X-Ray Production. . 108
Attenuation by Materials in the Beam
Path. .... . . . . 109
Anode Self-Attenuation. .. . . . 111
Effects Neglected in Model. . . . 116
General Features of the Calculated
Spectra . . . . . . . . 117
Testing the Modified Kramers' Formula
Model. . . . . . . . . 119
Exposure Rate Transmission
Measurements . . . . .. 119
Comparisons with Published Spectra. . 122
Other Methods to Determine X-Ray Spectra 126
Measurement . . . . . . 126
Monte Carlo Calculation . . . 130
Laplace Transform Pair Method ... 130

VI DETECTOR RESPONSE. . . . . . . 139

Plane Detector Code. . . . . . 141
Assumptions in the Plane Detector
Response Calculation . . . . . 144
Energy Deposition. . . . . . . 146
Case of Zero Degree Incidence . . 146
Case of Large Angle Incidence . . 149
Counts Per Incident Photon . . . . 151










TABLE OF CONTENTS continued


CHAPTERS


Discriminator Setting Corresponding
to 0 MeV. . . . . .. . .
Discriminator Setting Corresponding
to Energies Greater Than 0 MeV. . .
Validation of the Plane Detector Response
Calculations . . . . . . .
Iodine Escape Ratio . . . .
Measured Energy Spectra . . . .
Shield and Edge Effects. . . . .
Calculation of the Correction Factor.
Results of the Correction Factor
Calculation . . . . . .

MINE DETECTION MECHANISMS. . . . .

Backscattered Photon Signal Differences.


Fluence . . . . . .
Energy Fluence. . . .
Spatial Distribution. . .
Angular Distribution. . .
Energy Spectra. . . . .
Edge Effects. . . . .
Conclusions Based on Signal
Differences . . .
Irradiation Geometry and Optimum
Height of Detector. . . .
Angle of Incidence. . . .
Raster Gap Size . . . .
Detector Collimator Length .
Detector Panel Dimensions .
Segmented Detector Geometry
Source Beam Collimation . .
Source Energy Optimization. .
Depth of Burial . . . .
Polyenergetic Sources . .


Conclusions Based on Optimizat


Page


151

153

157
157
163
163
163

166

169

169
170
176
182
186
194
198


. . . 204
Energy. 208
. . . 208


. . .
. . .
. . .
. . .





ions. .


VIII APPLICATION TO IMAGING . . . .

Comparisons with Measurements. . .
Spatial Distribution of Detector
Response . . . . .
Detector Response with Mine Present
Edge Effects. . . . . . .
Energy Window Detector. . . .
Environmental Parameters . . . .
Height Sensitivity. . . .
Soil Density Variation. . . .
Soil Moisture Content . . .
Inhomogeneities . . . . .


209
216
222
223
227
229
232
241
244
246

248

249

249
251
258
262
266
266
272
277
283


vii


VII


















TABLE OF CONTENTS continued


CHAPTERS


Imaging. . . . . . . . .
Monte Carlo Generated Images . .
Measured Images . . . . .
Dual Energy Subtraction Technique .
Power Requirements . . . . .
Variables . . . . .
Fraction of Source Photons Reaching


the Detector. . . . .
Source Flux . . . .
Pixel Dwell Time. . . .
Calculation Technique . .
Power Calculations. . .


IX CONCLUSIONS. . . . . .


APPENDICES


CHARACTERISTICS OF LANDMINES .

Mine Classification. . . .
Metallic or Nonmetallic .
Antitank or Antipersonnel .
Conventional or Scatterable
Surface or Buried . . .
Fuzing Type . . . .
Employment of Landmines . .


HISTORICAL EXAMPLES OF MINE WARFARE .

Mine Development . . . . . .
Forerunners of Modern Mines . .
Mines of World War II . . . .
Countermine Warfare in World War II .
Mine Employment. . . . . . .
North Africa. . . . . . .
Eastern Front . . . . . .
Korea and Vietnam . . . . .

OTHER MINE DETECTION AND NEUTRALIZATION
METHODS. . . . . . . . .


Detector Technololgies . . .
General Considerations. . .
Microwaves. . . . . .
Neutrons. . . . .
Magnetic Resonance Techniques
Trace Gases . . . .
Animals . . . . .
Biochemical Methods . . .
Infrared Methods. . . .


viii


Page


287
287
296
342
347
348

350
350
353
353
357

363


368

368
371
372
372
373
375
376

378

378
378
379
380
380
380
382
383


385

385
385
386
388
390
391
392
392
393










oo

.o o o . .
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. . . .

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. .o o .


*


.*



















TABLE OF CONTENTS continued

APPENDICES

Neutralization . . .. . . .
Mechanical Systems. . . . . .
Explosive Methods . . . .
Magnetic Signature Duplication. . .

D X-RAY TRANSMISSION MEASUREMENTS. . . .

E GADOLINIUM OXYSULFIDE DETECTOR . . .

Detector Description . . . . . .
Detector Design . . . . . .
Screen Composition. . . . . .
Detector Response Matrix Calculation . .
Calculation Technique . . . . .
General Results of Calculations . .
Description of the Detector Response
Matrix . . . . .. . . .
Perpendicular Incidence . . . .
45 Degree Incidence . ... . .
75 Degree Incidence . . . . .
Comparison with Published Results . .
Response Matrix Relationship to
Detector Electronics . . . . .
Shortcomings of the Detector . . .
Sensitivity . . . . .
Fluorescence Decay Constant . . .
Corrective Actions . . ......
Comparison of Measured and Calculated
Responses . . . . . . .
Calculation Technique . . . .
Measurements. . . . . . . .

F X-RAY SPECTRA USED IN MEASUREMENTS . .


COMPUTER CODES . . . . .

Computer Hardware. . . . .
Personal Computers and Monte
Carlo Calculations. . . .
Computer Selection. . . .
Comparison with Cray X-MP/48
Supercomputer . . . .
Computer Software. . . . .
Computer Languages. . . .
Radiation Transport Codes .
X-Ray Spectra Codes . . .
Detector Response Codes . .
Imaging Codes . . . .
Utility Codes . . . .
Photon Interaction Data Files
Commercial Software . . .


Page


394
394
395
396

397

414

414
414
417
422
422
425

428
429
436
444
449

450
455
456
460
463

464
464
465

470

484

484

484
485

487
489
489
489
491
492
493
494
496
497




























TABLE OF CONTENTS continued


APPENDICES Page

H MONTE CARLO TECHNIQUES . . . . . 501

Angular Scattering Distributions . . 501
Momentum Transfer Variable. . . . 501
Incoherent Scattering . . .. .. 502
Sampling the Klein-Nishina
Distribution. . . ... . . .. 504
Coherent Scattering . . . . 506
Random Number Generators . . .. . 509
MCPHOT.PAS Generator . . .. 509
MCPHOT.P Generator . . . . 509
Fluorescent Emission . . . . 510
Application to Polyenergetic Sources . 512
Available Methods ........ 512
Application of the Fit Method .. .. 513

LIST OF REFERENCES. . . . . . . . . 516

BIOGRAPHICAL SKETCH . . . . . . . . 527
















LIST OF TABLES


TABLES Title Page

III.1 Geometry of the Sodium Iodide Detector
and Shield. . . . . . . . 32

111.2 Sources Used in Determining Lower Level
Discriminator Setting . . . .. 35

111.3 Composition of Soil Types. . . . ... 40

111.4 Characteristics of Common Warsaw Pact
Nonmetallic Antitank Mines. . . . 42

111.5 Ratios of the Linear Interaction
Coefficients of Sucrose to TNT. . .. 47

IV.1 Energy Mesh Structure for Mass
Interaction Coefficients. . . . 74

IV.2 Energy at Which Photoelectric and
Incoherent Scattering Mass Interaction
Coefficients Are Equal. . . . . 76

IV.3 Comparison of Number and Energy Albedo
Calculations for Iron . . . ... 92

IV.4 Comparison of Number Albedo
Calculations for Concrete . . . 93

IV.5 Comparison of Energy Albedo
Calculations for Concrete . . . 94

IV.6 Comparison of Number Albedo
Calculations for FTB Soil and
Buried DNB Mines. . . . . . 101

V.1 Energies of Tungsten K Characteristic
X Rays. . . ...... . . 110

V.2 Comparison of Exit Path Lengths from
Tungsten Anodes . . .. . . 115

VI.1 Energies of Iodine Fluorescent Emission
X Rays Used in the Detector Response
Calculations . . . . . 143










LIST OF TABLES continued


TABLES Page

VII.1 Comparison of the Linear Relationship
Between the Ratio of Number to Energy
Albedo and Source Energy at
Perpendicular Incidence . . . . 180

VII.2 Mine to Soil Response Ratios at Selected
Beam Angles of Incidence. . . . 211

VII.3 Front to Back Panel Fluence Ratios of
the Collimated Detector for 100 keV
Photon Beams Incident at 60 Degrees . 214

VII.4 Results of Calculations for the Geometric
Parameters of the Collimated Fluence
Detector. . . . . . . . 220

VII.5 Mine to Soil Fluence Ratio Dependence on
Panel Width and Raster Gap Size for an
Uncollimated Detector .. . . . 226

VII.6 Optimum Source Energies for the Uncolli-
mated Fluence Detector. . . . . 235

VII.7 Comparison of the Segmented and Unseg-
mented Uncollimated Fluence Detectors 238

VII.8 Mine to Soil Fluence Ratio at Selected
Depths of Burial of the TST Mine. . 242

VII.9 Mine to Soil Fluence Ratios Versus Depth
of Mine Burial for the Energy Window
Detector with Source Energy of 100 keV. 245

VIII.1 Parameters for Spatial Distribution
Comparison. . . . . . . . 250

VIII.2 Comparison of Calculated and Measured Mine
to Soil Detector Response/Ratio with the
TST Mine at 0.0 cm . . . . . 257

VIII.3 Energy Window Measurements for the TST
Mine at 2.54 cm Depth of Burial . . 265

VIII.4 Mine to Soil Fluence Ratio from the
Collimated Detector with Recently
Buried Mines. . . . . . . 276

VIII.5 Mine to Soil Fluence Ratio from the
Energy Window Detector with Recently
Buried Mines. . . . . . . 278


xii









LIST OF TABLES continued


TABLES

VIII.6 Mine to Soil Fluence Ratio of the
Uncollimated Fluence Detector for
Three Water Contents of HTL Soil
with the TST Mine at 2.5 cm Depth
of Burial . . . . . . . .

VIII.7 Mine to Soil Fluence Ratio of the
Collimated Fluence Detector for
Two Water Contents of HTL Soil
with the TST Mine at 2.5 cm Depth
of Burial . . . . . . . .


Page


280





281


VIII.8 Mine. to Soil Fluence Ratio of the
Energy Window Detector for Three
Water Contents of HTL Soil with
the TST Mine at 2.5 cm Depth of
Burial. . . . . .. . . 282

VIII.9 Object to Soil Fluence Ratio from
the Collimated Detector for
Selected Inhomogeneities. . . . 286

VIII.10 Object to Soil Fluence Ratio from
the Energy Window Detector for
Selected Inhomogeneities. . . . 288

VIII.11 Operational Requirements for a Vehicle-
Mounted Antitank Mine Detection
System. . . . . . . . ... 349

VIII.12 Photon Output of the GE Maxitron 300
X-Ray Therapy Unit. . . . . . 352

VIII.13 Imaging Quantities Necessary to Fulfill
Operational Requirements. . . . 354

VIII.14 Power and Signal to Noise Ratio Require-
ments for Imaging and Mine Detection
with the Uncollimated Detector . 358

VIII.15 Power and Signal to Noise Ratio Require-
ments for Imaging and Mine Detection
with the Collimated Detector. . . 362


E.1 Gadolinium Oxysulfide Screen Model . .


E.2


423


Energies of Fluorescent Photons Used
in the DETECT.PAS Code. . . . .


426


466


E.3 Calculated Ratios of Radiation Field
Quantities, 33Ba to 137Cs. . . .


xiii









LIST OF TABLES continued


TABLES Page

G.1 Benchmarks for Monte Carlo Transport
Codes. . . . . . . . . 488

G.2 Photon Interaction Data Files. . . . 498

H.1 Fluorescent Emission Probabilities . . 511


xiv

















LIST OF FIGURES

Title


FIGURES


Page


II.1 Conceptual large area backscatter detector
system. . . . ... . . . . 18

III.1 X-ray source, soil box and positioning
system and detector . . . ... 22

111.2 Detector electronics, computer and x-ray
source console. . . . . . 24

111.3 Lead shield for tube head and detector . 29

111.4 Geometry of sodium iodide detector and
shield. . . . . . . . 31

III.5 Components of the counting system. . . 37

III.6 Soil mass attenuation coefficients . . 41

III.7 TST mine used in measurements. . . . 45

111.8 Transmission comparison for TNT and
substitute. . . . . . . .. 49

111.9 Transmission comparison for NSL and
local soil. . . . . . . . 51

IV.1 Atomic form factor versus momentum
transfer variable. . . . . . 55

IV.2 Solid angle differential coherent
scattering cross section versus
scattering angle. . . . . . 57

IV.3 Coherent cross section versus photon
energy. . . . .. . . . ...... 58

IV.4 Fractional energy of Compton scattered
photons versus incident photon energy 60

IV.5 Solid angle differential Klein-Nishina
cross section versus scattering angle 62










LIST OF FIGURES continued


FIGURES Page

IV.6 Incoherent scattering function versus
momentum transfer variable. . . . 64

IV.7 Comparison of the solid angle differential
Klein-Nishina and incoherent scattering
cross sections. . . . .. .. 65

IV.8 Incoherent scattering cross section versus
photon energy . . . . . . 66

IV.9 Photoelectric interaction cross section
versus photon energy. . . . . 69

IV.10 Probability of K shell fluorescence
versus atomic number. ... . . .. 70

IV.11 Energies of K fluorescent photons versus
atomic number . . . . . . 72

IV.12 Mass interaction coefficients of aluminum
versus photon energy. . . . . 75

IV.13 Boundaries and materials of Monte Carlo
calculations. . . . . . . 84

IV.14 Number albedo versus energy for concrete 95

IV.15 Backscattered energy spectrum, 0.200 MeV
on aluminum . . . . . ... 96

IV.16 Backscattered energy spectrum, 0.6616 MeV
on aluminum . . . . . . . 97

IV.17 Backscattered energy spectrum, 0.6616 MeV
on iron . . . . . . . . 98

IV.18 Comparison of calculations of the solid
angle differential coherent cross
section . . ... . . .. 101

IV.19 Comparison of calculations of the solid
angle differential incoherent cross
section . . . . . . . . 102

V.1 Transmission curve without anode self-
attenuation . . . . . . . 112

V.2 Typical x-ray spectrum calculation . . 118


xvi










LIST OF FIGURES continued


FIGURES


VI.3 Plane detector response, discrimination
less than 0.03317 MeV . . . ..

VI.4 Plane detector response, discrimination
greater than 0.03317 MeV .. . ..

VI.5 Iodine escape peak ratio versus energy .

VI.6 Measured and calculated NaI(Tl) spectra.

VI.7 Plane detector response . . . .


V.3 Heel effect displayed by spectra . .

V.4 Heel effect displayed by half value
thickness . . . . . . .

V.5 Typical transmission curve comparison.

V.6 Spectrum comparison with Epp and Weiss
at 80 kVp . . . . . .

V.7 Spectrum comparison with Epp and Weiss
at 105 kVp. . . . . . .

V.8 Spectrum comparison with Fewell and
Shuping at 70 kVp . . . .

V.9 Spectrum comparison with Fewell and
Shuping at 80 kVp . . . .

V.10 Spectrum comparison with Fewell and
Shuping at 90 kVp . . . .

V.11 Archer-Wagner method fit to measured
transmission data . . . .

V.12 Comparison of modified Kramers' method
and the Archer-Wagner method at
80 kVp. . . . . . . .

V.13 Comparison of modified Kramers' method
and the Archer-Wagner method at
150 kVp . . . . . .

VI.1 Fraction of incident energy absorbed
perpendicular incidence . . .

VI.2 Fraction of incident energy absorbed
75 degree incidence . . . .


S 152


S 156

S 158

S 164

S 167


xvii


Page

. 120


. 121

. 123


. 124


. 125


. 127


. 128


. 129


. 134



. 136



. 137


. 147


. 150










LIST OF FIGURES continued


FIGURES

VI.8 Detector response with edge and shield
correction. . . . . . . .

VII.1 Number albedos versus energy for HTL soil
and two TST mine cases. . . . .

VII.2 Number albedo ratios versus energy for the
TST mine at 0.0 cm in three soils . .

VII.3 Number albedo ratios versus energy for the
TST mine at 2.5 cm in three soils . .


VII.4 Energy albedos versus energy for HTL soil
and two TST mine cases. . . . .

VII.5 Multiple scatter fraction versus energy
for HTL soil and two TST mine cases

VII.6 Ratio of number to energy albedo for HTL
soil and two TST mine cases . . .

VII.7 Spatial distribution of backscattered
fluence from 100 keV photons per-
pendicularly incident on HTL soil .

VII.8 Spatial distribution of backscattered
fluence from 100 keV photons per-
pendicularly on the center of the TST
mine at 0.0 cm. . . . . . .

VII.9 Spatial distribution of mine to soil
ratio of backscattered fluence from
perpendicularly incident 100 keV
photons . . . . . . . .


Page


168


172


174


175


S 177


S 179


S 181



183




184




185


VII.10 Spatial distribution of the single
scattered mine to soil ratio from
perpendicularly incident 100 keV
photons . . . . . . .

VII.11 Angular distribution of backscattered
fluence from 100 keV photons perpen-
dicularly incident on HTL soil and
two TST mine cases. . . . . .

VII.12 Angular distribution of the multiple
scattered fluence from 100 keV photons
perpendicularly incident on HTL soil
and two TST mine cases. . . . .


xviii


187




188




189










LIST OF FIGURES continued


FIGURES Page

VII.13 Mine to soil fluence ratio versus
collimator acceptance angle for 100
keV photons perpendicularly incident
on the TST mine at 0.0 cm in HTL soil 191

VII.14 Mine to soil fluence ratio versus
collimator acceptance angle for 100
keV photons perpendicularly incident
on the TST mine at 2.5 cm in HTL soil 192

VII.15 Multiple scatter fraction versus colli-
mator acceptance angle for 100 keV
photons perpendicularly incident on
the TST mine at 0.0 cm in HTL soil. . 193

VII.16 Differential energy spectra for 100 keV
photons perpendicularly incident on HTL
soil and two TST mine cases . . . 195

VII.17 Ratios of mine and soil integral energy
spectra for two TST mine cases in HTL
soil. . . . . ... .. . . .. 197

VII.18 Edge effect geometries . . . . . 199

VII.19 Spatial distribution of the single scat-
tered fluence from a 100 keV photon
beam perpendicularly incident on the
inside edge of the TST mine . . . 201

VII.20 Spatial distribution of the single scat-
tered mine to soil fluence response
ratio for a 100 keV photon beam perpen-
dicularly incident on the inside edge
of the TST mine . . . . . . 202

VII.21 Spatial distribution of the single scat-
tered mine to soil fluence response
ratio for a 100 keV photon beam per-
pendicularly incident on the outside
edge of the TST mine . . . . 203

VII.22 NaI(Tl) detector response and fluence
response versus source beam energy. . 206

VII.23 Ratio of NaI(Tl) detector response to
fluence response as a function of
source energy . . . . . . 207


xix









LIST OF FIGURES continued


FIGURES Page

VII.24 Ratios of integral energy spectra for
100 keV photons incident on the TST
mine at 2.5 cm in NSL soil for the
cases of 0 to 60 degree incidence . 212

VII.25 Spatial distribution of the fluence
response from a 100 keV beam inci-
dent at 60 degrees on the TST mine
at 2.5 cm in NSL soil . . . . 215

VII.26 Fluence response versus distance from
beam axis for 100 keV photons perpen-
dicularly incident on the TST mine at
2.5 cm in NSL soil. . . . . . 217

VII.27 Relationship between the raster gap size,
the length of the collimator, and the
spacing of the first collimator element
required to exclude single scattered
Photons from the detector . . . 224

VII.28 Geometry of the segmented fluence
detector. . . . . . . . 228

VII.29 Fluence response ratio matrices for the
segmented detector for perpendicularly
incident 150 keV photon beams on the
TST mine at 2.5 cm in HTL soil. . . 231

VII.30 Source energy optimization curve for the
uncollimated fluence detector with mine
depth of burial of 5 cm in NSL soil . 234

VII.31 Source energy optimization curve for the
segmented fluence detector with mine
depth of burial of 2.5 cm in NSL soil 237

VII.32 Source energy optimization curve for the
energy window detector with mine
depth of burial of 5 cm in NSL soil . 240

VIII.1 Calculated and measured spatial distribu-
tion of detector response from back-
scatter from sandy soil at 100 kVp. . 252

VIII.2 Calculated and measured spatial distribu-
tion of detector response from back-
scatter from sandy soil at 150 kVp. . 253










LIST OF FIGURES continued


Page


FIGURES


VIII.3 Calculated and measured spatial distribu-
tion of detector response from back-
scatter from sandy soil at 200 kVp..

VIII.4 Comparison of the number albedos of
sucrose and TNT . . . . . .

VIII.5 Three dimensional image diagram of
measured detector response for the
lucite annulus experiment . . .

VIII.6 Two dimensional image diagram of
measured detector response for the
lucite annulus experiment . . .

VIII.7 Three dimensional image diagram of
measured detector response for the
steel annulus experiment. . . .

VIII.8 Two dimensional image diagram of
measured detector response for the
steel annulus experiment. . . .

VIII.9 Fluence response as a function of
height above the soil surface for
selected panel widths of the
uncollimated detector . . . .

VIII.10 Fluence response as a function of
height above the soil surface for
selected acceptance angles of the
collimated detector . . . . .

VIII.11 Fluence response as a function of
height above the soil surface for
the energy window detector. . . .

VIII.12 Ratio of fluence responses for two
densities of HTL soil with the TST
mine at selected depths of burial
as a function of source energy for
the uncollimated detector . . .


S 254


S 256



S 260



S 261



S 263



S 264


268




270



273





274


VIII.13 Object to soil fluence response ratio
for selected materials as a function
of source energy for the uncolli-
mated detector. . . . . . .


284


xxi









LIST OF FIGURES continued


FIGURES

VIII.14 Monte Carlo generated image for the TST
mine buried flush to an NSL soil
surface for the uncollimated fluence
detector. . . . . . . .

VIII.15 Monte Carlo generated image for the TST
mine buried flush to an HTL soil
surface for the uncollimated fluence
detector . . . . .

VIII.16 Monte Carlo generated image for the TST
mine buried flush to an MCL soil
surface for the uncollimated fluence
detector. . . . . . . .


Page




S 290




S 291


292


VIII.17 Monte Carlo generated image for the TST
at 2.5 cm depth of burial in NSL soil
for the uncollimated fluence detector .

VIII.18 Low pass filtered Monte Carlo image for
the TST mine at 2.5 cm depth of burial
in NSL soil for the uncollimated
fluence detector. . . ... .

VIII.19 Monte Carlo generated image for the TST
mine at 5.0 cm depth of burial in NSL
soil for the uncollimated fluence
detector. . . . . . .. ..

VIII.20 Monte Carlo generated image for a simu-
lated water puddle on HTL soil with
20% water content by weight for the
uncollimated fluence detector . .

VIII.21 Monte Carlo generated image for an iron
disk buried flush to the surface of
NSL soil for the uncollimated fluence
detector. . . . .. . . .

VIII.22 Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine buried flush to
the soil surface. . . . . . .

VIII.23 Two dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine buried flush to
the soil surface. . . . . . .


xxii


294




295




297




298


299


301





302










LIST OF FIGURES continued


FIGURES Page

VIII.24 Three dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine buried flush to
the soil surface. . . . . . 303

VIII.25 Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm . . . . . 304

VIII.26 Low pass filtered image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm . . . . . 306

VIII.27 Three dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm . . . . . 307

VIII.28 Low pass filtered image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm . . . . . 308

VIII.29 Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine laid on the soil
surface . . . . . . . . 309

VIII.30 Two dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine laid on the soil
surface . . . . . . . . 310

VIII.31 Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm . . . . . 311


xxiii










LIST OF FIGURES continued


FIGURES

VIII.32 Two dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm . . . . .

VIII.33 Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 7.62 cm . . . . . .

VIII.34 Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine laid on the soil
surface . . . . . . . .

VIII.35 Two dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine laid on the soil
surface . . . . . . . .

VIII.36 Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array . . . . . . . . .

VIII.37 Three dimensional image diagram of the
measured uncollimated detector response
to a 150 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array . . . . . . . .

VIII.38 Three dimensional image diagram of the
measured uncollimated detector response
to a 150 kVp source beam filtered by
Sn for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array . . . . . . . . .

VIII.39 Three dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Sn for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array . . . . . . . .


xxiv


Page


312





314





315


316


318






319






321






322










LIST OF FIGURES continued


FIGURES

VIII.40 Three dimensional image diagram of the
measured collimated detector response
to a 150 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array . . . . . . . . .

VIII.41 Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array . . . . . . . . .

VIII.42 Irregular soil surface used in measure-
ments . . . . . . .

VIII.43 Three dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface . . . . . . . .

VIII.44 Two dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface . . . . . . . .


VIII.45 Three dimensional image diagram of the
measured collimated detector response
to a 100 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface . . . . . . . .

VIII.46 Three dimensional image diagram of the
*measured collimated detector response
to a 150 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface . . . . . . . .

VIII.47 Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface . . . . . . . .


XXV


Page


323






324


326


327






328


330






331






332










LIST OF FIGURES continued


FIGURES Page

VIII.48 Two dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface . . . . . . . . 333

VIII.49 Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for a wood disk buried flush to the
soil surface. . . . . . . 334

VIII.50 Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for a wood disk buried flush to the
soil surface. . . . . . . 335

VIII.51 Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for a steel disk buried flush to the
soil surface. . . . . . . 336

VIII.52 Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for a steel disk buried flush to the
soil surface. . . . . . . 337

VIII.53 Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for water contained in a thin plastic
container buried flush to the soil
surface . . . . . . . . 339

VIII.54 Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for water contained in a thin
plastic container buried flush to the
soil surface. . . . . . . 340

VIII.55 Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for a hole filled with loose soil. 341


xxvi










LIST OF FIGURES continued


FIGURES Page

VIII.56 Failure of the dual energy subtraction
technique . . . . ... . 345

VIII.57 Two dimensional image diagram of the
measured uncollimated detector
response to a 100 kVp source beam
filtered by Pb for the TST mine at
a depth of burial of 2.54 cm with
irregular soil surface. . . . . 346

A.1 Typical antitank mine. . . . . . 370

D.1 X-ray fluence spectrum, 80 kVp,
2.00 mm Al. . . . . . . . 398

D.2 Measured and calculated transmission of
exposure rate, 80 kVp, 2.00 mm Al.. .. 399

D.3 X-ray fluence spectrum, 80 kVp,
2.24 mm Al. . . . . . . . 400

D.4 Measured and calculated transmission of
exposure rate, 80 kVp, 2.24 mm Al . 401

D.5 X-ray fluence spectrum, 100 kVp,
2.00 mm Al. . . . . . . .. 402

D.6 Measured and calculated transmission
of exposure rate, 100 kVp, 2.00 mm Al 403

D.7 X-ray fluence spectrum, 100 kVp,
2.24 mm Al. . . . . . . . 404

D.8 Measured and calculated transmission of
exposure rate, 100 kVp, 2.24 mm Al. . 405

D.9 X-ray fluence spectrum, 150 kVp,
3.00 mm Al. . . . . . . .. 406

D.10 Measured and calculated transmission of
exposure rate, 150 kVp, 3.00 mm Al. . 407

D.11 X-ray fluence spectrum, 150 kVp,
3.34 mm Al. . . . . . . . 408

D.12 Measured and calculated transmission of
exposure rate, 150 kVp, 3.34 mm Al. . 409

D.13 X-ray fluence spectrum, 200 kVp,
3.00 mm Al. . . . . . . . 410


xxvii










LIST OF FIGURES continued


FIGURES


D.14 Measured and calculated transmission of
exposure rate, 200 kVp, 3.00 mm Al.

D.15 X-ray fluence spectrum, 200 kVp,
3.34 mm Al. . . . . . .

D.16 Measured and calculated transmission of
exposure rate, 200 kVp, 3.34 mm Al.


E.1 Gadolinium oxysulfide based detector .

E.2 Active region of the detector. . . .

E.3 Spectrum and transmission curve at
115 kVp . . . . . . .

E.4 Fraction of incident energy absorbed,
perpendicular incidence . . . .

E.5 Fraction of incident energy absorbed
in each screen, perpendicular
incidence . . . .. ..

E.6 Fraction of incident energy reflected,
perpendicular incidence . . . .

E.7 Fraction of incident energy transmitted
perpendicular incidence . . . .

E.8 Fraction of incident energy absorbed,
45 degree incidence . . . .

E.9 Fraction of incident energy absorbed
in each screen, 45 degree incidence .

E.10 Fraction of incident energy reflected,
45 degree incidence . . . . .

E.11 Fraction of incident energy transmitted,
45 degree incidence . . . . .

E.12 Fraction of incident energy absorbed,
75 degree incidence . . . . .

E.13 Fraction of incident energy absorbed in
each screen, 75 degree incidence. .

E.14 Fraction of incident energy reflected,
75 degree incidence . . . . .


*


.*


.*


xxviii


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S 411


S 412


S 413

416

S 418


S 421


S 430



S 431


S 432


433


S 437


438


S 440


S 441


445


S 446


447










LIST OF FIGURES continued


FIGURES

E.15


Fraction of incident energy transmitted
75 degree incidence . . . .


E.16 Emission spectrum of gadolinium
oxysulfide with 0.3 atom % terbium.

E.17 Emission spectrum of 3M Trimax
12 screens. . . . . . .

E.18 Average number of visible photons
produced per incident x-ray photon.

E.19 Dark pulse count rate versus time. .

E.20 Measured pulse height spectra . .

E.21 Response versus distance for 137Cs .
E.22 Response versus distance for 133Ba .


F.1 X-ray fluence spectrum, 100 kVp,
1.01 mm Al. . . . . .

F.2 X-ray fluence spectrum, 150 kVp,
1.01 mm Al. . . . . . .

F.3 X-ray fluence spectrum, 200 kVp,
2.67 mm Al. . . . . . .

F.4 X-ray fluence spectrum, 100 kVp,
9.52 mm Al. . . . . .

F.5 X-ray fluence spectrum, 150 kVp,
9.52 mm Al. . . . . . .

F.6 X-ray fluence spectrum, 150 kVp,
1.85 mm Sn. . . . . . .

F.7 X-ray fluence spectrum, 200 kVp,
1.85 mm Sn. . . . .

F.8 X-ray fluence spectrum, 100 kVp,
0.25 mm Al, 0.24 mm Pb. . . .

F.9 X-ray fluence spectrum, 100 kVp,
0.75 mm Pb. . . . . . .

F.10 X-ray fluence spectrum, 150 kVp,
0.25 mm Al, 0.75 mm Pb . . .


Page


. 448


. 452


. 453


. 454

. 459

. 462

. 468

. 469


. 471


. 472


. 473


. 474


. 475


. 476


. 477


. 478


. 479


. 480


xxix










LIST OF FIGURES continued


FIGURES Page

F.11 X-ray fluence spectrum, 200 kVp,
0.75 mm Pb. . . . . . . 481

F.12 X-ray fluence spectrum, 200 kVp,
0.25 mm Al, 0.75 mm Pb. . . . . 482

F.13 X-ray fluence spectrum, 200 kVp,
0.25 mm Al, 1.35 mm Pb. . . . . 483

H.1 The fit technique. . . . . .. .. 514


xxx















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


LANDMINE DETECTION BY SCATTER
RADIATION RADIOGRAPHY

By

John G. Campbell

August 1987

Chairman: Alan M. Jacobs
Major Department: Nuclear Engineering Sciences

The application of scatter radiation radiography to

the detection of buried nonmetallic antitank landmines is

examined. A combination of calculations and measurements

is used to address the problem. The primary calculation

tool is a Monte Carlo photon transport code. Measurements

are made with an x-ray source, sodium iodide detector, and

soil box positioning system. The soil box containing a

model of a nonmetallic antitank mine is moved beneath the

x-ray source to simulate both the forward motion of a

vehicle transporting the detection system and raster of the

beam to search a path of sufficient width to allow safe

passage. Calculations are used to suggest mine detection

mechanisms and to optimize geometric parameters and x-ray

beam quality. Measurements are used to validate the

calculation results for a small detector and produce images

of buried mines. The calculations are extended to large


xxxi










area detectors which are required to provide path searches

of approximately three meter widths. Environmental para-

meters, such as height sensitivity, soil density and mois-

ture content, and inhomogeneities are examined in both

calculations and measurements. Power requirements are also

addressed.

A system based upon detector collimation to emphasize

differences in the multiple scattered components, character-

istic of soil and the explosive found in mines, is found to

be capable of mine detection at depths of burial of at least

7.5 cm at power levels compatible with portability, and at

speeds, path widths, detection probabilities and false alarm

probabilities consistent with operational requirements. De-

tection at greater depths is possible in soil recently dis-

turbed by mine burial.

Images of holes refilled with loose soil can be dis-

tinguished from those of buried mines by their character-

istic features. However, the refilled hole images bear some

resemblance to those of mines laid on the soil surface. A

compound detector, consisting of both collimated and un-

collimated regions, can be used to overcome this problem and

increase the probability of detection of mines buried at

shallow depths.


xxxii
















CHAPTER I

INTRODUCTION


This research studies the use of backscattered x rays

to detect and image buried nonmetallic antitank mines. A

source of x-ray photons is directed at the soil surface.

After interacting with soil or a buried object, backscat-

tered photons strike a detector located above the soil

surface producing a response. Detection of a buried object

depends upon differences between the photon interaction

characteristics of soil and the object. The x-ray source is

rastered over the soil surface producing an array of respon-

ses, each of which carries information related to the mater-

ials through which photons passed before reaching the detec-

tor. This array of detector responses is manipulated to

produce an image characteristic of those materials. Calcu-

lations are performed to optimize the detection and imaging

process. A variety of detector geometries and types are

examined by these calculations. Measurements are made with

a small sodium iodide scintillation detector to examine the

predictions of the calculations and to produce images of

buried objects.

Chapter II provides a summary of the use of scattered

x-ray and gamma-ray photons to provide information about










materials they irradiate. The general concepts for the mine

detection and imaging system are also introduced in this

chapter. Three related appendices (A, B and C) provide

background on the characteristics of landmines, a short

history of landmine warfare, and a description of other

technologies which have been applied to mine detection.

Chapter III describes the equipment and materials used

in the research. Included in this chapter are descriptions

of soil and mine materials used in the calculations and

measurements.

Chapter IV describes the photon interaction character-

istics important to the mine detection problem. The single

scatter and Monte Carlo photon transport codes used in the

calculations are also described. Validation of the Monte

Carlo calculation method is presented.

Chapter V describes the method used to produce calcula-

tions of the x-ray source spectrum and the validation of the

technique. Other source calculation methods are discussed.

A related appendix (D) provides a graphical display of one

of the validation methods. Appendix F provides graphs of

spectra used in experiments.

Chapter VI describes the method used to calculate the

response function of the sodium iodide scintillation crystal

used in the experiments. Validation of the calculated re-

sponse function is provided. Response calculation for a

detector based on terbium activated gadolinium oxysulfide is

described in a related appendix (E). Detectors similar to









this could prove useful for covering the large areas neces-

sary to find vehicle paths through minefields.

In Chapter VII, results of the application of the Monte

Carlo transport code to the physics and geometry of mine

detection employing backscattered radiation are provided.

Based on these calculations, several detector types are

selected for further investigation. Optimization of the

geometry and source energy is made for each type of detector

selected.

Chapter VIII applies the results of the previous chap-

ter to producing images of mines. Calculated and measured

images are examined. The effects of environmental para-

meters on images are discussed, and power requirements are

estimated.

Chapter IX presents conclusions derived from this re-

search effort along with recommendations for directions for

future work.
















CHAPTER II

BACKSCATTER MINE DETECTION AND IMAGING


Conventional radiography uses the transmission of

photons through an irradiated object to produce an image.

The image depends upon the photon attenuation properties of

the internal structure of the object. Conventional radi-

ography cannot be used to examine objects buried in soil,

such as mines, because of the obvious inability to locate

the detector below the object. Backscatter radiography,

which depends upon differences in the photon scattering

properties of irradiated objects to produce an image, is

suited to the geometry of mine detection. Photons can

originate and be detected above the soil surface. Scattered

radiation has been used in medical and engineering applica-

tions to determine properties and form images of irradiated

objects. Nonmetallic mine detectors using backscattered

radiation have been constructed and tested, but have not

been considered useful enough for actual field use. The

detection and imaging principles investigated in this re-

search are designed to overcome problems inherent in the

previous work.










Previous Uses of Scattered Radiation

The first suggested use of Compton (incoherent) scat-

tering to determine characteristics of a material was by

Odeblad and Norhagen (1956). They showed that the intensity

of the scattered radiation for a fixed source energy and

scattering angle depends on the electron density of the

scattering medium. In a small volume of uniform composi-

tion, the electron density is proportional to the material

density. Using a collimated 6Co gamma-ray source and a

collimated scintillation detector, they were able to measure

the relative electron densities of materials in the small

volume defined by the intersection of the fields of view of

the detector and source collimators.
192
Lale (1959) used a collimated 92r source and a col-

limated detector positioned to receive forward scattered

Compton photons to measure electron density within trans-

verse cross sections in rabbits and guinea pigs. The sub-

jects were moved with respect to the beam to produce an

image of density variation. The process was very slow, and

subject to considerable quantum noise and attenuation of the

incident and scattered beams, but demonstrated that air in

organs would provide a large change in measured electron

density in images. In an extension of this work, Lale

(1968) used 5.6 MV x rays to reduce attenuation losses.

A patient platform was lowered through the beam. Forward

scattered photons were detected with a liquid scintillator.










Kondic and Hahn (1970) suggested the use of Compton

scattering to measure density variations in two-phase flow.

They examined collimated sources used with both collimated

and uncollimated detectors. With the uncollimated detector,

energy discrimination was used to determine the path taken

by a scattered photon. The relationship between energy and

angle in a Compton single scattering event determines the

position along the source beam from which the photon is

scattered, and the intensity (corrected for attenuation) at

that energy determines the electron density of the material

at that point. Farmer and Collins (1971) independently used

the same uncollimated detector technique in a medical appli-

cation. They used a collimated 1Cs source and an uncolli-

mated Ge(Li) detector to examine cross sectional structure.

Rather than move the patient or scan the beam, the energy

discrimination technique was used to determine origin of the

scattered photons. Problems with this method are attenua-

tion of both the primary and scattered photons, and resolu-

tion reduction caused by detection of multiply scattered

photons. Extensions of this method (Farmer and Collins,

1974) using two higher resolution Ge(Li) detectors, above

and below the patient, and focused to the plane of interest,

also suffered from attenuation and multiple scatter. Reiss

and Shuster (1972) and Dohring et al. (1974) used collimated
137
Cs sources and collimated detectors with patient motion

to determine lung function and measure lung density.

Problems with multiple scattering were again noted.









Clarke and Van Dyke (1973) and Garnett et al. (1973)

developed a two-source method to determine bone density.

The two source technique is used to eliminate the problem of

attenuation by tissue above the bone. The second source is

of the same energy as the single scattered beam of the first

for a selected scattering angle. Measurements of both

transmitted and scattered beams are made in two orientations

to allow correction for attenuation.

Battista et al. (1977) examined the physics of scatter

imaging and described the two major limitations to be atten-

uation of the single scattered photon fluence and contamina-

tion by multiply scattered photons. They provide methods

for obtaining a correction for the multiple scattering prob-

lem. Battista and Bronskill (1978) extended this investiga-

tion and concluded that multiple scatter is an inherent

limitation whose effect can be reduced, but not eliminated,

by improving the energy resolution of the detector. They

also showed that the use of forward scattered components

both reduces dose to patients and the effects of multiple

scatter. Anghaie (1982) showed that predictions of the

multiple scattered component could be used to improve image

resolution by subtracting it from the total signal.

Hanson et al. (1983) successfully used heavily filtered

x-ray beams in the two source densitometry method, taking

advantages of the high intensities and well-defined beams

available from x-ray machines. Errors from contamination by

multiple scattering were found to exceed those due to the

polychromatic nature of the source.









Jacobs et al. (1979) proposed an imaging scheme much

different than those discussed thus far. A collimated

scanning x-ray source with an uncollimated detector was used

to view large angle backscattered photons. Energy modula-

tion of the source was used to produce two images. The

image at the lower source energy is characteristic of the

overlying materials. When subtracted from the higher energy

image (after multiplication by an appropriate factor), the

result is an image characteristic of deeper layers within

the irradiated object. The technique was found to be sensi-

tive to regions of air within the object. This dual energy

approach was shown to allow irregular surface features to be

removed from the final image.

Backscattered Photon Mine Detection

A number of attempts have been made to use backscat-

tered photons to detect buried nonmetallic mines. With only

one exception, the published descriptions are from efforts

sponsored by the United States military. Detailed accounts

of these mine detection systems are contained in classified

documents. The descriptions provided here are from unclas-

sified summaries (Roder, 1975; Nolan et al., 1980). The

wide range of other technologies which have been examined as

possible mine detection methods are described in Appendix C.

Fluorescence Emission

Although fluorescent emission is not a backscatter

technique, attempts to use it as a mine detection mechanism

are similar. Between 1954 and 1957, the Armour Research









Foundation used a 150 kVp x-ray source to attempt to produce

fluorescent emission from the lead or mercury contained in

mine fuzes. These elements are found in approximately one

gram quantities of lead azide, lead styphnate or mercury

fulminate (U.S. Department of the Army, 1986). High resolu-

tion detectors were used to look for the energies of the

characteristic x rays of lead or mercury. The Compton scat-

tered fluence was found to completely obscure any fluores-

cent emission signal which might be present. Additional

efforts using more modern detectors produced this same re-

sult, and the technique was deemed infeasible.

Rayleigh Scattering

From 1958 to 1961, Tracerlab, Inc. attempted to use

Rayleigh (coherent) scattering from these same high atomic

number components of the mine fuze as a detection mechanism.

Because the probability of Rayleigh scattering decreases and

the direction of scattering becomes more forward peaked as

incident energy increases, the technique is limited to shal-

low depths of burial. A 120 kVp x-ray source was employed,

in an attempt to produce Rayleigh scattered photons when the

beam struck the high atomic number materials in the fuze.

Because the incident beam was polyenergetic, the Rayleigh

scattered photons were also produced in a spectrum of ener-

gies. Compton scattering was again the dominant source of

the detected signal. Two rastering detectors were tightly

collimated to focus on a very small volume which might con-

tain the mine fuze. Detection was signaled by a small shift









in the backscattered spectrum to higher energies. The very

small sampled volume, which led to scans on the order of

hours per square foot, was the cause for termination of this

effort. Unfortunately, this detection system was not tested

with a real mine. Had it been employed in such a fashion, a

large difference between cases of irradiation of soil only

and of soil containing a buried mine would have resulted.

The mine detection mechanism would have been the difference

between the photoelectric cross sections of soil and mine.

The higher photoelectric absorption of photons striking soil

results in fewer photons capable of being backscattered than

in the mine present case.

Compton Scattering

The first attempt to examine the contrast mechanism

afforded by the difference photoelectric cross sections of

soil and mine materials was made by the Naval Ordnance

Laboratory in 1960 to 1961. Unfortunately, 2 and 10 MV

bremsstrahlung sources were selected for the experiments.

At these energies the photoelectric cross sections of soil

and mine materials are both very small. The dominant inter-

action is Compton scattering, and the respective material

cross sections for this interaction at these energies are

nearly the same. Additionally, the material densities of

soil and explosive are similar. As a result no contrast

mechanism existed and only negative results were obtained.









Beginning in 1967 and extending until 1973, Texas

Nuclear Corporation conducted experiments to produce non-

metallic mine detection systems using backscatter of gamma

or x rays. These experiments culminated in a nonmetallic

antitank mine detector. A less successful nonmetallic anti-

personnel mine detector was also produced. Both systems

used vertically collimated sources and vertically collimated

detectors. Low energy x-ray sources were used to enhance

the photoelectric contrast between mine and soil. The

antitank mine detector used a 130 kVp x-ray source mounted

on the front of a 1/4-ton truck and four CsI(Tl) scintilla-

tion detectors. It was capable of operation at several

miles per hour. Field tests were conducted at a variety of

military installations with U.S. and Soviet mines filled

with dinitrobenzene (a nonexplosive substitute for trini-

trotoluene). Although depths of detection of up to 10 cm

were achieved, a number of conditions of the test were

optimized to enhance the mine detection process. The tests

were conducted in areas free of buried organic material,

such as tree roots, whose response was known to produce

false alarms in the detector. The areas of the tests were

also fairly level, minimizing sensitivity to irregular

surfaces. Deep ruts or depressions comparable to the size

of a mine were also capable of producing false alarms. The

test areas were free of vegetation, which if present would

have lowered the contrast between soil and soil with mine,

and if nonuniform, could have produced false alarms. The










extent of coverage was also a problem; mines located midway

between two detectors were missed unless they were on the

surface. A final objection to the system involved soil

density. It was found that the detector was sensitive to

density changes whether a mine was present or not. Concern

was expressed that dummy minefields could be produced by

simply digging and refilling holes. The act of emplacing a

mine significantly alters the soil density, reducing it, on

the average, to 75% of the undistrubed value (Roder, 1975).

After weathering had returned the soil to its normal

density, detection was no longer possible at 10 cm, and the

response difference at 7.5 cm was much reduced. Further

work on this detection system was terminated primarily as a

result of the apparent superiority of a competing techno-

logy, and secondarily as a result of the inadequacies de-

scribed (Nolan et al., 1980).

Coleman (1971) performed Monte Carlo calculations for

several cases in support of this effort. They are discussed

in Chapter IV. These calculations and the majority of Texas

Nuclear experiments were conducted with solid blocks of di-

nitrobenzene. The mines used in the field tests were filled

with dinitrobenzene, but it is unclear whether any air

space, characteristic of real mines (described in Appendix

A), was provided.

Preiss and Livnat (1973), working in Israel, provide

the only non-U.S. military publication of research on the

detection of nonmetallic mines by the backscatter of










ionizing radiation. The system consisted of an uncollimated

7Se source with a NaI(Tl) detector collimated to view a

10 cm diameter circle at the soil surface at a fixed detec-

tor height. The system was placed on a cart and pushed by

the operator over dirt road surfaces. The electronic com-

ponents of the detector were carried by backpack. This

research effort was the first to consider the effect of the

air space which exists at the top of mines. Experiments

with solid explosive filling the mine and with an actual

mine, containing an air space, revealed completely different

effects. In the case of the solid mine, the ratio of the

detector response with mine present to mine absent (soil

only) was found to be greater than 1.00. In the case of the

mine with air space, the ratio was less than 1.00. Mine

detection was accomplished by selecting an energy range in

the backscattered spectrum which enhanced the reduction in

response with the mine present.

Backscatter Radiation Radiography

Genesis of Current Research Effort

A high priority has been placed on research into the

detection of landmines (West et al., 1985; U.S. Department

of the Army, 1986). The increased interest in this research

is based upon a combination of factors, driven by the imple-

mentation of a new dynamic operational concept by the U.S.

Army. This new concept, termed the AirLand Battle, is

oriented primarily to the threat of a Warsaw Pact attack

into Western Europe. The superseded defensive concept,









termed the Active Defense, concerned itself with attrition

of numerically superior attacking forces by use of defensive

positions prepared in depth on the battlefield (DePuy, 1984;

Holder, 1985). Simulations indicated that this concept

would be successful against the first echelon of a Warsaw

Pact attack, but without extensive, rapid reinforcement

would be of doubtful utility against the following echelons.

The AirLand battle concept emphasizes the use of aggressive

engagement of the attacking force using both fire and man-

euver at varying depths on the battlefield. Counterattacks

into the flanks of the attacking force and into rear supply

and transport areas are encouraged to disrupt the rigid

plans and time tables characteristic of Soviet military

operations. These maneuvers are also designed to enhance

one of the few perceived advantages of Western military

forces in conventional combat with Soviet forces: the

capability of Western leaders of virtually any size unit to

use their initiative in fluid situations compared to the

discouragement (at least until recently) of any deviation

from detailed plans, regardless of tactical situation,

applied to Soviet leaders, especially of smaller sized units

(Suvorov, 1984; Walker, 1986; Baxter, 1986). Another key

factor in the development of the AirLand Battle concept is

the advent of a series of technological advances and equip-

ment modernizations which make rapid maneuver feasible

(RisCassi, 1986).










The landmine represents a serious challenge to rapid

maneuver. The employment of mines by the attacking force to

protect its flanks and rear areas could do much to neutral-

ize the new operational concepts. The effectiveness of

landmines is high. More than 20% of Allied tank casualties

in World War II were caused by mines. United Nations tank

casualties in the Korean conflict were as high as 70% in

offensive operations. In Vietnam (through 1970) 70% of all

U.S. vehicle losses were due to mines (U.S. Department of

the Army, 1973). The keystone manual of the U.S. Army, FM

100-5, Operations (U.S. Department of the Army, 1982),

emphasizes synchronized execution. Clearly, the capability

of mines to produce delays and disruptions is inconsistent

with the new maneuver oriented operational concepts.

Adding to this concern is the mine warfare capability

and experience of the Soviet Army, which is unsurpassed by

any army in history (Honeywell, 1981). Appendix B provides

examples of the Soviet experience with mines. The primary

mission assigned to Soviet engineer units is to insure the

momentum of maneuver mobility by rapidly overcoming natural

and manmade obstacles, while at the same time hindering

enemy force movement (Sidorenko, 1973). The second portion

of this mission, directly affecting the new U.S. Army oper-

ational concepts, is accomplished by Mobile Obstacle Detach-

ments, which provide countermobility support by laying mine-

fields and establishing other expedient obstacles along

enemy avenues of approach (Plyaskin et al., 1973; Uli,










1986). In short, the Soviet Army is aware of its vulner-

abilities on its flanks and in its rear areas, and is

organized to address the threat, in part, by employing

mines. Soviet doctrine has long included the rapid

emplacement of mines on the surface without burial (U.S.

Department of the Army, 1979a). In the 1970's, mechanical

minelayers and mine dispensing chutes for vehicles and

helicopters were fielded to allow rapid minefield emplace-

ment. More recently fielded scatterable mine systems fur-

ther enhance the capability to respond to the new U.S. op-

erational concepts (West et al., 1985).

Aside from manual probing, a hand-held nonmetallic mine

detector of questionable capability (the hand-held metallic

detector works well), and actual mine detonation in an

adverse encounter, the U.S. Army has no method for detecting

buried nonmetallic mines (U.S. Department of the Army,

1986). These slow or adverse detection mechanisms are

incompatible with the advent of new operational concepts

which rely upon maneuver mobility. Accordingly, reviews of

all previous detection technologies have been conducted by

the U.S. Army in an attempt to find systems which might be

made to work. One such review (Moler, 1985) examined the

range of nuclear techniques (x-ray backscatter is included

within this category, even though it is actually an atomic

technique). This review recommended imaging using x-ray

backscatter as the highest priority nuclear technique for

additional research.










Improvements on Previous X-Ray Backscatter Efforts

The shortcomings of the Texas Nuclear Corporation re-

search effort, described above, provide the basis for

improvements in the x-ray backscatter technique. The

concepts investigated in this dissertation differ from the

previous efforts in a number of areas. The major difference

is the examination of the formation of images of buried

objects, rather than detection based upon a single differ-

ence between soil and soil with buried object. Creating an

image requires capabilities that were unavailable in the

past. X-ray sources capable of long linear scans and the

image processing technology to allow real time analysis of

data have been developed since the Texas Nuclear Corporation

efforts. An image provides the important capability to

discriminate between buried mines and other buried objects

which have photon interaction characteristics similar to

mine materials. Coupling the scanning x-ray beam with a

detector large enough to assure coverage of width of the

largest vehicle which must traverse a mined area eliminates

another shortcoming of the previous effort. A diagram of a

conceptual detector is shown in Figure II.1.

Research Goals

The goals of this research effort are to optimize

the design parameters of a large area, x-ray backscatter

imaging system and to examine the effect of environmental

parameters on the detection and imaging process. The design

parameters available for optimization are the energies of













Source


direction of
motion of vehicle


raster direction


/ h

I/
soil /







d
s
mine
5--



Figure II.1. Conceptual large area backscatter detector
system. A pencil, incident x-ray beam strikes the soil
surface. The beam is scattered as it penetrates the soil
and mine. Some of the photons scattering within the mine
reach the panels of the detector after single or multiple
scatters. Distances indicated on the diagram are the height
of the detector above the soil, h; the depth of burial of
the mine, d; the size of the gap between the two panels, d ;
and the width of a panel, d.









the x-ray beams, beam angle of incidence, beam size, beam

collimation, detector geometry, and detector collimation.

Environmental parameters are soil type, soil density, soil

moisture content, inhomogeneities with the soil, surface

irregularities, mine geometry, and mine depth of burial.

The method for examining parameters is a combination of

calculations and measurements. The primary calculation tool

is a Monte Carlo photon transport code written specifically

for the mine detection problem. Measurements are made with

a small NaI(Tl) detector to validate the Monte Carlo pre-

dictions, allowing extension of the code to large area

detector configurations.
















CHAPTER III

EQUIPMENT AND MATERIALS


The apparatus used to perform measurements is designed

to simulate the raster of the x-ray beam across a soil sur-

face which may contain buried objects. This raster simula-

tion is accomplished by moving a soil box under a fixed

x-ray beam. The complete simulation system consists of the

x-ray machine, the soil box and its positioning system, the

detector and its related electronics, and the computer con-

trol devices. Figure III.1 shows the x-ray source, soil box

and positioning system, and detector. Figure III.2 shows

the detector electronics, computer control and x-ray source

control systems. Materials used for soil and buried objects

are selected to simulate those items found under field con-

ditions.

Equipment

X-Ray Source

An x-ray machine is selected as the source of the pho-

tons for backscatter imaging applications because of its

capability to produce intense photon beams which can be

rastered. Extremely high activity radionuclide sources

would be required to produce similar intensities in the

collimated beams necessary for the imaging process. Such























Figure III.1 X-ray source, soil box and positioning system, and detector. The GE
Maxitron 300 x-ray generator (top center) is held in a fixed position while the soil
box (center) is moved in raster mode by drive screws powered by DC motors with
controlled clutch/brakes. The positioning interface to the controlling computer is
on the right side of the photograph.










L "-






















Figure III.2. Detector electronics, computer and x-ray source console. This
photograph shows, from left to right, the detector high voltage supply, scaler and
timer, amplifier and single channel analyzer, count rate meter, the IBM PC computer,
and the GE Maxitron 300 control console with remote TV picture of exposure room.
















ii 2


; ,,,,,,,,,,,,,, I n I









sources require heavy shielding at all times and pose a

constant radiological safety concern. An x-ray machine

poses the same hazard only when in operation. Since the

mine detection problem requires a minimum path width equal

to the widths of following vehicles (on the order of 3

meters), rastering of the beam is required. Mechanical

systems are not practical for rastering a radionuclide

source at the speeds required for the imaging problem (on

the order of 103 m/s), or alternatively, moving a collimator

along a line source at those speeds. The electron beam of

an x-ray machine can be scanned along an extended anode at

very high speeds to provide the raster required. An addi-

tional advantage of an x-ray machine is the capability to

alter intensities by varying beam current and to alter beam

quality by varying tube voltage or filtration. Separate

radionuclide sources would be required to accomplish such

alterations.

The source of the photons used in the backscatter imag-

ing experiments is a General Electric Maxitron 300 X-Ray

Therapy Unit (General Electric, 1962). The unit is capable

of producing continuous beams of 70 to 300 kVp at beam cur-

rents between 5 and 20 mA. The primary voltage waveform

accelerating the electrons to the anode is single phase,

self-rectified at approximately 1200 Hz. The accelerated

electrons strike a 45 degree angle tungsten anode. If the

electron energy exceeds that of the K shell binding energy

of tungsten, K characteristic x rays are produced in









addition to the continuous x rays produced at all energies.

All beams pass through a 4.75 mm thick beryllium window.

Additional filtration can be provided both within and out-

side the head of the unit. Adjustable internal, rectangular

collimators are employed to shape the beam. When an ex-

ternal filter is used, an additional external collimator is

employed to prevent the majority of scattered or fluorescent

photons produced within the external filter from reaching

the soil plane.

The shielding of the head of the x-ray unit is supple-

mented by a 0.16 cm (1/16 inch) thick layer of lead. This

additional shielding was found to be required when measure-

ments were performed using an uncollimated detector with a

heavily filtered beam at higher accelerating potentials.

The higher accelerating potentials produce photons more

likely to penetrate the standard shielding of the unit.

This fact, combined with low intensity fields produced by

heavily filtered beams, results in a significant fraction of

the detector response being caused by head leakage scatter.

The lead shielding reduces the probability of head leakage

photons reaching the soil and subsequently scattering into

the detector. The shielding employed does not entirely

eliminate the problem, requiring two sets of measurements

to be made at high energies when an uncollimated detector is

used. The first image scan is made with the desired beam

filtration. A second scan is then made with a very thick

lead external filter which prevents beam photons from









reaching the soil. This second image scan is, therefore,

the result of the head leakage scatter. Subtraction of the

second scan from the first corrects the imaging data for the

head leakage scatter. Structural constraints caused by the

weight of the shield prevent thicker layers from being used.

Figure III.3 shows lead shielding covering the head of the

x-ray machine.

Soil Box Positioning System

The soil box positioning system was constructed accord-

ing to a design by Moss (1986). The control system was con-

structed by Moss. The soil box is positioned in the x-y

plane (the plane parallel to the floor of the exposure room)

beneath the source by a two level linear bearing system

driven by ball screws which are powered by DC motors with

controlled clutch/brakes. The scan motion is boustrophe-

donic. Both local and remote control of the positioning

system are available. Local control is used to provide the

initial beam-soil intercept position prior to irradiation.

Remote control of the soil box motion is through an RS-232

serial interface bus. It is used in the imaging process to

move the soil box through the array of measurement posi-

tions. Two soil boxes of dimensions of 66 cm by 66 cm by 45

cm deep and 122 cm by 91 cm by 45 cm deep are used. The

larger box is required for measurements with a collimated

detector. Both are filled with locally obtained sandy soil

typical of North Central Florida.






















Figure III.3. Lead shield for tube head and detector. The detector within its
shield and the shielding of the head of the x-ray generator are viewed from below.
The shielding is required to attenuate x-ray leakage from the generator head in
directions other than that of the beam. The filter holder with filter and external
collimator is also shown.







29



























































'I




ra.










Detector and Related Electronics

Two types of detectors have been used in the imaging

measurements. The x-ray sensing portion of the first de-

tector is based on terbium activated gadolinium oxysulfide

rare earth intensifying screens. This device was construct-

ed to provide an inexpensive, sensitive, large area detec-

tor. For reasons detailed in Appendix E, this detector is

found to be unsuitable for the detection and imaging tasks.

It is replaced by Bicron Model .5M.390/.5L-X, sodium iodide

detectors. This detector type is used in all imaging

measurements. The geometry of this detector is shown in

Figure III.4. Also included in this diagram is a composite

shield designed to allow the detector, when operated in an

uncollimated mode, to simulate small regions of a large area

plane detector by permitting photons to enter only through

the exposed face. Several regions of the detector (labeled

3, 4, 5 and 6 in Figure III.4) are not identified in the

diagram. Bicron Corporation, the manufacturer of the detec-

tor, provided the compositions and densities for these

materials with the understanding that they would not be

published due to their proprietary nature (Melocik, 1986).

They are included in the Monte Carlo calculations performed

to determine the detector response function (described in

Chapter VI). Table III.1 provides the dimensions of the

materials shown in Figure III.4.

Because a large area, plane detector is a possible can-

didate for an actual fielded system (Chapter II), it is




















10 9 10 9 9

81


9 9 10 9
- i


Figure III.4. Geometry of the sodium iodide detector and shield. A cross section of
the Bicron Model .5M.39Q/.5L-X NaI(Tl) detector (Melocik, 1986), and locally fabri-
cated shield is shown (not to scale). Numbers in detector and shield regions
correspond to materials and dimensions provided in Table III.1.


10


6=


I










TABLE III.1

Geometry of the Sodium Iodide
Detector and Shield


# Material Diameter or Thickness
Width (cm)

1 NaI(Tl) crystal 1.2700 0.9906

2 Quartz light pipe 1.2700 1.2700

3 Bicron proprietary 0.1588 a

4 Bicron proprietary 1.5875 a

5 Bicron proprietary 1.5875 a

6 Bicron proprietary 1.5875 a

7 Aluminum housing (face) 1.6383 0.0254

8 inner Air space 0.04 1.0643

9 inner Tin 0.07 1.0643

8 mid Air space 0.06 1.0643

9 mid Tin 0.07 1.0643

10 inner Lead 0.1588 15.0343

8 outer Air space 0.08 2.3343

9 outer Tin 0.07 2.3343

10 outer Lead 0.3175 2.3343

Dimensions of the Bicron Model .5M.390/.5L-X NaI(Tl) detec-
tor and locally fabricated shield used in measurements and
calculations. Numbers (#) in the table are keyed to Figure
III.4.

aMaterials and thicknesses are proprietary information of
Bicron Corporation.









desirable to retain as much similarity to such a configura-

tion as possible. The shield is employed to assist in re-

taining this similarity in the small sodium iodide detector

by preventing large numbers of photons from striking the

sides of the crystal. The responses of a small detector,

taken at a number of positions, can then be used to simulate

a large detector. Additionally, considerably greater detail

is available with a small detector than with a large detec-

tor which averages detailed response information over its

greater area. The purpose of the tin inner layer of the

shield is to prevent K fluorescent x rays produced in the

lead of the shield from entering the sides of the detector.

If this layer were not present and a lead layer was adjacent

to the detector, lead K fluorescent x rays from the lip of

the layer would enter through the side of the detector. The

high photoelectric cross section of tin at these energies

(72.794 to 87.343 keV) makes it an attractive material for

shielding lead x rays. The lower level discriminator of the

counting system is set high enough to preclude counting of

tin K fluorescent x rays (25.042 to 29.106 keV) (Storm and

Israel, 1970). The face of the NaI(Tl) crystal and the

bottom of the shield are at the same level to preclude

collimation of the detector. Collimators are attached to

the detector shield when such a configuration is desired. A

detailed description of the modeling of the detector

response function, including correction for edge effects and

the shield, is provided in Chapter VI.









The usual purpose of the lower level discriminator

setting of the counting system is to preclude pulse height

events corresponding to electronic noise. As described

above, an additional purpose in this detector system is to

prevent tin K fluorescent x rays, which could enter through

the sides of the detector, from being counted. A set of

radioactive sources is used to determine the relationship

between photon energy and lower level discriminator setting

(in combination with a fixed detector high voltage supply,

and amplifier and preamplifier settings). Sources and ener-

gies used for this calibration are given in Table III.2. A

discriminator setting corresponding to 35 keV was selected

to prevent counting of spillover of the tin K ray peak as a

result of the resolution of the detector. Based upon the

Monte Carlo spectral and number albedo calculations (Chapter

IV provides examples), this setting results in only a small

reduction of the total detector response compared to the

case when no discrimination is used. The fluence spectral

calculations show that only when the source energy is small

is there any significant contribution below 35 keV. The

number albedo (the fraction of incident photons which are

reflected from a surface) calculations show that low energy

source photons produce significantly less backscatter than

high energy photons (this is true up to about 300 keV).

Additionally, results of the detector response calculation,

provided and described in Chapter VI show that low energy

photons produce a much lower response than all others except






















TABLE III.2

Sources Used in Determining Lower
Level Discriminator Setting


Enerav (keV)a


(Ag Kal x ray)
(Cs Kl1 x ray)
(Ba K.l x ray)
(gamma)
(gamma from 109mAg)
(gamma)


22.162
30.970
32.191
80.999
88.037
122.06135


aphoton energy data are from Lederer and Shirley (1978).


Source


109Cd
133Bs
137Cs
133Ba
Ba
109Cd
57Co










very high energy photons (which pass through the detector

without significant interaction). The 35 keV value also

provides some safeguard for the lower level discriminator

setting determination from non-linearities observed in the

low energy response of NaI(Tl) (Aitken et al., 1967). The

light output and hence pulse height is not proportional to

the amount of energy deposited in the NaI(Tl) crystal for

low photon energies. Figure III.3 shows the detector and

shield. The slotted wooden structure supporting the

detector allows the distance between the beam axis and the

detector to be varied.

The detector is operated in a pulse counting mode. The

detector high voltage is supplied at -900 volts. Figure

III.5 provides a diagram of the components of the counting

system. Remote control of the counting system is by an

IEEE-488 General Purpose Interface Bus (GPIB).

Computer Control System

An IBM PC personal computer controls both the RS-232

serial interface bus, which operates the soil box position-

ing system, and the IEEE-488 GPIB, which operates the

counting system. Software for these two functions was

provided by Moss (1986). The RS-232 serial interface bus

transmits the direction, distance and axis of motion to the

motor controllers. The GPIB controls the counting channel

and time through the counter/timer. The two systems are

integrated by the computer to allow complete automation of

the scanning and counting tasks required to produce an












Bicron
.5M.39Q/.5L-X
NaI(Tl) Detector


ORTEC 556
High Voltage
Power Supply


ORTEC 113
Preamplifier




ORTEC 590A
Amplifier and Single
Channel Analyzer


ORTEC 974
Timer and Quad
Counter




IEEE 488
General Purpose
Interface Bus



IBM PC XT
Personal Computer


ORTEC 449
Log/Linear
Rate Meter


Figure III.5. Components of the counting system.


I r


I


H









image. Independent operation of the positioning and count-

ing systems is also possible.

Simple graphical display programs, written in Turbo

Pascal (Borland, 1985), are used to rapidly analyze the

image data. These programs accept the data files produced

by the counting system control program.

Materials

Soils

Three soil types are selected for calculations to

represent a range of soil properties. Norfolk sandy loam

(Jaeger, 1975) has a high silicon dioxide content and is

similar to the North Central Florida sandy soil used in the

measurements. Hagerstown loam (Bear, 1955) is close to the

average of all soil types examined in elemental composition.

Malatula clay loam is a lateritic soil with high iron con-

tent. Lateritic soils are produced under conditions of high

rainfall and high temperatures. These conditions, over geo-

logic periods of time, lead to the decomposition of organic

materials and selected minerals. The result is a soil low

in silicon dioxide and high in hydrated oxides of iron and

aluminum (Bear, 1955). A global average soil constructed

from the average elemental composition of the crust of the

earth is also used in some calculations (Jaeger, 1975).

This global average soil is very similar in its photon in-

teraction properties to Hagerstown loam. Hereafter, these

soils will be referred to as NSL (Norfolk sandy loam), HTL

(Hagerstown loam), MCL (Malatula clay loam) and GAD (global









average). The elemental compositions, densities and weight

percentages of water of these soils are given in Table

III.3. A comparison of the mass attenuation coefficients of

the NSL, HTL and MCL soils is given in Figure III.6. The

coefficients are calculated from Hubbell's data (1982).

Nonmetallic Antitank Mine Model

Nonmetallic antitank mines of the Warsaw Pact are the

subject of the mine detection effort. Nonmetallic mines are

important subjects for study because of the difficult prob-

lem they present to all current mine detector types and

because their implications to changes in U.S. operational

doctrine. Metallic mines are not considered since other

techniques are more applicable to their detection. While

nonmetallic antipersonnel mines are also very difficult to

detect, they are a secondary concern for mounted armor

combat operations. Also, while buried, surface laid, and

scatterable mines would be employed in any large scale

conflict in Europe, this study concerns itself primarily

with the buried mine, the more difficult detection problem.

Table III.4 provides characteristics of several common

conventional Warsaw pact nonmetallic landmines. The TST

mine, listed in the table for the purpose of comparison, is

the model used in experiments and calculations. As indi-

cated by the table, it is representative of common Warsaw

pack nonmetallic antitank mines.

The TST model consists of a lucite, right circular

cylinder, with 0.635 cm thick walls and outside diameter of









TABLE III.3

Composition of Soil Types


Element Weight Percentage of Elements in Dry Soilsa
NSL HTL GAD MCL

H 0.070 0.185
C 0.502 1.320 -
O 52.627 49.637 47.330 38.702
Na 0.082 0.629 2.840 0.052
Mg 0.054 0.674 2.110 0.784
Al 1.095 6.236 8.240 18.955
Si 44.142 34.330 28.100 1.730
P 0.026 0.086 0.493
S 0.028 0.162 -
K 0.083 2.327 2.640 0.075
Ca 0.278 0.688 3.650 0.129
Ti 0.425 0.626 8.035
Mn 0.008 0.040 0.504
Fe 0.580 3.061 5.090 30.578


aData for NSL and GAD are from Jaeger (1975). Data for HTL
and MCL are from Bear (1955).


Density and Moisture Ranges

Soil Type Density Range Moisture Range
(g/cm ) (%)
NSL 1.40 1.96 5 25

HTL 0.96 2.17 8 25

GAD 0.96 2.17 10 30

MCL 0.080 1.80 15 30

bData from Hough (1957) and Chilton et al. (1984).







102


10
0


S\ Largest to Smallest:
< MCL, HTL, NSL, TNT

Ca 1





10-1
10 -2 10 -1 1
Photon Energy (MeV)

Figure III.6. Soil mass attenuation coefficients. The mass attenuation coefficients
(cm /g) of the three soils used in the majority of the calculations, Malatula clay
loam (MCL), Hagerstown loam (HTL), and Norfolk sandy loam (NSL) are displayed. The
mass attenuation coefficients for trinitrotoluene (TNT), the explosive contained in
most mines, are also shown for comparison.


















TABLE III.4

Characteristics of Common Warsaw Pact
Nonmetallic Antitank Mines


Mine Country Mass Diameter Height Expl. Expl.
(kg) (cm) (cm) Type Mass (kg)

PM-60 GDR 11.3 32 12 TNT 8.6

TM-60 USSR 11.3 32 11.7 TNT 7.5

TMB-2 USSR 7.0 27.4 15.5 TNT or 5.0
AMATOL

PT-Mi- CZECH 9.9 32.2 10.2 TNT 5.6
Ba-III

TST N/A 10.3 30.2 variable sucrose 7.5


Table adapted from U.S. Department of the Army, TRADOC
Threat Monograph, Comparison of Selected NATO and Warsaw
Pact Engineer Organizations and Equipment (U.S. Army
Training and Doctrine Command, Fort Monroe, VA, 1979b),
p. 88.









30.16 cm. The cylinder is 14.60 cm high and has two 0.635

cm thick covers for the top and bottom. An aluminum cylin-

der with 0.24 cm thick walls, outside diameter of 28.89 cm

and height of 8.57 cm fits inside the lucite cylinder and

holds the explosive substitute material. Only the top 7.50

cm of the aluminum cylinder is filled with explosive mater-

ial. Its lower portion is separated from this material by a

0.24 cm thick base plate. The 0.83 cm high curtain below

the aluminum base plate is drilled with three holes at 120

degree intervals. These holes align with five sets of three

holes in the lucite cylinder and are used to allow variable

setting of the air gap located between the top lucite cover

and the explosive substitute material. The aluminum con-

tainer of the model provides structural support for the

heavy explosive substitute portion of the mine. Addition-

ally, it served as the mold for the molten substitute

material when it was prepared. Aluminum is very similar to

soil in its photon scattering properties, and, as such, is

an acceptable wall material for the backscatter radiation

method of mine detection. Due to its metallic content, it

would be an unacceptable model for many other detection

methods. Figure III.7 shows the TST mine used in the

measurements.

Since actual explosive materials present safety and

administrative problems, a substitute material is required.

Since TNT is the most commonly used explosive in landmine,

it serves as the standard against which substitute materials






















Figure III.7. TST mine used in measurements. The TST mine is designed to simulate
nonmetallic antitank mines. The upper layer of the mine cylinder, whose thickness
can be varied, contains air. The lower portion contains the explosive substitute
material. A detailed description of the geometry and materials of the TST mine is
provided in the text.















~ZI Cr
-;I-~.-
,
~~t^U
~-? `t~!:
r; 3C~-PILL~;
2~~-'' ;z i,.
'' "~'~,~kiS-C;;`-l.-:


- r
._.. r.

"-


17LZ4









are compared. Previous studies made use of dinitrobenzene

as a TNT substitute. Unfortunately, this material is toxic.

Evaluation of a number of common nontoxic materials is made

by comparing linear interaction coefficients with those of

TNT. Sucrose is selected as the substitute. Table III.5

shows the comparison of the interaction coefficients of TNT

and sucrose.

The explosive substitute is solidified KaroTM Light

Corn Syrup. While this material is not sucrose, it has

similar elemental composition and photon interaction

characteristics. Upon heating, a portion of the fructose

contained in the syrup is converted to sucrose. A number of

test batches of the substitute are made by removing water

from the syrup by heating. When the capability to consis-

tently obtain the same material density (1.56 g/cm3) is

achieved, samples are used in the tests described below and

found to be an acceptable substitute for TNT.

Materials Tests

Tests of photon interaction characteristics of the

explosive substitute and soil materials are conducted to

insure that the cross section sets used in the Monte Carlo

photon transport calculations are adequate. As described

above, the TNT substitute is solidified KaroTM Light Corn

Syrup with a density of 1.56 g/cm The soil used in the

experiments is obtained locally. Its high sand content

suggests that it is similar to the Norfolk Sandy Loam (NSL)

soil described above. Samples of each of these materials









TABLE III.5

Ratios of the Linear Interaction
Coefficients of Sucrose to TNT


Energy Interaction Coefficient Ratiosa
(MeV) Coherent Incoherent Photoelectric Total


0.010

0.015

0.020

0.030

0.040

0.050

0.060

0.080

0.100

0.150

0.200

0.300

0.400

0.500

0.600

0.800

1.000


0.9379

0.9346

0.9336

0.9335

0.9334

0.9334

0.9334

0.9334

0.9335

0.9333

0.9338

0.9338

0.9339

0.9339

0.9339

0.9340

0.9339


1.0257

1.0171

1.0117

1.0062

1.0037

1.0024

1.0017

1.0008

1.0004

1.0000

0.9998

0.9997

0.9996

0.9996

0.9996

0.9996

0.9996


0.9505

0.9520

0.9528

0.9540

0.9545

0.9547

0.9559

0.9548

0.9571

0.9571

0.9572

0.9572

0.9572

0.9583

0.9586

0.9581

0.9583


0.9524

0.9581

0.9652

0.9789

0.9873

0.9919

0.9944

0.9967

0.9978

0.9987

0.9991

0.9994

0.9994

0.9995

0.9995

0.9995

0.9996


a Sucrose density: 1.588 g/cm3; TNT density: 1.654 g/cm3
(Weast, 1967). For the purpose of backscatter radiation
effects, the two interaction coefficient ratios of the most
importance in evaluating a substitute material are the
incoherent and total coefficients. Coefficient data are
from Hubbell et al. (1975) and Hubbell (1982).









are placed in the beams of various spectra produced by the

GE Maxitron 300 X-Ray Therapy Unit. Before the materials

tests are conducted, each of the four energy spectra

utilized in the measurements is itself tested using exposure

attenuation by added aluminum filtration as described in

Chapter V. The conditions required for formal half value

layer measurements are observed in these measurements and in

the materials tests (Johns and Cunningham, 1983). The

transmission of exposure rate is also calculated using the

method described in Chapter V for NSL (three sets of data

for NSL at different density and moisture contents) and TNT.

Seven thicknesses of the solidified KaroTM Light Corn

Syrup are each subjected to the four spectra: 80, 100, 150,

and 200 KVp, each filtered by 4.75 mm of beryllium inherent

filtration, 0.25 mm aluminum equivalent monitor chamber,

3.19 mm of aluminum added filtration, and an air path of

67.31 cm. Figure III.8 compares the measured exposure rate

transmissions with those calculated. Perfect agreement

would occur if the ratio for each sample of measurement to

calculation is 1.00 or, in terms of the figure, if the plot-

ted points lie on the line of slope equal to 1.00.

Agreement is very good, and the explosive substitute is

deemed adequate.

For each of the four beam energies listed above, three

sets of five soil samples are prepared (60 samples in to-

tal). Multiple samples are used because of the variability

in composition, density and moisture content characteristic







0.7


0.6
0
0.5

~0.4

0.3

0.2

( 0.1


0 .0 1 1 1 1 1 1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Calculated TNT Transmission
Figure II.8. Transmission comparison for TNT and substitute. A comparison of the
measured transmission of exposure rates produced by samples of the explosive sub-
stitute material, and the calculated attenuation of exposure rates of TNT for the
same thicknesses as the substitute samples is shown. Calculations were performed by
the XRSPEC.PAS code (described in Chapter V).









of the soil. Two of the sets of samples differed only in

density; the compacted set density is measured to be 1.579

g/cm and the loose soil set, 1.450 g/cm3. Both have an

average moisture content of 3.26%. The third set differs

both in moisture content and density. It is prepared by

heating the soil to remove all moisture. The density of

this soil is 1.62 g/cm The increase in density with loss

of water is a result of combustion of low density organic

matter in the soil during heating. All samples are of the

same thickness. Exposure transmission measurements and

calculations are compared in Figure III.9. Agreement is

very good, indicating that the local soil is, as suspected,

close to NSL soil in its photon interaction properties.









0.4-




0.3
CA)

CO
| 0.2


(

(0.1




0.0
-j



0.0 0.1 0.2 0.3 0.4
Calculated NSL Soil Transmission
Figure III.9. Transmission comparison for NSL and local soil. A comparison of the
measured transmission of exposure rates produced by sets of samples of the locally
available soil, and the calculated attenuation of exposure rates of NSL soil for the
same thicknesses as the local soil samples is shown. Calculations were performed by
the XRSPEC.PAS code (described in Chapter V).















CHAPTER IV

RADIATION TRANSPORT


In the mine detection system, photons, originating from

an x-ray source, travel through air, and strike the soil.

The photons then undergo interactions with the soil and

objects buried within it. Some photons are scattered back

through the soil surface and strike the detector. This

chapter describes the fundamental photon interactions of

importance to the mine detection problem, the radiation

transport models used to simulate those interactions, and

their validation.

Photon Interactions

Photons interact with matter through a variety of

mechanisms. The energy range of interest for mine detection

and imaging (described in Chapter VII) results in only three

photon interactions of importance: coherent scattering,

incoherent scattering and the photoelectric effect. A brief

description of each of these interaction types is provided.

Coherent Scattering

Thomson gave the first description of the interaction

of an electromagnetic wave with a free electron (Jammer,

1966). Applying purely classical physics to the interac-

tion, he showed that the time varying electric field









associated with the electromagnetic wave would cause the

electron to oscillate with the same frequency as the field.

The resulting accelerated charged particle would then radi-

ate an electromagnetic wave of this same frequency. Since

the frequency of the photon is unchanged, there is no change

in photon energy as a result of the coherent scattering

interaction. This elastic scattering process is known as

Thomson scattering. The solid angle differential cross

section (the probability of scatter into a unit solid angle

per electron per unit fluence incident on the electron) for

Thomson scattering is given by

daT re 2
d--- = 2- (1 + cos a ,

da
where dQ is the solid angle differential Thomson

scattering cross section,

re is the classical radius of the electron,

e is the scattering angle.


When the photon energy is such that its associated

wavelength is comparable in size to the atoms in the mater-

ial in which it scatters, the interaction can no longer be

considered to be with a single free electron. The inter-

action is now collectively with all the electrons of an

atom. These atomic electrons oscillate and radiate in

phase. The process is called coherent or Rayleigh scatter-

ing. In this case the solid angle differential cross

section becomes










r (2
dacoh _e 2 2
-d 2e (1 + cos 28)F2(xZ)
d 2'


do
dcoh
where d- is the solid angle differential coherent

scattering cross section,

F(x,Z) is the atomic form factor, which depends

upon the atomic number, Z, of the material,

and the momentum transfer variable, x, given

by


Os
sin-

where is the wavelength of the photon.
where A is the wavelength of the photon.


The integral of the solid angle differential coherent

cross section gives the probability of coherent scattering

per atom per unit incident fluence,


coh = rr2
coh e


(1 + cos2 )sin F2 (x,Z)d ,
(os s s


where acoh is the total coherent scattering cross section

per atom. Coherent scattering cross sections and atomic

form factors are provided in tabular form for all elements

by Hubbell et al. (1975). The square of the atomic form

factor represents the probability that the electrons of an

atom take up the recoil momentum of the interaction without

absorbing any of the incident photon's energy. Figure IV.1

shows a graph of the atomic form factors of aluminum (Z=13)








30.0


\
\

20.0 -
x \ Dashed line: Iron
SSolid line: Aluminum

1

10.0







0.0 1.0 2.0 3.0
x (Reciprocal Angstroms)
Figure IV.1. Atomic form factor versus momentum transfer variable. Atomic form
factors for aluminum and iron are shown as a function of the momentum transfer
variable. Data are from Hubbell et al. (1975).









and iron (Z=26) as a function of x. At large values of x,

the atomic form factor and, hence, the probability of coher-

ent interaction, is small. Large values of x correspond to

small photon wavelengths or high photon energies. The high-

er the atomic number of the material, the larger the atomic

form factor at a given energy and scattering angle. Hence,

at a given energy, coherent scattering is more probable in

high Z materials than in low Z materials. The effect of the

atomic form factor term is to strongly peak the coherent

scattered photons in the forward direction. This forward

peaking is largest in low Z materials and at high energies.

Figure IV.2 displays these effects. Because of the forward

peaking and lack of change in energy, the typical coherently

scattered photon closely resembles the incident photon, and

many calculations ignore this interaction mechanism." In

terms of the mine detection problem, coherent backscatter

will be important only at relatively low energies, and will

have a larger effect in the soils containing the highest

portion of high Z elements Figure IV.3 shows the coherent

cross section of aluminum and iron as a function of photon

energy.

It should be noted that atomic form factors are avail-

able only for individual atoms and a very few compounds.

Since coherent scattering is a cooperative process involving

all the electrons of an atom and the spatial distribution of

the electron density about an atom in a molecule is altered

relative to the free atom, the use of the available atomic








102


-: -1 U
0 10 -.

S" -- 20 keV

(n - -
c 20 keV
0 -

o 10 -


m 10 3 Al 100 keV
Q \^ --------___----



0


0 20 40 60 80 100 120 140 160 180

Scattering Angle (degrees)
Figure IV.2. Solid angle differential coherent scattering cross section versus
scattering angle. The graph shows that for a given material, coherent scattering is
more forward peaked at higher energy, and for a given energy, coherent scattering in
any direction is greatest in the material with the higher atomic number.











10

0 Fe
0 1 -


0
S= Al
U)
10

U 10 -2-


10 -3
10 -2 10 1
Energy (MeV)
Figure IV.3. Coherent cross section versus photon energy. The coherent scattering
cross section of aluminum and iron are shown. The material having the higher atomic
number has the higher coherent scattering cross section at all energies. Data for
the graph are from Hubbell et al. (1975).


10 3









form factors for compounds is only an approximation to

physical reality.

Incoherent Scattering

Compton (1923) first described photon inelastic scat-

tering from a free electron. In his model of this inter-

action, the photon strikes a free, stationary electron pro-

ducing a new, lower energy, scattered photon and a recoil

electron. This free electron case will be approximately

correct if the energy of the incident photon is very large

in comparison with the binding energy of the electron to its

atom. Compton's formula for the dependence of the scattered

photon's energy on the energy of the incident photon and the

scattering angle is

E
E' =
l+a(l-coses)


where E' is the energy of the scattered photon,

E is the energy of the incident photon,

8s is the scattering angle, and

a = E/mec2, where mec2 is the rest mass energy of the

electron (0.511 MeV).

This relationship plays a very important role in the

mine detection problem/ Figure IV.4 shows the fractional

energy (E'/E) in a Compton interaction as a function of in-

cident photon energy for several scattering angles. The

fractional loss is greatest at high energies, and at a fixed

energy, for large scattering angles backscatteringg). Since








1.00

>0.90
,.

i 0.80

0.70
-D

S0.60
4-
0
c 0.50
0

S0.40
LL


0.30 tT
0.00


Scattering Angle
(degrees)
45


90


180


I I I I I I I I I I I I I i i I I I I I I 1 I- I-I I I-
0.05 0.10 0.15 0.20 0.25 0.30
Incident Photon Energy (MeV)


Figure IV.4. Fractional energy of Compton scattered photons versus incident photon
energy. The graph shows that the fraction of energy retained by the scattered photon
is greatest for small scattering angles, and for low incident photon energies.









/igh photon energies are required for deep penetration,

these two factors combine to make backscatter from signifi-

cant depths in the soil difficult./

The Klein-Nishina formula (Evans, 1955) gives the solid

angle differential scattering cross section for the inelas-

tic scattering of an unpolarized photon from a free elec-

tron,


do r2 1+cos28
KN e s
d 2 [l+a(l-cos8s)]2


2 2
a (1-coses) 2
+ -.3
[1+a(l-cos9 )]3


dKN
In this equation d is the solid angle differential
dQ
Klein-Nishina cross section per electron. Figure IV.5 shows

the differential Klein-Nishina cross section as a function

of scattering angle for three energies. At low energies

forward scatter and backscatter are approximately equally

probable. As energy increases, scattering becomes more

forward peaked. This fact increases the difficulty of the

backscatter detection of mines The use of higher energy

photons, which are capable of penetrating to great depths in

soil, will eventually lead to a lower backscattered fluence

due to this forward peaking and the two factors discussed

above with respect to Compton's energy/angle relationship.

In reality, photons are bound, and inelastic events at

energies at which the incident photon energy is not very









0.08

-C
20 keV

0.06
J




C
100 keV
00.04



C)
a 0.02 500 keV
0

0
O 0.00
0 0 .0 0 .i | | i i i l i i i i i i i i i i i i i i i i i i , i I i i i
0 20 40 60 80 100 120 140 160 180
Scattering Angle (degrees)
Figure IV.5. Solid angle differential Klein-Nishina cross section versus scattering
angle. The variation of the cross section with scattering angle is shown for three
incident photon energies. As the incident energy increases, backscattering becomes
less probable.









large compared to the atomic binding energy are not cor-

rectly accounted for by the Klein-Nishina formula. The

Klein-Nishina formula is corrected by multiplication by the

incoherent scattering function, S(x,Z),


inc KN
d d S(x,Z)
dQ d i

do
inc
where dc is the solid angle differential incoherent
dQ
scattering cross section.

The incoherent scattering function represents the

probability that an atomic electron struck by a photon will

absorb energy and be excited or removed from the atom.

Figure IV.6 shows the incoherent scattering function for

aluminum and iron as a function of the momentum transfer

variable. The function has the effect of decreasing the

Klein-Nishina cross section (per electron) with the re-

duction being greatest at low energies and in high Z mater-

ials. Figure IV.7 displays these effects. The incoherent

scattering cross section is given by the integral over solid

angle of the differential cross section


[2 dc
KN
ainc = da S(x,Z)sin9 dsd ,
*0 'O

where inc. is the total incoherent scattering cross section

per atom.

Tabulated values of the incoherent scattering cross

section are provided by Hubbell et al. (1975). Figure IV.8








30.0





20.0 ---

N
x :
C/)

10. -



Dashed line: Iron
Solid line: Aluminum
0.0 i- -- -
0.0 1.0 2.0 3.0
x (Reciprocal Angstroms)
Figure IV.6. Incoherent scattering function versus momentum transfer variable. To
account for incoherent scattering from bound electrons, the Klein-Nishina cross
section is multiple by the incoherent scattering function. Data are from Hubbell et
al. (1975).









c 0.08
L.
o
Lj 0.06

a-


o
0.04
0


&0
0.02
(n


2 0.00
o

S0.08
0

0
EL 0.06


0.04


0
C
0
,-
o
00.02
vC,


0 0.00
0


Klein-Nishina


20 keV


20 40 60 80 100 120 140 160 180
Scattering Angle (degrees)


Klein-Nishina


100 keV


25 50 75 100 125 150 175
Scattering Angle (degrees)


Figure IV.7. Comparison of the solid angle differential
Klein-Nishina and incoherent scattering cross sections. The
solid angle differential Klein-Nishina and incoherent scat-
tering cross sections per electron (in units of barns per
steradian per electron) of aluminum and iron are compared at
20 keV (a) and 100 keV (b).









CO
0.8



S ~ Klein-Nishina

S0.6






0O
Q 0.4 -
0



O-


10 -2 10 -1 1
Energy (MeV)
Figure IV.8 Incoherent scattering cross section versus photon energy. The inco-
herent scattering cross section per electron of aluminum and iron are compared to the
Klein-Nishina cross section. The reduction from the Klein-Nishina cross section is
greatest at low energy and in the material with the higher atomic number. Data are
from Hubbell et al. (1975).









shows the incoherent scattering cross section per electron

of aluminum and iron, and that calculated from the integral

of the unmodified Klein-Nishina formula. /The Klein-Nishina

cross section overestimates the true incoherent cross sec-

tion at low energy. The error in the Klein-Nishina cross

section is larger in high Z materials. Because the effect

of the incoherent scattering function is important only at

low energies, it is often neglected in calculations/ The

same caveat described in the discussion of the atomic form

factor, regarding atomic and molecular electron density

configurations, applies to the incoherent scattering func-

tion.

Photoelectric Effect

In the photoelectric effect, an incident photon strikes

an atomic electron and is completely absorbed. The electron

is emitted from the atom with kinetic energy equal to the

difference in the incident photon energy and the binding

energy of the electron to the atom. If the interaction is

with an inner shell electron, the vacancy remaining after

the interaction will be filled, either producing a fluor-

escent emission photon(s) or Auger electrons. In the energy

region of interest to the mine detection problem, the cross

section per atom for the photoelectric interaction varies

approximately as

Zn/E3

where n varies between 4.0 and 5.0 depending on photon

energy (Anderson, 1984). This approximation indicates the









photoelectric cross section will be large at low energies

and in high atomic number materials. Figure IV.9 shows the

variation of the photoelectric cross section of iodine

(Z=53), gadolinium (Z=64) and lead (Z=82) as a function of

photon energy (each of these materials plays a role in this

research). Superimposed on the variation with atomic number

and energy, discussed above, are edges. These sharp discon-

tinuities in the cross sections are the result of the dis-

crete binding energies of electrons in their atomic shells.

Below an edge energy, the incident photon does not possess

sufficient energy to overcome the binding energy of the

electrons in a particular shell. As photon energy increases

to just above the edge energy, this is no longer the case

and the cross section increases dramatically as a result of

the capability to remove the newly available electrons. As

a result of these edges, a lower atomic number material may

have a higher cross section for the photoelectric inter-

action in an energy range below the edge energy of a higher

atomic number material.

Figure IV.10 shows the probability of K shell fluores-

cent emission following the filling of a vacancy in the

inner atomic shell./In low atomic number materials, this

probability is small; the alternate radiationless emission

of Auger electrons dominates (Evans, 1955). Since soil

and explosive materials contain generally low atomic number

elements, fluorescent emission from these materials is not

very probable/ Even in those few instances in which




Full Text
18
Source
surface. The beam is scattered as it penetrates the soil
and mine. Some of the photons scattering within the mine
reach the panels of the detector after single or multiple
scatters. Distances indicated on the diagram are the height
of the detector above the soil, h; the depth of burial of
the mine, d; the size of the gap between the two panels, d ;
and the width of a panel, d ^


LIST OF FIGURES continued
FIGURES Page
E.15 Fraction of incident energy transmitted,
75 degree incidence 448
E.16 Emission spectrum of gadolinium
oxysulfide with 0.3 atom % terbium. . 452
E.17 Emission spectrum of 3M Trimax
12 screens 453
E.18 Average number of visible photons
produced per incident x-ray photon. . 454
E.19 Dark pulse count rate versus time 459
E.20 Measured pulse height spectra 462
137
E.21 Response versus distance for Cs . . 468
133
E.22 Response versus distance for Ba . . 469
F.l X-ray fluence spectrum, 100 kVp,
1.01 mm A1 471
F.2 X-ray fluence spectrum, 150 kVp,
1.01 mm A1 472
F.3 X-ray fluence spectrum, 200 kVp,
2.67 mm Al 473
F.4 X-ray fluence spectrum, 100 kVp,
9.52 mm Al 474
F.5 X-ray fluence spectrum, 150 kVp,
9.52 mm Al 475
F.6 X-ray fluence spectrum, 150 kVp,
1.85 mm Sn 476
F.7 X-ray fluence spectrum, 200 kVp,
1.8 5 mm Sn 477
F.8 X-ray fluence spectrum, 100 kVp,
0.25 mm Al, 0.24 mm Pb. 478
F.9 X-ray fluence spectrum, 100 kVp,
0.7 5 mm Pb 479
F.10 X-ray fluence spectrum, 150 kVp,
0.25 mm Al, 0.75 mm Pb 480
xxxx


343
The technique is not applicable to cases where the mine is
positioned above the surface or buried flush to the top of
the soil. In these cases, there are no irregularities or
inhomogeneities other than the mine itself. Because the
addition of a second energy beam greatly complicates the
mine detection system and increases power requirements,
principally by shortening the time the source beam inter
cepts a position on the mine at constant vehicle speed and
by increasing the noise in the subtracted image, it is not
desirable to use the technique in cases in which, despite
the presence of irregularities or inhomogeneities, the
signal from the mine is large enough to provide unmistakable
detection. Examples of this situation for buried mines have
been illustrated for the collimated detector with both
inhomogeneities (Figures VIII.40 and VIII.41) and surface
irregularities (Figures VIII.45 through VIII.48) for mines
buried at 2.54 cm. For the uncollimated detector, which
produces a small mine to soil ratio even at relatively
shallow depths of burial, the technique would appear
applicable. Eventually, even with the collimated detector,
a depth will be reached where the mine to soil ratio is too
small to allow unmistakable recognition due to irregulari
ties or inhomogeneities.
Unfortunately, the dual energy technique is incompat
ible with the backscatter mine detection irradiation
geometry. The problem lies with the positioning of the
detector with respect to the source. As was described in


£Z
O
*OT
CO
E
to
c
D
L.
I
Figure D.6. Measured and calculated transmission of exposure rate, 100 kVp, 2.00 mm
Al. A comparison of measured and calculated transmission of exposure rate of a 100
kVp beam produced by the GE Maxitron 300 X-Ray Therapy Unit with 4.75 mm beryllium
inherent filtration, 2.00 mm aluminum added filtration and air path length of 90.17
cm is shown. The calculated transmission of exposure rate is based upon the spectrum
shown in Figure D.5.
403


78
optionally to the computer terminal screen, hardcopy, disk
file and three-dimensional graphical display.
Interaction Modelling
The code uses the fine energy mesh mass interaction
coefficient data described previously in this chapter.
Log-log interpolation is used to determine values of the
coefficients at energies not provided within the fine mesh
tables. Coherent scattering is not included in the model.
Incoherent scattering includes modification of the Klein-
Nishina distribution by the incoherent scattering function.
Contributions due to fluorescent emission from soils or mine
following photoelectric interactions are neglected based
upon their low probability of occurrence in low Z materials,
and the very low energies (and, therefore, high attenuation)
characteristic of such photons when an infrequent emission
occurs. For example, the probability of K fluorescent emis
sion following a photoelectric interaction of a photon,
whose energy exceeds the K edge energy, with an aluminum
atom in soil is less than 2%. If a fluorescent photon were
produced (part of the less than 2%), its energy would be
1.486 keV (Storm and Israel, 1970) and would have a mean
-4
free path of about 2 x 10 cm in soil.
Monte Carlo Model
The majority of the calculations supporting this
research have been made with Monte Carlo computer codes.
Two versions of the radiation transport code have been used.
MCPHOT.PAS is written in Turbo Pascal (Borland, 1985) for


493
DETNAIP.PAS is a Monte Carlo code which is used to
determine the lead shielding requirements for the Nal(Tl)
detector.
NAISPEC.PAS is a Monte Carlo code which calculates
Nal(Tl) energy spectra on a one keV increment.
SPRESOL.PAS modifies the output of the NAISPEC.PAS code
to account for the energy dependent resolution of the
Nal(Tl) detector using the recommendations of Berger and
Seltzer ( 1972) .
DETISO.PAS is a Monte Carlo code which calculates the
response of a detector to an isotropic point source. It is
used to compare the results of detector response matrix
calculations to experiments with radionuclide sources.
COLLIM.PAS computes the relationship between detector
collimator acceptance angle, collimator height and width of
the gap in the large area fluence detector.
Imaging Codes
COUNTER.BAS controls detector system electronics for
count rate measurements with the GE Maxitron X-Ray Therapy
Unit. It is used without soil box motion for multiple
measurements at a single position. The code was written by
Moss (1986).
OPS.BAS controls the detector system electronics and
soil box positioning system for measurements with the GE
Maxitron 300 X-Ray Therapy Unit to produce images of buried
objects. This code was also written by Moss (1986).


267
height. Figure VII.26 indicates that because of the rapid
decrease of the backscattered fluence with distance from the
beam axis, panel widths of approximately 70 cm (without a
raster gap) would be nearly equivalent to an infinite
detector. Of course, a raster gap is required for the beam,
and the central minimum in the mine to soil fluence ratio
makes gaps on the order of 10 to 30 cm attractive. The
principle reason for selecting a 10 cm gap for the uncolli
mated detector, in the discussion in Chapter VII, is to
intercept a substantial fraction of the backscatter fluence.
A 30 cm raster gap provides a slightly better mine to soil
fluence ratio, but at the cost of allowing a sizeable
fraction of the backscattered fluence to escape through the
gap (see Table VII.5). Wide panels increase the probability
of the detector striking the soil surface while moving over
rough terrain. Figure VIII.9 shows the variation in the
number of photons striking an uncollimated fluence gap
detector per source photon for the case of 100 keV photons
perpendicularly incident on the center of the TST mine at a
depth of burial of 1.0 cm in NSL soil as a function of
height of the detector above the soil. The raster gap is 10
cm, and the beam size is 1.27 cm by 1.27 cm when the source
is at a height of 64.48 cm above the soil. The source is
fixed at a height of 29.87 cm above the detector plane.
Source height and beam size are varied to correspond to
detector height. The response curves for selected panel
widths are shown. The shapes of the curves are similar.


TABLE OF CONTENTS
continued
CHAPTERS Page
Discriminator Setting Corresponding
to 0 MeV 151
Discriminator Setting Corresponding
to Energies Greater Than 0 MeV 153
Validation of the Plane Detector Response
Calculations 157
Iodine Escape Ratio 157
Measured Energy Spectra 163
Shield and Edge Effects 163
Calculation of the Correction Factor. 163
Results of the Correction Factor
Calculation 166
VII MINE DETECTION MECHANISMS 169
Backscattered Photon Signal Differences. 169
Fluence 170
Energy Fluence 176
Spatial Distribution 182
Angular Distribution 186
Energy Spectra 194
Edge Effects 198
Conclusions Based on Signal
Differences 204
Irradiation Geometry and Optimum Energy. 208
Height of Detector 208
Angle of Incidence 209
Raster Gap Size 216
Detector Collimator Length 222
Detector Panel Dimensions 223
Segmented Detector Geometry 227
Source Beam Collimation 229
Source Energy Optimization 232
Depth of Burial 241
Polyenergetic Sources 244
Conclusions Based on Optimizations. . 246
VIII APPLICATION TO IMAGING 248
Comparisons with Measurements. ...... 249
Spatial Distribution of Detector
Response 249
Detector Response with Mine Present . 251
Edge Effects 258
Energy Window Detector 262
Environmental Parameters 266
Height Sensitivity 266
Soil Density Variation 272
Soil Moisture Content 277
Inhomogeneities 283


354
TABLE VIII.13
Imaging Quantities Necessary to
Fulfill Operational Requirements
Quantity
Operational Requirement
Desired
Level3
Useful
Number of pixels
per line scan
350
254
Line scan rate
105.51 s"1
18.11 s"1
Single line scan
time
9.48 ms
55.22 ms
Pixel dwell time
27.05 ps
217.11 us
a
Based on vehicle speeds and scanned widths of Table
VIII.11.


505
where G is a constant. Kahn introduces a change of variable
at this point to
z
a_
a
This parameter can take on values between 1 and 1 + 2 a,
corresponding to scatter at zero and 180 degrees. The
resulting probability density function for z is given by
p(z) = (w2-l + i + z),
G'z2 2
where G' is another constant. Kahn applies the rejection
method to two independent components of this distribution.
The distribution becomes
p(z) = K [A-l H1(z) gx(z) + A2 h2(z) g2(z)],
where K is a constant,
A^ = (1 + 2a)/(9 + 2a),
h1(z) = 4(1/z 1/z2),
gx(z) = l/(2a)/
A2 = 8/(9 + 2a),
h2(z) = (1/z + w2)/2, and
g2(z) = (1 + 2a)/(2az2).
These components are chosen so that g^(z) and <32^z^ are
themselves probability density functions, and so that the
h^(z) and h2(z) functions have maximum values of 1 in the
range of z. Sampling begins by selecting a random number


Figure E.14. Fraction of incident energy reflected, 75 degree incidence. The
fraction of incident x-ray photon energy escaping into the relection hemisphere of
the detector system constructed from two halves of 3M Trimax 12 screen B 184048 as a
function of incident x-ray photon energy (MeV) for the case of 75 degree incidence is
shown.
447


222
to edge of detector distance exceeds the diameter of the
mine), detection will be difficult because no medium (other
than air) is available to scatter photons outside the walls
of the mine. A compound detector, which includes an
uncollimated portion placed inside the collimated panels
(producing a smaller raster gap), could be used to overcome
this problem. As shown in Chapter VIII, the uncollimated
detector is well-suited to detection of surface laid mines
(see Figures VIII.29 and VIII.30).
Detector Collimator Length
Because of the requirement for the mine detection
system to travel over rough terrain, care must be taken to
insure that the length of the collimator is not excessive
for the detector height. The purpose of the collimator is
to prevent single scattered photons from reaching the
detector. There is a fixed geometric relationship between
the height of the detector, the collimator length, the
raster gap size, the collimator spacing, and the acceptance
angle. In the case of a compound (collimated and
uncollimated regions) detector, the raster gap discussed
here is equivalent to twice the distance from the beam axis
to the nearest edge of a collimated panel. If the raster
gap is small, very long collimators are required at the
panel edge nearest the beam to preclude significant amounts
of single scatter from entering the detector. As the raster
gap size increases, the required collimator lengths de
crease. If the spacing between adjacent elements is large,


3
this could prove useful for covering the large areas neces
sary to find vehicle paths through minefields.
In Chapter VII, results of the application of the Monte
Carlo transport code to the physics and geometry of mine
detection employing backscattered radiation are provided.
Based on these calculations, several detector types are
selected for further investigation. Optimization of the
geometry and source energy is made for each type of detector
selected.
Chapter VIII applies the results of the previous chap
ter to producing images of mines. Calculated and measured
images are examined. The effects of environmental para
meters on images are discussed, and power requirements are
estimated.
Chapter IX presents conclusions derived from this re
search effort along with recommendations for directions for
future work.


Energy (keV)
Figure F.9. X-ray fluence spectrum, 100 kVp, 0.75 mm Pb. The x-ray fluence spectrum
at 100 kVp calculated by the XRSPEC.PAS code for the GE Maxitron 300 X-Ray Therapy
Unit with 4.75 mm beryllium inherent filtration, 0.75 mm lead added |iltration and
air path length of 60 cm is shown. Fluence units are photons per cin per keV. Total
fluence is normalized to 1 photon per cm .
479


CHAPTER II
BACKSCATTER MINE DETECTION AND IMAGING
Conventional radiography uses the transmission of
photons through an irradiated object to produce an image.
The image depends upon the photon attenuation properties of
the internal structure of the object. Conventional radi
ography cannot be used to examine objects buried in soil,
such as mines, because of the obvious inability to locate
the detector below the object. Backscatter radiography,
which depends upon differences in the photon scattering
properties of irradiated objects to produce an image, is
suited to the geometry of mine detection. Photons can
originate and be detected above the soil surface. Scattered
radiation has been used in medical and engineering applica
tions to determine properties and form images of irradiated
objects. Nonmetallic mine detectors using backscattered
radiation have been constructed and tested, but have not
been considered useful enough for actual field use. The
detection and imaging principles investigated in this re
search are designed to overcome problems inherent in the
previous work.
4


106
Kramers' Formula
Kramers' formula is a simple relationship between the
energy associated with an electron accelerating potential and
the intensity or energy fluence spectrum of the x rays
produced when the electrons strike a target, in this case the
anode of an x-ray machine. The formula is based upon the
nonrelativistic, semiclassical physics of electron energy
loss, neglecting electron scattering. It applies only to the
continuous portion of the x-ray spectrum produced by the
bremsstrahlung process. Despite these simplifying assump
tions, its use in calculations of x-ray spectra is well es
tablished. The International Commission on Radiological
Units and Measurements (1964) finds the method to perform
well over a wide range of energies, provided that modifica
tions for self-absorption in the anode and attenuation by
other materials in the path of the beam are made.
One form of Kramers' formula is
1(E) = k (Eq E),
where I is the intensity or energy fluence of x-ray photons
of energy, E,
k is a constant of proportionality dependent on the
anode material,
Eq is the energy of the electrons striking the anode,
and
E is the energy of an x-ray photon within the
spectrum.


47
TABLE III.5
Ratios of the Linear Interaction
Coefficients of Sucrose to TNT
Energy
(MeV)
Coherent
Interaction Coefficient Ratios3
Incoherent Photoelectric
Total
0.010
0.9379
1.0257
0.9505
0.9524
0.015
0.9346
1.0171
0.9520
0.9581
0.020
0.9336
1.0117
0.9528
0.9652
0.030
0.9335
1.0062
0.9540
0.9789
0.040
0.9334
1.0037
0.9545
0.9873
0.050
0.9334
1.0024
0.9547
0.9919
0.060
0.9334
1.0017
0.9559
0.9944
0.080
0.9334
1.0008
0.9548
0.9967
0.100
0.9335
1.0004
0.9571
0.9978
0.150
0.9333
1.0000
0.9571
0.9987
0.200
0.9338
0.9998
0.9572
0.9991
0.300
0.9338
0.9997
0.9572
0.9994
0.400
0.9339
0.9996
0.9572
0.9994
0.500
0.9339
0.9996
0.9583
0.9995
0.600
0.9339
0.9996
0.9586
0.9995
0.800
0.9340
0.9996
0.9581
0.9995
1.000
0.9339
0.9996
0.9583
0.9996
aSucrose density: 1.588 g/cm3; TNT density: 1.654 g/cm3
(Weast, 1967). For the purpose of backscatter radiation
effects, the two interaction coefficient ratios of the most
importance in evaluating a substitute material are the
incoherent and total coefficients. Coefficient data are
from Hubbell et al. (1975) and Hubbell (1982).


166
calculation do not include coherent scattering, since these
events do not deposit energy and, generally, do not greatly
change the direction of travel of a photon. The model
implicitly assumes that the variation in fluence over the
size of the detector is small, which is a good approximation
for the small detector being used.
Results of the Correction Factor Calculations
Results of the calculations show that except at high
energies (200 keV or greater), the effect of photons pene
trating the shield into the side of the crystal outweighs
that of photons leaking through the side wall of the crys
tal, making the correction factor a number greater than
1.00. The reason for this phenomenon is twofold. Photons
in the low energy range under consideration are very rapidly
attenuated by the Nal(Tl) crystal, reducing the impact of
leakage to only those photons which strike very close to the
bottom edge of the crystal. The protrusion (see Figure
III.l) of the detector face below the shield (to avoid col-
limation), combined with the layer of low atomic number
material, which is packed around the sides of the crystal
within the aluminum housing (proprietary material), plays a
significant role. This side region is relatively poorly
shielded and allows significant numbers of photons to
penetrate into Nal(Tl) crystal through the side wall.
Figure VI.7 and VI.8 display, respectively, the plane
detector response function and the result of correcting it
for shield and edge effects.


LIST OF FIGURES
continued
FIGURES Page
VII.24 Ratios of integral energy spectra for
100 keV photons incident on the TST
mine at 2.5 cm in NSL soil for the
cases of 0 to 60 degree incidence . 212
VII.25 Spatial distribution of the fluence
response from a 100 keV beam inci
dent at 60 degrees on the TST mine
at 2.5 cm in NSL soil 215
VII.26 Fluence response versus distance from
beam axis for 100 keV photons perpen
dicularly incident on the TST mine at
2.5 cm in NSL soil 217
VII.27 Relationship between the raster gap size,
the length of the collimator, and the
spacing of the first collimator element
required to exclude single scattered
Photons from the detector 224
VII.28 Geometry of the segmented fluence
detector 228
VII.29 Fluence response ratio matrices for the
segmented detector for perpendicularly
incident 150 keV photon beams on the
TST mine at 2.5 cm in HTL soil 231
VII.30 Source energy optimization curve for the
uncollimated fluence detector with mine
depth of burial of 5 cm in NSL soil . 234
VII.31 Source energy optimization curve for the
segmented fluence detector with mine
depth of burial of 2.5 cm in NSL soil 237
VII.32 Source energy optimization curve for the
energy window detector with mine
depth of burial of 5 cm in NSL soil . 240
VIII.1 Calculated and measured spatial distribu
tion of detector response from back-
scatter from sandy soil at 100 kVp. . 252
VIII.2 Calculated and measured spatial distribu
tion of detector response from back-
scatter from sandy soil at 150 kVp. . 253
xx


Figure E.12. Fraction of incident energy absorbed, 75 degree incidence. The
fraction of incident x-ray photon absorbed in the two phosphor layers of the detector
system constructed from two halves of 3M Trimax 12 screen B 184048 as a function of
incident x-ray photon energy (MeV) for the case of 75 degree incidence is shown.
445


Figure F.13. X-ray fluence spectrum, 200 kVp, 0.25 nun Al, 1.35 mm Pb. The x-ray
fluence spectrum at 200 kVp calculated by the XRSPEC.PAS code Cor the GE Maxitron 300
X-Ray Therapy Unit with 4.75 mm beryllium inherent filtration, 0.25 mm aluminum
equivalent monitor ionization chamber, 1.35 mm lead added filtration and air path
length of 60 cm is shown. Fluence units are photons per cm per keV. Total fluence
is normalized to 1 photon per cm .
483


4.0
0.0 iiiiir~i| iii|mr~|mi|r-1i|r~ii|r~ir
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40
Collimator Acceptance Angle (radians)
Figure VII.14. Mine to soil fluence ratio versus collimator acceptance angle for 100
keV photons perpendicularly incident on the TST mine at 2.5 cm in HTL soil. A 25 cm
radius central section of the detection plane has been removed. The plane is located
34.6075 cm above and parallel to the soil surface.
192


15
The landmine represents a serious challenge to rapid
maneuver. The employment of mines by the attacking force to
protect its flanks and rear areas could do much to neutral
ize the new operational concepts. The effectiveness of
landmines is high. More than 20% of Allied tank casualties
in World War II were caused by mines. United Nations tank
casualties in the Korean conflict were as high as 70% in
offensive operations. In Vietnam (through 1970) 70% of all
U.S. vehicle losses were due to mines (U.S. Department of
the Army, 1973). The keystone manual of the U.S. Army, FM
100-5, Operations (U.S. Department of the Army, 1982),
emphasizes synchronized execution. Clearly, the capability
of mines to produce delays and disruptions is inconsistent
with the new maneuver oriented operational concepts.
Adding to this concern is the mine warfare capability
and experience of the Soviet Army, which is unsurpassed by
any army in history (Honeywell, 1981). Appendix B provides
examples of the Soviet experience with mines. The primary
mission assigned to Soviet engineer units is to insure the
momentum of maneuver mobility by rapidly overcoming natural
and manmade obstacles, while at the same time hindering
enemy force movement (Sidorenko, 1973). The second portion
of this mission, directly affecting the new U.S. Army oper
ational concepts, is accomplished by Mobile Obstacle Detach
ments, which provide countermobility support by laying mine
fields and establishing other expedient obstacles along
enemy avenues of approach (Plyaskin et al., 1973; Uli,


246
x-ray sources must be used to achieve rapid detection over
wide paths, some discussion of the effect of polyenergetic
sources is required. The presence of non-optimum energy
photons will degrade the mine to soil ratios. This implies
efforts to shape the source x-ray spectra to place a major
ity of the source photons near the monoenergetic optimum
energy to lessen the effects of the other photons. The
combination of two methods is generally used to shape
spectra. Increasing the peak kilovoltage accelerating
electrons across the x-ray tube increases the average and
peak energies of the beam. Addition of filters to selec
tively remove low energy components (as discussed for the
energy window detector) can also be used for this purpose.
Filtration must be used with care, since too much filtra
tion, while producing a more appropriate spectrum, also
removes useful photons, increasing power requirements.
Spectra calculated by the XRSPEC.PAS code for various filter
and voltage combinations can be compared by using the fit
technique described in Appendix H, with the response per
source photon for a particular detector at a given depth of
burial of the TST mine replacing the detector response at a
specific detector position. This technique is applied to
the calculation of power requirements in Chapter VIII.
Conclusions Based on Optimizations
The results of the optimization calculations presented
above indicate that only the collimated detector offers the
possibility of exceeding th minimum useful depth for mine


489
Computer Software
Brief descriptions of the computer codes written for
this research are provided. Descriptions of the validation
of the major codes are provided within the chapters of the
dissertation. A separate document (Campbell, 1987) contains
listings of the major codes used in this research.
Computer Languages
Computer codes for the research are written in Micro
soft BASIC, version 2.10 (Compaq, 1984b); Turbo Pascal,
version 3.01A (Borland, 1985); or Green Hills Pascal,
version GS-1.2a (Green Hills, 1985). In the file naming
scheme used, file extensions identify the language in which
a particular program is written. The extension, BAS, refers
to a BASIC program; PAS, to a Turbo Pascal program; and, P,
to a Green Hills Pascal program. All files with the
extension, COM, are object code, generated by the Turbo
Pascal compiler. These object codes are primarily used on
the IBM Personal Computer for processing imaging data. All
other file extensions refer not to programs, but to data.
Radiation Transport Codes
SGLMIN.PAS is a single scatter photon transport code.
It is described in detail in Chapter IV.
MCPHOT.PAS and MCPHOT.P are Monte Carlo photon trans
port codes. They are described in detail in Chapter IV.
PBSCAT.PAS is a Monte Carlo photon transport code used
to calculate scatter and fluorescent emission contributions
to the x-ray source beam from lead filters employed in some
of the experiments.


CHAPTER III
EQUIPMENT AND MATERIALS
The apparatus used to perform measurements is designed
to simulate the raster of the x-ray beam across a soil sur
face which may contain buried objects. This raster simula
tion is accomplished by moving a soil box under a fixed
x-ray beam. The complete simulation system consists of the
x-ray machine, the soil box and its positioning system, the
detector and its related electronics, and the computer con
trol devices. Figure III.l shows the x-ray source, soil box
and positioning system, and detector. Figure III.2 shows
the detector electronics, computer control and x-ray source
control systems. Materials used for soil and buried objects
are selected to simulate those items found under field con
ditions .
Equipment
X-Ray Source
An x-ray machine is selected as the source of the pho
tons for backscatter imaging applications because of its
capability to produce intense photon beams which can be
rastered. Extremely high activity radionuclide sources
would be required to produce similar intensities in the
collimated beams necessary for the imaging process. Such
20


Photons/Radian/Source Photon
Figure VII.11. Angular distribution of backscattered fluence from 100 keV photons
perpendicularly incident on HTL soil and two TST mine cases.
188


425
taken by averaging the three actual edge energies. Five
characteristic photons are allowed from gadolinium and three
from titanium, provided edge energies are exceeded. These
photon energies are given in Table E.2. The probabilities
of emission of a particular photon are computed using the
method recommended by Carter and Cashwell. Secondary
fluorescence following or K ^ emission is included in
the model. All fluorescent emissions are isotropic.
General Results of Calculations
The DETECT.PAS code is used to perform calculations of
the energy deposited in the phosphor layers of the screen
configuration shown in Figure E.2. The screen layer compo
sitions, thicknesses and densities used in the code are
shown in Table E.l. A 0.3 cm thick cardboard layer, which
provides support, separates the two screens. Ten thousand
photon histories were followed for 20 photon energies inci
dent on the screen at nine different angles. The quantity
recorded in the response matrix is the energy deposited in
the phosphor layers per incident photon at a particular
energy and angle. As discussed below, this quantity is
directly proportional to the electronic signal produced in
the complete detector system by an incident photon.
Two phenomena occur at the K edge energy of gadolinium
(50.239 keV) which profoundly influence the detector re
sponse. At the edge energy the cross section for photo
electric interaction in gadolinium increases rapidly. This
results in an increase in the number of photoelectric




25
sources require heavy shielding at all times and pose a
constant radiological safety concern. An x-ray machine
poses the same hazard only when in operation. Since the
mine detection problem requires a minimum path width equal
to the widths of following vehicles (on the order of 3
meters), rastering of the beam is required. Mechanical
systems are not practical for rastering a radionuclide
source at the speeds required for the imaging problem (on
3
the order of 10 m/s), or alternatively, moving a collimator
along a line source at those speeds. The electron beam of
an x-ray machine can be scanned along an extended anode at
very high speeds to provide the raster required. An addi
tional advantage of an x-ray machine is the capability to
alter intensities by varying beam current and to alter beam
quality by varying tube voltage or filtration. Separate
radionuclide sources would be required to accomplish such
alterations.
The source of the photons used in the backscatter imag
ing experiments is a General Electric Maxitron 300 X-Ray
Therapy Unit (General Electric, 1962). The unit is capable
of producing continuous beams of 70 to 300 kVp at beam cur
rents between 5 and 20 mA. The primary voltage waveform
accelerating the electrons to the anode is single phase,
self-rectified at approximately 1200 Hz. The accelerated
electrons strike a 45 degree angle tungsten anode. If the
electron energy exceeds that of the K shell binding energy
of tungsten, K characteristic x rays are produced in


Energy (keV)
Figure D.5. X-ray fluence spectrum, 100 kVp, 2.00 mm Al. The x-ray spectrum at 100
kVp calculated by the XRSPEC.PAS code for the GE Maxitron 300 X-Ray Therapy Unit with
4.75 mm beryllium inherent filtration, 2.24 mm aluminum added filtration (includes
0.25 mm aluminum equivalent monitor ionization2chamber) and air path length of 90.17
cm is shown. Fluence units are photons per cin per keV. Total fluence is normalized
to 1 photon per cm.
402


355
mine and for the effects of a real detector. The maximum
number of independent 1.27 cm by 1.27 cm beam intercepts on
the mine is more than 400. Many of these samples, however,
will produce responses very unlike that of the center of the
mine. Again, being conservative, only the central 50 sam
ples are used in the detectability determination. This
presupposes a system to recognize and group together high
count pixels occurring in regions the size of a mine.
The fraction of source photons striking the detector
multiplied by the flux per beam current, the pixel dwell
time, and the area of the beam on the soil surface gives the
number of photons reaching the detector divided by the beam
current for a pixel near the center of the mine. Dividing
this number into the required 10000 counts for imaging
yields the required beam current. Using this current, the
power and number of counts characteristic of soil can be
calculated. To determine if this power level can also lead
to mine detection, the Neyman-Pearson criterion is applied.
This test maximizes the probability of detection while
holding the false alarm probability to a fixed level by
determining a threshold for deciding if a signal is present.
The criterion is modified to allow a variable signal to
noise ratio. The false alarm probability is given by
where Pn is the false alarm probability
erf is the error function,


110
TABLE V.l
Energies of Tungsten K Characteristic X Rays
X Ray
Actual Energy3
(keV)
Code Energy Bin
(keV)
Kcd
59.321
59
Ka2
57.984
58
KB1
67.244
67
KS2
69.081
69
K63
66.950
67
aActual energies of K characteristic x rays are from
Storm and Israel (1970).


0.96 ~|1 II1T11 | ¡-Tjj | i ; p-j [t~ f~[ I ~1 [~-[ [ | [ | TT | | II |
30 50 70 90 110 130 150 170 190 210
Energy (keV)
Figure VIII.12. Ratio of fluence responses for disturbed to in-place density of HTL
soil with the TST mine at selected depths of burial as a function of source energy
for the uncollimated detector. Calculations are for 100 keV photon beams perpendi
cularly incident on the centers of TST mines. The uncollimated detector consists of
two panels of 30 cm width and 210 cm length, separated by a raster gap of 10 cm, and
located 34.6075 cm above and parallel to the soil surface. Soil densities are 1.27
g/cmJ for disturbed soil, and 1.70 g/cin for in-place soil.
274


130
the response of the detector employed in the measurement
(Baird, 1981). As noted above, serious discrepancies in
published measurements of x-ray spectra are noted in the
literature (Fewell and Shuping, 1977), indicating that the
relative difficulty of the technique is high. For these
reasons, a measurement technique is not selected. However,
as described above, comparisons of calculated results with
published measurements of spectra, which have been deter
mined by reviewers to be reliable, have been useful in
testing the modified Kramers' formula method.
Monte Carlo Calculation
Implementation of a Monte Carlo code to calculate x-ray
spectra requires a good understanding of the bremsstrahlung
interaction cross sections for thick targets. Unfortunate
ly, these cross sections are not well known for the diagnos
tic and therapeutic x-ray energy ranges which are of in
terest in the mine detection problem (Koch and Motz, 1959).
Results of Monte Carlo calculations of x-ray spectra are
generally considered inferior to other techniques (Huang et
al., 1981). As a result this method is not selected.
Laplace Transform Pair Method
This technique was first introduced by Silberstein
(1932, 1933). It requires that exposure transmission meas
urements be made by placing varying thicknesses of materials
in the path of the beam (usually aluminum or copper). The
resulting exposure rate transmission versus thickness data
is then fit to a function of the attenuation coefficient of


148
reaching the Nal(Tl) crystal, resulting in an increase in
the fraction of energy absorbed in the crystal.
At the K edge of iodine (0.03317 MeV), there is a dis
continuous decrease in the fraction of energy absorbed in
the Nal(Tl) crystal. Below this energy, incident photons
are unable to remove K shell electrons in iodine; above it,
they are. The removal of a K shell electron is frequently
followed by emission of a K fluorescent x ray (radiationless
Auger electron emission is also possible). The decrease in
the fraction of energy absorbed in the crystal at the K edge
energy is caused by the escape of these iodine K fluorescent
x rays from front surface of the crystal.
Above the K edge, the absorbed fraction increases to a
maximum at about 0.100 MeV. This increase is due primarily
to the increasing depth of penetration of the incident pho
tons. The deeper into the Nal(Tl) crystal that photons
interact, the more difficult it is for the K fluorescent x
rays to escape the crystal. As depth of penetration in
creases, they are reabsorbed in the crystal with increasing
efficiency. A secondary mechanism for the increase in ab
sorbed fraction is the enhanced capability for penetration
of the material layers in front of the crystal.
As incident energy increases above the peak at approxi
mately 0.100 MeV, there is a decrease in the absorbed frac
tion. This is primarily a result of transmission of photons
through the crystal without interaction and small angle
(forward) Compton scattering events in which the scattered


30
Detector and Related Electronics
Two types of detectors have been used in the imaging
measurements. The x-ray sensing portion of the first de
tector is based on terbium activated gadolinium oxysulfide
rare earth intensifying screens. This device was construct
ed to provide an inexpensive, sensitive, large area detec
tor. For reasons detailed in Appendix E, this detector is
found to be unsuitable for the detection and imaging tasks.
It is replaced by Bicron Model .5M.390/.5L-X, sodium iodide
detectors. This detector type is used in all imaging
measurements. The geometry of this detector is shown in
Figure III.4. Also included in this diagram is a composite
shield designed to allow the detector, when operated in an
uncollimated mode, to simulate small regions of a large area
plane detector by permitting photons to enter only through
the exposed face. Several regions of the detector (labeled
3, 4, 5 and 6 in Figure III.4) are not identified in the
diagram. Bicron Corporation, the manufacturer of the detec
tor, provided the compositions and densities for these
materials with the understanding that they would not be
published due to their proprietary nature (Melocik, 1986).
They are included in the Monte Carlo calculations performed
to determine the detector response function (described in
Chapter VI). Table III.l provides the dimensions of the
materials shown in Figure III.4.
Because a large area, plane detector is a possible can
didate for an actual fielded system (Chapter II), it is


LANDMINE DETECTION BY
SCATTER RADIATION RADIOGRAPHY
by
JOHN G. CAMPBELL
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1987


Figure VII.7. Spatial distribution of backscattered fluence from 100 keV photons
perpendicularly incident on HTL soil. The fluence (photons/(incident photon-cin ))
striking a plane located 34.6075 cm above and parallel to the soil surface is shown.
The source beam is incident at the origin of the x-y plane at the soil surface.
183


266
clear, but, as expected, the magnitudes of the ratios are
much reduced from those produced by monoenergetic sources in
Chapter VII as a result of the presence of low energy pho
tons in each spectrum (see Figures F.9 and F.ll) and partial
energy deposition events in the small Nal(Tl) detector.
Environmental Parameters
In a fielded system, the mine detection process is
complicated by a number of environmental influences. This
section examines conditions which would be frequently
encountered by a mine detection system on the battlefield.
Height Sensitivity
The calculations described in Chapter VII are all based
upon a detector height of 34.6075 cm. This height is ap
proximately the minimum possible to allow operation over
moderately rough terrain without causing the detector panels
to strike the ground. Implied in this precaution is the
variation of height of the detector as the vehicle moves
across such terrain. Of much less importance are the
corresponding variation in the height of source and the
resulting changes in the beam size intersecting the soil,
provided perpendicular incidence and a fairly tightly
collimated source beam are employed.
The optimum uncollimated detector, in terms of height
sensitivity, has panels of infinite extent and no raster
gap. This detector, disregarding air attenuation, would be
completely insensitive to height variation because it would
intercept the entire backscattered fluence independent of


Figure IV.14. Number albedo versus energy for concrete. Calculated values of the
number albedo for the case of perpendicular incidence as a function of incident
photon energy are compared. The Berger and Raso (1960) values agree well with the
simple MCPHOT code calculations. Both neglect coherent scattering, and use only the
Klein-Nishina scattering distribution. The full MCPHOT code calculation includes
coherent scattering and incoherent scattering from bound electrons.
U1


Figure VIII.39. Three-dimensional image diagram of the measured uncollimated
detector response to a 200 kVp source beam filtered by Sn for the TST mine at a depth
of burial of 2.54 cm with overlying rock array. The response is sampled at a 2.54 cm
increment.
322


46
are compared. Previous studies made use of dinitrobenzene
as a TNT substitute. Unfortunately, this material is toxic.
Evaluation of a number of common nontoxic materials is made
by comparing linear interaction coefficients with those of
TNT. Sucrose is selected as the substitute. Table III.5
shows the comparison of the interaction coefficients of TNT
and sucrose.
TM
The explosive substitute is solidified Karo Light
Corn Syrup. While this material is not sucrose, it has
similar elemental composition and photon interaction
characteristics. Upon heating, a portion of the fructose
contained in the syrup is converted to sucrose. A number of
test batches of the substitute are made by removing water
from the syrup by heating. When the capability to consis-
tently obtain the same material density (1.56 g/cm ) is
achieved, samples are used in the tests described below and
found to be an acceptable substitute for TNT.
Materials Tests
Tests of photon interaction characteristics of the
explosive substitute and soil materials are conducted to
insure that the cross section sets used in the Monte Carlo
photon transport calculations are adequate. As described
TM
above, the TNT substitute is solidified Karo Light Corn
3
Syrup with a density of 1.56 g/cm The soil used in the
experiments is obtained locally. Its high sand content
suggests that it is similar to the Norfolk Sandy Loam (NSL)
soil described above. Samples of each of these materials


104
1.5%. With the exception of one low energy bin, all energy
spectra results are within expected statistical variation.
The fractional contribution of fluorescent emission photons
to the fluence at the disk was found to be 0.00027, justify
ing their neglect in the MCPHOT.P code. Further, since
these photons appeared in the 5 to 10 keV bin of the energy
spectrum, and most real detectors employ some type of dis
crimination against low energy noise, these photons would
not be detected.


429
keV is used to demonstrate the effects. For each angle,
four graphs are shown. These graphs display the fraction of
incident photon energy absorbed in the phosphor layers of
the detector, the fractions of incident photon energy
absorbed in each layer of the detector, the fraction of
incident photon energy lost into the reflection hemisphere,
and the fraction of the incident photon energy lost into the
transmission hemisphere. The fraction of incident photon
energy deposited in non-phosphor layers of the detector is
generally less than 0.01 and is not shown.
Perpendicular Incidence
Figure E.4 shows the fraction of the incident photon
energy absorbed in the phosphor layers of the detector for
the case of perpendicular incidence. At very low energies
(below 0.020 MeV), virtually all of the incident energy is
captured by the phosphor layers as a result of the very high
photoelectric cross section of gadolinium. Figure E.5
indicates that the first phosphor layer absorbs nearly all
the energy, shielding the second phosphor layer from any
significant number of interactions. Figure E.6 shows that
the fraction of incident photon energy lost in the reflected
direction is small (and remains so, up to the K edge). All
that can escape in this energy range are a few L x rays and
contributions from the few coherent and incoherent scatter
ing events. Figure E.7 shows that virtually no photon
energy is able to penetrate the screen, as would be expected
by the very high absorption of the first phosphor layer.


Figure VIII.40. Three-dimensional image diagram of the measured collimated detector
response to a 150 kVp source beam filtered by Al for the TST mine at a depth of
burial of 2.54 cm with overlying rock array. The response is sampled at a 2.54 cm
increment.
323


84
A
A


Figure IV.13. Boundaries and materials of Monte Carlo
calculations. Triangles indicate boundaries; circles/
materials. The boundaries are the detector plane (1)/ the
soil surface (2), the top of the mine (3), the air-explosive
interface in the mine (4), the bottom of the mine (5), the
cylinder wall in the air region of the mine (6), and the
cylinder wall in the explosive region of the mine (7). The
materials are air above the soil (1)/ soil (2), air within
the mine (3), and explosive (4). The detector plane boun
dary exists only for photons travelling upward/ away from
the soil plane.


*
Figure IV.18. Comparison of calculations of the solid angle differential coherent
cross section. Analytical and Monte Carlo calculations of the solid angle coherent
scattering cross section are compared for 20 keV photons on aluminum. The Monte
Carlo sampling technique used here is also employed in the MCPHOT codes. 100,000
photon histories are used in the Monte Carlo calculation.
101


Figure III.6. Soil mass attenuation coefficients. The mass attenuation coefficients
(cm /g) of the three soils used in the majority of the calculations, Malatula clay
loam (MCL), Hagerstown loam (HTL), and Norfolk sandy loam (NSL) are displayed. The
mass attenuation coefficients for trinitrotoluene (TNT), the explosive contained in
most mines, are also shown for comparison.


145
crystal, the charged particles of interest are again the
secondary electrons described above, and the electric field
is primarily that of the nuclei of iodine atoms. In the
energy range of interest in the mine detection problem, the
probability of producing bremsstrahlung photons is small.
Any bremsstrahlung produced would be of very low energy
resulting in rapid local reabsorption. For these reasons,
bremsstrahlung escape is not considered in the detector
response calculations of the DETNAI.P code.
Fluorescent emissions following photoelectric interac
tions near the surface of the Nal(Tl) crystal may escape the
crystal. This effect is included in the DETNAI.P code (and
in NAISPEC.PAS). It plays an important role in the shape of
the response function and serves as a method for checking
the response calculations against published values of the
iodine escape ratio (described below). This effect is more
important for low energy photons (above the K edge of io
dine) because high photoelectric cross sections make inter
actions near the surface of the crystal and the subsequent
fluorescent escape more probable.
Scatter of source photons from surrounding materials
will obviously effect the detector response if not accounted
for. Shielding the head of the x-ray machine and the sides
of the detector reduces this effect. The DETNAI.P code
assumes no scatter off of surrounding materials. As is de
scribed in Chapter VIII, the initial problem in reconciling
measured and calculated response was determined to be caused


M


Figure VIII.33. Three-dimensional image diagram of the measured collimated detector
response to a 200 kVp source beam filtered by Al for the TST mine at a depth of
burial of 7.62 cm. The response is sampled at a 2.54 cm increment.
314


Source Photon Energy (keV)
Figure VII.23. Ratio of Nal(Tl) detector response to fluence response as a function
of source energy. This figure shows the ratio of the two responses displayed in
Figure VII.22.


275
on TST mines at various depths of burial in HTL soil. The
detector is located 34.6075 cm above the soil and consists
of two panels, each 30 cm wide with a 10 cm raster gap. The
3
disturbed soil density is 1.27 g/cm ; the in-place soil
density, 1.70 g/cm The ratio displayed in the figure
should not be confused with the mine to soil fluence ratio.
The ratio displayed, multiplied by the in-place mine to soil
fluence ratio, gives the mine to soil fluence ratio in the
reduced density soil. The peak in the density enhancement
ratio lies in generally the same energy region as the peak
in the mine to soil fluence ratio. For the mine buried at
2.5 cm, the peak is shifted somewhat to lower energy reflec
ting the new-found capability of relatively low energy
photons to reach the soil surface. There is no change in
the conclusions regarding optimum energy for the uncolli
mated detector, but detection becomes easier at 5.0 cm.
Detection at 7.5 cm remains beyond the capability of the
uncollimated fluence detector, even in low density soil.
The effect of reduced density on the collimated detec
tor is much more dramatic. Table VIII.4 compares calcula
tions for the collimated detector for in-place and disturbed
soil. The conclusion reached is that detection is possible
at 10.0 cm with the reduced soil density. In fact, detec
tion is possible at any depth. The final entry in the table
indicates that the collimated configuration detects density
differences in the soil without the presence of the mine.
This conclusion is consistent with results obtained by Texas


456
for deeply buried mines. Double layers of the intensifying
2
screens with areas of 255 cm each are employed to maximize
light output. The geometry of the reflecting coating on the
interior of the detector is designed to direct a large
fraction of the visible light created by the screens to the
photocathode of the photomultiplier tube. A large diameter
bialkali photomultiplier tube is selected for its high
sensitivity and its ability to match the spectral character
istics of the visible light falling on the photocathode.
The combination of these items produces a detector which is
extremely sensitive to photon radiation in the energy range
of interest for mine detection. The detector is readily
capable of distinguishing between different scattering
materials placed in an x-ray beam in the mine detection
geometry. However, the count rates so obtained bear no
relationship to the calculated detector response matrix. A
series of measurements were made to define the causes for
this discrepancy. Two causes are found, high sensitivity
and the fluorescence decay time of the terbium activated
gadolinium oxysulfide phosphor used in the Trimax 12
screens.
Sensitivity
The high sensitivity of the detector system is a result
of two design factors. The first factor is the high visible
light output of the intensifying screens. This high output
is due to the inherently high efficiency of the screens to
absorb x-ray photon energy and emit visible light, and the


Figure VIII.46. Three-dimensional image diagram of the measured collimated detector
response to a 150 kVp source beam filtered by Al for the TST mine at a depth of
burial of 2.54 cm with irregular soil surface. The response is sampled at a 2.54 cm
increment.
331


Figure VII.27. Relationship between the raster gap size, the length of the
collimator, and the spacing of the first collimator element required to exclude
single scattered photons from the detector.
224


286
TABLE VIII.9
Object to Soil Fluence Ratios Produced by the
Collimated Detector for Selected Inhomogeneities
Collimator
Acceptance
Angle
Object
Wood
to Soil Fluence
Material
Aluminum
Ratio3
Iron
90.0b
1.041
0.916
0.197
0.013
0.012
0.005
36.9
1.054
0.881
0.175
0.026
0.023
0.009
25.8
1.280
0.887
0.121
0.076
0.060
0.019
23.1
1.400
0.759
0.081
0.133
0.088
0.025
Calculations are for 100 keV photon beams perpendicularly
incident on NSL with a density of 1.54 g/cm The beam
intercepts the objects at their centers. Diverging source
beams are 1.27 cm by 1.27 cm at the soil surface and are
produced by a point source at 64.48 cm above the soil sur
face. The detector consists of two panels/ each 210 cm long
by 30 cm wide, separated by a raster gap of 30 cm, located
parallel to and 34.6075 cm above the soil surface.
bSame as an uncollimated detector.


199
left source right
left source right
detector detector
Figure VII.18. Edge effect geometries. (a) Edge effect
produced by a beam intercept just inside the mine wall.
(b) Edge effect produced by a beam intercept just outside
the mine wall.


510
positive or negative numbers. If a negative number is
generated, it is converted to a positive number by adding
the magnitude of the largest negative integer, which is
equivalent to the largest positive number plus one. The
algorithm used is as follows.
BEGIN.
random seed < random seed*a + b.
if random seed < 0, then
random seed < random seed + 2147483647 + 1.
random number < c*random seed.
END.
In this algorithm, a = 843314861; b = 453816693; and c =
0.46566128752458E-9. The number, 2147483647, is 231-1.
These constants are from Forsythe et al. (1977).
Flourescent Emission
Fluorescent emission routines, based on the
recommendations of Carter and Cashwell (1977), are used in
the detector response codes. The calculated probabilities
of emission associated with the fluorescent emission photons
used in this research are shown in Table H.l. Data for the
calculations is from Storm and Israel (1970), with the ex
ception of total yields, which are taken from Fink et al.
(1966) or Bambynek et al. (1972). The more current data of
Bambynek et al. are used wherever available. Data for the L
shell yields are poorly known. Fortunately, the low ener
gies of the L fluorescent photons makes this shortcoming
unimportant in the mine detection problem.


522
Lederer, C. M., and Shirley, V. S. Table of Isotopes. New
York: Wiley, 1978.
Lickly, A. Applied Reasoning Corporation, Cambridge, MA.
Personal communications, June 6 and 11, 1986.
Macksey, K. Africa Corps. New York: Ballintine, 1968.
Marshall, T. G.; Scolaro, G.; Rand, D. L.; King, T.; and
Williams, V.P. "The DSI-32 Coprocessor Board." Byte, 10:
120-136, 1985.
Melocik, G. Bicron Corporation, Newbury, OH. Personal com
munication, November 21, 1986.
Minato, S. "Low Energy Components of Scattered Gamma Radi
ation." Nucl. Sci. Engr. 51:32-40, 1973.
Moler, R. B. "Workshop Report, Nuclear Techniques in Mine
Detection Research." Fort Belvoir, VA: Belvoir Research
and Development Center, 1985.
Moss, D. C. "An X-Ray Backscatter Imaging System: Hardware
and Software Development." Unpublished Master of Science
Degree Project Report. University of Florida, Gaines
ville, FL, 1986.
Nolan, R. V. ; Egghart, H. C.; Mittleman, L.; Brooke, R. L.;
Roder, F. L.; and Gravitte, D. L. MERADCOM Mine Detec
tion Program: 1960-1980. Fort Belvoir, VA: U.S. Army
Mobility Equipment Research and Development Command,
1980.
Norton, P. Inside the IBM PC. New York, NY: Prentice-
Hall, 1986.
Odeblad, E., and Norhagen, A. "Electron Density in a Local
ized Volume by Compton Scattering." Acta Radiolgica
45:161-167, 1956.
Petzold, C. "Accelerator Boards, Power for a Price." PC
Magazine 5(15):125-165, 1986.
Plyaskin, V. Ya.; Lysukhin, I. F.; Ruvinskiy, V. A.
Engineer Support of Combined-Arms Combat. Moscow:
Voyenizat, 1970. Translated from Russian and published
by the U. S. Army Foreign Science and Technology Center,
Charlottesville, VA, 1973.
Preiss, K., and Livnat, R. "Detection of Plastic Mines by
Gamma-Ray Backscatter." Trans. Israel Nucl. Soc.
1:30-33, 1973.


204
Conclusions Based on Signal Differences
The differences in the backscattered signals for mine
present and absent suggest the examination of four detector
types. These detector types are a simple, uncollimated
detector to exploit differences in fluence; a collimated
detector to exploit differences in the angular distribution
of the fluence; an energy window detector to exploit the
differences in the low energy spectra; and a segmented
fluence detector to exploit differences caused by edge
effects. Each of these detector types must be capable of
rapidly detecting mines over a path wide enough to allow
passage of an armored vehicle. This requirement results in
detector configurations similar to that shown in Figure
II.1, that is, large area detectors which allow rastering of
an x-ray source beam. The existence of the raster gap and
practical considerations of reasonable size result in
configurations different than those employed in the simple
physical arguments described above. The geometry of these
more realistic configurations is examined later in this
chapter. Despite the increase in geometric complexity,
calculations for the more realistic configurations are shown
to closely follow the general results presented above. Each
of the more realistic detector types is modelled as two
panels of detecting material located above and parallel to
the soil surface, and separated by a gap to allow raster of
the source beam. The collimated detector adds the capabil
ity to limit the acceptance angle of photons incident on the


Energy (keV)
Figure F.12. X-ray fluence spectrum, 200 kVp, 0.25 mm Al, 0.75 mm Pb. The x-ray
fluence spectrum at 200 kVp calculated by the XRSPEC.PAS code for the GE Maxitron 300
X-Ray Therapy Unit with 4.75 mm beryllium inherent filtration, 0.25 mm aluminum
equivalent monitor ionization chamber, 0.75 mm lead added filtration and air path
length of 60 cm is shown. Fluencje units are photons per cm per keV. Total fluence
is normalized to 1 photon per cm .
482


82
To obtain a random number between 0 and 1, the result of the
above operation is divided by m + 1. In a multiplicative
congruential generator, c is equal to zero. Unless care is
taken to avoid improper selection of the values of the con
stants, seriously flawed generators can be produced (Press
et al., 1986). The constants used in the random number
generators (detailed in Appendix H) in the MCPHOT.PAS and
MCPHOT.P codes are well established and recommended.
The Compaq Deskpro (Compaq, 1984a) used for the MCPHOT.
PAS calculations is based upon the Intel 8086 computer chip.
The 16 bit words of this machine allow only 65,535 distinct
integer values. Employment of a linear congruential method
on such a machine results in a maximum period of the same
size, provided optimum values of a, c, and m are chosen.
This is clearly unacceptable for the problem at hand. The
method selected for use in the MCPHOT.PAS code is a multi
plicative congruential form, which uses real numbers, sug
gested by Cheney and Kincaid (1980). An 8087 math coproces
sor (8087-2 for the Compaq Deskpro) and the 8087 supported
version of Turbo Pascal must be employed with this method to
obtain 16 digit real precision (Borland, 1985) required by
the algorithm. The maximum period of this generator is on
30
the order of one billion (2 ) random numbers (Cheney and
Kincaid, 1980). The penalty paid for this long period is
reduced speed due to real number arithmetic (Norton, 1986) .
The Definicon DSI-32 coprocessor used with the MCPHOT.P code
is based upon the National Semiconductor 32032 computer chip


162
Sharma et al. use the mass interaction coefficient data
of Grodstein (1957). The NAISPEC.PAS code uses the most
current published interaction data (Hubbell et al., 1975;
Hubbell, 1982; Storm and Israel, 1970). The incoherent
interaction coefficients in the Grodstein data are simply
calculated from the Klein-Nishina relationship. As a result
they are too high at low energies. Additionally, below 40
kev, the photoelectric data of Grodstein is very poor (15 to
20% low). The correct (lower) incoherent data will reduce
the escape ratio. The correct photoelectric data (higher)
will increase the escape ratio.
The model of Sharma et al. uses the broad energy mesh
of the Grodstein tables (14 energies between 10 and 300 keV)
and employs linear interpolation to obtain other values.
The NAISPEC.PAS code uses a fine mesh table constructed from
a cubic spline interpolation of the more modern data (183
energies between 1 and 300 keV), and uses log-log interpola
tion to obtain other values. Linear interpolation over
estimates the photoelectric interaction data in a coarse
mesh table leading to interactions nearer the crystal sur
face. The more accurate procedure of the NAISPEC.PAS code
will, therefore, lower the escape ratio.
The calculations of Sharma et al. are based on 10000
photon histories; the NAISPEC.PAS calculations are based on
50000 photon histories. The number of histories by itself
has no effect on the value of the escape ratio, but on how
precisely it is calculated.


Figure VIII.10. Fluence response as a function of height above the soil surface for
selected acceptance angles of the collimated detector. Calculations are for 100 keV
photon beams perpendicularly incident on the center of TST mines buried flush to the
surface in HTL soil. Collimated detectors consists of two panels of 30 width and 210
cm length, separated by a raster gap of 30 cm.
270


Figure IV.2. Solid angle differential coherent scattering cross section versus
scattering angle. The graph shows that for a given material, coherent scattering is
more forward peaked at higher energy, and for a given energy, coherent scattering in
any direction is greatest in the material with the higher atomic number.


APPENDIX F
X-RAY SPECTRA USED IN MEASUREMENTS
This appendix contains a catalog of calculations of the
x-ray spectra used in the experimental portion of the re
search described in Chapter VIII. These spectra are also
used for the discussion of power requirements contained in
that same chapter. The calculations of the spectra are
provided by the XRSPEC.PAS code described and validated in
Chapter V and Appendix D.
The source of the x-ray spectra used in the experiments
is the GE Maxitron 300 X-Ray Therapy Unit (General Electric,
1962). It is described in Chapter III. The spectra dis
played in this appendix are for peak kilovoltages of 100,
150 and 200 kVp. Beam filtration varies from very light to
very heavy, providing a fair representation of the range of
possible beam qualities available from this machine. The
spectra are displayed in terms of the fluence per unit
2
energy (photons per cm per keV) as a function of photon
energy. All spectra are normalized to a total fluence of 1
photon per cm^.
470


521
Jacobs, A. M.; Towe, B. C.; and Harkness, J. E. "Backscat-
ter X-Ray Radiography: Medical Applications." Proc. of
the SPIE, Medical Imaging 11:206-211, 1979.
Jaeger, R. G., ed. Engineering Compendium on Radiation
Shielding. Vol. II. New York: Springer-Verlag, 1975.
Jammer, M. The Conceptual Development of Quantum Mechanics.
New York: McGraw-Hill, 1966.
Johns, H. E., and Cunningham, J. R. The Physics of
Radiology. 4th ed. Springfield, IL: Thomas, 1983.
Jones, D. E. A. "The Determination from Absorption Data of
the Distribution of X-Ray Intensity in the Continuous
X-Ray Spectrum." Brit. J. Radiol. 13:95-101, 1940.
Joseph, P. M. "Mathematical Method for Determining kVp from
X-Ray Attenuation Measurements." Med. Phys. 2:201-207,
1975.
Kahn, H. Applications of Monte Carlo. Report AECU-3259.
Santa Monica, CA: The Rand Corp., 1956.
Knoll, G. F. Radiation Detection and Measurement. New
York: Wiley, 1979.
Koch, H. W., and Motz, J. W. "Bremsstrahlung Cross Section
Formulas and Related Data." Rev. Mod. Phys. 31:920-955,
1959.
Kodak Corporation. "Technical Information for General
Publication: Kodak Lanex Regular Screen/4864, Kodak
Lanex Medium Screen/4863, Kodak Lanex Fine Screen/4869."
Kodak Technical Information Coordination Office, Kodak
Park, NY, 1980.
Kondic, N. N., and Hahn, O. J. "Theory and Application of
the Parallel and Diverging Beam Method in Two-Phase
Systems." 4th International Heat Transfer Conference,
Paris 7:MT-1.4, 1970.
Kramers, H. A. "On the Theory of X-Ray Absorption and of
the Continuous X-Ray Spectrum." Philos. Mag. J. Sci.
46:836-871, 1923.
Lale, P. G. "The Examination of Internal Tissues Using
Gamma-Ray Scatter with Possible Extension to Megavolt
Radiography." Phys. Med. Biol. 4:159-167, 1959.
Lale, P. G. "Examination of Internal Tissues by High-Energy
Scattered X-Radiation." Radiol. 90:510-517, 1968.


492
XRGREEN.PAS calculates x-ray spectra by Greening's
Laplace transform pair method (Greening, 1950).
FITARCH.PAS calculates the fitting parameters for the
Archer-Wagner Laplace transform pair (Archer and Wagner,
1982) using the Levenberg-Marquardt method (Press et al.,
1986).
FITRUBIO.PAS calculates the fitting parameters for the
Rubio-Mainardi modification of the Archer-Wagner Laplace
transform pair (Rubio and Mainardi, 1984) by the Levenberg-
Marquardt method.
ARCHER.PAS computes the transmission of exposure rate
by the Archer-Wagner method, given the fitting parameters
found by the FITARCH.PAS code. The output of this code is
compared to the original exposure rate transmission measure
ments as a check of the FITARCH.PAS code results.
Detector Response Codes
DETECT.PAS is a Monte Carlo code which is used to cal
culate the detector response matrix for the gadolinium
oxysulfide x-ray intensifying screen based detector. The
code is described in Appendix E.
DETNAI.PAS and DETNAI.P are Monte Carlo codes employed
to calculate the plane detector response function for the
Bicron Corporation Nal(Tl) detector used in the measure
ments. The codes are described in Chapter VI.
DETCOR.PAS corrects the plane detector response func
tion calculated by the DETNAI.PAS code for the shield and
finite size of the actual detector. The correction tech
nique is described in Chapter VI.


61
/high photon energies are required for deep penetration,
these two factors combine to make backscatter from signifi
cant depths in the soil difficulty/
The Klein-Nishina formula (Evans, 1955) gives the solid
angle differential scattering cross section for the inelas
tic scattering of an unpolarized photon from a free elec
tron ,
da
KN
1+cos 0
[l+a(1-cose )]
O
a2(1-cose )2
o
[l+a(l-cos0 )]
s
da
In this equation
KN
d fl
is the solid angle differential
Klein-Nishina cross section per electron. Figure IV.5 shows
the differential Klein-Nishina cross section as a function
of scattering angle for three energies. At low energies
forward scatter and backscatter are approximately equally
probable. As energy increases, scattering becomes more
forward peakedy/This fact increases the difficulty of the
backscatter detection of mines/ The use of higher energy
photons, which are capable of penetrating to great depths in
soil, will eventually lead to a lower backscattered fluence
due to this forward peaking and the two factors discussed
above with respect to Compton's energy/angle relationship^
In reality, photons are bound, and inelastic events at
energies at which the incident photon energy is not very


Figure IV.19. Comparison of calculations of the solid angle differential incoherent
cross section. Analytical and Monte Carlo calculations of the solid angle incoherent
scattering cross section are compared for 50 keV photons on aluminum. The Monte
Carlo sampling technique used here is also employed in the MCPHOT codes. 100,000
photon histories are used in the Monte Carlo calculation.
102


Figure E.4. Fraction of incident energy absorbed, perpendicular incidence. The
fraction of incident x-ray photon energy absorbed in the two phosphor layers of the
detector system constructed from two halves of 3M Trimax 12 screen B 184048 as a
function of incident x-ray photon energy (MeV) for the case of perpendicular inci
dence is shown.
430


85
without interaction, and then, which of those boundaries is
closest and its distance.
Based upon the material in which the photon is travel
ing, a calculation of the distance to interaction is made.
While the distance any single photon travels before inter
acting is not predictable, the distribution of the distances
for a large number of photons is
p(x) = yexp(-yx),
where p(x) is the probability density function describing
the distribution of distances travelled to an
interaction,
y is the linear attenuation coefficient for the
material in which the photon travels at the
photon's energy,
x is the distance to first interaction.
This distance- distribution is sampled using random numbers
by the relationship
x = -(1.0/y) ln(rn),
where rn is a random number uniformly distributed between 0
and 1. The linear attenuation coefficient is obtained by
summing the mass interaction coefficients at the photon
energy for the appropriate material and then multiplying by
the material density.
The distances to the next boundary and to interaction
are then compared. If the boundary distance is smaller, the
photon is placed at the boundary and allowed to continue in


356
m is the number of samples,
d is the decision threshold level,
A is the number of counts due to irradiation of a
s
single pixel of soil, and
f is the reciprocal of the signal to noise ratio of
soil.
Using the desired and useful false alarm probabilities of
Table VIII.11, this equation is solved for the decision
threshold level, d, which is then substituted into the
expression for the probability of detection,
where is the probability of detection
A is the number of counts due to irradiation of a
m
single pixel characteristic of a beam intercept
near the center of the mine, and
f is the reciprocal of the signal to noise ratio of
the mine.
This formulation makes the probability of detection
independent of the power level. This is the actual case
since the majority of the noise is produced by height
variations, soil surface irregularities or inhomogeneities.
Increasing the power level simply increases the magnitude of
these sources proportionately. Since the majority of the
noise is produced by the soil, for mines buried below the
surface, f and f are similar. They are set equal in the
m
s


509
Random Number Generators
MCPHOT.PAS Generator
The MCPHOT.PAS code uses a real number modification of
a multiplicative congruential random number generator
suggested by Cheney and Kincaid (1980). The generator is
implemented by the following algorithm.
BEGIN.
random seed < (fraction[(a*random seed)/b])*b
random number < random seed/c
END.
In the algorithm, a = 16807.0; b = 2147483647.0; and c =
2147483648.0. The fraction operation provides the real
fractional portion of the bracketed quantity.
MCPHOT.P Generator
The MCPHOT.P code uses an integer based linear
congruential random number generator designed for 32-bit
word computers (Dyck et al., 1984). A straight forward
algorithm for this technique would be of the following form.
BEGIN.
random seed < [random seed*a + c] (mod m)
random number < random seed/m
END.
The algorithm actually employed takes advantage of the
automatic performance of (mod 2n) integer calculations by
computers, where n is the bit-word length of the computer
and m is 2n Because of the method by which computers
manipulate integers, these calculations can produce either


Figure E.l. Gadolinium oxysulfide based detector.


108
where VQ is the time dependent accelerating potential of
electrons striking the anode, and
Vmax t^te max;*-muin accelerating potential of
electrons striking the anode or the peak tube
potential.
To account for the self-rectified nature of the potential,
the value of the cosine is permitted to take on only posi
tive values by constraining its argument to -tt/2 to tt/2.
The resulting 201 values of the intensity are summed in 1
keV intervals. Negative values of the quantity, VQ V,
result in no contribution to the intensity.
Characteristic X-Ray Production
If the energy of the accelerated electrons exceeds the
binding energy of electrons of the anode material, charac
teristic x rays may be produced. Only K characteristic
photon emission from the tungsten anode is modelled by the
XRSPEC.PAS code; that is, only interactions with the K or
inner shell atomic electrons of tungsten are considered.
This presents no problem as long as sufficient filtration of
the beam is applied to remove the low energy L characteris
tic radiation. For the mine detection application, even
this filtration requirement is unnecessary, since virtually
no L x rays survive interaction with the soil to contribute
to the scattered fluence. The filtration is important,
however, in tests of the code which rely on transmission
measurements of the uncollided beam in which thin layers of
attenuating material are employed.


LIST OF FIGURES
FIGURES Title Page
II.1Conceptual large area backscatter detector
system 18
111.1 X-ray source, soil box and positioning
system and detector 22
111.2 Detector electronics, computer and x-ray
source console 24
111.3 Lead shield for tube head and detector . 29
111.4 Geometry of sodium iodide detector and
shield 31
III. 5 Components of the counting system 37
III.6 Soil mass attenuation coefficients .... 41
III. 7 TST mine used in measurements 45
111.8 Transmission comparison for TNT and
substitute 49
111.9 Transmission comparison for NSL and
local soil 51
IV.1 Atomic form factor versus momentum
transfer variable 55
IV.2 Solid angle differential coherent
scattering cross section versus
scattering angle 57
IV. 3 Coherent cross section versus photon
energy 58
IV.4 Fractional energy of Compton scattered
photons versus incident photon energy 60
IV.5 Solid angle differential Klein-Nishina
cross section versus scattering angle 62
xv


Figure VIII.4 Comparison of the number albedos of sucrose and TNT. Monte Carlo
calculations for the TST mine containing sucrose and TNT are compared. Calculations
are provided by the MCPHOT.P code.
256


Figure VII.29 Fluence response ratio matrices for the segmented detector for
perpendicularly incident 150 keV photon beams on the TST mine at 2.5 cm in HTL soil.
Each matrix value is with respect to the right rear panel of the segmented fluence
detector. All intercepts, except that at the center of the mine, are located either
1.00 cm inside or outside of the mine wall. The ratios are calculated at a detector
height of 34.6075 cm above the soil surface. Mine to soil ratios at 100 keV for an
unsegmented, uncollimated detector at each intercept are indicated in parentheses.


I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
'faf' A
>'^''2 1
Alan M.Jacobs,Chairman
Professor of Nuclear Engineering
Sciences
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree oJi-HDoctor-of Philosophy.
Edward E. Carroll,/Jr.
Professor of Nuclear Engineering
Sciences
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
/
J1
Edward T. Dugan //
Associate Professor" of Nuclear
Engineering Sciences
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
ohn Staudhammer
Professor of Electrical
Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
_ -,/ < > --v-
Mark C. Yang
Professor of Statistics


o
-4-J
O
C
0
OT
C
O
Q.
0
0
C
0
o
c
0
JD
Li_
Energy (keV)
Figure VIII.13. Object to soil fluence response ratio for selected materials as a
function of source energy for the uncollimated detector. Calculations are for 100
keV photon beams perpendicularly incident on the centers of selected objects
(described in text) buried flush with the soil surface. The uncollimated detector
consists of two panels of 30 cm width and 210 cm length, separated by a raster gap of
10 cm, and located 34.6075 cm above and parallel to the soil surface.
284


386
incompatible with rapid maneuver by mechanized forces.
Detection methods can be described as active or passive.
Active systems input energy of some form into the soil and
attempt to detect changes caused by the presence of the
mine. Passive systems rely on characteristics of mines
which produce emissions either from the mine itself or as a
result of soil disturbances.
Microwaves
A number of active detector types based on microwaves
have been examined. These systems consist of microwave
transmitters and receivers. The balanced bridge concept
uses two transmitters or receivers to compare the reflected
signal produced by adjacent areas simultaneously. The
reflected signal from the mine is much smaller than those
produced by reflection from the soil surface and by direct
coupling between transmitter and receiver. If the soil is
uniform in the vicinity of the buried mine and the detector
electronics are symmetric, the soil reflection and direct
coupling signals should be of the same amplitude and phase.
Any difference resulting from subtraction of these signals
represents the buried mine. The hand held nonmetallic mine
detector in use today in the U.S. Army operates on this
principle. The major problems with this detector are sur
face irregularities, soil attenuation, and soil inhomogenei
ties. False alarms can be generated by tree roots or air
pockets. When used with visual inspection and probing, the
detector is useful. The detector operates by producing


LIST OF TABLES continued
TABLES Page
G.l Benchmarks for Monte Carlo Transport
Codes 488
G.2 Photon Interaction Data Files 498
H.l Fluorescent Emission Probabilities .... 511
xiv


F(x.Z)
Figure IV.1. Atomic form factor versus momentum transfer variable. Atomic form
factors for aluminum and iron are shown as a function of the momentum transfer
variable. Data are from Hubbell et al. (1975).


138
technique as a part of this dissertation research effort
with four K characteristic x rays failed when applied to
real data. Values of the fluence for a characteristic x-ray
energy are as likely to be negative (without physical
meaning) as not. Conclusions regarding the limitation of
the usefulness of the Archer-Wagner method to cases of
little or no characteristic radiation are unchanged by the
extension proposed by Rubio and Mainardi.


423
TABLE E.l
Gadolinium Oxysulfide Screen Model
Screen Layer
Composition
Thickness
(cm)
Density
(g/cm3)
Protective
Lucite
.00100
1.000
Phosphor
Gd 9 s in
lucite
0.02694
4.526
Reflecting
Ti02
0.001905
4.260
Base
Lucite
0.0254
1.000


90
of the problem parameters, summary statistics, energy
spectrum of the backscattered fluence, and angular spectral
information to support calculations for collimated detector
geometries (MCPHOT.P only). The diskette file output is the
spatial distribution of the backscattered fluence and
detector response.
Validation of the Monte Carlo Codes
The MCPHOT.PAS and MCPHOT.P codes include detailed
consideration of coherent and incoherent scattering because
of the importance of low energy photons to the backscatter
mine detection problem. Published literature on backscatter
effects is rarely concerned with the low energy regime of
interest in this research. When such results at low energy
are published, these detailed effects are ignored. In order
to allow comparison with published results, the more sophis
ticated coherent and incoherent scattering routines must be
replaced by routines which neglect coherent scatter entirely
and use the Klein-Nishina distribution for incoherent scat
ter. Two separate comparisons are made with published re
sults. One is made at the simplified level; a second, with
the fully developed scattering routines employed. This dual
comparison also provides information on the range of appli
cability of the simplified approach. The fully developed
scattering routines are validated separately from the Monte
Carlo transport codes, and by comparison with a general
purpose, mainframe computer code.


Figure E.6. Fraction of incident energy reflected, perpendicular incidence. The
fraction of incident x-ray photon energy escaping into the relection hemisphere of
the detector system constructed from two halves of 3M Trimax 12 screen B 184048 as a
function of incident x-ray photon energy (MeV) for the case of perpendicular
incidence is shown.
432


283
Inhomogeneities
To this point, the only inhomogeneity considered in the
calculations has been the mine itself. Other objects will
be present in real applications. Calculations have been
performed for wood, aluminum and iron. Since aluminum is
similar in density and atomic number to common minerals,
calculations for it also provide information concerning
rock.
Figure VIII.13 shows the results of calculations, in
terms of the object to soil fluence ratio of the uncolli
mated fluence detector, for objects composed of these
three materials as a function of source beam energy. The
irradiation condition is for the standard heights and beam
sizes used throughout the calculation examples, for the
object buried flush to the surface in NSL soil. The wooden
object is a disk 8.57 cm in radius and 1.87 cm thick of
3
density, 0.522 g/cm These dimensions correspond to a
wooden disk used in imaging experiments. The aluminum and
iron disks are 10 cm in radius and 2 cm thick. The figure
shows that wood responds simiJ^aruL-y-, but less strongly than
the mine at low energy, but unlike the mine, at higher ener
gies becomes indistinguishable from soil; The similarity
to the mine at low energy is due to the low average atomic
number of wood as compared to soil. The dissimilarity in
response at high energy is due to the low density of the
wood compared to explosive. The high energy photons pass
through the wood without significant interaction. This


29


131
the material which has a known inverse Laplace transform.
This inverse transform function, multiplied by the deriva
tive of the attenuation coefficient with respect to energy
to transform variables from attenuation coefficient to
energy, constitutes the x-ray spectrum. Silberstein pro
vided the first such Laplace transform pair.
Significant improvements to Silberstein's original
transform pair were made by Bell (1936) and Jones (1940) to
account for the known physics of x-ray spectra and photon
attenuation. Greening (1947) provided an approximation
technique for accounting for the characteristic portion of
the x-ray spectrum and also produced the first definition of
the general properties required of other Laplace transform
pairs for use in spectral reconstruction (Greening, 1950).
The original Silberstein pair, though modified by additional
parameters, continued to be used even though its fits to
transmission data were often not particularly good. Better
Laplace transform pairs were identified (Saylor, 1969;
Huang et al., 1981? Archer and Wagner, 1982), but with their
use, the capability to approximate the characteristic por
tion of the spectrum was lost. Baird (1981) provides a
theoretical analysis of the general Laplace transform pair
technique. Ahuja et al. (1986), provide a summary of the
Laplace transform pair models which have been used up to
1986. The International Commission on Radiological Units
and Measurements (1964) cautions that the usefulness of this
technique depends upon the accuracy of measurement of the


200
large number of incident photons results in the response of
the detector on the left being higher than that on the
right. The lower half of the figure shows the analogous
basis for the edge effect of a beam striking just outside
the mine. Here, the path on the left includes air, while
the path on the right is entirely through soil.
Figure VII.19 shows the single scatter spatial distri
bution resulting from a perpendicularly incident, 100 keV
photon beam striking just inside of the edge of the mine
buried at 2.5 cm. Examination of this figure reveals an
asymmetric spatial distribution of the backscattered fluence
response. Fewer photons are backscattered into the positive
y half of the plane than into the negative y portion.
Figures VII.20 and VII.21 more clearly display this type of
asymmetry by showing the spatial distribution of the single
scatter mine to soil fluence ratios for this inside inter
cept, and an intercept just outside the edge. A detector
occupying the left front portion of the plane of Figure
VII.20 will record a response less than that of soil alone.
This is a result of the air layer allowing photons to reach
depths normally not attainable. These deeply located pho
tons are then unable to reach the detector through the long
slant paths through soil. The reduction in response occurs
because these photons produce essentially no contribution to
the backscattered fluence as they traverse the low density
air.


1.0
The
fraction of incident x-ray photon energy escaping into the transmission hemisphere of
the detector system constructed from two halves of 3M Trimax 12 screen B 184048 as a
function of incident x-ray photon energy (MeV) for the case of perpendicular
incidence is shown.
h
433


223
long collimators will again be needed. Figure VII.27 shows
the relationships for a detector height of 34.6075 cm. This
graph shows the required length of the collimator element
closest to the beam axis to prevent single scattered photons
from reaching the detector as a function of the raster gap
size and the distance to the next nearest element. To ob
tain an overall 30 cm clearance above flat soil surfaces,
the detector height must be increased to accommodate the
collimator. As can be seen from the graph, unless care is
taken with the geometry of the system, very long collimators
will preclude practical employment at useful heights of the
detector. With the small detector used in the experiments,
employed at distances from the beam axis of approximately 20
cm (analogous to one-half of the raster gap size), colli
mator lengths of 3 to 5 cm are appropriate.
Detector Panel Dimensions
The length of the detector panels is determined by the
requirement to cover the full width of an armored vehicle.
This vehicle width is typically on the order of three
meters, but the detector must extend beyond the sides of the
vehicle in order to provide mine detection information in
those locations. Given that detector heights of approxi
mately 30 cm are to be used, Figure VII.26 indicates that
this overhang on each end need not be more than about 70 cm.
The rapid fall off in backscattered fluence with distance
from the beam axis allows calculations performed for a
truncated section of the detector about the axis to be


LIST OF TABLES continued
TABLES Page
VII.1 Comparison of the Linear Relationship
Between the Ratio of Number to Energy
Albedo and Source Energy at
Perpendicular Incidence 180
VII.2 Mine to Soil Response Ratios at Selected
Beam Angles of Incidence 211
VII.3 Front to Back Panel Fluence Ratios of
the Collimated Detector for 100 keV
Photon Beams Incident at 60 Degrees . 214
VII.4 Results of Calculations for the Geometric
Parameters of the Collimated Fluence
Detector 220
VII.5 Mine to Soil Fluence Ratio Dependence on
Panel Width and Raster Gap Size for an
Uncollimated Detector 226
VII.6 Optimum Source Energies for the Uncolli
mated Fluence Detector 235
VII.7 Comparison of the Segmented and Unseg
mented Uncollimated Fluence Detectors 238
VII.8 Mine to Soil Fluence Ratio at Selected
Depths of Burial of the TST Mine. . 242
VII.9 Mine to Soil Fluence Ratios Versus Depth
of Mine Burial for the Energy Window
Detector with Source Energy of 100 keV. 245
VIII.1 Parameters for Spatial Distribution
Comparison 250
VIII.2 Comparison of Calculated and Measured Mine
to Soil Detector Response/Ratio with the
TST Mine at 0.0 cm 257
VIII.3 Energy Window Measurements for the TST
Mine at 2.54 cm Depth of Burial .... 265
VIII.4 Mine to Soil Fluence Ratio from the
Collimated Detector with Recently
Buried Mines 276
VIII.5 Mine to Soil Fluence Ratio from the
Energy Window Detector with Recently
Buried Mines 278
Xll


277
Nuclear Corporation in their mine detection efforts (Roder
and Van Konyenburg, 1975)/ as described in Chapter II. The
possibility of dummy minefields being constructed by simply
digging and refilling holes with loose soil exists with this
detector/ though imaging should be helpful in determining
whether sizes and shapes are characteristic of mines.
The energy window detector also experiences an enhance
ment in its capability to detect mines due to reduced soil
density. Table VIII.5 displays results for this detector
for the same example considered above with the collimated
detector. The energy window detector is capable of detec
tion down to at least 5 cmf and probably to 7.5 cm, in soil
recently disturbed by mine emplacement. Unlike the colli
mated detector, it is not subject to detecting refilled
holes.
Soil Moisture Content
The addition of water lowers the effective atomic
number of soil, making it a better scattering medium. As a
result, each of the detector types, all of which depend on
some form of differences in the scattering properties
between the mine and soil, would be expected to be degraded
in their ability to detect mines. This would be true if the
average atomic number were the only change in the soil, but
added water also results in higher density. As is seen in
the preceding section, the collimated detector is particu
larly sensitive to density, so that mixed results for it
might be expected.


Energy (keV)
Figure V.6. Spectrum comparison with Epp and Weiss at 80 kVp. The measured spec
trum, from Epp and Weiss (1966), is generated by a diagnositc x-ray unit operated at
80 kVp with 0.5 mm inherent aluminum filtration, 2.00 mm aluminum a^ded filtration
and an air path length of 2.13 m. Fluence units are photons per cin per keV. The
calculated spectrum is generated by the XRSPEC.PAS code. Total fluence is normalized
to 1 photon per cm.
124


467
up tail). The measured value for the ratio was 4.892
0.346, which compares well with the calculated value of
4.725 0.223. Response versus distance curves were made
under the same conditions as the first ratio comparison
above. These curves are shown in Figures E.21 and E.22.
In these figures, each set of calculated data has been
normalized to the measured data by multiplication by a
constant. The value of the constant for a data set is
determined by calculating the single best value for the
measured to calculated ratio considering unequal uncertain
ties in each ratio (Knoll, 1979). The cesium results are
good; the barium results show significant departure from
measured values closer to the detector, probably reflecting
the non-linear nature of the pulse pile up with variation of
source strength. This effect would be expected to play a
larger role for barium than cesium because of the higher
flux of the source and the higher response of the detector
to its lower energy photons.


249
the preceding chapter and the imaging results are applied to
estimations of the power requirements for the x-ray
generator.
Comparisons with Measurements
The experimental apparatus described in Chapter III is
used to perform a series of measurements to test the
accuracy of the calculation techniques. The calculation
techniques are described in detail in Chapters IV, V and VI,
and Appendix H. Graphs of the calculated x-ray spectra used
in the measurements described in this chapter are shown in
Appendix F.
Spatial Distribution of Detector Response
Measurements of the spatial distribution of the detec
tor response due to soil alone are made for three source
spectra at 100, 150 and 200 kVp, filtered by varying amounts
of lead, by varying the distance of the uncollimated Nal(Tl)
detector from the beam axis. The spectra used are shown in
Figures F.8, F.10 and F.12. Spectra are calculated by the
XRSPEC.PAS code. Table VIII.1 summarizes the experimental
and calculation parameters. Lead filtration is used in
these experiments to keep the backscattered fluence rate at
levels which can be handled by the Nal(Tl) detector without
producing dead time effects. Initial attempts at
comparisons with soil were very good at 100 kVp, but became
progressively worse as beam energy increased. A series of
experiments determined that the head leakage of the x-ray
machine provides a considerable contribution to the source


Figure VIII.55. Three-dimensional image diagram of the measured collimated detector
response to a 200 kVp source beam filtered by Al for a hole filled with loose soil.
The response is sampled at a 2.54 cm increment. The hole is 15 cm in radius and 15
cm deep.
341


TABLE OF CONTENTS continued
CHAPTERS Page
Single Scatter Model 73
Computation Scheme 73
Interaction Modeling 78
Monte Carlo Model 78
Problem Parameters and Data 80
Random Number Generators 81
Computation Scheme 83
Modelling Scattering Interactions ... 87
Russian Roulette 89
Code Output 89
Validation of the Monte Carlo Codes. ... 90
Number and Energy Albedo Calculations 91
Energy Spectra Comparisons 91
Comparison with Buried Mine
Calculations 91
Testing the Scattering Routines .... 99
V X-RAY SOURCE 105
Kramers' Formula Method 105
Kramers' Formula 106
Time Dependent Accelerating Potential 107
Characteristic X-Ray Production. . 108
Attenuation by Materials in the Beam
Path 109
Anode Self-Attenuation Ill
Effects Neglected in Model 116
General Features of the Calculated
Spectra 117
Testing the Modified Kramers' Formula
Model 119
Exposure Rate Transmission
Measurements 119
Comparisons with Published Spectra. . 122
Other Methods to Determine X-Ray Spectra 126
Measurement 126
Monte Carlo Calculation 130
Laplace Transform Pair Method 130
VI DETECTOR RESPONSE 139
Plane Detector Code 141
Assumptions in the Plane Detector
Response Calculation 144
Energy Deposition 146
Case of Zero Degree Incidence 146
Case of Large Angle Incidence 149
Counts Per Incident Photon 151
vi


LIST OF FIGURES continued
FIGURES Page
V.3 Heel effect displayed by spectra 120
V.4 Heel effect displayed by half value
thickness 121
V.5 Typical transmission curve comparison. . 123
V.6 Spectrum comparison with Epp and Weiss
at 80 kVp 124
V.7 Spectrum comparison with Epp and Weiss
at 105 kVp 125
V.8 Spectrum comparison with Fewell and
Shuping at 70 kVp 127
V.9 Spectrum comparison with Fewell and
Shuping at 80 kVp 128
V.10 Spectrum comparison with Fewell and
Shuping at 90 kVp 129
V.ll Archer-Wagner method fit to measured
transmission data 134
V.12 Comparison of modified Kramers' method
and the Archer-Wagner method at
80 kVp 136
V.13 Comparison of modified Kramers' method
and the Archer-Wagner method at
150 kVp 137
VI.1 Fraction of incident energy absorbed
perpendicular incidence 147
VI.2 Fraction of incident energy absorbed
75 degree incidence 150
VI.3 Plane detector response, discrimination
less than 0.03317 MeV 152
VI.4 Plane detector response, discrimination
greater than 0.03317 MeV 156
VI.5 Iodine escape peak ratio versus energy . 158
VI.6 Measured and calculated Nal(Tl) spectra. 164
VI. 7 Plane detector response 167
xvii


466
TABLE E.3
Calculated
Ratios of
133
Radiation
137
Ba to Cs
Field
Quantities,
Quantity
Ratio
a
)
Activity*3
0.744
+
0.032
Fluence rate (flux)
2.075
+
0.088
Energy fluence rate
0.522
+
0.022
Detector response
4.725
+
0.223
aSources located 3.016 cm from the center of the detector
plane.
^On August 14, 1986.


position
328
y position
1 3 5 7 9 11 13 15 17
Figure VIII.44. Two-dimensional image diagram of the
measured uncollimated detector response to a 200 kVp source
beam filtered by Pb for the TST mine at a depth of burial of
2.54 cm with irregular soil surface. The response is sam
pled at a 2.54 cm increment.


141
angles of incidence, ranging from 0 to 89.9 degrees. Ten
thousand photon histories are followed for each energy/angle
mesh point. A correction to this response matrix is then
calculated for the effect of the shield and edge leakage for
the same energy/angle mesh.
Plane Detector Code
The plane detector response is calculated by the
DETNAI.P code, written in Green Hills Pascal (Green Hills
Software, 1984) and implemented on the DSI-32 coprocessor
(Marshall et al., 1985). Cross sections for all materials
are calculated for a fine energy mesh by cubic spline
interpolation of data by Hubbell et al. (1975), Hubbell
(1982), and Storm and Israel (1970) when detailed informa
tion concerning photoelectric edge effects is required.
Full coherent, incoherent and photoelectric interactions,
including fluorescent emission from iodine are included.
The atomic form factors and incoherent scattering factors
are from Hubbell (1975). Implementation of the coherent
scattering routine is based on the techniques of Carter and
Cashwell (1977), and Williamson and Morin (1983a, 1983b).
Implementation of the incoherent scattering routine is also
based on the recommendations of Carter and Cashwell (1977),
utilizing the Kahn method (1956) for sampling the Klein-
Nishina relationship as a first step in the technique. The
atomic fluorescent yield of iodine is from Bambynek et al.
(1972). Four iodine fluorescent emission K x rays and one L
x ray are allowed, in accordance with the recommendations of


113
is more strongly attenuated. Soole shows that uncertainties
in the amount of characteristic radiation produced cannot
account for the discrepancy, and concludes that self-attenu
ation in the anode is the cause. The high photoelectric
interaction cross section of tungsten preferentially removes
the lower energy components resulting in the harder spec
trum. Soole makes use of the concept of mean effective
depth of production of x rays, originally presented by
Hanson and Salem (1961). While x rays are not produced at a
single point at depth within the anode, Hanson and Salem
show that for the purpose of calculations, a mean effective
depth can be defined. This depth is very small, on the
order of microns for tungsten. Soole independently deter
mines this depth using Kramers' formula by iteratively
adding small amounts of tungsten to materials through which
the beam passes. The mean effective depth is that which
provides the least squares deviation between calculated and
measured transmission data. His tungsten depths, derived in
this manner, are somewhat higher than published mean effec-
2
tive depths (in mg/cm of any target material). The pub
lished data are for a variety of smooth surface metal tar
gets, but do not include tungsten. The surface of a
tungsten anode, especially one which has been in operation
for an extended period of time, is far from smooth at the
micron level, so the differences are not surprising.
The least squares fitting technique employed by Soole
and described above, is used with exposure transmission


247
detection using an x-ray source. The uncollimated detectors
are capable of detection only if the mine is close to the
surface. The major problem with collimated and energy
window detectors is that the magnitude of the backscatter
signal sensed is small in comparison with that sensed by the
uncollimated detector. The problem is worse with the energy
window detector because the heavy filtration required fur
ther reduces the efficiency of the system. These considera
tions are directly related to a series of fundamental prac
tical concerns about the feasibility of a mine detection
system which center about the power requirements of the
x-ray source. The key variables which influence the power
requirement are the fluence spectrum, detection efficiency,
the speed of forward motion, the width of the path scanned,
noise characteristics, and beam size. Power calculations
are made in Chapter VIII.


Figure IV.12. Mass interaction coefficients of aluminum versus photon energy. Mass
interaction coefficients (in units of cm /g) for coherent scattering (coh), incoher
ent scattering (inc), and photoelectric interaction (pe) of aluminum are shown. The
sum of these coefficients is the mass scatter coefficient total).


position
316
y position
1 3 5 7 9 11 13 15 17
Figure VIII.35. Two-dimensional image diagram of the
measured collimated detector response to a 200 kVp source
beam filtered by A1 for the TST mine laid on the soil
surface. The response is sampled at a 2.54 cm increment.


LIST OF FIGURES continued
FIGURES Page
F.ll X-ray fluence spectrum, 200 kVp,
0.75 mm Pb 481
F.12 X-ray fluence spectrum, 200 kVp,
0.25 mm Al, 0.75 mm Pb 482
F.13 X-ray fluence spectrum, 200 kVp,
0.25 mm Al, 1.35 mm Pb 483
H.l The fit technique 514
xxx


Figure VIII.3. Calculated and measured spatial distribution of detector response
from backscatter from sandy soil at 200 kVp. Responses are normalized to 1.00 at
19.775 cm from the beam axis. Geometry and source details are provided in Table
VIII.1.
254


CHAPTER VII
MINE DETECTION MECHANISMS
The detection of a buried, nonmetallic antitank mine
using backscattered ionizing radiation depends upon dif
ferences between the characteristics of the reflected
photons for the cases of mine present and absent. These
differences derive from the simple physical characteristics
of the two cases. The mine represents a low atomic number
inclusion within the higher atomic number soil. Addition
ally, the mine has a definite geometric shape and includes a
region of air near its upper surface. While soil and ex
plosive densities are similar, the soil and air densities
are very dissimilar. This chapter describes the implica
tions of these physical differences in producing dissimilar
ities in the backscattered photon signals and provides the
basis for mine detection mechanisms to exploit them. Re
sults provided are from calculations using the SGLMIN.PAS
and MCPHOT.P codes.
Backscattered Photon Signal Differences
The physical differences discussed above lead to dissi
milarities in the fluence, energy fluence, spatial distri
bution, angular distribution, and energy spectra of the
backscattered photon signals. Additionally, the geometry of
169


Figure E.10. Fraction of incident energy reflected, 45 degree incidence. The frac
tion of incident x-ray photon energy escaping into the relection hemisphere of the
detector system constructed from two halves of 3M Trimax 12 screen B 184048 as a
function of incident x-ray photon energy (MeV) for the case of 45 degree incidence is
shown.
440


UT


42
TABLE III.4
Characteristics of Common
Nonmetallic Antitank
Warsaw Pact
Mines
Mine
Country
Mass
(kg)
Diameter
(cm)
Height
(cm)
Expl.
Type
Expl.
Mass (kg)
PM-60
GDR
11.3
32
12
TNT
8.6
TM-60
USSR
11.3
32
11.7
TNT
7.5
TMB-2
USSR
7.0
27.4
15.5
TNT or
AMATOL
5.0
PT-Mi-
Ba-III
CZECH
9.9
32.2
10.2
TNT
5.6
TST
N/A
10.3
30.2
variable
sucrose
7.5
Table adapted from U.S. Department of the Army, TRADOC
Threat Monograph, Comparison of Selected NATO and Warsaw
Pact Engineer Organizations and Equipment (U.S. Army
Training and Doctrine Command, Fort Monroe, VA, 1979b),
p. 88.


419
variability in composition is indicated. Communications
with 3M Corporation indicate that this variation in mass is
not unusual (Frank, 1986). Additional information concern
ing the screen composition was provided in those communica
tions and by 3M product brochures (3M, 1985a). Unfortunate
ly, that information is incompatible with the measured
masses of the screens. 3M Corporation suggests that the
discrepancy may be due to entrained air in the phosphor
layer (Frank, 1986).
Given the mass variability and the apparent discrepan
cies in the compositions and thicknesses, x-ray attenuation
measurements were performed to determine the actual thick
nesses of gadolinium oxysulfide in the screens. Preliminary
Monte Carlo calculations indicated that the attenuation pro
perties of the screens depend almost entirely on only the
gadolinium oxysulfide in the phosphor layer. With this in
mind, a model of the screen was constructed using the in
formation provided by 3M for all layers except the phosphor.
To determine the phosphor layer composition and thickness, a
modification of a method used by Venema (1979) to address
the same lack of information for x-ray intensifying screens
due to proprietary reasons is employed. Venema assumes that
screens under investigation are composed of pure gadolinium
oxysulfide. He then measures the attenuation produced by
the screens when subjected to an x-ray source, and based
upon these results, calculates the thicknesses of the gado-
2
linium oxysulfide in mg/cm The method used m this


279
Table VIII.6 shows results/ in terms of the mine to
soil fluence ratio, for the uncollimated fluence detector
for three different moisture contents of HTL soil with the
TST mine at a depth of burial of 2.5 cm. The example is for
100 keV source photons incident perpendicularly on the mine
center. The table shows a slight degradation in the mine to
soil fluence ratio as a result of increasing water content
for this detector.
Table VIII.7 shows results of calculations for the
collimated detector for two different soil moisture contents
of HTL soil as a function of source beam energy. --At low ,
energies^the effect of additional moisture is tolower the jf
(mine to soil fluence ratio; at higher energies, to increase I
(it. At the lower energies the dominant mechanism for change
is the reduction in the photoelectric scattering cross
section of the soil with increasing moisture content, re
sulting in increased incoherent scattering, which degrades
the ratio. At higher energies, where the photoelectric
cross section is already low, the dominant mechanism is the
increased density of the soil with the higher water content.
The increase in density serves to enhance the attenuation
difference between the mine and soil.
Table VIII.8 shows the results of calculations for the
energy window detector for HTL soil of three different soil
moisture contents. The results indicate the mine detection
capability of the energy window technique is degraded more
by moisture than either of the other two detector configura
tions .


Figure E.9. Fraction of incident energy absorbed in each screen, 45 degree inci
dence. The fraction of incident x-ray photon energy absorbed in the two phosphor
layers of the detector system constructed from two halves of 3M Trimax 12 screen B
184048 as a function of incident x-ray photon energy (MeV) for the case of 45 degree
incidence is shown. The first screen is that nearest the incident photon when it
first encounters the detector.
438


position
346
y position
1 3 5 7 9 11 13 15 17
Figure VIII.57. Two-dimensional image diagram of the
measured uncollimated detector response to a 100 kVp source
beam filtered by Pb for the TST mine at depth of burial of
2.54 cm with irregular soil surface. The response is
sampled at a 2.54 cm increment. Compare to Figure VIII.44.


TABLE OF CONTENTS
continued
APPENDICES Page
H MONTE CARLO TECHNIQUES 501
Angular Scattering Distributions 501
Momentum Transfer Variable 501
Incoherent Scattering 502
Sampling the Klein-Nishina
Distribution 504
Coherent Scattering 506
Random Number Generators 509
MCPHOT.PAS Generator 509
MCPHOT.P Generator 509
Fluorescent Emission 510
Application to Polyenergetic Sources . 512
Available Methods 512
Application of the Fit Method 513
LIST OF REFERENCES 516
BIOGRAPHICAL SKETCH 527
x


4
direction
of motion
90 cm
-j30 cm}-
90 cm
Front
Left
Panel
Front
Right
Panel
/ , ,
Lduur axis
Beam/ ouii j-iiLCivjt:p u iasctsi yap
T
30 cm
1
10
T
30
1
30 cm
i
vehicle
Figure VII.28. Geometry of the segmented fluence detector.
228


Figure VIII.53. Three-dimensional image diagram of the measured uncollimated
detector response to a 100 kvp source beam filtered by Pb for water contained in a
thin plastic container buried flush to the soil surface. The response is sampled at
a 1.27 cm increment. The container is 5 cm in radius and 7 cm deep.
339


59
form factors for compounds is only an approximation to
physical reality.
Incoherent Scattering
Compton (1923) first described photon inelastic scat
tering from a free electron. In his model of this inter
action, the photon strikes a free, stationary electron pro
ducing a new, lower energy, scattered photon and a recoil
electron. This free electron case will be approximately
correct if the energy of the incident photon is very large
in comparison with the binding energy of the electron to its
atom. Compton's formula for the dependence of the scattered
photon's energy on the energy of the incident photon and the
scattering angle is
E' =
E
l+a(l-cose ) '
S
where E' is the energy of the scattered photon,
E is the energy of the incident photon,
0g is the scattering angle, and
2 2
a = E/m c where me is the rest mass energy of the

electron (0.511 MeV).
This relationship plays a very important role in the
mine detection problem^ Figure IV.4 shows the fractional
energy (E'/E) in a Compton interaction as a function of in
cident photon energy for several scattering angles. The
fractional loss is greatest at high energies, and at a fixed
energy, for large scattering angles (backscattering). Since


Figure VIII.18. Low pass filtered Monte Carlo image for the TST mine at 2.5 cm depth
of burial in NSL soil for the uncollimated fluence detector. This figure is the
result of two-dimensional low pass filtration of the image of Figure VIII.17.
295


x (Reciprocal Angstroms)
Figure IV.6. Incoherent scattering function versus momentum transfer variable. To
account for incoherent scattering from bound electrons/ the Klein-Nishina cross
section is multipled by the incoherent scattering function. Data are from Hubbell et
al. (1975).
a\


426
TABLE E.2
Energies of Fluorescent Photons Used
in the DETECT.PAS Code
X-Ray
Energy (keV)
Titanium
Gadolinium
Weighted average
of 3 L x rays
not considered
6.642
Kal
4.510
42.996
Ka2
4.504
42.309
kB1' weighted
average of M2,M3,M4
to K transitions
4.931
48.6485
k82' weighted
average of N2,N3
to K transitions
not applicable
49.9595


351
conditions. The code can then be used for calculations with
different beam filtrations at this same peak kilovoltage and
at this single position. Values of the flux at other posi
tions at this same peak kilovoltage are calculated using the
inverse square law. Separate exposure rate measurements are
required for each peak kilovoltage of interest to determine
the appropriate flux normalization constant. The flux di
vided by the beam current applied during the exposure rate
measurement provides the desired quantity for the power
calculations. Since the voltage is specified by the beam
energy, the beam current becomes the quantity of interest in
fixing the power.
The ratios of fluence to exposure from the work of
Fewell and Shuping (1977), produced by a similar single
phase x-ray machine, are used to test the calculations of
the XRSPEC.PAS code. Differences of less than 2% between
the calculated and published fluence to exposure ratios are
found for three spectra (Figures F.8 through F.10) from this
paper. Table VIII.12 provides calculated results for the
various spectra used in the measurements. These values are
typical of x-ray generators having tungsten anodes, and are
used in the power calculations. A significant improvement
in the number of source photons available can be made by
lowering the source to the height of the detector while
maintaining the same beam size at the soil surface. There
is virtually no change in the characteristics of the
backscatter radiation due to the larger angular dispersion


Energy (eV)
Figure E.16. Emission spectrum of gadolinium oxysulfide with 0.3 atom % terbium.
The relative intensities of the discrete line emission spectrum of a terbium acti
vated gadolinium oxysulfide x-ray intensifying screen containing 0.3 atom % terbium
replacing gadolinium (here, the 3M Alpha 8 screen) and the relative sensitivity of
the Hamamatsu R877 photomultiplier tube versus photon energy (eV) are shown.
452


o
D
tu
O
"O
0
J3
<
L_
0
jQ
E
n
20 60 100 140 180 220
Energy (keV)
Figure VII.2. Number albedo ratios versus energy for the TST mine at 0.0 cm in three
soils. The ratio of the number albedos of mine present to soil only are shown for
three soil types for perpendicularly incident photon beams striking the center of the
TST mine buried flush with the soil surface.
174


Detector Response
5.0E-005 -i
Figure H.l. The fit technique. A typical example o| the fit technique for the
detector response (in counts per source photon per cin of detector face area) as a
function of source energy for the Bicron Model .5M.39Q/.5L-X Nal(Tl) detector. The
solid line is a cubic spline fit to the data; the dashed line, a fourth order
polynomial least squares fit.
514


ACKNOWLEDGMENTS
A number of individuals and organizations have played
an important role in my research. First and foremost, I
thank my wife, Becky, for her support, understanding, and
patience.
Dr. Alan Jacobs, who was my research advisor, was
always willing to help, whether the assistance required
discussion of new ideas or manual labor. The basic concept
of the project, using imaging techniques for mine detection,
was his. The generous amount of time he took from a very
busy schedule is greatly appreciated. I thank the other
members of my committee, Dr. Edward Carroll, Dr. Edward
Dugan, Dr. John Staudhammer, and Dr. Mark Yang, for their
time and guidance.
Two graduate students, who worked on other aspects of
the research problem, also contributed to my efforts.
Captain Dale Moss designed the soil box positioning system
and its computer control. Linda Hipp was an equal partner
in the assembly of the positioning system and spent many
long hours performing measurements.
I thank Bill Coughlin of the Radiation Control
Department for the loan of an ionization chamber for the
exposure rate transmission experiments, and Harvey Norton,
11


503
dgKH
p(fi) = dfl S (x, Z ).
a _
me
Multiplying this expression by unity in the form of several
factors and rearranging gives
da
P() = S(xmax'Z)
0inc
KN
S(x,Z)
S(x ,Z)
max
dfl
TKN
The probability density function is now in a generalized
form for applying rejection sampling. The expression
contains three parts, a term which is independent of the
scattering angle, a term involving the ratio of incoherent
scattering functions, and a new probability density
function. This new probability density function is that of
the angular scattering distribution of the Klein-Nishina
cross section. The ratio of the incoherent scattering
functions is always a number between 0 and 1, since S(x,Z)
is a monotonically increasing function (see Figure IV.6).
Determining the incoherent scattering angle begins by
sampling the Klein-Nishina probability density function for
the scattering angle (described below). This trial sampled
value, along with the energy of the incident photon, is used
to calculate a trial sample momentum transfer variable. A
table of the momentum transfer variables and associated in
coherent scattering function values of the appropriate
material is entered. The values of the incoherent scatter
ing function at x and x are found. The ratio of these
3 m z* v


186
ratio is greater than 1.00 everywhere, it is higher at posi
tions further from the beam axis because, for equal slant
paths through their respective materials, photons traveling
through explosive are less attenuated than those travelling
through soil. The existence of the central minimum is es
sentially due to the single scattered component. Figure
VII.10 shows the same quotient for the single scattered
component only, more clearly revealing its origin. This
result implies that a detector will be better able to detect
mines if the regions corresponding to the central minimum
are not included within it. As a practical matter, part of
the central region must be removed to allow raster of the
beam.
Angular Distribution
The angular distribution referred to in this section is
that of the photons striking a plane above the soil surface
after backscatter from soil or mine. Figure VII.11 shows
the differential angular spectra for the cases under discus
sion for a perpendicularly incident 100 keV beam. Zero
radians or 0 degrees is equivalent to perpendicular inci
dence on the plane. Figure VII.12 shows the same spectra
for the multiply scattered photons only. Greater differ
ences in ratios between the soil and mine cases in the
multiple scatter spectra suggests that a detector which is
capable of removing the single scatter component would be
more sensitive to mine detection. The differences in the
multiple scattered spectra are a result of the much lower


258
calculations predict that for a surface buried mine, the low
energy beams are more efficient at displaying contrast
between mine and soil. This prediction is verified by the
measurements. Additionally, the calculations predict that
the mine to soil ratio has a relative minimum in its spatial
distribution. The measurements confirm the increase in
ratio with distance from the beam axis.
Edge Effects
Calculations predict the existence of edge effects when
the source beam strikes near the wall of the mine. The
first measured images are designed to test this prediction.
To amplify the existence of any such effects, two non-mine
targets are selected. These objects are annuli composed of
lucite and steel. Each is buried with its top surface flush
with the soil, and the soil in the center removed. The
lucite annulus has an outer diameter of 15.24 cm, inner
diameter of 12.70 cm, and height of 7.62 cm. The steel
annulus has an outer diamter of 17.78 cm, an inner diameter
of 15.24 cm, and a height of 7.62 cm. Both objects are,
therefore, considerably smaller than an antitank mine. In
order to resolve the 1.27 cm thick walls of each target, the
backscattered fluence is sampled at an increment of the same
size. The 100 kVp spectrum shown in Figure F.8 is used for
the image. The detector is located 19.775 cm from the beam
axis, and is uncollimated. All other experimental condi
tions are the same as indicated in Table VIII.1. The
purpose of the air space in the centers of the annuli is to


Photons/MeV/Incident Photon
Figure IV.16. Backscattered energy spectrum, 0.6616 MeV on aluminum. Calculations
are for perpendicular incidence of 0.6616 MeV photons on aluminum by Minato (1973)
and the simple MCPHOT are compared.


220
TABLE VII. 4
Results of Calculations for the Geometric Parameters
of the Collimated Fluence Detector
Mine to Soil Fluence Ratio3
Energy Gap Size Collimator Acceptance Angle
(keV)
(cm)
90.0
36.9
25.8
23.1
19.9
40
30
1.006
0.020
0.996
0.039
_b
_b
_b
40
1.022
0.022
1.023
0.065
_b
_b
_b
50
30
1.047
0.021
1.130
0.046
1.353
0.178
2.058
0.773
_b .
40
1.059
0.023
1.161
0.074
2.485
1.260
1.826
1.025
_b
60
30
1.090
0.022
1.178
0.049
1.570
0.184
3.975
1.235
_b
40
1.076
0.024
1.141
0.071
2.895
1.419
1.896
1.092
_b
80
30
1.149
0.019
1.297
0.042
1.867
0.163
3.606
0.588
5.034
1.456
40
1.126
0.021
1.336
0.066
2.749
0.725
3.721
1.457
2.330
1.072
100
30
1.131
0.016
1.240
0.033
1.650
0.114
2.474
0.294
4.047
0.876
40
1.141
0.019
1.285
0.055
2.829
0.582
2.738
0.775
3.247
1.189
120
30
1.155
0.016
1.289
0.035
1.679
0.114
2.167
0.234
2.262
0.366
40
1.130
0.018
1.357
0.053
3.025
0.509
2.535
0.556
2.958
0.907
150
30
1.092
0.015
1.169
0.030
1.415
0.084
1.907
0.173
2.047
0.277
40
1.087
0.016
1.332
0.049
2.440
0.333
2.262
0.413
1.986
0.494


422
gadolinium oxysulfide thickness estimate and the model of
the other portions of the screens. Using these calculated
values for the binder material the entire screen model,
minus the gadolinium oxysulfide, is introduced into the
XRSPEC.PAS calculations. Thicknesses of gadolinium
oxysulfide are added to these calculations and varied until
the computed exposure rate transmission matches that of the
experiments. Using this second value for the thickness of
the gadolinium oxysulfide, the mass balance equation is
again used to obtain a second estimate of the binder
thickness. The entire process continues until convergence
is obtained. Convergence is very rapid, and the final
result confirms that Venema's assumption of pure gadolinium
oxysulfide is fairly good; the difference between this
assumption and the final result of the iterative process is
only 2.2%. Table E.l gives the thicknesses and densities of
the screen used in the detector (one back screen was divided
into halves to produce the two layers).
Detector Response Matrix Calculation
Calculation Technique
A Monte Carlo code, DETECT.PAS, written in Turbo Pascal
(Borland, 1985), is used to construct the detector response
matrix for the gadolinium oxysulfide based screen materials.
The code is a modification of the MCPHOT.PAS photon trans
port code discussed in Chapter IV. The major differences
between the codes, other than materials and geometry, is
that photoelectric interactions with subsequent fluorescent
emission are modelled in DETECT.PAS.


194
It is significant that an optimum collimation angle may
occur for a particular combination of photon energy, detec
tor height, and mine geometry. If the collimator acceptance
angle is too large, single scattered photons are admitted,
making the ratio low. As noted in Chapter II, many early
applications of scatter imaging made use of the fact that
the single scattered fluence is very nearly independent of
all variables except density. Since the mine and soil
densities are similar, the single scattered fluences are
roughly alike. If the collimator acceptance angle is too
small, the area viewed by the collimated region of the
detection plane shrinks. When the geometry is such that the
area viewed is at the edge of the mine, the ratio drops.
This edge effect is caused by the air layer in the mine.
The photons scattering in the explosive enter the soil at
depths which prevent them from reaching the surface. The
average photon scattering in the soil, which eventually
reaches the collimated plane, is always close to the
surface. In extreme cases, the ratio may fall below unity.
Energy Spectra
Figure VII.16 shows the differential energy spectra for
100 keV photons perpendicularly incident on the problem
cases. The major difference in the spectral shapes with the
mine present occurs in the lower energy region and is due to
the increased multiple scatter in the lower atomic number
materials. The break in the smoothness of the spectral
curves at high energy is due to coherent backscatter. The


383
At the pivotal battle of Kursk during the summer of
1943, mines played a decisive role. The German attack into
the Kursk salient was expected; the Soviet forces, under
Zhukov, were completely prepared (Zhukov, 1969). Six belts
of fortified positions, each 175 km long, were protected by
minefields of linear densities of up to 8000 mines per kilo
meter (Caidin, 1974). Minefields were positioned to chan
nelize the attacking German forces into fire traps where
concentrated direct fires and artillery were applied.
German forces attempting to advance did not find it unusual
to have to remove 40,000 mines per day in the sector of a
Corps (Von Mellenthin, 1956). Such German efforts to remove
minefields were met by heavy Soviet resistance, including
snipers dedicated to protecting the fields. When German
armor did manage to break through, the Soviets mined behind
them and then counterattacked (Caidin, 1974). The first
appearance of specialized engineer units designed to protect
Soviet flanks in the offense with mines occurred at Kursk
(Baxter, 1986).
At the end of the war, Soviet expertise in both mine
and countermine warfare was unequaled. In most aspects (a
notable exception is scatterable mines), this is also true
today (Nolan et al., 1980; Honeywell, 1981).
Korea and Vietnam
In Korea, low density, random mining proved effective
in slowing the movement of U.S. forces. Mine rollers,
pushed by tanks and designed to detonate pressure mines,


77
computes the fluence per incident photon. This quantity is
obtained by calculating a series of probabilities. These
probabilities are of survival while passing through air from
the source to the soil plane, of survival while passing
through soil or mine to a scattering point, of undergoing an
incoherent scattering interaction in a small incremental
volume about a scattering point, of scattering into an in
cremental solid angle about a point in the detector array,
of survival while passing from the scattering point through
the soil or mine towards a point in the detector plane, and
of survival while passing through air from the soil plane to
a point in the detector plane. The product of these prob
abilities gives the desired fluence per incident photon at a
single point in the detector plane from a single incremental
scattering volume. The summation of such results from in
crements along the photon's path to a depth where the incre
mental response is negligible gives the total single scat
tered fluence per incident photon at a single point in the
detector array. This process is carried out for all points
in the detector array. Typically, the array consists of 421
points at a 10 cm increment within a 200 cm by 200 cm de
tector plane. A geometry routine calculates the distances
along the photon path through the various materials en
countered. A full three dimensional representation of the
TST mine with air and explosive layers is included in the
geometry routine. Output of results of calculations is


171
Figure VII.1 shows number albedos as a function of source
beam energy for perpendicular incidence on HTL soil, and the
centers of TST mines buried in HTL soil with their top sur
faces 0.0 (flush to the surface) and 2.5 cm below the
ground. The number albedo, representing the fraction of all
incident photons which are reflected, is directly propor
tional to the backscattered fluence. In all three cases,
the shapes of the number albedo curves are similar. The
number albedo is low at low energies because photoelectric
interactions are dominant. At these energies, photons are
much more likely to be absorbed than scattered. As source
photon energy increases, the probability of incoherent
scattering increases, accounting for the rise in the number
albedo. At higher energies the rate of increase slows and
the curves level off. This is a result of the preference in
incoherent scattering for forward scatter as energy in
creases. The case of the mine buried flush with the surface
shows the greatest difference from the soil alone. This is
expected since it presents the low atomic number explosive
directly to the beam. The difference for the case of the
mine buried at 2.5 cm is much smaller. At low energy there
is little difference from the soil only case. This is a
result of the inability of the low energy photons to pene
trate the soil layer in both entrance and exit directions.
As energy increases, photons are able to penetrate, but soil
attenuation reduces the backscattered signal. Since the
incoherent cross section per electron is only weakly


54
where is the solid angle differential coherent
scattering cross section,
F(x,Z) is the atomic form factor, which depends
upon the atomic number, Z, of the material
and the momentum transfer variable, x, given
by
x
where X is the wavelength of the photon.
The integral of the solid angle differential coherent
cross section gives the probability of coherent scattering
per atom per unit incident fluence,
2
(1 + cos20_)sin F2(x,Z)d6
s s s
e
b
where a ^ is the total coherent scattering cross section
per atom. Coherent scattering cross sections and atomic
form factors are provided in tabular form for all elements
by Hubbell et al. (1975). The square of the atomic form
factor represents the probability that the electrons of an
atom take up the recoil momentum of the interaction without
absorbing any of the incident photon's energy. Figure IV. 1
shows a graph of the atomic form factors of aluminum (Z=13)


Photons/MeV/lncident Photon
20 40 60 80 100
Scattered Photon Energy (keV)
Figure VII.16. Differential energy spectra for 100 keV photons perpendicularly in
cident on HTL soil and two TST mine cases. Differential energy spectra (photons/
(source photon MeV)), calculated for the soil and mine present cases. The major
difference between soil and mine is at low energy.
195


146
by scatter of head leakage photons. The detector response
calculation played the key role in identifying this
previously unnoticed scatter path.
If two pulses arrive during the resolving time of the
detector, the sum of the pulses will be detected, resulting
in a single count at an incorrect energy. This is avoided
by measuring at count rates where such sum events are im
probable. One of the criteria for selection of the energy/
filtration combinations being used is to avoid high count
rate situations.
Energy Deposition
As explained above, gross energy deposition is not the
primary quantity of interest in Nal(Tl) response. It is,
however, instructive to examine the energy absorption
process to obtain a better physical feel for the nature of
the interactions occurring in the detection process.
Case of Zero Degree Incidence
Figure VI.1 shows the fraction of the incident photon
energy absorbed in the Nal(Tl) crystal as a function of
incident photon energy for the case of 0 degree incidence on
the outer aluminum layer of the detector. The shape of the
curve is explained by examining the photon interaction
characteristics of the crystal.
At low energy the fraction of incident energy absorbed
is low due to absorption of photons in the material layers
in front of the crystal. As incident energy increases, more
photons are capable of penetrating the front layers and


Number Albedo/Energy Albedo
Energy (keV)
Figure VII.6. Ratio of number to energy albedo for HTL soil and two TST mine cases.
The relationship between the number to energy albedo ratio as a function of energy is
linear.
181


89
routine in the Monte Carlo codes then uses the precollision
direction cosines and the scatter direction cosines with
respect to the initial direction to calculate the new
direction cosines with respect to the coordinate system of
the problem. An algorithm given by Carter and Cashwell
(1977) is used for this pupose.
Russian Roulette
Before allowing a scattered photon to recycle through
the scheme described, the photon is examined to determine if
Russian roulette should be played. The criteria for
subjecting the photon to Russian roulette are that the
photon be located well outside or below the mine and be
moving away from the mine, or that the photon be at least 1
cm below the soil surface and have an energy of 20 keV or
less, or that the photon has a weight of 0.05 or less. The
Russian roulette method used in the code selects a random
number and compares it to 0.5. If the random number is less
than 0.5, the photon's weight is increased by a factor of
two, and it is allowed to travel to the next boundary or
interaction. If the random number is greater than 0.5, the
photon is terminated and a new photon is started. The
Russian roulette routine is used to save computation time
from being applied to photons which are not likely to
contribute significantly to the backscattered fluence.
Code Output
Code output is to terminal screen, printer, and dis
kette files. The hardcopy output includes a recapitulation


420
research uses the same technique as a first estimate of the
gadolinium oxysulfide thickness and then employs an itera
tive method to include the effects of the other materials
present in the screen.
In order to perform the calculations for the iterative
procedure, an accurate knowledge of the x-ray source spec
trum used is required. The XRSPEC.PAS code is used for this
purpose. Preliminary measurements with the desired spectrum
are made to verify the spectrum using attenuation of expo
sure rate by aluminum. Other examples of this type of
measurement check are given in Appendix D. The calculation
of the fluence spectrum used in the measurements to deter
mine the phosphor layer composition is shown in Figure E.3
along with its exposure rate transmission curves. The
agreement between the measured and calculated curves is ex
cellent. Additional exposure rate transmission measurements
with this spectrum are made with Trimax 12 sheets in the
beam. The XRSPEC.PAS is used to calculate the exposure rate
transmission produced by screens of pure gadolinium oxysul
fide of thicknesses varying from 0.05 mm to 0.50 mm in in
crements of 0.01 mm. The measured transmission values are
then compared to the calculations to determine the thickness
of pure gadolinium oxysulfide which produces the observed
results. This value is used as a first estimate of the
gadolinium oxysulfide thickness. Using a mass balance
equation, the masses, volumes and thicknesses of the binder
material in the phosphor layer are calculated using the


63
large compared to the atomic binding energy are not cor
rectly accounted for by the Klein-Nishina formula. The
Klein-Nishina formula is corrected by multiplication by the
incoherent scattering function, S(x,Z),
da
inc
dfi
da
KN
d fi
S(x,Z)
/
where
doinc
dft
is the solid angle differential incoherent
scattering cross section.
The incoherent scattering function represents the
probability that an atomic electron struck by a photon will
absorb energy and be excited or removed from the atom.
Figure IV. 6 shows the incoherent scattering function for
aluminum and iron as a function of the momentum transfer
variable. The function has the effect of decreasing the
Klein-Nishina cross section (per electron) with the re
duction being greatest at low energies and in high Z mater
ials. Figure IV.7 displays these effects. The incoherent
scattering cross section is given by the integral over solid
angle of the differential cross section
'2ir
ainc
"o
IT
da
KN
dft
S(x,Z)sin0 d0 d ,
s s
where a. is the total incoherent scattering cross section
xnc
per atom.
Tabulated values of the incoherent scattering cross
section are provided by Hubbell et al. (1975). Figure IV.8


353
in the beam. While the maximum angular spread in the beam
nearly doubles, it is still less than 1.4 degrees from
perpendicular incidence. A source height of 34.6075 cm (the
same as the detector) is used in the power calculations.
Pixel Dwell Time
The combination of forward speed and the raster of the
beam determine the amount of time the beam spends on the
mine. If an image is to be produced, the scan must be
broken into smaller time segments to form pixels. The time
the beam spends irradiating a single pixel is the pixel
dwell time. Arguments presented in Chapter VII indicate
that the size of the beam at the mine surface should not be
much larger than the 1.27 cm by 1.27 cm used in the measure
ments to allow sufficient resolution to determine the
circular shape of the mine. The time required for the beam
to sweep through an area of this size can be calculated from
the speed and raster lengths. Table VIII.13 provides the
results of such calculations for a 1.27 cm by 1.27 cm beam
using the desired and useful operational requirements given
in Table VIII.11.
Calculation Technique
The fraction of source photons striking the detector is
taken from Monte Carlo calculations for beam intercepts at
the center of the mine. To be conservative, the fraction is
adjusted so that the difference between mine and soil
backscattered signals is reduced by 20% to account for lower
responses at other beam intercepts near the center of the


c
o
*(/)
en
£
en
c
a
L_
t
Figure D.12. Measured and calculated transmission of exposure rate, 150 kVp, 3.34 mm
Al. A comparison of measured and calculated transmission of exposure rate of a 150
kVp beam produced by the GE Maxitron 300 X-Ray Therapy Unit with 4.75 mm beryllium
inherent filtration, 3.34 mm aluminum added filtration and air path length of 90.07
cm is shown. The calculated transmission of exposure rate is based upon the spectrum
shown in Figure D.ll.
409


LIST OF FIGURES
continued
FIGURES
VIII.40
VIII.41
VIII.42
VIII.43
VIII.44
VIII.45
VIII.46
VIII.47
Page
Three dimensional image diagram of the
measured collimated detector response
to a 150 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array 323
Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array 324
Irregular soil surface used in measure
ments 326
Three dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface 327
Two dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface 328
Three dimensional image diagram of the
measured collimated detector response
to a 100 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface 330
Three dimensional image diagram of the
measured collimated detector response
to a 150 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface 331
Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface 332
xxv


119
the beam. Calculations using the XRSPEC.PAS code show this
feature. Figure V.3 shows the results of calculations of
the fluence spectra for three portions of an x-ray beam
generated at 80 kVp. The spectrum associated with the por
tion of the beam nearest the anode is reduced in magnitude
and shifted to higher energies by the heel effect. Figure
V. 4 displays the effect in a form often found in medical
physics texts (Hendee, 1984). Here the effect is shown in
the variation of half value thickness, the thickness of
material (aluminum in this case) required to reduce the
exposure rate of the x-ray beam by a factor of two. The
calculation of this figure uses the geometry required for
formal half value measurements (Johns and Cunningham, 1983).
As shown in the figure, greater thicknesses of aluminum are
required for portions of the beam nearest the anode.
Testing the Modified Kramers' Formula Model
The validity of the modified Kramers' formula method
for calculating x-ray spectra is tested by comparisons with
exposure rate transmission measurements and published
measurements of spectra.
Exposure Rate Transmission Measurements
The transmission of exposure rate of x-ray beams pro
duced by the GE Maxitron 300 is measured for a variety of
combinations of maximum accelerating potentials and filia
tions Beams produced by these energy and filtration com
binations are transmitted through varying thicknesses of
aluminum to develop transmission curves. These measured


68
photoelectric cross section will be large at low energies
and in high atomic number materials. Figure IV.9 shows the
variation of the photoelectric cross section of iodine
(Z=53), gadolinium (Z=64) and lead (Z=82) as a function of
photon energy (each of these materials plays a role in this
research). Superimposed on the variation with atomic number
and energy, discussed above, are edges. These sharp discon
tinuities in the cross sections are the result of the dis
crete binding energies of electrons in their atomic shells.
Below an edge energy, the incident photon does not possess
sufficient energy to overcome the binding energy of the
electrons in a particular shell. As photon energy increases
to just above the edge energy, this is no longer the case
and the cross section increases dramatically as a result of
the capability to remove the newly available electrons. As
a result of these edges, a lower atomic number material may
have a higher cross section for the photoelectric inter
action in an energy range below the edge energy of a higher
atomic number material.
Figure IV.10 shows the probability of K shell fluores
cent emission following the filling of a vacancy in the
inner atomic shell. /In low atomic number materials, this
probability is small; the alternate radiationless emission
of Auger electrons dominates (Evans, 1955). Since soil
and explosive materials contain generally low atomic number
elements, fluorescent emission from these materials is not
very probable./ Even in those few instances in which


276
TABLE VIII.4
Mine to Soil Fluence Ratio from the Collimated
Detector with Recently Buried Mines
Depth of
Burial
(cm)
£
Mine to Soil Fluence Ratio
Collimator Acceptance Angle
25.8 b
Density
Normal Low
23.1
Density
Normal Low
19.9
Density
Normal Low
0.0
3.007
3.086
4.453
4.562
6.165
6.469
0.203
0.208
0.512
0.531
1.333
1.394
2.5
1.650
2.030
2.474
3.344
4.047
6.079
0.114
0.145
0.294
0.402
0.876
1.316
5.0
1.197
1.461
1.516
2.099
2.379
3.368
0.095
0.111
0.206
0.269
0.569
0.770
7.5
1.028
1.268
1.142
1.673
1.724
2.778
0.084
0.071
0.165
0.223
0.435
0.650
10.0
1.005
1.190
0.926
1.554
1.039
2.396
0.072
0.083
0.121
0.188
0.254
0.528
15.0
1.000
1.156
1.000
1.266
1.000
1.673
without
0.081
0.158
0.382
mine
a
Calculations are for 100 keV photon beams perpendicularly
incident on HTL soil with 10% water by weight. The beam
intercepts TST mines at their centers. Diverging source
beams are 1.27 cm by 1.27 cm at the soil surface and are
produced by a point source at 64.48 cm above the soil sur
face. The detector consists of two panels, each 210 cm long
by 30 cm wide, separated by a raster gap of 30 cm, located
parallel to and 34.6075 cm above the soil surface.
L. n
The density of the normal, undisturbed soil is 1.80 g/cm ;
that of the disturbed soil is 1.35 g/cm The disturbed
soil density is characteristic of that surrounding a
recently emplaced mine.
Q
This calculation was made for a cylindrical hole of^depth
15 cm and radius 15 cm filled with soil at 1.35 g/cnr
density.


position
302
y position
1 3 5 7 9 11 13 15
Figure VIII.23. Two-dimensional image diagram of the
measured uncollimated detector response to a 100 kVp source
beam filtered by Pb for the TST mine buried flush to the
soil surface. The response is sampled at a 2.54 cm incre
ment .


159
ratio. Calculations performed for this comparison modelled
the detector used by Dell and Ebert (1969) in the experimen
tal portion of their work. This detector consisted of a 2.5
cm (diameter) by 2.5 cm (thickness) Nal(Tl) crystal with a
0.013 cm beryllium window. All photon beams were tightly
collimated, small in diameter and incident perpendicularly
on the center of the face of the detector. These condi
tions, combined with the low energies of the photons used
(40 to 100 keV), make scatter out of the crystal negligible.
Therefore, a plane detector approximation for calculation
purposes is acceptable. As shown in Figure VI.5, the
NAISPEC.PAS calculations agree well with these other
efforts. The discrepancies which exist are a result of
differences in the basic data, assumptions, and techniques
used in the calculations. The Sharma paper provides an
excellent discussion of the calculation techniques they
used; the Dell and Ebert calculations are poorly docu
mented, but are probably very similar in nature to those of
Sharma et al. The effect of the various differences are in
some instances to increase, and others to decrease the
iodine escape ratio.
Sharma et al. assume a bare Nal(Tl) crystal suspended
in vacuum. The NAISPEC.PAS code models the beryllium wall
suspended in air. The effect of the presence of a low
atomic number material wall is to produce incoherent scat
ters which alter photon directions producing interactions,
on the average, closer to the surface of the Nal(Tl) crystal


255
34.77 cm for the case with mine. Measurements were made at
three detector positions for each source energy. The slight
differences in height above the soil in the two measurements
are due to the removal and addition of soil during placement
of the mine. The calculations employ the interaction char
acteristics of sucrose as the explosive material. Measure
ment comparisons of the attenuation properties of TNT and
sucrose, described in Chapter III (see Figure III.9), indi
cate sucrose is a good substitute material. Figure VIII.4
shows a comparison of calculations of the number albedo of
sucrose and TNT at eight energies, indicating that the
scattering properties of the two materials are also very
similar. Exact agreement would exist if the data points lay
directly on the line of slope equal to 1.00. Results of the
measurement to calculation comparison are expressed as the
ratio of mine to soil detector response in Table VIII.2.
Agreement is seen to be very good. The relatively large
uncertainties in the measured ratios derive from instabili
ties in the General Electric Maxitron 300, not quantum
statistics. Correction for head leakage contributions is
required in the 200 kVp measurements. As described in
Chapter III, due to structural constraints, it is not
possible to provide sufficient lead shielding to completely
remove the head leakage contribution for higher beam
energies.
These measurements confirm several key conclusions
from the calculations described in Chapter VII. Those


269
All have relatively low response when the height is small.
In this case the bulk of the photons are escaping through
the raster gap. Since the gap size is the same in all the
cases, the responses are also essentially the same. Each of
the curves go through a maximum and then drop off at large
heights above the soil. For large heights, the bulk of the
photons are escaping beyond the detector panels. Not sur
prisingly, the broadest maximum and largest response is
associated with the largest panels. The broader the maxi
mum, the less the sensitivity of the detector configuration
to height variation.
The collimated detector presents a different height
sensitivity mechanism. The variation in height alters the
size of the area of the soil surface from which the detector
can receive photons. Tight collimation reduces the varia
tion in the size of the area viewed. Since the detection
mechanism depends on the differential attenuation by soil
and explosive of multiplj^scattered photons reaching a
collimated detector, large detector areas are not required
to gather the bulk of the available photons. It is only the
region near the beam side of the panel that is of great
importance in a collimated detector which is configured to
exclude the bulk of the single scattered fluence. Figure
VIII.10 shows the sensitivity of collimated detector to
height variation. The calculation is for the 100 keV
photons perpendicularly incident on the center of the TST
mine buried flush to the soil surface. The detector


Figure VI.4. Plane detector response, discrimination greater than 0.03317 MeV. The
calculated detector response (number of counts per incident photon striking the
detector) for the case of perpendicular incidence on a plane model of a Bicron Model
.5M.39Q/.5L-X detector is shown. Calculations were performed by the DETNAI.P Monte
Carlo code for the cases of lower level discriminator settings corresponding to 0.000
and 0.035 MeV.
156


Figure VIII.52. Three-dimensional image diagram of the measured collimated detector
response to a 200 kVp source beam filtered by Al for a steel disk buried flush to the
soil surface. The response is sampled at a 1.27 cm increment. The disk is 5 cm in
radius and 2 cm thick.
337


163
Measured Energy Spectra
Figure VI.6 compares an energy spectrum measurement
made by Dell and Ebert (1969) as part of their iodine escape
work. The calculated energy spectrum is from the NAISPEC.
PAS code and employs a gaussian distribution to smear the
discrete energies calculated into the resolution of the
Nal(Tl) crystal employed in the measurements. Assumptions
on the variation of resolution with energy are from Berger
and Seltzer (1972). Agreement between the measured and
calculated spectra is seen to be good.
Shield and Edge Effects
The plane detector response described above is adjusted
for two types of photon events, which occur in the real de
tector, but not in the plane model. These effects are
caused by photons which penetrate the detector shield, enter
the side wall, and deposit energy in the Nal(Tl) crystal,
increasing the observed count rate above that which is
predicted by the plane detector response calculations; and
photons, which enter the bottom face of the detector and
exit the side wall of the detector without depositing
sufficient energy to produce a count, decreasing the ob
served count rate predicted by the plane detector response
calculations.
Calculation of the Correction Factor
A computer code DETCOR.PAS was written in Turbo Pascal
(Borland, 1985) to make a first order approximation of the
correction factor at each energy/angle mesh point in the


375
supported so that they are 10 to 14 cm from the snow surface
(.S. Department of the Army, 1973).
Soviet instructions for the burial of landmines are
similar to those described in the preceding paragraph
(Radevich et al., 1965). In vegetated areas, the sod is cut
to a depth of 5 to 8 cm, and peeled back. Soil is removed,
the mine emplaced, and finally, the sod replaced covering
the mine. In areas of solid soil or in well travelled dirt
roads, 2 to 3 cm of the mine must protrude above the surface
to allow the crushing action which begins the detonation
chain in a pressure fuzed mine. In soft, nonvegetated
soils, the mine is buried flush to the surface. In snow
less than 25 cm deep, mines are placed on the soil surface.
In depths of snow, greater than 25 cm, and less than 60 cm,
snow is compacted under the mine so that the depth of snow
(not compacted) above the emplaced mine is 10 to 15 cm. In
depths greater than 60 cm, other materials are employed to
build a firm foundation under the mine.
Mines emplaced by mechanical mine layers are generally
more deeply buried than those emplaced by hand. The Soviet
PMR-3 mechanical minelayer is capable of either surface
placement or burials, in soft soils, of 30 to 40 cm (U.S.
Department of the Army, 1979a). Large bombs converted for
use as mines may be buried at even greater depths.
Fuzing Type
A wide variety of fuze types exist. For antitank
mines, some aspect (or several) of the vehicle signature is


214
TABLE VII.3
Front to Rear Panel Ratios of the Collimated Detector
for 100 keV Beams Incident on the TST Mine at 60 Degrees
Front to Rear.Panel Fluence Ratioa
Soil Only DOB -2.5 cm DOB=7.5 cm
Collimator
Acceptance
Angle
90.0
36.9
25.8
23.1
19.9
16.3
11.5
1.095 0.019
1.661 0.060
4.671 0.487
6.102 0.924
5.030 0.938
3.777 0.935
2.774 0.909
1.159 0.020
2.044 0.072
6.426 0.599
6.715 0.787
6.819 1.015
8.307 1.701
8.978 2.958
1.088 0.014
1.754 0.046
4.655 0.149
5.618 0.561
5.266 0.670
3.590 0.588
2.514 0.614
cl
The calculation example is for a 100 keV photon beam of
radius of 1 cm, incident at 60 degrees on NSL soil of
density 1.54 g/cm with the TST mine at depths of burial of
2.5 and 7.5 cm. In each case the beam is incident at the
center top of the mine, and the detector height is 34.6075
cm. The detector consists of two 30 cm wide by 210 cm long
panels, separated by a raster gap of 30 cm, parallel to the
soil surface and centered on the beam/soil intercept
position.
to
uDepth of burial of the top surface of the mine in soil.


280
TABLE VIII.6
Mine to Soil Fluence Ratio of the Uncollimated
Fluence Detector for Three Water Contents of HTL
Soil with the TST Mine at 2.5 cm Depth of Burial
Source Beam
Energy
(keV)
a
Mine to Soil Fluence Ratio
Water content by Weight0
0%
10%
20%
40
1.007
1.011
1.010
0.024
0.016
0.016
50
1.058
1.047
1.042
0.021
0.017
0.017
60
1.108
1.094
1.081
0.021
0.013
0.018
80
1.138
1.138
1.116
0.018
0.016
0.015
100
1.133
1.116
1.099
0.016
0.013
0.012
120
1.142
1.113
1.088
0.018
0.013
0.013
150
1.103
1.081
1.068
0.014
0.012
0.012
200
1.075
1.067
1.047
0.016
0.012
0.012
Calculations are for photon beams perpendicularly incident
on HTL soil with selected water content and densities. The
beam intercepts TST mines at their centers. Diverging
source beams are 1.27 cm by 1.27 cm at the soil surface and
are produced by a point source at 64.48 cm above the soil
surface. The detector consists of two panels, each 210 cm
long by 30 cm wide, separated by a raster gap of 10 cm,
located parallel to and 34.6075 cm above the soil surface.
Coil density varies with water gontent. The densities used
in the calculation are 1.70 g/cnr for the dry soil (0%),
1.80 g/cin for the 10% soil, and 1.90 g/cm for the 20%
soil.


Figure D.11. X-ray fluence spectrum, 150 kVp, 3.34 mm Al. The x-ray spectrum at 150
kVp calculated by the XRSPEC.PAS code for the GE Maxitron 300 X-Ray Therapy Unit with
4.75 mm beryllium inherent filtration, 3.34 mm aluminum added filtration (includes
0.25 mm aluminum equivalent monitor ionization2Chamber) and air path length of 90.07
cm is shown. Flue^ce units are photons per cin per keV. Total fluence is normalized
to 1 photon per cm.
408


519
Epp, E. R., and Weiss, H. "Energy Spectrum of Primary
Diagnostic X Rays." Phys. Med. Biol. 11:225-238, 1966.
Evans, R. D. The Atomic Nucleus. Eleventh printing. New
York: McGraw-Hill, 1955.
Farmer, F. T., and Collins, M. P. "A New Approach to the
Determination of Anatomical Cross-Sections of the Body by
Compton Scattering of Gamma-Rays." Phys. Med. Biol.
16:577-586, 1971.
Farmer, F. T., and Collins, M. P. "A Further Appraisal of
the Compton Scatter Method for Determining Anatomical
Cross-Sections of the Body." Phys. Med. Biol.
19:808-818, 1974.
Fewell, T. R., and Shuping, R. E. "Photon Energy Distribu
tion of Some Typical Diagnostic X-Ray Beams." Med. Phys
4:187-197, 1977.
Fink, R. W. ; Jopson, R. C.; Mark, H.; and Swift, C. D.
"Atomic Fluorescence Yields." Rev, of Mod. Phys.
38:513-540, 1966.
Forsythe, G. E.; Malcom, M. A.; and Moler, C. B. Computer
Methods for Mathematical Computations. Englewood Cliffs,
NJ: Prentice-Hall, 1977.
Frank, W. X-Ray Products Division, 3M Corporation, St.
Paul, MN. Personal communications, May 23 and June 3,
1986.
Garnett, E. S.; Kennett, T. J.; Kenyon, D. B.; and Webber,
C. E. "A Photon Scattering Technique for Measurement of
Absolute Bone Density in Man." Radiol. 106:209-213,
1973.
General Electric Corporation. Maxitron 300 X-Ray Therapy
Unit Operation, Maintenance. General Electric X-Ray
Department, 1962. Milwaukee, WI, General Electric
Directions No. 12338C.
Golden Software, Inc. Grapher. Golden, CO: Golden
Software, 1986.
Golden Software, Inc. Surfer. Golden, CO: Golden
Software, 1987.
Green Hills Software, Inc. Green Hills Software User's
Guide, Pascal Language. Glendale, CA: Green Hills
Software, 1984.


100
TABLE IV.6
Comparisons of Number Albedo
Calculations for FTB Soil and Buried DNB Mines
Energy
Depth of
Number
Albedo
(MeV)
Burial (cm)
Coleman
(1971)
MCPHOT.P
0.070
Soil only
0.117
+
0. 002
0.1162

0.0110
0.120
Soil only
0.2094
+
0.0014
0.215
+
0.003
0.130
Soil only
0.2204
0.0015
0.200
Soil only
0.256
+
0.004
0.2634

0.0016
0.070
5.08
0.119

0.002
0.1196
+
0.0011
0.120
5.08
0.227
+
0.003a
0.2257

0.0015
0.130
5.08
0.2380

0.0009
0.200
10.16
0.259
+
0.004
0.2627
+
0.0016
aColeman
provides a calculation
for
a range
between
0
.120
and 0.130 MeV with uniform distribution of source energies.


271
consists of two panels of width of 30 cm, separated by a 30
cm raster gap. The figure indicates this detector is very
height sensitive. The sensitivity decreases as the accept
ance angle becomes smaller. The sensitivity is even more
serious than the figure indicates. The strong dependence of
this detector on the geometry of the system with respect to
soil is discussed above. Varying the height of the detector
destroys the geometric relationship determined to provide
optimum mine detection. This is particularly important when
the detector height is above 34.6075 cm, that for which the
geometry was optimized. Above this height the collimator
begins to allow single scattered photons to enter the detec
tor degrading its capability to detect mines. There are
three options to remedy this problem. First, the collimator
acceptance angle may be made very small, so that only
photons backscattered close to perpendicular to the soil
surface can reach the detector. The major problem arising
from this remedy is the increase in the power requirements
of the x-ray generator due to the further reduction in the
number of photons reaching the detector. The second remedy
is to insure a fixed height relationship to the soil through
some servo mechanism or by restricting use of the detector
to moderately flat surfaces such as roads. A third approach
is signal processing based on correlation of single line
scans. As shown later in this chapter, the operational re
quirements for the speed of the vehicle carrying the mine
detection system and the width of the path to be searched


515
than the K edge energy (as is the case in the measurements),
there is only one region of discontinuity above the energy
corresponding to the discriminator level setting rather than
two for a setting corresponding to energies below the K
edge. Further, the region of discontinuity is actually a
staircase because of the four possible K x rays which are
emitted, which softens the transition. Also, the detector
response discussion was in terms of the energy of the
photons striking the detector. The discussion now centers
around the relationship with the energy of the source
photons. The incoherent scattering process serves to
further decouple the source energy from the discontinuities
arising from K edge effects, smearing the scattered photon
energy. The effect of the discontinuity in the detector
response matrix at the energy corresponding to the lower
level discriminator setting is of little consequence because
of the small magnitude of the response near this energy.
The fitted response versus energy relationships (a different
relationship exists for each detector position of interest)
can be coupled directly to any energy spectrum to predict
the response at a given position.
The fit method has the advantage of conserving computer
time while providing a more accurate solution than the
multigroup method. The number of monoenergetic calculations
used to determine the fitted curve is important to the
accuracy of the solution. Eight to ten energies are used in
this research and appear to be more than adequate to express
the desired relationship accurately.


Pulse Height (volts)
Figure E.20. Measured pulse height spectra. The pulse height spectra using the
terbium activated gadolinium oxysulfide detector system for background (dark pulses)
and two radionuclide sources are shown.
462


c
o
en
en
£
en
c
a
i
I
Figure V.5. Typical transmission curve comparison. A comparison of measured and
calculated transmission of exposure rate of a 150 kVp beam produced by the XRSPEC.PAS
code for the GE Maxitron 300 X-Ray Therapy Unit with 4.75 mm beryllium inherent fil
tration, 3.44 mm aluminum added filtration (includes 0.25 mm aluminum equivalent
monitor ionization chamber) and air path length of 91.44 cm.
123


area detectors which are required to provide path searches
of approximately three meter widths. Environmental para
meters, such as height sensitivity, soil density and mois
ture content, and inhomogeneities are examined in both
calculations and measurements. Power requirements are also
addressed.
A system based upon detector collimation to emphasize
differences in the multiple scattered components, character
istic of soil and the explosive found in mines, is found to
be capable of mine detection at depths of burial of at least
7.5 cm at power levels compatible with portability, and at
speeds, path widths, detection probabilities and false alarm
probabilities consistent with operational requirements. De
tection at greater depths is possible in soil recently dis
turbed by mine burial.
Images of holes refilled with loose soil can be dis
tinguished from those of buried mines by their character
istic features. However, the refilled hole images bear some
resemblance to those of mines laid on the soil surface. A
compound detector, consisting of both collimated and un
collimated regions, can be used to overcome this problem and
increase the probability of detection of mines buried at
shallow depths.
XXXI1


221
TABLE VII.4 continued
Mine to Soil Fluence Ratio3
Energy Gap Size Collimator Acceptance Angle
(keV)
(cm)
\o
o
.
o
o
to
(Tt

o
o
00
.
in
CN
23.1
19.9
200
30
1.080
1.124
1.324
1.506
1.786
0.014
0.028
0.072
0.117
0.197
40
1.080
1.261
2.147
2.441
2.247
0.015
0.044
0.239
0.357
0.427
The calculations are for photon beams perpendicularly
incident on HTL soil with.jlO% water content by weight and
soil of density 1.80 g/cm with the TST mine at a depth of
burial of 2.5 cm. The diverging source beams are 1.27 cm by
1.27 cm at the soil surface and are produced by a point
source 64.48 cm above the soil surface. In each case the
beams are incident at the center top of the mine, and the
detector height is 34.6075 cm. Detector panels are 30 cm
wide and 210 cm long, sepatated by raster gaps of either 30
or 40 cm, each centered on the source beam axis.
b
Uncertainties are too large to allow meaningful compari
sons .


265
TABLE VIII.3
Energy Window Measurements for
the
TST Mine
at
. 2.54
cm Depth of Burial
Source Energy
Window
Mine to Soil Detector
(kVp)
(keV)
Response Ratio
100b
35.0
-
39.7
1.208 0.172
35.0
-
48.9
1.138 0.062
35.0
-
58.3
1.115 0.026
35.0
-
67.6
1.092 0.027
35.0
-
open
1.092 0.021
200
35.0
-
40.1
1.168 0.034
35.0
-
50.2
1.122 0.018
35.0
-
60.4
1.123 0.014
35.0
-
70.5
1.104 0.008
35.0
-
open
1.075 0.007
aSee text for description of experimental configuration.
filtered by 4.75 mm Be and 0.75 mm Pb. Source spectrum is
shown in Figure F.9.
cFiltered by 4.75 mm Be and 0.75 mm Pb. Source spectrum is
shown in Figure F.ll.


99
1971) or 8.890 cm (Roder and Van Konyenburg, 1975). The
mine is composed entirely of dinitrobenzene (DNB) at a
3
density of 1.44 g/cm ; no air space is considered. The soil
(hereafter identified as FTB) composition used in the cal
culations is from samples taken at Fort Belvoir, Virginia.
3
The soil density used is 1.30 g/cm The code used for the
calculations does not consider coherent scattering and uses
the Klein-Nishina distribution without modification by the
incoherent scattering factor. Photon interaction data sets
were constructed for FTB soil and DNB to allow calculations
using the MCPHOT.P code. Coleman's values of the number
albedo from soil only and with mine present are compared
with calculations by the MCPHOT.P code in Table IV.6. The
comparisons are very good.
Testing the Scattering Routines
The sampling techniques used for coherent and incoher
ent scattering are tested by comparison with analytical cal
culations of the respective solid angle differential scat
tering cross section as a function of the cosine of the
scattering angle. The same routines employed in the MCPHOT.
PAS and MCPHOT.P codes are used to sample the cosine of the
scattering angle for coherent and incoherent scattering.
These codes are run for 100,000 samples with the cosines of
the scattering angles binned in increments of 0.02. Figures
IV.18 and IV.19 compare the analytical and Monte Carlo cal
culations of the solid angle differential scattering cross
section as a function of the cosine of the scattering angle


392
Animals
Animals appear to be much more sensitive detectors of
the vapors of TNT than any man-made device. The actual
detection mechanism used by animals is unknown, but the
sense of smell probably plays an important role. Properly
trained dogs were shown to be able to detect mines over a
wide range of environments. Field test showed detection
rates as high as 90% with false alarm rates below 15%. The
program was terminated by the Army because of perceived
incompatibility of dogs and mechanized warfare, and their
vulnerability.
A wide range of other animals have also been used in
attempts to detect TNT. These include badger, coatimundi,
coyote, deer, ferret, fox, hog, javelina, miniature pig,
opossum, raccoon, three skunk species and timber wolf. A
complex detection system, based on training rats to detect
TNT vapor by direct stimulation of the pleasure center of
the brain has been studied. TNT detection was accomplished
by monitoring the electroencephalograph of the rat for a
feature characteristic of activity in the pleasure center.
The system is said to be ready for field testing, but
primarily in an anti-terrorist explosives detection role.
Biochemical Methods
Experiments with bioluminescent bacteria were conducted
by RPC Corporation, which demonstrated that certain bacteria
produced visible light in the presence of TNT vapor which
had been heated to 100C. Bacteria were grown in nutrient


Figure VI.1. Fraction of incident energy absorbed, perpendicular incidence. The
calculated fraction of incident photon energy absorbed in the Nal(Tl) crystal of a
plane model of a Bicron Model .5M.39Q/.5L-X detector for the case of zero degree
incidence is shown. Calculations were performed by the DETNAI.P Monte Carlo code.
147


293
No attempt is made to provide polyenergetic calculations due
to the rather significant time required to generate an
image. Figure VIII.14 shows the NSL calculation; Figure
VIII.15, the HTL soil calculation; and Figure VIII.16, the
MCL soil calculation. In each figure the presence of the
mine is clear, as would be expected from the large mine to
soil fluence ratios from mines buried flush to the surface.
The origin of the high ratio is clear if the responses for
the two average soil calculations (NSL and HTL) are compared
to that for MCL soil. The magnitudes of the response from
the mines are nearly the same in all three cases. The
magnitude of the responses from the soils are very differ
ent. This is the photoelectric effect contrast mechanism,
more evident for MCL soil due to its higher average atomic
number.
Figure VIII.17 shows the results of calculations for
the TST mine at a depth of burial of 2.5 cm. Given the same
numbers of photon histories as followed with the mine buried
flush to the soil surface and the reduction in the differ
ence between mine and soil responses, the statistical vari
ation in backscatter fluence becomes more noticeable.
Figure VIII.18 shows the application of a two-dimensional
low pass filter to the image displayed in Figure VIII.17.
This filter averages the response of nearest neighbors in
the image to remove high frequency content. The image is
reduced in size, losing the outer border which does not
possess a full set of nearest neighbors. Figure VIII.19


TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ii
LIST OF TABLES xi
LIST OF FIGURES XV
ABSTRACT xxxi
CHAPTERS
I INTRODUCTION 1
II BACKSCATTER MINE DETECTION AND IMAGING . 4
Previous Uses of Scattered Radiation ... 5
Backscattered Photon Mine Detection. ... 8
Fluorescence Emission 8
Rayleigh Scattering 9
Compton Scattering 10
Backscatter Radiation Radiography 13
Genesis of Current Research Effort. . 13
Improvements on Previous X-Ray
Backscatter Efforts 17
Research Goals 17
III EQUIPMENT AND MATERIALS 20
Equipment 20
X-Ray Source 20
Soil Box and Positioning System .... 27
Detector and Related Electronics. ... 30
Computer Control System . 36
Materials. 38
Soils 38
Nonmetallic Antitank Mine Model .... 39
Materials Tests 46
IV RADIATION TRANSPORT 52
Photon Interactions 52
Coherent Scattering 52
Incoherent Scattering 59
Photoelectric Effect 67
Mass Interaction Coefficients 71
v


486
General Purpose Interface Bus, was used for gathering data
from measurements. Analysis of measurement data was per
formed on both computer systems.
The Compaq Deskpro with math coprocessor is an excel
lent tool for floating point intensive calculations, but
increased speed was desired to allow a wider range of Monte
Carlo calculations to be performed. Two options for in
creasing the speed of calculations were examined. First,
accelerator boards operating with high speed 80286 central
processor units and high speed math coprocessors were ex
amined. The fastest of these accelerator boards (Petzold,
1986), the PC-elevATor family, produced by Applied Reasoning
Corporation, were tested using a MCPHOT.PAS problem as a
benchmark (Lickly, 1986). Results of the benchmark showed
only a modest gain in speed when compared to the Compaq
Deskpro. The reason for the poor showing by these devices
lies in the relative inefficiency of the 80286/80287 combi
nation to perform floating point intensive calculations
(Petzold, 1986). The second option examined was the Defini-
con Systems DSI-32 coprocessor. This device uses a 10 MHz
32032 central processing unit with a 32081 math coprocessor
to achieve speeds comparable to mid-sized VAX minicomputers
(Marshall et al., 1985). The DSI-32 coprocessor plugs into
an expansion slot in the Compaq Deskpro. The disadvantage
to the system is the requirement to recode programs to run
on the new central processing unit. To ease the recoding
process from Turbo Pascal, a Pascal compiler was selected.


444
previously explained. Transmission losses increase (Figure
E.ll) as a result of decrease in the photoelectric cross
section.
75 Degree Incidence
Figure E.12 shows the fraction of incident energy ab
sorbed in the phosphor layers for the case 75 degree inci
dence. The low energy region (below 0.035 MeV) is flat and
greatly extended. The apparent thickness of the phosphor
layer to an incident photon is now 3.864 times the true
thickness. Virtually all photons are stopped in the first
phosphor layer; the second layer is well shielded (Figure
E.13). Reflection losses are higher than in previous cases
due to backscatter from the screens, but are still relative
ly low (Figure E.14). Transmission losses in this energy
region do not occur (Figure E.15).
From 0.035 MeV to the K edge, the fraction of energy
absorbed in the first screen decreases with the falling
photoelectric cross section; the fraction absorbed by the
second layer increases as photons manage to reach it through
the first layer (Figure E.13). The second layer fraction
does not pass through a maximum in this energy range as it
did in the previously discussed cases. The extreme
shielding afforded by the first layer accounts for this
effect at 75 degree incidence. Reflection and transmission
losses remain low (Figures E.14 and E.15).
At the K edge, an inversion in previous results is
seen. The low energy side has higher fractional energy


236
side of the mine in the positions shown in Figure VII.29.
Because of symmetry, only four of the intercepts displayed
in the figure produce different responses. For the purpose
of this discussion, the intercepts will be referred to as
inside or outside and front or lateral, where front is the
direction of motion of the vehicle transporting the system
(perpendicular to the long axis of the detector), and
lateral is perpendicular to the direction of motion (along
the direction of beam raster). The presence of soil in all
beam intercepts outside of the mine results in optimum
energies even for mines buried flush to the surface. There
is a strong tendancy towards higher energies in this tech
nique, especially at greater depths of burial. The cone of
forward scattered photons produced by scatter in the soil
before the mine is reached, intercepts the edge of the mine
producing dissimilar responses in the asymmetrically (with
respect to the intercept position) located detector panels.
The ratios produced are not large, but shift the optimum
energy higher. Figure VII.31 shows an example of this
behavior. Optimum energies for the segmented detector range
from 80 keV to 200 keV or greater. It is not possible to
find a single energy which provides good results for all
cases, but 150 keV is the best for the range of soil types
and densities examined. Table VII.7 provides a typical
comparison of the ratios achieved by this method with the
mine to soil ratios achieved by the unsegmented detector
with 100 keV photons (compromise optimum for that detector)


296
shows the response from a TST mine buried at 5.0 cm in NSL
soil. As the mine center intercept calculations indicate,
the uncollimated detector has difficulty imaging below 2.5
cm.
Figure VIII.20 shows the response of a simulated water
puddle. The puddle is modeled as a cylinder of radius of 10
cm and height of 5 cm, placed flush to the surface of HTL
soil with 20% water by weight. The response image is very
similar to that of the TST mine. The capability of imaging
to determine the shape and size of objects is important in
avoiding false alarms due to low atomic number soil inclu
sions such as water or tree roots. Figure VIII.21 shows the
image response of a iron disk of 5 cm radius and 2 cm thick
ness buried flush to the surface in NSL soil, displaying the
effect of a high atomic number inclusion.
Measured Images
Images of buried and surface laid mines, and other
objects have been produced using the GE Maxitron 300 X-Ray
Therapy Unit as the source with the Bicron Nal(Tl) detector.
Chapter III describes these pieces of equipment, and the
soil box positioning and computer control systems employed
in the measurements. The geometry of the measurements
closely follows that which is used in the calculations.
With the exception of energy spectra, Table VIII.1 contains
basic information concerning the irradiation geometry. All
figures of measured images are for a detector positioned
21.5 cm from the beam axis. For the measured images which


451
energies of the discrete visible energy photons emitted and
their relative intensities. The atom percentage of terbium
replacing gadolinium determines the relative intensities of
the components of the visible spectrum emitted. The major
ity of terbium activated gadolinium oxysulfide intensifying
screens use a 0.3 atom % of terbium replacing gadolinium.
The result is emission dominated by photons in the green
region of the visible spectrum (Buchanan et al., 1972;
Kodak, 1980). Figure E.16 shows a typical emission spectrum
for screens of this type. The Trimax 12 screens contain
less than 0.3% atom percent terbium which alters the
relative intensities, producing more photons from the blue
region of the visible spectrum (Frank, 1986). Figure E.17
shows the emission spectrum from a Trimax 12 phosphor (3M,
1985b). The number of visible photons produced is, there
fore, also directly proportional to the energy deposited in
the phosphor. Figure E.18 shows the average number of
visible photons produced (based on the intensity weighted
average energy of the visible emission spectrum of the
Trimax 12 screens and an intrinsic conversion efficiency of
0.15) per x-ray photon incident on the screens as a function
of energy of the incident x-ray photon. Results similar to
this figure but for thinner screens and, therefore, of lower
magnitude are reported by Dick and Motz (1981). The next
step in the chain of events is the efficiency of the mylar
reflector surrounding the screens to direct the visible
photons onto the photocathode of the photomultiplier tube.


382
Throughout the campaign both sides used mines to con
solidate positions on newly captured terrain. Minefields
were placed to cover all avenues of approach to secure
positions against counterattack. In the desert mines became
the most important means of restricting enemy maneuver.
Eastern Front
During World War II, the Red Army developed sound doc
trine for the employment of mines in the defensive and of
fensive operations. Each individual Soviet unit position
was protected by mines when available. Mining began only
ten meters to the front of the most forward unit element,
and was considered so important that it was even conducted
under fire. When forced to withdraw mines were left behind
to produce casualties in the attacking force. At Kiev and
Vyborg in 1941 and Sevastopol in 1942, radio controlled
mines were used as German forces entered the cities (Honey
well, 1981).
Soviet histories claim the use of 222 million mines
during World War II. The immense transportation burden
imposed by mine warfare was alleviated by requiring each
soldier going to the front to carry a minimum of two anti
tank mines (Honeywell, 1981). The mass of the mines, on the
order of ten kilograms each, is a strong testimonial to the
importance the Red Army placed on mines. Field fabrication
of mines using wooden cases also helped reduce the
logistical problem.


Figure A.l. Typical antitank mine. The device shown in the photograph is a U.S.
Army training model of the East German PM-60 nonmetallic antitank mine.


417
of two screens. The screen which is normally placed nearest
the x-ray source contains less gadolinium oxysulfide than
the other. The screen nearest the source is called the
front screen; the other, the back screen. To increase the
sensitivity of the mine detection system, two back screens
are used in the detector constructed by Moss. A diagram of
the active region is shown in Figure E.2. The two intensi
fying screens are placed back to back with the phosphor
sides facing away from each other. Normally, the two phos
phor layers, covered by their protective coatings, face each
other with an x-ray film sandwiched between. In the outward
facing configuration, visible light photons resulting from
x-ray interactions in the phosphor are collected by angled
mylar reflectors, and directed to the face of a large
photomultiplier tube. The lower half of the reflector is
attached to thin cardboard to allow x-ray photons scattered
by soil or buried materials to reach the screens without
significant attenuation.
Screen Composition
The 3 M Trimax 12 screens were selected because of
their large phosphor thickness and their emission spectrum
(described below). For proprietary reasons, little
information is available concerning the composition of the
screens. To make matters worse, the two sets of screens
purchased have back screens which differ in mass by more
than 6%. Since the serial numbers of the two back screens
reveal that they are from the same batch, considerable


12
extent of coverage was also a problem; mines located midway
between two detectors were missed unless they were on the
surface. A final objection to the system involved soil
density. It was found that the detector was sensitive to
density changes whether a mine was present or not. Concern
was expressed that dummy minefields could be produced by
simply digging and refilling holes. The act of emplacing a
mine significantly alters the soil density, reducing it, on
the average, to 75% of the undistrubed value (Roder, 1975).
After weathering had returned the soil to its normal
density, detection was no longer possible at 10 cm, and the
response difference at 7.5 cm was much reduced. Further
work on this detection system was terminated primarily as a
result of the apparent superiority of a competing techno
logy, and secondarily as a result of the inadequacies de
scribed (Nolan et al., 1980).
Coleman (1971) performed Monte Carlo calculations for
several cases in support of this effort. They are discussed
in Chapter IV. These calculations and the majority of Texas
Nuclear experiments were conducted with solid blocks of di
nitrobenzene. The mines used in the field tests were filled
with dinitrobenzene, but it is unclear whether any air
space, characteristic of real mines (described in Appendix
A), was provided.
Preiss and Livnat (1973), working in Israel, provide
the only non-U.S. military publication of research on the
detection of nonmetallic mines by the backscatter of


position
264
y position
Figure VIII.8. Two dimensional image diagram of measured
response for the steel annulus experiment.


0.0 ~|~i ~T'i"T~r r~r~f 1 1 r |~r~r~i rrn"l i t rr T~r~r ~i r r >
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40
Collimator Acceptance Angle (radians)
Figure VII.13. Mine to soil fluence ratio versus collimator acceptance angle for 100
keV photons perpendicularly incident on the TST mine at 0.0 cm in HTL soil. A 25 cm
radius central section of the detection plane has been removed. The plane is located
34.6075 cm above and parallel to the soil surface.
191


30 40 50 60 70 80 90 100
Upper Window Energy (keV)
Figure VII.24. Ratios of integral energy spectra for 100 kev photons incident on the
TST mine at 2.5 cm in NSL soil for the cases of 0 and 60 degree incidence. The lower
energy window level is set at 35 keV.
212


O 20 40 60 80 100 120 140 160
Energy (keV)
Figure F.2. X-ray fluence spectrum, 150 kVp, 1.01 mm Al. The x-ray fluence spectrum
at 150 kVp calculated by the XRSPEC.PAS code for the GE Maxitron 300 X-Ray Therapy
Unit with 4.75 mm beryllium inherent filtration, 1.01 mm aluminum added filtration
and air path length of 60 cm is shown. Fluence units are photons per cm2 per keV.
Total fluence is normalized to 1 photon per cm2.
472


365
detector to sense soil density changes and an image response
to surface laid mines which differs considerably from that
of buried mines. The concern imposed by the detection of
density differences is the possibility of constructing dummy
minefields by simply digging holes and refilling them with
loose soil. The image produced by such refilled holes
differs considerably from that of a mine. Without an image,
however, this situation would produce false alarms. The
concern produced by the image of the surface laid mine is
that it might be confusing to an operator looking for re
sponses characteristic of buried mines. The image response
for the surface laid mine is very strong, but has similari
ties to that of the refilled hole. Since surface laid mines
are an important consideration on the modern battlefield, a
composite detector, using an uncollimated detector as a
supplement, could be useful.
An uncollimated detector consisting of two large area
panels with a raster gap of 10 cm is marginally capable of
detecting mines buried at only 2.5 cm. It is, however, an
excellent detector for mines laid on the soil or buried
flush to the surface. The lightly filtered beams, found to
be necessary for the .collimated detector to meet reasonable
power requirements, are particularly useful when used with
the uncollimated detector for mines either laid on the
surface or buried flush to the soil. The very high back-
scattered fluence available to this detector, as compared to
the collimated detector, allows the possibility of combining


251
at the high beam energies. This result is a combination of
the increased capability of high energy photons to leak
through the standard shielding of the head of the x-ray
machine and the lead filtration, which reduces beam
intensity considerably. In order to correct for the head
leakage contribution, additional measurements at each
detector position are conducted at the higher energies by
placing 1.03 cm of lead in the beam path. Due to this very
large thickness of lead, the measurements taken in this
configuration are now due only to head leakage. Subtraction
of the head leakage from the original measurement data
produces the detector response due to the source beam only.
Figures VIII.1 through VIII.3 show the excellent agreement
between calculation and measurement. The success of the
code in predicting a problem in the experimental conditions
testifies to its value. As a result of the discovery of the
head leakage problem additional shielding now encloses the
head.
Detector Response with Mine Present
A series of measurements with the TST mine buried flush
to the soil surface with the beam intercept at the center of
the mine provide an additional test of the calculation
technique. The measurements are made with the 100 and 200
kVp spectra shown in Figures F.8 and F.12. Other parameters
of the measurements are the same as those presented in Table
VIII.1 with the exception of the height of the detector
above the soil, which was 34.29 cm for the soil case, and


434
As incident photon energy increases (0.020 MeV to below
the K edge), the photoelectric interaction cross section is
still dominant, but is decreasing rapidly in magnitude. As
a consequence, fewer photons and less energy are absorbed in
the first phosphor layer. The second phosphor layer begins
to see and absorb more photons as they increasingly survive
absorption in the first. These effects are seen in Figure
E.5. The fraction of energy absorbed in the first phosphor
layer decreases, and the fraction absorbed in the second
phosphor layer increases. The fraction of energy reflected
(Figure E.6) remains low, but the fraction transmitted
increases with energy (Figure E.7). The net result, as seen
in Figure E.4, is a decrease in the fraction of energy
absorbed. The increase of absorption in the second phosphor
layer is insufficient to make up for the loss of absorption
in the first and the increasing transmission losses. In
fact, at about 0.035 MeV, the photoelectric cross section
has fallen so low that the fraction absorbed in the second
phosphor layer also begins to fall (Figure E.5).
At the K edge there is a sudden large increase in the
photoelectric interaction cross section as a result of
reaching the threshold energy for ionizing the K shell of
gadolinium. There is an immediate, discontinuous increase
in the fraction of incident energy absorbed in the phosphor
layers (Figure E.4). Figure E.5 shows that the fraction
absorbed in the first phosphor layer increases greatly,
again shielding the second phosphor layer, which reaches a


80
Problem Parameters and Data
Each of the Monte Carlo codes begins with the input of
problem data. These inputs are the photon interaction data
of air, soil and explosive, material densities, mine ge
ometry, and problem parameters. The photon interaction data
are the mass interaction coefficient files for coherent
scattering, incoherent scattering and the photoelectric
effect, the atomic form factors, incoherent scattering
functions and an integral used for sampling the coherent
scattering distribution (described in Appendix H). The mass
interaction data are read from files constructed using the
fine energy mesh described previously. The atomic form
factors and incoherent scattering functions are read from
files constructed in the same 45 value format as the tables
which appear in Hubbell et al. (1975). The integral asso
ciated with coherent scattering is also read from files
arranged in a 45 value format. Interactive input provides
the parameters for the particular problem. The parameters
available are initial photon energy, angle of incidence,
source height, beam geometry, soil type, height and extent
of detector plane, mine type, explosive type, depth of
burial of mine, beam/soil/mine intercept position, and
number of photon histories to be followed. Three beam
geometries are allowed: parallel beam, diverging circular
beam and diverging rectangular beam.


485
incurring any cost above wasted time encourages experimen
tation with the code. This ability to make mistakes is, of
course, a major disadvantage if they go undetected. Com
parisons with published data, experimental measurements, and
standard codes run on mainframe computers are important to
avoiding coding and logic errors.
The flexibility to write a code specific to the problem
at hand can do much to overcome speed advantages of main
frame computers used with standard codes. The standard
codes are generally large and somewhat unwieldy because they
must have the capability to provide almost any imaginable
desired type of output over a very large range of problem
types and parameters. An additional flexibility is accrued
because a small computer can be dedicated entirely to the
problem at hand and not have to compete in a multiple user
environment.
Computer Selection
A Compaq Deskpro (Compaq, 1984a), equipped with 640
kilobytes of random access memory, two 360 kilobyte floppy
diskette drives, a 20 megabyte hard disk drive, a 8087-2
math coprocessor and a Definicon Systems DSI-32 32032
coprocessor (Definicon, 1986) with 32081 math coprocessor
and 1 megabyte of random access memory, was used for the
calculations presented in this dissertation. An IBM
Personal Computer (Norton, 1986), equipped with 640 kilo
bytes of random access memory, two 360 kilobyte floppy
diskette drives, a 8087 math coprocessor, and an IEEE


0.91
0.91
(1
0.93
1.00
0.93
1.00 (1.05)
1.07
1.00
1.07
1.00
(1.05)
231


329
before scattering. Scattering positions, which require the
longest paths through soil to reach the detector produce the
minima. Figures VIII.45 through VIII.47 show the use of a
collimated detector with acceptance angle of 21.6 for three
source beam energies filtered by aluminum. Figure VIII.45
is for a 100 kVp beam; Figure VIII.46 for a 150 kVp beam;
and Figure VIII.47 for a 200 kVp beam. Spectra for these
images are given by Figures F.l through F.3. While each of
these images produced by the collimated detector shows the
influence of the irregular soil surface, there is no ques
tion as to the presence of the buried mine. Figure VIII.48
provides a two-dimensional image for the 200 kVp case with
collimated detector to show that the distortions in the
image shape of the mine are not large.
Figure VIII.49 shows the image response of a disk of
wood buried flush to the soil surface as produced by a 100
kVp beam filtered by lead (Figure F.8) and an uncollimated
detector. The edge effect at the side of the disk furthest
from the detector is produced by the relative transparency
of the low density wood to photons. Figure VIII.50 shows
the response of the collimated detector with acceptance
angle of 18.1 degrees to the same wood disk using the source
spectrum shown in Figure F.3. The response is similar to
that of a mine buried at approximately 7.5 cm. Figures
VIII.51 and VIII.52 show the uncollimated and collimated
images of an iron disk of radius of 5 cm and height of 2 cm
buried flush to the soil surface. The same set of source


79
use on personal computers. MCPHOT.P is written in Green
Hills Pascal (Green Hills, 1984) for use with the Definicon
DSI-32 coprocessor (Marshall et al., 1985) which provides
increased speed of calculation. Appendix G provides addi
tional information about this device. The two codes are
essentially identical in most respects, although calcula
tions of angular spectra are included in the MCPHOT.P code
to support computations for collimated detectors.
The Monte Carlo transport codes follow the histories of
monoenergetic photons from their source to the detector
plane. The detector response function, described in detail
in Chapter VI, which is also the result of a Monte Carlo
calculation, couples directly to the energies and angles of
incidence of the photons striking the detector plane. The
results of the calculation of the x-ray spectrum, described
in Chapter V, are used to weight the monoenergetic Monte
Carlo transport calculations to account for polychromatic
sources. This technique allows the monoenergetic calcula
tions to be used with any x-ray source spectrum, producing a
considerable reduction in computation time from the alter
native of sampling of a spectrum within the transport
calculation.
Appendix H provides details for the techniques used to
sample the more complex probability density functions
encountered in the Monte Carlo code. Also included in this
appendix are details concerning the random number generators
used in the Monte Carlo codes and the technique for applying
the monoenergetic source results to polychromatic sources.


TABLE IV.2
Energy at Which Photoelectric
and Incoherent Scattering Mass Interaction
Coefficients Are Equal
Material
Effective Z
Energy (MeV)
Wood
6.525
0.025
Sucrose
6.704
0.026
TNT
6.919
0.026
Air
7.374
0.029
Quartz
10.805
0.046
NSL soil
10.905
0.048
HTL soil
11.381
0.053
Concrete
11.576
0.055
GAD soil
11.912
0.055
Aluminum
13.000
0.052
MCL soil
15.856
0.080
Iron
26.000
0.115
Sodium iodide
46.558
0. 260
Lead
82.000
0.550


115
TABLE V. 2
Comparison of Exit Path Lengths Through Tungsten
Anodes Which Provide the Best Fit to Measured
Exposure Rate Transmission Data as Calculated
Using Kramers' Formula.
Beam Energy
(kVp)
Filtration
(mm of Al)
Exit Path
Soole (1971)
Length (microns)
GE Maxitron 300
80
2.00
6.99
5.63
80
2.24
-
5.86
80
3.00
6.01
-
100
2.00
6.99
5.81
100
2.24
-
5.75
100
3.00
4.04
-
150
3.00
-
5.20
150
3.34
-
5.32
150
3.44
-
5.79
200
3.00
-
4.07
200
3.34

4.90


34
The usual purpose of the lower level discriminator
setting of the counting system is to preclude pulse height
events corresponding to electronic noise. As described
above, an additional purpose in this detector system is to
prevent tin K fluorescent x rays, which could enter through
the sides of the detector, from being counted. A set of
radioactive sources is used to determine the relationship
between photon energy and lower level discriminator setting
(in combination with a fixed detector high voltage supply,
and amplifier and preamplifier settings). Sources and ener
gies used for this calibration are given in Table III.2. A
discriminator setting corresponding to 35 keV was selected
to prevent counting of spillover of the tin K ray peak as a
result of the resolution of the detector. Based upon the
Monte Carlo spectral and number albedo calculations (Chapter
IV provides examples), this setting results in only a small
reduction of the total detector response compared to the
case when no discrimination is used. The fluence spectral
calculations show that only when the source energy is small
is there any significant contribution below 35 keV. The
number albedo (the fraction of incident photons which are
reflected from a surface) calculations show that low energy
source photons produce significantly less backscatter than
high energy photons (this is true up to about 300 keV).
Additionally, results of the detector response calculation,
provided and described in Chapter VI show that low energy
photons produce a much lower response than all others except


Figure VI.2. Fraction of incident energy absorbed, 75 degree incidence. The
calculated fraction of incident photon energy absorbed in the Nal(Tl) crystal of a
plane model of a Bicron Model .5M.39Q/.5L-X detector for the case of 75 degree
incidence is shown. Calculations were performed by the DETNAI.P Monte Carlo code.
150


Energy (keV)
Figure D.7. X-ray fluence spectrum, 100 kVp, 2.24 mm Al. The x-ray spectrum at 100
kVp calculated by the XRSPEC.PAS code for the GE Maxitron 300 X-Ray Therapy Unit with
4.75 mm beryllium inherent filtration, 2.24 mm aluminum added filtration (includes
0.25 mm aluminum equivalent monitor ionization2chamber) and air path length of 90.17
cm is shown. Fluerjce units are photons per cin per keV. Total fluence is normalized
to 1 photon per cm.
404


LIST OF FIGURES
continued
FIGURES
VIII.32
VIII.33
VIII.34
VIII.35
VIII.36
VIII.37
VIII.38
VIII.39
Page
Two dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
A1 for the TST mine at a depth of
burial of 2.54 cm 312
Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 7.62 cm 314
Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine laid on the soil
surface 315
Two dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine laid on the soil
surface 316
Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array 318
Three dimensional image diagram of the
measured uncollimated detector response
to a 150 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array 319
Three dimensional image diagram of the
measured uncollimated detector response
to a 150 kVp source beam filtered by
Sn for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array 321
Three dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Sn for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array 322
xxiv


Figure VII.10. Spatial distribution of th<
perpendicularly incident 100 keV photons,
to soil fluence ratio intercepting a plane
the soil surface is shown.
single scattered mine to soil ratio from
The single scatterer component of the mine
located 34.6075 cm above and parallel to
187


210
inclusion of this region unattractive. Table VII.2 shows an
example of the effect of angles of incidence other than zero
degrees on the mine to soil ratio for collimated and uncol
limated fluence detectors. A number albedo detector is
included in the table for reference. The detector geometry
used in these calculations consists of two 30 cm wide panels
separated by a raster gap of 30 cm, located 34.6075 cm above
the soil surface and centered on the beam/soil intercept.
This geometry allows the beam incident at 20 degrees to pass
through the raster gap, while the 60 degree beam passes
under the rear panel from behind, when used in conjunction
with the source height employed in the measurements. Non
zero degree incident beams are shown to degrade the fluence
response ratios. Energy window detectors are also adversely
affected. Since the average soil penetration depth de
creases with increasing angle of incidence, the low energy
scatter contribution due to the mine decreases. Increasing
the angle of incidence increases the number of reflected
photons, primarily because their shallower penetration also
produces easier escape to the soil surface. This increased
scatter, however, is characteristic of the soil, not the
buried mine. As a result, the mine to soil ratio in the
energy window detector is lower for non-zero angles of
incidence. This effect is shown by Figure VII.24 which
displays the ratios of the integral energy spectra of mine
present to soil cases for angles of incidence of zero and 60


208
over all angles of incidence, presented in Chapter VI (com
pare this figure with Figure VI.4). The low ratio at low
source energies is not of major consequence because such
source photons do not contribute strongly to either of the
responses. The energy window detector, which uses low
energy photons as its detection mechanism, is a possible
exception to these comments. If significant differences in
the energy distributions of the mine and soil cases exist
within energy bin widths (5 keV) used in the calculations,
errors will be introduced as a result of the rapid variation
in the detector to fluence response ratio at low energy.
Irradiation Geometry and
Optimum Energy Considerations
A combination of practical concerns, and the physics of
the backscatter problem limit the geometric relationship
between detector and soil surface. With the large area,
panel detector configuration as a basis, the irradiation
geometry is examined. Optimum source energies are also
discussed.
Height of Detector
The height of the detector above the soil surface must
allow for operation over rough terrain. From a purely
theoretical standpoint the optimum height would be deter
mined as that which maximizes the ratio of mine present to
mine absent response while providing the largest possible
fluence striking the detector. This height depends on the


225
accurate. Calculations performed in this research are for
210 cm long panels centered on the beam axis.
The optimum width of the detector panels depends on the
beam energy, raster gap size, and operational considera
tions. Minimizing the width helps prevent the possibility
of damage to the detector system while operating over rough
terrain. The key advantage to larger widths lies in in
creasing the total fluence sensed, improving the detection
statistics, and allowing lower x-ray generator power levels.
For the uncollimated detectors there is the added advantage
of reducing sensitivity to variations in height.
The optimum width of the collimated detector is not
found through calculations because of the very low fluences
striking small detector strips. Experiments using the
Nal(Tl) detector, however, indicate that even very small
detectors can be successfully used with this technique. The
most important variables for the collimated detector are the
size of the raster gap and the acceptance angle of the
collimator, which have already been discussed. Widths of 30
cm have been used for collimated detectors in the calcula
tions to allow meaningful comparisons of the low fluences
sensed by these detectors per source photon.
Table VII.5 shows a typical set of calculations for an
uncollimated fluence detector, used in determining panel
width. The information provided by this table indicates
that the improvement in the mine to soil ratio achievable by
varying the panel width and raster gap size is small.


233
beams are 1.27 cm by 1.27 cm in size at the soil surface,
and are produced by a point source at 64.48 cm above the
soil surface. Detector panels, located 34.6075 cm above the
soil, are 210 cm long and centered on the source beam axis.
A beam/mine intercept at the center of the TST mine is used
for the unsegmented detector; four intercepts inside and
outside the mine are used for the segmented detector.
Optimum energies for the energy window detector are examined
by Monte Carlo calculations of the ratios of integral energy
spectra at various source beam energies.
Figure VII.30 shows an example of an optimization curve
for NSL soil for the uncollimated fluence detector. Curves
obtained by this method are very similar to the number
albedo versus energy graphs (Figures VII.2 and VII.3), as
are the explanations for their shapes. The ratios are
higher as a result of removal of the central minimum. The
application of this same method to a range of soil condi
tions provides the results summarized in Table VII.6 for
this detector type. A compromise energy of 100 kev provides
reasonably good mine to soil ratios in all cases. Any
energy within the range of 40 to 200 keV is capable of
detecting mines buried flush to the soil surface. For this
case, the lowest energy in the range provides the greatest
ratio.
The uncollimated, segmented fluence detector presents a
much wider range of optimum energies for the beam intercepts
examined. These intercepts are located 1.00 cm from the


381
campaign entended from June 1940 to May 1943. The early
portions of the campaign were fought between British and
Italian forces, with the German Africa Corp, commanded by
Rommel, arriving in February, 1941.
During the spring of 1942, British forces at Ain El
Galaza near Tobruck used one million mines in field of
depths of thousands of meters to strengthen their defensive
positions (Rommel, 1953). It was during this battle that
Rommel developed a respect for and understanding of the
utility of mines in the defense, which he would use in the
future (Macksey, 1968). The British minefields in support
of fortified positions were very effective in delaying, dis
rupting and sometimes defeating German attacks.
In June of 1941, Operation Battleaxe, a British attack
against an inferior German force resulted in a total British
defeat, largely because of the extensive use of mines. The
mines slowed the attacking vehicles, making them easy tar
gets for accurate German antitank weapon fire (Honeywell,
1981).
In August, 1942, the British defense at El Alamein em
ployed 150,000 mines. In October, with the Germans then on
the defensive, 500,000 mines, many captured from the
British, were employed in "Devil's Gardens," large complex
minefields with depths up to 6.4 kilometers. While these
were formidable obstacles, the German failure to employ
sufficient numbers of antipersonnel mines in the fields
allowed the British to clear lanes or alter minefield
patterns at night (Rommel, 1953).


CHAPTER V
X-RAY SOURCE
A number of techniques are available for determining or
modelling the spectra produced by x-ray machines. The
method selected for use in the mine detection calculations
is presented and other techniques are discussed.
Kramers1 Formula Method
The technique selected for calculating the x-ray spec
tra of the GE Maxitron 300 Therapy Unit is based upon a
modification of Kramers' formula (Kramers, 1923). The model
is implemented by an interactive computer code, XRSPEC.PAS,
written in Turbo Pascal (Borland, 1985) for use on personal
computers. The code calculates 1 keV increment spectra for
fluence, energy fluence and exposure, and the integrals of
these quantities. The relative values of integral quantities
calculated by varying the amount of attenuating material in
the beam can be used to simulate transmission experiments,
which can then be checked against actual measurements. Since
the values are relative, it is equally valid to consider the
calculated quantities to be fluence rate, energy fluence rate
and exposure rate. Fluence files created for use with the
photon transport calculations of the mine detection problem
are normalized so that the integrated fluence is 1.00 pho-
2
tons/(source photon cm ).
105


465
angles of incidence. To allow higher energy photons to be
considered, the detector response matrix was extended to
1.00 MeV using the DETECT.PAS code. The sources used in the
133 137
calculations were Ba and Cs. Energies and frequencies
of emission per decay were taken from Unger and Trubey
(1982). These two nuclides were chosen for their very dif
ferent photon emission characteristics.
133
The Ba source emits low energy photons while the
137
emissions of the Cs source are dominated by a 0.6616 MeV
gamma. Because of the high energy of this photon,
significant deposition of energy in the phosphor layers of
the detector occurs only for large angles of incidence. Two
types of calculation results are provided, the ratio of the
detector responses of the two nuclides and response versus
distance from the detector curves. Table E.3 shows the
ratios of various radiation field quantities for the two
nuclides used. The largest contributing factor in the
uncertainties given in the table lies in the activities of
the sources. As can be seen from these numbers, the
detector response function plays a major role in increasing
the relative importance of the low energy photons of the
barium source.
Measurements
The detector responses for each nuclide were measured
at the face (3.016 cm from the plane of the face of the
front screen) of the detector with a lower level discrimi
nator level setting of 1.10 volts (far out on the pulse pile


376
sensed by the fuze to begin the detonation sequence. Among
the signatures available are velocity, ground pressure,
specific impulse, local disturbance of the magnetic field of
the earth, seismic impulse, noise, radio frequency radia
tion, visual recognition, and infrared radiation. Pressure
fuzes are among the most common employed. They may operate
on a single or multiple impulse method (to attack the third
vehicle in a column on a road, for instance), or in a delay
mode to defeat attempts to detonate mines with rollers pre
ceding the vehicle. Other simple types include tilt rods
and disturbance fuzes. Complex fuze types include magnetic
anomaly, acoustic, vibration, active or passive infrared,
and photon backscatter. Magnetic fuzes may be triggered by
a threshold, a rate of change or by the magnetic signature
associated with a particular vehicle type. Mines may also
be detonated on command by an observer.
Employment of Landmines
Mines are employed in offensive, defensive and retro
grade operations. In the offense they are primarily used to
provide flank protection during movement, to block with
drawal routes of an enemy force under pursuit, and to
protect against counterattacks. They also provide economy
of force by defending areas which are only lightly held as a
result of concentration elsewhere for the offensive opera
tion. In the defense and in retrograde operations, they are
employed as obstacles to delay and channelize enemy move
ment. In all operations they may be employed to harass and


32
TABLE III.l
Geometry of the Sodium Iodide
Detector and Shield
#
Material
Diameter
Width
or Thickness
(cm)
1
Nal(Tl) crystal
1.2700
0.9906
2
Quartz light pipe
1.2700
1.2700
3
Bicron proprietary
0.1588
a
4
Bicron proprietary
1.5875
a
5
Bicron proprietary
1.5875
a
6
Bicron proprietary
1.5875
a
7
Aluminum housing (face)
1.6383
0.0254
8 inner
Air space
0.04
1.0643
9 inner
Tin
0.07
1.0643
8 mid
Air space
0.06
1.0643
9 mid
Tin
0.07
1.0643
10 inner
Lead
0.1588
15.0343
8 outer
Air space
0.08
2.3343
9 outer
Tin
0.07
2.3343
10 outer
Lead
0.3175
2.3343
Dimensions of the Bicron Model .5M.390/.5L-X Nal(Tl) detec
tor and locally fabricated shield used in measurements and
calculations. Numbers (#) in the table are keyed to Figure
III.4.
aMaterials and thicknesses are proprietary information of
Bicron Corporation.


Figure VIII.29. Three-dimensional image diagram of the measured uncollimated
detector response to a 100 kVp source beam filtered by Pb for the TST mine laid on
the soil surface. The response is sampled at a 2.54 cm increment.
309


325
photons are rarely able to perform the required multiple
scattering through long paths in soil or explosive, the
response at the detector is primarily due to the higher
energy components. Since the detector operates on the
difference in attenuation of the two materials, the lowest
energy photons capable of reaching the detector in signi
ficant numbers provide the best detection mechanism. The
higher energy photons, provide slightly less contrast
between the two media, reducing the overall ratio in the 200
kVp case.
Figures VIII.42 through VIII.48 show the effect of ir
regularities in the soil surface on mine detection using the
uncollimated and collimated detectors. Figure VIII.42 shows
the positions with respect to the sampling array of six,
2.54 cm high mounds of soil protruding above a smooth soil
surface. Buried beneath the soil at a depth of 2.54 cm and
centered within the array is the TST mine. Figure VIII.43
shows an image produced for this configuration by a 200 kVp
beam filtered by lead (Figure F.12) and used in conjunction
with an uncollimated detector. The image is completely
dominated by the effects of the soil surface irregularities.
Figure VIII.44, which provides a two-dimensional represen
tation of the image, shows more clearly that the image
consists of minima and maxima of the same geometric pattern
as the soil mounds. The positions of these image features
with respect to the soil mound locations are determined by
the average path lengths travelled by photons into soil


218
The optimization of the gap size for the collimated
fluence detector proceeds in the same fashion. The optimum
gap size is very dependent upon the source energy, the soil
type and density, and collimator acceptance angle since the
technique differentiates between the multiple scattering
properites of the medium. A decision based on the calcula
tions is complicated by the poor statistics of the results
caused by the very small fraction of the source photons
which produce a response in a useful collimated detector.
Attempts to use a correlated sampling technique within the
Monte Carlo method, such as that employed by Coleman (1971),
are inappropriate on two counts. First, the existence of
air within the mine (not present in Coleman's work) violates
the variance criterion for applying correlation techniques
to the interaction coefficients. This criterion basically
requires that the interaction coefficients of the materials
in the correlation calculation be similar. The great
difference in the densities of air and the other problem
materials violates this requirement. The second problem
with the method is that the correlation technique does not
apply to any atomic number dependent quantities other than
the interaction coefficients. Thus, even if the air layer
were neglected, the scattering routines would have to be
altered. No coherent scattering could be permitted, and the
Klein-Nishina cross section would have to be substituted for
the incoherent scattering cross section. Demonstrated
inaccuracies with such substitutions in the energy range of


36
very high energy photons (which pass through the detector
without significant interaction). The 35 keV value also
provides some safeguard for the lower level discriminator
setting determination from non-linearities observed in the
low energy response of Nal(Tl) (Aitken et al., 1967). The
light output and hence pulse height is not proportional to
the amount of energy deposited in the Nal(Tl) crystal for
low photon energies. Figure III.3 shows the detector and
shield. The slotted wooden structure supporting the
detector allows the distance between the beam axis and the
detector to be varied.
The detector is operated in a pulse counting mode. The
detector high voltage is supplied at -900 volts. Figure
III.5 provides a diagram of the components of the counting
system. Remote control of the counting system is by an
IEEE-488 General Purpose Interface Bus (GPIB).
Computer Control System
An IBM PC personal computer controls both the RS-232
serial interface bus, which operates the soil box position
ing system, and the IEEE-488 GPIB, which operates the
counting system. Software for these two functions was
provided by Moss (1986). The RS-232 serial interface bus
transmits the direction, distance and axis of motion to the
motor controllers. The GPIB controls the counting channel
and time through the counter/timer. The two systems are
integrated by the computer to allow complete automation of
the scanning and counting tasks required to produce an


347
deeper penetration of the high energy photon produces a very
different path to the detector. The extension of these
different paths to a polyenergetic spectrum, leads to the
same conclusion as for the uncollimated detector; the high
energy components of the higher energy beam are uncorrected.
The previous application of this technique (Jacobs et al.,
1979) used detectors positioned as close to the source as
possible to produce nearly vertical paths through overlying
materials.
Power Requirement
The data derived from calculations and imaging experi
ments provide the information required to make estimates of
the power requirements for mine detection using backscatter
radiation radiography. Two criteria are used to assess the
capability of portable generators to provide the power re
quired to produce images and detect buried mines. The first
criterion derives from experience with the imaging experi
ments. Those experiments reveal that approximately 10000
counts with the mine present are required for each pixel in
the image to produce readily recognizable patterns for mines
buried at depth. This number of counts effectively deter
mines the power requirement, but does not address the ques
tion of detectability, the second criterion. Detection is
determined by the magnitude of the difference in the mine
and soil responses in the presence of noise. The Neyman-
Pearson criterion (Schwartz and Shaw, 1975) is used as the
vehicle for the determination of detectability. These two


227
Considerations regarding height sensitivity, examined
quantitatively in Chapter VIII, encourage the use of small
raster gaps to maximize the fluence striking the detector.
Table VII.5 also provides the fraction of the total back-
scattered fluence intercepted by the various detector con
figurations. Given the small differences in the mine to
soil ratio, the 10 cm gap size is selected for calculations.
Increase of panel width beyond 30 cm produces virtually no
change in the mine to soil ratio, so the smallest width is
used in the majority of the calculations for the uncolli
mated detector to satisfy the operational requirement to
minimize the total size of the detector. Other widths are
examined with respect to height sensitivity in Chapter VIII.
Segmented Detector Geometry
The geometry of the segmented detector is shown in
Figure VII.28. The principle of operation of this detector
is to remove an additional portion of the central minimum in
the mine to soil ratio. A central section of each panel
with respect to the beam axis is removed from the detector.
Since the x-ray beam is rastered, the section removed must
also be rastered. This could be accomplished electroni
cally. Rather than simply comparing the backscattered
responses with and without mine present, an amplification is
achieved by comparing the ratios of the responses of each of
the four detector segments. Over perfectly uniform soil and
with beam intercept at the center of the mine, the ratios,
taken with respect to any one of the segments, would be


Figure E.ll. Fraction of incident energy transmitted, 45 degree incidence. The
fraction of incident x-ray photon energy escaping into the transmission hemisphere of
the detector system constructed from two halves of 3M Trimax 12 screen B 184048 as a
function of incident x-ray photon energy (MeV) for the case of 45 degree incidence is
shown.
441


c:
o
to
(ft
E
(ft
c
a
f-
Figure D.2. Measured and calculated transmission of exposure rate, 80 kVpf 2.00 mm
Al. A comparison of measured and calculated transmission of exposure rate of a 80
kVp beam produced by the GE Maxitron 300 X-Ray Therapy Unit with 4.75 mm beryllium
inherent filtration, 2.00 mm aluminum added filtration and air path length of 90.17
cm is shown. The calculated transmission of exposure rate is based upon the spectrum
shown in Figure D.l.
399


518
Chilton, A. B.; Shultis, J. K.; and Shaw, R. E. Principles
of Radiation Shielding. Englewood Cliffs, N.J.:
Prentice-Hall, 1984.
Clarke, R. L., and Van Dyk, G. "A New Method for Measure
ment of Bone Mineral Content Using Both Transmitted and
Scattered Beams of Gamma-Rays." Phys. Med. Biol.
18:532-539, 1973.
Coleman, W. A. "Monte Carlo Calculation of the Effect of
Subterranean Perturbations on Refexed X-Rays." Nucl.
Sci. Engr. 46:12-21, 1971.
Compaq Computer Corporation. Compaq Deskpro Personal Com
puter Operations Guide. Houston, TX: Compaq Computer
Corporation, 1984a.
Compaq Computer Corporation. BASIC Version 2 Reference
Guide. Houston, TX: Compaq Computer Corporation, T984b.
Compton, A. H. "A Quantum Theory of the Scattering of
X-Rays by Light Elements." Phys. Rev. 21:483-502, 1923.
Definicon Systems. DSI-32 Manual. West Lake Village, CA:
Definicon Systems, 1986.
Dell, J. R., and Ebert, P. J. "Nal(Tl) Escape Peak to
Photopeak Ratios." Nucl. Instr. and Meth. 68:335-336,
1969.
Denison, J. T. SCIPLOT. Houston, TX: Techdata Engineering
Programs, 1984.
DePuy, W. E. "Toward a Balanced Doctrine." Army
34(11):18-25, 1984.
Dick, C. E., and Motz, J. W. "Image Information Transfer
Properties of X-Ray Fluorescent Screens." Med. Phys.
8:337-346, 1981.
Dohring, W.; Reiss, K. H.; and Fabel, H. "Lokale in vivo
Dichtesbestimmungen der Lunge mit Hilfe der Compton-
Streuung." ("Compton Scatter for Local in vivo Assessment
of Density in the Lung.") Pneumonologie 150:345-359,
1974. Abstract in English.
Dyck, V. A.; Lawson, J. D.; and Smith, J. A. FORTRAN 77, An
Introduction to Structured Problem Solving. Reston, VA:
Reston Publishing, 1984.
Dyson, N. A. "Characteristic X RaysA Still Developing
Subject." Phys. Med. Biol. 20:1-29, 1975.


Ill
the L and K edges is required, the cross section data of
Storm and Israel (1970) are used. The mass attenuation data
are constructed for energies between 1 and 300 keV with a 1
keV increment. These data sets have been constructed for
the following materials: tungsten, beryllium, aluminum,
copper, iron, lead, lucite, air, gadolinium oxysulfide,
sucrose, TNT and a soil type (Norfolk sandy loam) similar to
that used in the mine detection and imaging experiments.
Anode Self-Attenuation
Since x-ray photons are produced by electron interac
tions within the anode, they are subjected to attenuation by
tungsten as they exit. Correction for anode attenuation is
accomplished using the method suggested by Soole (1971).
Soole compares calculations using Kramers' formula without
correction for anode self-attenuation to published exposure
transmission data. He finds the resulting calculated expo
sure transmission curves to indicate a softer (lower energy)
spectrum than the measured values implied. Figure V.l shows
a typical calculation by the XRSPEC.PAS code without anode
self-attenuation. The figure shows measured and calculated
exposure rate transmission produced by placing varying
thicknesses of aluminum in the x-ray beam. The geometry of
the measurements conforms to the requirements for formal
half value layer determination (Johns and Cunningham, 1983).
The discrepancy between the calculation and measurement is
the same as is observed by Soole. The steeper slope of the
calculated curve implies a softer beam, that is, one which


CHAPTER IV
RADIATION TRANSPORT
In the mine detection system, photons, originating from
an x-ray source, travel through air, and strike the soil.
The photons then undergo interactions with the soil and
objects buried within it. Some photons are scattered back
through the soil surface and strike the detector. This
chapter describes the fundamental photon interactions of
importance to the mine detection problem, the radiation
transport models used to simulate those interactions, and
their validation.
Photon Interactions
Photons interact with matter through a variety of
mechanisms. The energy range of interest for mine detection
and imaging (described in Chapter VII) results in only three
photon interactions of importance: coherent scattering,
incoherent scattering and the photoelectric effect. A brief
description of each of these interaction types is provided.
Coherent Scattering
Thomson gave the first description of the interaction
of an electromagnetic wave with a free electron (jammer,
1966). Applying purely classical physics to the interac
tion, he showed that the time varying electric field
52


126
to 25% of the constant potential term. This waveform would
be expected to produce a harder spectrum than the single
phase waveform of the GE Maxitron 300 when operated at the
same peak kilovoltage. Comparisons at 80 and 105 kVp are
shown. The lack of characteristic x rays in the measured 80
kVp spectrum casts some doubt on the quality of these mea
surements. The characteristic x rays should be more intense
in this spectrum than in the corresponding GE Maxitron 300
spectrum as a result of the waveform. Overall, however, the
comparisons are generally good.
Figures V.8, V.9 and V.10 show the comparison with the
measurements of Fewell and Shuping (1977). The voltage
waveform of the x-ray machine used in these measurements is
single phase, as is the GE Maxitron 300. Comparisons are
made at 70, 80 and 90 kVp. The comparisons in all three
cases are excellent. The presence of characteristic x rays
in the measured 80 kVp spectrum reinforces the lack of
confidence in the Epp and Weiss measurements described
above.
Other Methods to Determine X-Ray Spectra
Several other methods are frequently applied to the
problem of determining x-ray spectra.
Measurement
The most direct method for determining x-ray spectra is
measurement. Unfortunately, this method is an extremely
difficult, expensive, and time consuming endeavor requiring
highly specialized equipment and detailed corrections for


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
LANDMINE DETECTION BY SCATTER
RADIATION RADIOGRAPHY
By
John G. Campbell
August 1987
Chairman: Alan M. Jacobs
Major Department: Nuclear Engineering Sciences
The application of scatter radiation radiography to
the detection of buried nonmetallic antitank landmines is
examined. A combination of calculations and measurements
is used to address the problem. The primary calculation
tool is a Monte Carlo photon transport code. Measurements
are made with an x-ray source, sodium iodide detector, and
soil box positioning system. The soil box containing a
model of a nonmetallic antitank mine is moved beneath the
x-ray source to simulate both the forward motion of a
vehicle transporting the detection system and raster of the
beam to search a path of sufficient width to allow safe
passage. Calculations are used to suggest mine detection
mechanisms and to optimize geometric parameters and x-ray
beam quality. Measurements are used to validate the
calculation results for a small detector and produce images
of buried mines. The calculations are extended to large
xxxi


526
Zhukov,
York:
. K. Marshall Zhukov's Greatest Battles New
Harper and Rowe, 1969.


424
Photoelectric events are eliminated in the MCPHOT.PAS
code by a weighting scheme which allows only scattering
interactions to be considered. This is justifiable because
of the low atomic number of the materials present in the
mine and soil. In the case of the detector response calcu
lation, energy deposition is the quantity of interest and
photoelectric events become extremely important. Addition
ally, in a thin detector containing a relatively high atomic
number material (64 for gadolinium oxysulfide), fluorescent
emission also plays an important role. Detailed photoelec
tric interaction cross sections and information concerning
fluorescent emissions are taken from Storm and Israel
(1970). Atomic fluorescence yields are taken from Fink et
al. (1966). The method used to model fluorescent emission
is that suggested by Carter and Cashwell (1977). Using
their recommendations, titanium in the reflecting layer, and
gadolinium in the phosphor layer are permitted to have
fluorescent emissions. The terbium in the phosphor layer is
neglected because it is present in very small quantities
(less than 0.3 atom % replacing gadolinium), and because it
is very close to gadolinium in the energies of its fluores-
cently emitted photons (the atomic number of terbium is 65).
Only K characteristic emissions of titanium are considered
since its L x rays have energies on the order of only 500
eV, and can be considered to be effectively absorbed at the
locations of the photoelectric interactions which precede
their production. An effective L edge of gadolinium is


Figure VII.17. Ratios of mine and soil integral energy spectra for two TST mine
cases in HTL soil. The energy value appearing in the graph is that of the upper end
of the energy window with the lower end set at zero.
197


364
1.27 cm by 1.27 cm at the soil surface to allow shape reso
lution of the mine. The optimum size of the raster gap
depends on detector type.
Of the four types of detectors which have been examined
for feasibility, only a large area detector, consisting of
panels of sensing material separated by a 30 cm gap to allow
beam raster and using collimation to remove the single scat
tered component, is capable of detecting mines at depths of
burial greater than 5.0 cm. Higher mine to soil ratios can
be obtained with larger raster gaps, but the reduction in
backscattered fluence makes the power requirement unreason
able. Heavy filtration of the source beam to force its
spectrum to possess a higher proportion of the monoenergetic
optimum energy photons is counterproductive because of
greatly increased power requirements. Lightly filtered 200
kVp beams are found to provide good results. The collimated
detector is capable of mine detection and imaging to at
least 7.5 cm. This conclusion is reached for realistically
available portable power supplies with acceptable detection
and false alarm probabilities for vehicle speeds and path
widths compatible with operational requirements in the
presence of moderate amounts of noise. In soil recently
disturbed by burial of mines, larger depths are possible.
The major drawback of the collimated detector system is
its sensitivity to height variation. This issue is dis
cussed in the section below covering future research direc
tions. Less important concerns include the ability of the


313
y-direction is a result increasing numbers of photons cross
ing into soil after exiting the mine as the source beam
moves closer to the wall nearest the detector. Figure
VIII.33 shows the image formed for a mine at a depth of
burial of 7.62 cm with the Bicron Nal(Tl) detector colli
mated to an acceptance angle of 18.1. The mine to soil
detector response ratio is approximately 1.2 at this depth.
This is higher than the ratio achieved by the uncollimated
detector at a depth of burial of 2.54 cm. Figures VIII.34
and VIII.35 show the response for a mine laid on the surface
of the soil. As with the image of the surface-laid mine for
the uncollimated detector, the three-dimensional image dis
play has been rotated 180 to allow features that would
otherwise be hidden to be seen. The considerably different
image is a result of the multiple scatter requirement before
detection. Just as in the uncollimated case, photons
striking outside the mine wall furthest from the detector
are shielded by the mine, producing a depression in the
detector response associated with these beam intercepts.
Photons striking inside the wall furthest from the detector
initially show decreasing response as distance into the mine
increases. The cause is photons traveling roughly parallel
to the soil surface within the mine. Such photons increas
ingly escape the mine as the beam intercepts move towards
the near wall and lateral paths exceed the distance to that
wall. Upon escaping, they encounter primarily air, which
only very rarely is able to scatter a photon to the


Figure VIII.20. Monte Carlo generated image for a simulated water puddle on HTL soil
with 20% water content by weight for the uncollimated fluence detector. The water
puddle is 10 cm in radius and 5 cm deep.
298


0.25
to
§ 0.20
CL
to
0
C£
0
O
§ 0.15
EE
0.1 o -\iiiiiiiiiiiiiiiiiiiiiiii
0 10 20 30 40 50 60
Height (cm)
Figure VIII.9. Fluence response as a function of height above the soil surface for
selected panel widths of the uncollimated detector. Calculations are for 100 kev
photon beams perpendicularly incident on the center of TST mines at 1.0 cm depth of
burial in NSL soil. The uncollimated detector consists of two panels of various
widths and 210 cm length, separated by a raster gap of 10 cm. Fluence response units
are photons/source photon.
268


463
probability of a given number of visible photons reaching
the photocathode within the detector resolving time
decreases continuously as a function of that number. For
the dark pulses, the interpretation is that the probability
that a given number of electrons are thermionically emitted
from the photocathode within the detector resolving time
decreases continuously as a function of that number.
Corrective Actions
Some corrective actions can be taken to allow the de
tector to function as a tool for the measurements, however,
the long fluorescence decay constant makes any detector
based on this phosphor unusable in a real operating landmine
detector system. The reason for this conclusion lies in the
rapid scanning rate required to meet reasonable rates of
travel for the vehicle carrying the detector system. Pixel
irradiation times in such a real system are estimated to be
on the order of 10 to 100 microseconds (Moler, 1985).
Corrections, which can be applied to the terbium activated
gadolinium oxysulfide detector, to allow its use in imaging
measurements for laboratory experiments are reducing the
detector sensitivity, reducing the dark pulses, and applying
low energy discrimination. The simplest methods to reduce
sensitivity are to reduce the area of the detector and the
diameter of the photomultiplier tube. This will result in
lower count rates and decreased photomultiplier tube persis
tence. Since the amount of thermionic emission is directly
proportional to the area of the photocathode, reduction in


50
of the soil. Two of the sets of samples differed only in
density; the compacted set density is measured to be 1.579
3 3
g/cm and the loose soil set, 1.450 g/cm Both have an
average moisture content of 3.26%. The third set differs
both in moisture content and density. It is prepared by
heating the soil to remove all moisture. The density of
3
this soil is 1.62 g/cm The increase in density with loss
of water is a result of combustion of low density organic
matter in the soil during heating. All samples are of the
same thickness. Exposure transmission measurements and
calculations are compared in Figure III.9. Agreement is
very good, indicating that the local soil is, as suspected,
close to NSL soil in its photon interaction properties.


449
absorption than the high energy side. Figure E.13 shows
that the first phosphor layer displays this same behavior.
This is a result of the same effect responsible for the
maximum above the K edge energy in the 45 degree case, the
loss of K fluorescent photons with corresponding small
energy deposition for incident photons with energies near
the K edge energy. Figure E.14 shows that at the K edge,
approximately 21% of the incident energy is lost into the
reflection hemisphere. This energy loss is a combination of
K fluorescent x rays (dominant portion) and backscatter.
The fraction of energy deposited in the second layer de
creases also (Figure E.13). The cause is the same as in
previous discussions: shielding by the first phosphor
layer. It is more obvious that a good deal of that shielding
is in the form of fluorescent emission into the reflection
hemisphere. Transmission losses remain low (Figure E.15).
*
Above the K edge, the effects are the same as discussed for
the case of 45 degree incidence, but enhanced by the larger
apparent phosphor thickness seen by the incident photons.
Comparison with Published Results
Chan and Doi (1984) have performed Monte Carlo calcu
lations for x-ray intensifying screens. While their calcu
lations are for only a single screen composed of pure phos
phor, they do show graphs of the fraction of energy absorbed
per incident x-ray photon for the cases of zero and 80 de
gree incidence. The shapes of these curves for the Lanex
Regular screen, which is based on gadolinium oxysulfide


372
Antitank or Antipersonnel
Antitank (AT) mines are designed to destroy or disable
tanks. They are also employed against other tracked and
wheeled vehicles. Their fuzing is generally designed to
prevent an individual soldier from causing detonation.
These are generally large mines, containing several
kilograms of explosives. Of these two mine types, they
represent the greatest threat to new U.S. operational
concepts, and are also the subject of this dissertation.
Antipersonnel (AP) mines are designed to kill or injure
soldiers operating on foot. They are generally very small
mines and may contain less than a tenth of a kilogram of
explosive. Doctrine in most armies requires that anti
personnel mines be employed whenever antitank mines are
emplaced to discourage their disarming by foot soldiers
(U.S. Department of the Army, 1979a, Radevich et al., 1965).
Alternatively, antihandling devices or boobytraps may be
employed in conjunction with antitank mines for the same
purpose.
Conventional and Scatterable
A conventional mine is placed in or on the ground by
hand or by mechanical mine laying systems. Scatterable
mines are delivered remotely by aircraft, artillery or
rockets. Scatterable mines are employed to protect flanks,
in enemy rear areas, or in response to enemy maneuver.
(U.S. Department of the Army, 1979a). Scatterable mines
will always be located on the surface of the ground;


116
Effects Neglected in the Model
In addition to the simplifying assumptions inherent in
Kramers' formula, several other effects are neglected.
These include the effect of the filter in producing secon
dary photons in the beam, and the effect of the external
collimator in preferentially hardening the outer portions of
the beam.
When a photon interacts in the filter, a number of out
comes are possible. The XRSPEC.PAS model, by its use of
simple attenuation coefficients, assumes that any interact
ing photon is removed from the beam. In reality, coherent
scatter, incoherent scatter and fluorescent emission photons
can be produced and may contribute to the beam. The exter
nal collimator exists to remove these photons, but it cannot
fulfill this function if the photons pass through the col
limator opening.
Since the walls of the collimator are parallel to the
centerline of the beam, and the beam is diverging, a higher
fraction of photons striking the lower walls will penetrate
the collimator. This results in an unwanted penumbra about
the defined beam, which will be spectrally harder than the
center.
These effects are highly dependent upon the geometry
and materials involved. Detailed calculations made for the
actual geometry and materials used in the mine detection
experiments show the effects to be negligible, producing a
maximum shift in the average energy of a spectral distribu
tion of 20 eV.


524
Shelkin, M., and Purdy, J. P. "The Counter Obstacle Ve
hicle." The Military Engineer 78:362-364, 1986.
Sidorenko, A. A. The Offensive, A Soviet View. Washington,
DC: U.S. Government Printing Office, 197 3.
Silberstein, L. "Determination of the Spectral Composition
of X-Ray Radiation from Filtration Data." J. Opt. Soc.
Am. 22:265-280, 1932.
Silberstein, L. "Spectral Composition of an X-Ray Radiation
Determined by its Filtration Curve." Phil. Mag. 15:375,
1933.
SoftLogic Solutions, Inc. DoubleDos. Manchester, NH:
SoftLogic, 1986.
Soole, B. W. "The Attenuation of X-Radiation Generated at
Constant Potentials Sufficient to Excite K-Radiation in a
Tungsten Target." Phys. Med. Biol. 16:427-437, 1971.
Stanton, L. ; Day, J. L.; Lightfoot, D. A.; Villafana, T.;
and Rauch, P. L. "Rapid Computation of Diagnostic X-Ray
Bremsstrahlung Spectra." Radiol. 130:477-484, 1979.
Storm, E., and Israel, H. I. "Photon Cross Sections from 1
keV to 100 MeV for Elements Z=1 to Z=100." Nuclear Data
Tables, Section A A7:565-681, 1970.
Sundararaman, V.; Prasad, M. A.; and Vora, R. B. "Computed
Spectra from Diagnostic and Therapeutic X-Ray Tubes."
Phys. Med. Biol. 18:208-218, 1973.
Suvorov, V. Inside the Soviet Army. London: Hamilton,
1982.
3M Corporation. "Trimax Intensifying Screens." X-Ray
Products Brochure. St. Paul, MN, 1985a.
3M Corporation. "Spectral Emission of Screens and Log
Sensitivity of Film." Information paper. St. Paul, MN,
1985b.
TurboPower Software. Programmer's Utilities. Campbell, CA:
TurboPower Software") 1985.
Uli, P. J. "Soviet Engineers." The Military Engineer
78:510-513, 1986.
Unger, L. M., and Trubey, D. K. Specific Gamma-Ray Dose
Constants for Nuclides Important to Dosimetry and
Radiological Assessment. Report ORNL/RSIC-45/R1. Oak
Ridge, TN: Oak Ridge National Laboratory, 1982.


87
since the cross section for the photoelectric effect becomes
larger as energy decreases, the weighting factor decreases
with each incoherent scattering interaction. The type of
interaction is forced by this weighting procedure to either
be a coherent or incoherent scattering event. The type of
interaction is determined by finding the ratio,
^coh
and comparing it to a random number. In this ratio, y is
the linear photoelectric interaction coefficient. This
ratio is the probability that the scattering event is co
herent. If the random number is less than the ratio, the
interaction is a coherent scattering event; otherwise, it is
an incoherent scattering event.
Modeling Scattering Interactions
If the interaction is determined to be a coherent scat
tering event, the probability density function,
p(^)
da
coh
d?r
coh
f
must be sampled to determine the direction of the scattered
photon. Conventional rejection techniques are inefficient
for sampling this distribution (Williamson, 1983a). The
technique used is a combination of inversion and rejection
sampling (Carter and Cashwell, 1977; Williamson and Morin,
1983a). It is described in detail in Appendix H.


Fraction of Incident Energy
Figure IV.4. Fractional energy of Compton scattered photons versus incident photon
energy. The graph shows that the fraction of energy retained by the scattered photon
is greatest for small scattering angles, and for low incident photon energies.


427
interactions occurring in the phosphor layer. At this same
energy, K fluorescent x rays are first capable of being
produced. Below the K edge energy, only L characteristic
photons can be emitted. They are produced with a much lower
probability than the K x rays, and their low energies result
in many being absorbed before escaping the phosphor layer in
which they originate. In contrast, because of their higher
energies and the thinness of the phosphor layers, many K
characteristic photons escape the phosphor layers in which
they originate. Most of the K x rays escaping into the
hemispheres of the screens which face one another are ab
sorbed in the other (non-origin) screen. Those escaping
into the hemispheres facing outward from the screen layers
are lost, carrying away a substantial portion of the initial
photons energy. Complicating the K x ray loss phenomenon
is the fact that the first phosphor layer (the layer closest
to the source of the incident photon) effectively shields
the second phosphor layer. This shielding effect is a func
tion of incident photon energy. An asymmetry in energy
deposition in the phosphor layers occurs which is greatest
at low energies. In general, more energy is deposited in
the first phosphor layer than in the second. This effect
also occurs at energies above the K edge, but with an addi
tional asymmetry. Since more photoelectric events are oc
curring in the first phosphor layer, more K fluorescent
photons are being produced. As a result, the loss of K x
rays into the reflected direction (into the hemisphere from


Table IV.1. Supplementing this structure are table entries
for energies just above and just below edges.
73
> Figure IV.12 shows the mass interaction coefficients of
aluminum as a function of photon energy. The energy ranges
of dominance of the interactions are dependent on the atomic
number of the absorber. /The photoelectric effect dominates
at low energies; incoherent scattering, at higher energies.
In no case does coherent scattering dominate. Table IV.2
gives the approximate energy at which the photoelectric and
incoherent mass interaction coefficients are equal for
materials of interest to the mine detection problem^/
Single Scatter Model
A single scatter photon transport computer code,
SGLMIN.PAS, written in Turbo Pascal (Borland, 1985) provides
a simple introduction to the variables associated with the
mine detection problem. While multiple scatter plays a very
important role, this simple model has been used to provide
insights into many aspects of the mine detection problem.
Computation Scheme
The code computes the single scattered fluence to an
array of detector positions located above and parallel to
the soil surface. The parameters which can be varied in
calculations are energy of the incident photon beam, angle
of incidence of the beam, height of the detector plane above
the soil, soil type and density, depth of burial of the
mine, and the beam/soil/mine intercept position. For each
position in the array in the detector plane, the code


455
Regardless of the value of this collection efficiency, it
will be a constant. The next step is the conversion of the
visible light energy to electron kinetic energy by the
photocathode of the photomultiplier tube. Given a constant
relative intensity, incident visible spectrum, this will
also be a constant, as will be the amplification of the
electron signal as it passes through the dynodes of the
photomultiplier tube. The signal output from the anode of
the photomultiplier, therefore, is directly proportional to
the energy deposited in the phosphor layer of the screen
material. Accordingly, the usefulness of a response matrix,
which provides the amount of energy deposited within the
phosphor layers per incident x-ray photon, becomes apparent.
The response matrix (with appropriate interpolation rou
tines) can be coupled directly to the fluence output of the
MCPHOT.PAS code to produce results directly proportional to
the measured electrical signal output of the detector
system. The difference in emission spectrum, noted above,
allows selection of a high efficiency photomultiplier tube
with a better match of the spectral sensitivity of the
photocathode. Figures E.16 and E.17 also show the spectral
sensitivity of the Hamamatsu R877 photomultiplier tube used
in measurements with the screens (Hamamatsu, 1985).
Shortcomings of the Detector
The gadolinium oxysulfide based detector is designed to
obtain high count rates to assist in reducing the x-ray gen
erator power requirements by improving counting statistics


357
power calculations. This quantity is allowed to vary to
determine how the detection probability changes with noise.
Tolerance levels are determined by the desired and useful
levels of Table VIII.11.
A series of calculations are performed by a computer
code, POWER.PAS. The error function is calculated from its
complement, which is in turn computed from a routine pro
vided by Press et al. (1986). This routine is also used to
produce a table of the error functions used to find its
inverse as a part of the solution of the false alarm equa
tion for the decision threshold. The code also computes the
minimum mine to soil ratio required to allow detection at
the desired and useful operational levels.
Power Calculations
Several examples are used to examine the power require
ment. The uncollimated detector is examined for depths of
burial of 0.0, 2.5 and 5.0 cm; the collimated detector at
2.5 and 7.5 cm. Both detectors are examined at the desired
vehicle speed and desired path width with the desired proba
bilities of false alarm and detection from Table VIII.11.
Table VIII.14 shows results for the uncollimated
detector. A number of conclusions can be derived from the
table. The generally reasonable power levels are a result
of the high fraction of source photons reaching the uncol
limated detector. The addition of filtration is seen to
increase the power requirement. The low signal to noise
ratios for the mines buried flush to the surface indicate


241
Depth of Burial
As a first comparison of the relative merit of the
alternative detector types, the capability to detect mines
buried at depth is examined. Mines are typically buried at
shallow depths, normally flush with the surface, or in
vegetated areas as deep as 8 cm. Regardless of these facts
and the increasing importance of surface laid mines, a key
criterion in all past research has been the ability to
detect mines buried much deeper (Nolan et al., 1980). The
most recently stated goal is for detection at 20.32 cm (8
inches), with the minimum useful depth being 5.08 cm (2
inches) (Moler, 1985). Table VII.8 compares the mine to
soil fluence ratios for the optimum configurations of three
of the four detectors at selected depths of burial in HTL
soil with 10% water by weight. The moisure content and
relatively high density of this soil make it a difficult
medium for mine detection. The segmented detector, which is
compared and shown to be approximately equivalent to the
uncollimated, unsegmented detector in Table VII.7, is not
included. The collimated detector is clearly superior for
detection at depth. None of the configurations remotely
approaches the capability of detection at the 20.32 cm goal.
The unsegmented, uncollimated detector will be unable to
detect mines even at the minimum useful depth of 5.08 cm
without significant signal processing effort. The seg
mented, uncollimated detector improves upon the unsegmented
detector only slightly. Detection at 5 cm remains


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TITLE: Landmine detection by scatter radiation radiography (record number:
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389
capable of covering a path width of only 20 cm. This mass
did not include biological shielding. A technique was
developed to subtract the contribution from neutron capture
in oxygen. Attempts at improving the system centered on the
use of the then newly available Ge(Li) solid state detec
tors. The only positive result of this change was reduction
in the shielding weight. The very small size crystals then
available was the primary cause for this reduction, not a
hoped for improvement in resolution. The resolution
advantages of the Ge(Li) detectors were of no practical use
because of Doppler broadening of the inelastically produced
gamma rays. Additionally, neutron irradiation destroyed the
Ge(Li) detectors after only after a few hours of use. The
use of larger Ge(Li) detectors and time of flight methods
did not overcome the problems of the system.
14 15
The use of the thermal N(n,y) N reaction had been
considered, but rejected because of two problems. First,
the count rate for the 10.8 MeV gamma ray produced in the
reaction was very low, and second, the resolution of a
Nal(Tl) detector was not adequate to separate this gamma
from a 10.6 MeV gamma ray of silicon. With the advent of
Ge(Li) detectors, this second problem vanished. The low
count rate problem remained. Solving it required a much
higher thermal neutron flux than was feasible at the time.
In 1970, Triangle Research Institute proposed the use of
252
Cf as the neutron source. This approach was rejected
because of weight requirements of the biological shield and


1
c
o
ot
(n
E
cn
c
a
L_
I-
10
T "I1 | I I T | I 1 I | H I | I I I | l I
0.2 0.4 0.6 0.8 1.0
~i r i i t I r i | i rr | i i i |
1.2 1.4 1.6 1.8 2.0
g/cm2 Of Aluminum
Figure V.11. Archer-Wagner method fit to measured transmission data. The excellent
capability of the Archer-Wagner fitting equation (Archer and Wagner, 1982) is
demonstrated.
M
OJ


180
TABLE VII.1
Comparison of the Linear Relationship
Between the Ratio of Number to Energy Albedo
and Source Energy at Perpendicular Incidence
Bulatov and Berger and MCPHOT.P
Andrushin (1967) Raso (1960)
Concrete
slope (MeV 1)
4.28
4.45
4.47
intercept
1.00
0.94
0.95
Iron .
slope (MeV-1)
3.55
3.59
3.53
intercept
1.00
0.96
0.98
HTL soil ,
slope (MeV-1)
-
-
4.58
intercept


0.93
HTL soil with TST
mine flush with
surface slope (MeV j
-
-
5.27
intercept


0.98
HTL soil with TST
mine at 2.5 cm depth_^
of burial slope (MeV x)
_
4.78
intercept
-
-
0.94


107
Since electron energy is related to accelerating potential
by the relation
E = e V/
where e is the charge of the electron, and
V is the accelerating potential,
Kramers' formula is alternatively written as
I(V) = k"* (VQ V),
where k" is k/e.
Application of this formula results in an unattenuated
bremsstrahlung spectrum which declines linearly from a maxi
mum of k'V^^ at V equal to zero, to a value of zero when V is
equal to V In order to apply Kramers' formula to the case
of the GE Maxitron 300 Therapy Unit, a number of modifica
tions are necessary. These modifications are described in
the following paragraphs.
Time Dependent Accelerating Potential
Since the accelerating potential of the GE Maxitron 300
is self-rectified, single phase, it varies in time. As a
result, the VQ term in Kramers' formula must be replaced
with an expression which accounts for the time dependence of
the accelerating potential. This time dependence is model
led as a sinusoid based upon waveforms associated with the
GE Maxitron 300 (General Electric, 1962). The expression
used to model the single phase nature of the accelerating
voltage is
V = v cosTr(t/200), t =-100,... ,100,
O ill cl X


345
uncolliraated
detector
Figure VIII.56. Failure of the dual energy subtraction
technique. (a) High and low energy photon paths to the
uncollimated detector produce unrelated responses due to
surface irregularities and inhomogeneities. (b) The same
problem exists for the collimated detector.


232
experiments is 1.27 cm by 1.27 cm. This size, used in
conjunction with a sampling interval of 2.54 cm, is capable
of resolving the circular shape of the large antitank mine
and providing edge effect information at mine/soil boun
daries. Given the 64.48 cm height of the source, the
angular spread of the beam is very small. Increasing the
beam size to 5.08 cm by 5.08 cm, a factor of 16 in area,
with this source height, produces only a 1.4% degradation of
the mine to soil fluence ratio, in HTL soil examples. As a
result beam sizes larger than those used in the experiments
can be employed with little penalty in response ratio near
the center of the mine, as long as the height of the source
is not changed. Image resolution would suffer, however.
Source Energy Optimization
The method used to determine the optimum source energy
for the collimated detector is addressed above in conjunc
tion with geometry considerations. The optimum source ener
gies of the other detector types depend less strongly on
geometry, and are determined in this section. For the un
collimated detectors, both segmented and unsegmented, the
technique employed is Monte Carlo calculations of the flu
ence responses for each of the three soil types with and
without the TST mine, using the values of the geometric
parameters discussed above. The calculations are for photon
beams perpendicularly incident on the soils with various
densities and moisture contents with the TST mine at a depth
of burial of 0.0, 2.5, 5.0 and 7.5 cm. Diverging source


67
shows the incoherent scattering cross section per electron
of aluminum and iron, and that calculated from the integral
of the unmodified Klein-Nishina formula. /The Klein-Nishina
cross section overestimates the true incoherent cross sec
tion at low energy. The error in the Klein-Nishina cross
section is larger in high Z materials. Because the effect
of the incoherent scattering function is important only at
low energies, it is often neglected in calculations^" The
same caveat described in the discussion of the atomic form
factor, regarding atomic and molecular electron density
configurations, applies to the incoherent scattering func
tion.
Photoelectric Effect
In the photoelectric effect, an incident photon strikes
an atomic electron and is completely absorbed. The electron
is emitted from the atom with kinetic energy equal to the
difference in the incident photon energy and the binding
energy of the electron to the atom. If the interaction is
with an inner shell electron, the vacancy remaining after
the interaction will be filled, either producing a fluor
escent emission photon(s) or Auger electrons. In the energy
region of interest to the mine detection problem, the cross
section per atom for the photoelectric interaction varies
approximately as
Zn/E3
where n varies between 4.0 and 5.0 depending on photon
energy (Anderson, 1984). This approximation indicates the


379
invented tank and to the increasing importance of mechanized
vehicles. Though explosive devices were never employed in
the form of extensive minefields, pipes filled with explo
sives and placed in roadways, and buried, modified artillery
shells were used ((U.S. Department of the Army, 1986). In
the years following World War I and before World War II, the
German Army pioneered the development of landmines
(Honeywell, 1981).
Mines of World War II
Modern mine development stems chiefly from German and
Soviet innovations. The German Army developed a wide range
of mine types including the Teller plate antitank mine, the
bounding shrapnel antipersonnel mine, a variety of nonmetal-
lic mines, mines employing shaped charges, and scatterable
mines. The Soviets produced the first nonmetallic mine in
response to a shortage of metal, rather than as an antide-
9*
tection mechanism; however, they also produced the first
device, a tar paper cased mine, specifically designed for
that purpose. The Soviets were also the first to use wooden
cased mines, flame mines, projectile mines, and a wide
variety of fuze types, including vibratory, magnetic
influence, and an antidetector fuze to attack mine detectors
based on frequency induction. Other nations copied and
modified the German and Soviet designs (U.S. Department of
the Army, 1973).
While modern mines are in some cases more sophisticated
than those employed in World War II, they are, with the


o
o
o
O
0
.o
<
L-
0
JD
E
rj
Energy (keV)
Figure VII.3. Number albedo ratios versus energy for the TST mine at 2.5 cm in three
soils. The ratio of the number albedos of mine present to soil only are shown for
three soil types for perpendicularly incident photon beams striking the center of the
TST mine at a depth of burial of 2.5 cm.
175


Q)
<0
O
&
$
cP
Figure VII.21. Spatial distribution of the single scattered mine to soil fluence
response ratio for a 100 keV photon beam perpendicularly incident outside the edge of
the TST mine. The TST mine is buried at a depth of 2.5 cm in NSL soil. The ratio is
shown at a height of 34.6075 cm above the soil plane.
203


143
TABLE VI. 1
Energies of Iodine Fluorescent Emission X Rays
Used in the Detector Response Calculations
X Ray
Weighted average of 3 L x rays
K.
kal
K
a2
KBl'
K
32
weighted average of M2,
M4 to K transitions
weighted average of N2,
to K transitions
Energy (keV)
4.206
28.613
28.318
M3,
32.276
N3
33.041


TABLE G.l
Benchmarks for Monte
Carlo Transport
Codes
Computer
Code
cl
Speed Factor
IBM PC/XT with 8087
MCPHOT.PAS
1.00
IBM PC/AT (6 MHz)
with 5.33 MHz 80287
MCPHOT.PAS
1.57
Compaq Deskpro with
8087-2
MCPHOT.PAS
1.98
PC-elevATor with 8 MHz
80286 and 8 MHz 80287
MCPHOT.PAS
2.75
PC-elevATor with 10 MHz
80286 and 8 MHz 80287
MCPHOT.PAS
3.17
PC-elevATor with 12.5 MHz
80286 and 8 MHz 80287
MCPHOT.PAS
4.12
Definicon DSI-32
MCPHOT.P
7.65
Cray X-MP/48
MCNP
271.04
aSpeed factor is with respect to the IBM PC. It is calcu
lated by dividing the program execution time on the IBM PC
by the execution time for other computer and code combina
tions.


103
for coherent and incoherent scattering. The comparisons are
very good.
An additional test of the scattering routines and the
entire code was made by comparing MCPHOT.P results with
those of the MCNP code (Briesmesiter, 1986). MCNP is a
general purpose Monte Carlo code developed at Los Alamos
National Laboratory for neutron and photon transport. It is
a widely accepted standard code for mainframe computer use
in nuclear engineering and weapons applications. An option
in the MCNP code allows full treatment of photon scattering
using atomic form factors and the incoherent scattering
function. A buried mine problem was run using the MCNP code
on a Cray X-MP/48 computer and compared to the same calcula
tion using the MCPHOT.P code on the Definicon DSI-32. In
order to conserve central processing unit time on the Cray
computer, the problem was limited to a cylinder of 50 cm
radius about the beam axis. The MCPHOT.P code was modified
for this same constraint. The only difference between the
two calculations was to allow the MCNP code to model photo
electric interactions with subsequent fluorescent emissions.
This was done to test the assumption in the MCPHOT.P code
that fluorescent emission from soil and mine materials could
be ignored. Comparisons were made with the number of pho
tons striking a 50 cm radius disk above the soil, the total
energy of those photons and their energy spectrum. In each
case the comparison was excellent. Differences in the
number and energy of photons striking the disk are less than


Figure VIII.15. Monte Carlo generated image for the TST mine buried flush to an HTL
soil surface for the uncollimated fluence detector.
291


Figure V.12. Comparison of modified Kramers' method and the Archer-Wagner method at
80 kVp. A comparison of two calculated x-ray spectra for an 80 kVp beam generated by
the GE Maxitron 300 X-Ray Therapy Unit with 4.75 mm beryllium inherent filtration,
2.00 mm aluminum added filtration (includes 0.25 mm aluminum equivalent monitor ioni
zation chamber^, and an air path length of 90.17 cm is shown. Fluence u^its are
photons per cni per keV. Total fluence is normalized to 1 photon per cm.
136


Figure VIII.26. Low pass filtered image diagram of the measured uncollimated
detector response to a 100 kVp source beam filtered by Pb for the TST mine at a depth
of burial of 2.54 cm. This figure is the result of two-dimensional low pass
filtration of the image of Figure VIII.25.
306


Figure E.13. Fraction of incident energy absorbed in each screen, 75 degree
incidence. The fraction of incident x-ray photon energy absorbed in the two phosphor
layers of the detector system constructed from two halves of 3M Trimax 12 screen B
184048 as a function of incident x-ray photon energy (MeV) for the case of 75 degree
incidence is shown. The first screen is that nearest the incident photon when it
first encounters the detector.
446


Energy (keV)
Figure VII.30. Source energy optimization curve for the uncollimated fluence
detector with mine depth of burial of 5 cm, in NSL soil. The ratio of mine to soil
fluence response striking an uncollimated detector consisting of two panels of 30 cm
width and 210 cm length, separated by a raster gap of 10 cm and located 34.6075 cm
above and parallel to the soil surface is shown as a function of source energy of
perpendicularly incident beams. The beams intercept the mine at its center.
234


495
MUCBSX.BAS converts the wide energy mesh mass interac
tion coefficients created by the MIXCS.BAS code to the one
keV increment mass attenuation coefficients used by the
XRSPEC.PAS code.
MIXFS.BAS creates files of atomic form factors and
incoherent scattering functions for compounds and mixtures.
SURFACE.PAS produces a three-dimensional display of the
spatial distribution of fluence or detector response calcu
lated by the photon transport codes.
READF.PAS manipulates the fluence and detector response
outputs of the photon transport codes. Manipulations in
clude filtration, symmetry operations, integration, and
addition, subtraction and division of matrices.
POSDATA.PAS reads spatial response files created by
MCPHOT.PAS and MCPHOT.P codes, applies any available sym
metries to improve statistics, and creates a file of re
sponse versus distance from beam axis for a monoenergetic
source beam.
PTRESP.PAS, PTRESPLN,PAS, AND PTRESPSP.PAS use, re
spectively, least squares polynomial fits, least squares
log-log fits and cubic spline fits of detector response
versus energy at a particular detector position used in com
bination with x-ray spectra produced by the XRSPEC.PAS code
to give the detector or fluence response at a position due
to the polyenergetic source beam.


86
the same direction of travel in the new material. A routine
in the code determines the new material index by examining
the position and direction of travel of the photon. This is
true unless the boundary is that of the detector plane. In
this case the photon is scored. A number of pieces of in
formation are extracted during the scoring process. They
include the weight and energy of the photon, the detector
response produced by the photon, the number of scattering
events the photon has undergone, the position in the
detector plane of the photon intercept, and the angle of
incidence of the photon on the detector plane.
If the interaction distance is smaller, the position of
interaction is calculated, and the type of interaction is
determined. Because photoelectric effect interactions
cannot contribute to the scattered fluence at the detector,
and fluorescent emission is not important, a weighting
technique is used to force all photons to scatter, greatly
increasing the efficiency of the calculation. The weighting
factor applied at each scattering event is given by
^coh + ^inc
t
u
where each of the interaction coefficients is found by
table look-up at the photon energy in the material of the
interaction. This weighting factor represents the proba
bility that the interaction is a scattering event and is,
therefore, a number less than one. Since incoherent scat
tering events lower the energy of the resulting photon and


235
TABLE VII.6
Optimum Source Energies for the
Uncollimated Fluence Detector
Depth
Soil Type Burial
of
(cm)
Optimum Mine to Soil
Fluence Response
Energy (keV) Ratio3
NSL
2.5
80
1.176 0.018
5.0
80
1.052 0.016
7.5
80
1.016 0.016
HTL
2.5
100
1.133 0.016
5.0
120
1.042 0.015
MCL
2.5
150
1.174 0.026
5.0
200
1.046 0.015
HTL b
2.5
60
1.227 0.021
low density
5.0
120
1.064 0.015
7.5
120
1.022 0.014
NSL
r 2.5
80
1.187 0.014
small air gap
c
5.0
80
1.044 0.015
HTL
2.5
80
1.139 0.011
10% h2o
HTL
2.5
80
1.116 0.015
20% H20
aSee text for
description
of calculation
parameters.
^Density of 1
3
.27 g/cm .
CAir layer in
mine
is 1.0
cm, instead of
the normal 2.5 cm.


226
TABLE VII.5
Mine
and
to Soil Fluence
Raster Gap Size
Ratio Dependence On
for an Uncollimated
Panel Width
Detector
a
Mine to Soil Fluence Ratio
(% of Backscattered Fluence Detected)
Raster Gap
Size (cm)
10
Panel width
30
(cm)
50
10
1.112 0.020
(23.5)
1.175 0.024
(18.6)
1.174 0.030
(12.5)
20
1.139 0.016
(42.1)
1.175 0.019
(31.2)
1.190 0.023
(21.1)
30
1.147 0.014
(54.6)
1.183 0.017
(39.7)
1.176 0.020
(26.5)
40
1.156 0.012
(63.2)
1.176 0.016
(45.1)
1.180 0.019
(30.2)
50
1.153 0.012
(68.6)
1.178 0.015
(48.9)
1.176 0.018
(32.7)
60
1.156 0.012
(72.3)
1.176 0.015
(51.3)
1.174 0.018
(34.5)
The calculations are for 100 keV photon beams perpendicu
larly incident on NSL soil of density 1.54 g/cm with the
TST mine at a depth of burial of 2.5 cm. The diverging
source beams are 1.27 cm by 1.27 cm at the soil surface and
are produced by a point source at 64.48 cm above the soil
surface. In each case the beams are incident at the center
top of the mine, and the detector height is 34.6075 cm.
Detector panels are 210 cm long and centered on the source
beam axis.


Figure VI.7. Plane
Model .5M.39Q/.5L-X
angle of incidence.
detector response. The response of the plane model of a Bicron
Nal(Tl) detector is displayed as a function of photon energy and
167


Energy (keV)
Figure V.10. Spectrum comparison with Fewell and Shuping at 90 kVp. The measured
spectrum, from Fewell and Shuping (1977), is generated by a diagnositc x-ray unit
operated at 90 kVp with 0.7 mm aluminum equivalent inherent filtration, 4.00 mm
aluminum added2filtration and an air path length of 100 cm. Fluence units are
photons per cni per keV. The calculated spectrum is generated by the XRSPEC.PAS
code. Total fluence is normalized to 1 photon per cm.
129


LIST OF FIGURES continued
FIGURES
VIII.24
VIII.25
VIII.26
VIII.27
VIII .28
VIII.29
VIII.30
VIII.31
Page
Three dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine buried flush to
the soil surface 303
Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm 304
Low pass filtered image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm 306
Three dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm 307
Low pass filtered image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm 308
Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine laid on the soil
surface 309
Two dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine laid on the soil
surface 310
Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm 311
xxm


83
(Definicon Systems/ 1986). This machine allows for more
. . 32
than four billion distinct integers (2 -1), and makes the
use of fast, integer based random number generators with
long periods possible. The algorithm selected is a linear
congruential method suggested by Dyck et al. (1984). The
maximum period of this generator is approximately one-half
billion (Forsythe et al./ 1977).
Computation Scheme
Based upon selection of a particular beam geometry and
angle of incidence/ photons are individually started from
the source position. Random numbers are used to determine
the position, and in the case of diverging beams, the direc
tion of the photon within the beam. Each photon begins its
history with the initial energy assigned in the input, a
weight of 1.00, and series of integer codes which indicate
that it has not yet been involved in a scattering event,
that it is initially traveling in air, and that it is not at
any of the material boundaries of the problem.
Based upon the photon's position and direction of
travel, the distance to the next material boundary is com
puted. In the case of the photon just emitted from the
source, this first boundary is the soil, but thereafter any
of seven boundaries are possible. Figure IV.13 shows the
boundaries and material indices used in the calculation. A
series of geometry routines determine which of the boundar
ies the photon will intercept if it continues on its path


Figure VIII.1. Calculated and measured spatial distribution of detector response
from backscatter from sandy soil at 100 kVp. Responses are normalized to 1.00 at
19.775 cm from the beam axis. Geometry and source details are provided in Table
VIII.1. Uncertainties in measured results are too small to plot.
252


242
TABLE VII.8
Mine
to Soil Fluence
Ratio
at Selected
Depths
of Burial
of the
TST Mine
Detector Type
Depth of
Uncollimateg,
Collimated*3
Energy
Burial (cm)
Unsegmented3
Window
0.0
1.750
6.165
13.825
0.017
1.333
1.751
2.5
1.117
4.047
2.925
0.010
0.876
0.391
o

in
1.019
2. 379
1.310
0.014
0.569
0.186
7.5
1.003
1.724
1.004
0.011
0.435
0.148
10.0
1.001
1.039
0.979
0.011
0.254
0.145
aThe calculations are for 100 keV photon beams perpendicu
larly incident on HTL soil with 10% water by weight and
density of 1.80 g/crrr with the TST mine at various depths
of burial. The diverging source beams are 1.27 cm by 1.27
cm at the soil surface and are produced by a point source at
64.48 cm above the soil surface. The detector height is
34.6075 cm. Detector panels are 30 cm wide and 210 cm long,
separated by a raster gap of 10 cm, centered on the source
beam axis.
^The calculations are for 100 keV photon beams perpendicu
larly incident on HT^ soil with 10% water by weight and
density of 1.80 g/cin with the TST mine at various depths
of burial. The diverging source beams are 1.27 cm by 1.27
cm at the soil surface and are produced by a point source at
64.48 cm above the soil surface. In each case the beams are
incident at the center top of the mine, and the detector
height is 34.6075 cm. Detector panels are 30 cm wide and
210 cm long, separated by a raster gap of 30 cm, centered on
the source beam axis. Collimator acceptance angle is 19.9
degrees.


Energy Albedo
0.00 -jiii|iii|iii|iiiiiii|
20 60 100 140 180 220
Energy (keV)
Figure VII.4. Energy albedos versus energy for HTL soil and two TST mine cases,
energy albedos displayed in this figure are for perpendicularly incident photon
beams.
The
177


151
At high energies, the decrease in fraction absorbed is
much less than in the zero degree incidence case. This is a
result of the much thicker Nal(Tl) layer seen by an uncol
lided photon (long slant path through the crystal). Few, if
any, photons are transmitted through the crystal without
interaction. The primary transmission mechanism becomes
Compton scatter.
Counts Per Incident Photon
As described above, it is not the gross energy absorbed
which determines the number of counts recorded, but the
total energy absorbed in the crystal as a result of all
interactions of each individual incident photon and its
progeny. A further modification to the number of counts
recorded is the setting of the lower level discriminator.
Figure VI.3 shows the response of the plane detector in
counts per incident photon striking the outer case of the
detector for two discriminator level settings corresponding
to 0 and 0.025 MeV.
Discriminator Setting Corresponding to 0 MeV
This discriminator setting results in a count being
recorded for any energy depositing photon event occurring in
the crystal. The effect of the iodine K edge, so prominent
in the energy deposition curves, is removed by this criter
ion. Any deviation from a value of 1.00 counts per incident
photon is a result of photons completely missing the crystal
or undergoing only coherent interactions in the crystal.
Several mechanisms are responsible for such misses.


460
Fluorescence Decay Constant
The fluorescence decay constant refers to the amount of
time required for the induced luminescence from the phosphor
to decay by a factor of 1/e (e = 2.7182818...). For scin
tillation counting, especially at high count rates, the
pulse decay time should be short, so that fast signal pulses
can be generated. The results of pulse height spectra
measurements indicate that the fluorescence decay time
(which may include phosphorescence or delayed fluorescence)
for terbium activated gadolinium oxysulfide is long, on the
order of tenths of seconds. This long decay constant leads
to a long time period (relative to any realistic high count
rate electronics) during which visible light is emitted from
the phosphor layers. This results in the pulse of electrons
produced at the photocathode extending over a long period of
time. In low count rate situations, the ultimate result is
very small pulse amplitudes characteristic of single elec
tron events, that is, having exactly the same characteri
stics as the dark pulses described above. Hence, there is
no simple way to discriminate against noise events. As
count rate increases the number of visible light photons
reaching the photocathode within a short time interval
increases, and multiple electron pulses are generated,
leading to larger pulse height amplitudes. This is the
phenomenon of pulse pile up. It should be understood that
in general, these larger pulse pile up amplitudes are
produced (ultimately) by different incident photon


442
of energy absorbed in both phosphor layers decreases due to
increasing transmission losses. Comparison of Figures E.7
and E.11 reveals that at any given energy, the transmission
losses are smaller at 45 degree incidence than at 0 degrees,
as would be expected from the increased phosphor absorption.
At the K edge (Figure E.8), there is again a discrete
jump in the fraction of energy absorbed in the phosphor
layers as a result of the increase in the photoelectric
cross section. Comparison of Figures E.5 and E.9 shows that
the first phosphor layer at 45 degrees absorbs a higher
fraction of the incident energy; and the second phosphor
layer, a lower fraction (as a result of better shielding by
the first) than at 0 degree incidence. In fact, there is a
small step decrease in the fraction absorbed by the second
phosphor layer at the edge. Comparison of Figures E.6 and
E.10 shows an increase at 45 degree incidence in the
fraction of energy lost to the reflection hemisphere as a
consequence of increased incident photon absorption in the
first phosphor layer and hence increased K fluorescent
photon production. Fluorescent emission losses in this
direction are also enhanced by shallower average depth in
the phosphor at which photoelectric interactions take place.
The net result of increased absorption in the first phosphor
layer, decreased absorption in the second, and increased
losses into the reflection hemisphere is a slight increase
in fractional energy absorption at the K edge over the 0
degree incidence case. As would be expected, there is a


71
fluorescent emission does occur, the emitted photons will be
very low in energy due to the small binding energy of K
shell electrons in low Z materials. Figure IV.11 shows this
effect. These very low energy photons will be rapidly ab
sorbed near their point of origin and produce a negligible
contribution to the backscattered fluence. In materials
such as those of Figure IV.9, fluorescent emission plays an
important role and cannot be neglected. These materials are
associated with the detection of the scattered photons and
are discussed in Chapter VI and Appendix E. Emission of
fluorescent photons is isotropic.
Mass Interaction Coefficients
The interaction cross sections described above are
converted into mass interaction coefficients for use in the
transport models. For compounds and mixtures, the cross
section data from Hubbell et al. (1975) and elemental weight
fractions are used to construct the mass interaction co
efficients. In cases where edge effects are important,
the photoelectric data of Storm and Israel (1970) are also
used. These sets of mass interaction data are then expanded
by cubic spline interpolation into fine energy mesh tables
for use in the models. In cases where edge effects are
important, the cubic spline interpolations are performed
separately above and below the edges and then merged. The
mass interaction coefficient tables cover an energy range
from 1 keV to 1 MeV. The mesh structure used is given in


394
gains heat more rapidly during the day than surrounding
undisturbed soil. In very dry soils, the thermal conducti
vities are approximately the same and no temperature dif
ferences occur. Additionally, very moist soils, air tem
peratures below freezing, shadows, long duration cloud
cover, vegetation, and wind were also found to adversely
affect this detection mechanism. Detection was best at
night or first light due to thermal clutter during daylight
hours. A number of infrared based detector systems were
built and tested. Under favorable environmental conditions,
the technique worked well for rapid detection of mines
buried in roads.
Mine Neutralization
An alternative to the detection of mines is their
neutralization. When a minefield is adversely encountered
or detected by some other means, devices which destroy or
move mines to clear a path through them can be employed. As
was the case for the detection mechanisms, a wide range of
methods have been tried.
Mechanical Systems
Three mechanical devices have been used by various ar
mies to neutralize mines. In each case the device precedes
the vehicle to which it is attached into a minefield. Rol
lers are heavy metal wheels designed to detonate pressure
fuzed mines. Delayed fuzing or fuzing on a second pressure
pulse are simple methods to defeat the roller (Shelkin,
1986). The number of mine encounters is limited before the


Energy (keV)
Figure D.15. X-ray fluence spectrum, 200 kvp, 3.34 mm Al. The x-ray spectrum at 200
kVp calculated by the XRSPEC.PAS code for the GE Maxitron 300 X-Ray Therapy Unit with
4.75 mm beryllium inherent filtration, 3.34 mm aluminum added filtration (includes
0.25 mm aluminum equivalent monitor ionization2chamber) and air path length of 90.07
cm is shown. Fluence units are photons per crn per keV. Total fluence is normalized
to 1 photon per cm.
412


Figure VIII.50. Three-dimensional image diagram of the measured collimated detector
response to a 200 kVp source beam filtered by Al for a wood disk buried flush to the
soil surface. The response is sampled at a 1.905 cm increment. The disk is 8.57 cm
in radius and 1.87 cm thick.
335


Energy (keV)
Figure V.7. Spectrum comparison with Epp and Weiss at 105 kVp. The measured spec
trum, from Epp and Weiss (1966), is generated by a diagnositc x-ray unit operated at
105 kVp with 0.5 mm inherent aluminum filtration, 2.00 mm aluminum added filtration
and an air path length of 2.13 m. Fluence units are photons per cin per keV. The
calculated spectrunj is generated by the XRSPEC.PAS code. Total fluence is normalized
to 1 photon per cm.
125


TABLE OF CONTENTS continued
APPENDICES Page
Neutralization 394
Mechanical Systems 394
Explosive Methods 395
Magnetic Signature Duplication 396
D X-RAY TRANSMISSION MEASUREMENTS 397
E GADOLINIUM OXYSULFIDE DETECTOR 414
Detector Description 414
Detector Design 414
Screen Composition 417
Detector Response Matrix Calculation . 422
Calculation Technique 422
General Results of Calculations .... 425
Description of the Detector Response
Matrix 428
Perpendicular Incidence 429
45 Degree Incidence 436
75 Degree Incidence 444
Comparison with Published Results . 449
Response Matrix Relationship to
Detector Electronics 450
Shortcomings of the Detector 455
Sensitivity 456
Fluorescence Decay Constant 460
Corrective Actions 463
Comparison of Measured and Calculated
Responses 464
Calculation Technique 464
Measurements 465
F X-RAY SPECTRA USED IN MEASUREMENTS .... 470
G COMPUTER CODES 484
Computer Hardware 484
Personal Computers and Monte
Carlo Calculations 484
Computer Selection 485
Comparison with Cray X-MP/48
Supercomputer 487
Computer Software 489
Computer Languages 489
Radiation Transport Codes 489
X-Ray Spectra Codes 491
Detector Response Codes 492
Imaging Codes 493
Utility Codes 494
Photon Interaction Data Files 496
Commercial Software 497
IX


16
1986). In short, the Soviet Army is aware of its vulner
abilities on its flanks and in its rear areas, and is
organized to address the threat, in part, by employing
mines. Soviet doctrine has long included the rapid
emplacement of mines on the surface without burial (U.S.
Department of the Army, 1979a). In the 1970's, mechanical
minelayers and mine dispensing chutes for vehicles and
helicopters were fielded to allow rapid minefield emplace
ment. More recently fielded scatterable mine systems fur
ther enhance the capability to respond to the new U.S. op
erational concepts (West et al., 1985).
Aside from manual probing, a hand-held nonmetallic mine
detector of questionable capability (the hand-held metallic
detector works well), and actual mine detonation in an
adverse encounter, the U.S. Army has no method for detecting
buried nonmetallic mines (U.S. Department of the Army,
1986). These slow or adverse detection mechanisms are
incompatible with the advent of new operational concepts
which rely upon maneuver mobility. Accordingly, reviews of
all previous detection technologies have been conducted by
the U.S. Army in an attempt to find systems which might be
made to work. One such review (Moler, 1985) examined the
range of nuclear techniques (x-ray backscatter is included
within this category, even though it is actually an atomic
technique). This review recommended imaging using x-ray
backscatter as the highest priority nuclear technique for
additional research.


Figure VIII.34. Three-dimensional image diagram of the measured collimated detector
response to a 200 kVp source beam filtered by Al for the TST mine laid on the soil
surface. The response is sampled at a 2.54 cm increment.
315


359
TABLE VIII.14 continued
3
Calculations are for perpendicularly incident beams of the
indicated qualities originating from a diverging point
source 34.6075 cm above an HTL soil surface. Beam size at
the soil surface is 1.27 cm by 1.27 cm. The uncollimated
detector consists of two panels, each 30 cm wide, separated
by a 10 cm raster gap, and located 34.6075 cm above the soil
surface.
u
dA11 include 4.75 mm Be inherent filtration.
The power is that required to produce 10000 fluence counts
on the detector per pixel near the center of the mine.

The minimum signal to noise ratio (SNR) required to allow
mine detection by a system transported on a vehicle moving
at 1.34 m/s, searching a path 3.05 m wide, while maintaining
a false alarm probability of 0.00075 and a detection proba
bility of 0.99. See text for details of calculation.
eAlso includes 0.25 mm Al equivalent monitor ionization
chamber.


27
reaching the soil. This second image scan is, therefore,
the result of the head leakage scatter. Subtraction of the
second scan from the first corrects the imaging data for the
head leakage scatter. Structural constraints caused by the
weight of the shield prevent thicker layers from being used.
Figure III.3 shows lead shielding covering the head of the
x-ray machine.
Soil Box Positioning System
The soil box positioning system was constructed accord
ing to a design by Moss (1986). The control system was con
structed by Moss. The soil box is positioned in the x-y
plane (the plane parallel to the floor of the exposure room)
beneath the source by a two level linear bearing system
driven by ball screws which are powered by DC motors with
controlled clutch/brakes. The scan motion is boustrophe-
donic. Both local and remote control of the positioning
system are available. Local control is used to provide the
initial beam-soil intercept position prior to irradiation.
Remote control of the soil box motion is through an RS-232
serial interface bus. It is used in the imaging process to
move the soil box through the array of measurement posi
tions. Two soil boxes of dimensions of 66 cm by 66 cm by 45
cm deep and 122 cm by 91 cm by 45 cm deep are used. The
larger box is required for measurements with a collimated
detector. Both are filled with locally obtained sandy soil
typical of North Central Florida.


8
Jacobs et al. (1979) proposed an imaging scheme much
different than those discussed thus far. A collimated
scanning x-ray source with an uncollimated detector was used
to view large angle backscattered photons. Energy modula
tion of the source was used to produce two images. The
image at the lower source energy is characteristic of the
overlying materials. When subtracted from the higher energy
image (after multiplication by an appropriate factor), the
result is an image characteristic of deeper layers within
the irradiated object. The technique was found to be sensi
tive to regions of air within the object. This dual energy
approach was shown to allow irregular surface features to be
removed from the final image.
Backscattered Photon Mine Detection
A number of attempts have been made to use backscat
tered photons to detect buried nonmetallic mines. With only
one exception, the published descriptions are from efforts
sponsored by the United States military. Detailed accounts
of these mine detection systems are contained in classified
documents. The descriptions provided here are from unclas
sified summaries (Roder, 1975; Nolan et al., 1980). The
wide range of other technologies which have been examined as
possible mine detection methods are described in Appendix C.
Fluorescence Emission
Although fluorescent emission is not a backscatter
technique, attempts to use it as a mine detection mechanism
are similar. Between 1954 and 1957, the Armour Research


498
TABLE G.2
Photon Interaction Data Files
Material
File
Extension
Code
Availability by
MUCBS MUCBSM
File Type3
MUSBSX
Air
AIR
X
X
X
Aluminum
AL
X
X
X
Beryllium
BE
X
X
X
Concrete13
CON
X
X
Copper
CU
X
Dinitrobenzene
DNB
X
X
FTB soil0
FTB
X
X
GAD soild
GAD
X
X
Gd202S phosphore
HTL soilf
GOS
HTL
X
X
X
X
X
HT1 soil9
HT1
X
X
HT2 soilh
HT2
X
X
Iron
FE
X
X
X
Lead
PB
X
X
X
Lucite
LUC
X
X
X
MCL soil1
MCL
X
X
NSL soil^
NSL
X
X
X
Rubber
CUS
X
X
sio2
SIO
X
X
Sucrose
sue
X
X
X
Nal
NAI
X
X
Ti02
TDO
X
X
X
Teflon
TEF
X
X
Trinitrotoluene
TNT
X
X
X
Tungsten
W
X
Water
WAT
X
X
Wood
WOD
X
X
a
See text of this appendix for a description of these file
types.


238
TABLE VII.7
Comparison of the Segmented and Unsegmented,
Uncollimated Fluence Detectors
Beam Intercept3
and Depth of
Burial (cm)
u
Fluence Response Ratio0
Segmented Unsegmented
At Intercept At Mine
Center
Inside Front
0.0
1.654
0.043
1.186
0.017
1.753
+
0.026
in

CM
1.153
0.026
1.024
0.015
1.133
+
0.016
5.0
1.052
0.026
1.004
0.014
1.037

0.016
Outside Front
0.0
1.201
0.040
1.196
0.018
1.753

0.026
2.5
1.072
0.029
1.050
0.015
1.133
+
0.016
5.0
0.974
0.021
1.018
0.015
1.037
+
0.016
Inside Lateral
0.0
2.107
0.057
1.220
0.018
1.753
+
0.026
2.5
1.218
0.027
1.037
0.015
1.133
+
0.016
5.0
1.064
0.024
0.999
0.014
1.037
+
0.016
Outside Lateral
0.0
1.511
0.030
1.239
0.018
1.753
+
0.026
2.5
1.101
0.023
1.056
0.015
1.133

0.016
5.0
1.035
0.022
1.019
0.015
1.037
+
0.016
See text for description of location of intercept posi
tions .
^The calculations are for photon beams perpendicularly
incident on HTL soil of density 1.70 g/cm with the TST
mine at various depths of burial. The diverging source
beams are 1.27 cm by 1.27 cm at the soil surface and are
produced by a point source at 64.48 cm above the soil sur
face. The detector height is 34.6075 cm. Detector panels
are 210 cm long and centered on the source beam axis. Beam
energy for the segmented detector is 150 keV; for the un
segmented detector, 100 keV.


443
slight decrease in the fraction of energy transmitted when
compared to the 0 degree case (Figures E.7 and E.ll).
Above the K edge, comparison of Figures E.4 and E.8
shows a major difference in curvature. While the perpendi
cularly incident case resulted in a monotonically decreasing
function above the K edge, the 45 degree case gives a
relative maximum at about 0.058 MeV. The effect is not
rooted in any increase of efficiency of the screen with
increasing energy, but rather with a loss of efficiency in
the vicinity of the K edge at larger angles of incidence.
The site of this loss of efficiency is the first phosphor
layer. As has been previously discussed, as the angle of
incidence increases, the apparent phosphor thickness the
incident photon encounters becomes larger, resulting in more
absorptions and more K fluorescent photons and an average
shallower depth of production. Thus as angle of incidence
increases, the fraction of energy loss into the reflection
hemisphere increases. This increase is augmented by
increasing backscatter from the screen surface with
increasing angle of incidence, but the main effect is the
loss of K fluorescent photons, which is greatest at energies
near the K edge (Figure E.10). The effect is magnified by
the fact that events in which the incident photon energy is
close to that of the K edge, and in which the K x ray
escapes, deposit very little energy in the phosphor. The
result is the relative maximum observed in Figure E.8. Once
this maximum is passed, the remaining effects have been


c
o
*cn
M
E
CO
c
D
L_
f-
Figure D.4. Measured and calculated transmission of exposure rate, 80 kVp, 2.24 mm
Al. A comparison of measured and calculated transmission of exposure rate of a 80
kVp beam produced by the GE Maxitron 300 X-Ray Therapy Unit with 4.75 mm beryllium
inherent filtration, 2.24 mm aluminum added filtration and air path length of 90.17
cm is shown. The calculated transmission of exposure rate is based upon the spectrum
shown in Figure D.3.
401


81
Random Number Generators
The Monte Carlo codes are prolific users of random
numbers uniformly distributed on an interval between 0 and
1. For example, tests at 150 keV with the TST mine at 1.5
cm depth of burial in HTL soil showed that an average of 80
random number calls were made per photon. Since calcula
tions employing 200,000 photons are not unusual, it is
apparent that the period of the random number generator used
should be long. Random number generators are not actually
random; all follow fixed rules for producing a sequence of
numbers with a cycle length characteristic of the technique
used. The period of the generator refers to how many random
numbers can be generated before the sequence repeats. Prob
lems with short periods of random number generators employed
on personal computers are common (Whitney, 1984; Wichmann
and Hill, 1987). In the interest of speed of computation,
multiplicative and linear congruential random number gener
ators are used. Implementations of these types of random
number generators, which use integer arithmetic, are effi
cient and fast, but subject to machine dependent period
constraints. The general form of these generators is
Ij+-^ = [alj + c] mod m ,
where m is the modulus, a is the multiplier and c is the
increment. The modulus operator (mod) requires division of
the bracketed quantity by m and retention of the remainder.


450
(Kodak, 1980), including complex features such as the
inversion at the K edge for large angles of incidence,
correspond very well to results presented in this section.
Response Matrix Relationship to Detector Electronics
Deposition of energy in the phosphor is a single step
in a chain of events which leads to the electrical signal
produced by the detector system. The x-ray photon energy
deposited within the phosphor layer is converted into
kinetic energy of electrons within the layer. Some of these
electrons interact with the terbium impurity ions in the
phosphor layer, resulting in the emission of a discrete
spectrum of visible light photons. A discrete spectrum is
obtained because the interaction producing the visible light
photons is with electrons in the 4f shell of terbium, which
is shielded from external charge distributions (Anderson,
1984). The intrinsic conversion efficiency (defined as
watts of optical power output divided by watts of x-ray
power absorbed) for production of visible light photons in
terbium activated gadolinium oxysulfide screens is given as
0.18 by Buchanan et al. (1972) for excitation by electrons.
A value of 0.15 is generally favored for excitation by
x-rays (3M, 1985a; Anderson, 1984). Regardless of the
value used, the visible light output is directly proportion
al to the energy deposited in the phosphor. Given the
amount of energy deposited in the phosphor and its conver
sion efficiency into optical energy, the number of visible
light photons which are produced depends only upon the


418
Figure E.2. Active region of the detector. The layers of
the active region of the detector are shown (not to scale).
This portion of the detector is constructed from two 3M
Trimax 12 terbium activated gadolinium oxysulfide x-ray
intensifying screens. Thicknesses, compositions and
densities of the layers are given in Table E.l.


0.030
c
o
H-
O
JZ
Q_
Q)
O
L_
ZJ
o
co
0.025
0.020
Q>
Q.
CO
0.015
O
O
o.oio Hiiiiiiiiiiii
0 10 20 30 40 50 60
Detector Height (cm)
Figure VIII.11. Fluence response as a function of height above the soil surface for
the energy window detector. Calculations are for 100 keV photon beams perpendicular
ly incident on the center of TST mines buried flush to the surface in HTL soil. The
uncollimated detector with an energy window of 35 to 55 keV, consists of two panels
of 30 cm width and 210 cm length, separated by a raster gap of 30 cm, and located
various heights above and parallel to the soil surface intercepts the backscattered
fluence.
273


6
Kondic and Hahn (1970) suggested the use of Compton
scattering to measure density variations in two-phase flow.
They examined collimated sources used with both collimated
and uncollimated detectors. With the uncollimated detector,
energy discrimination was used to determine the path taken
by a scattered photon. The relationship between energy and
angle in a Compton single scattering event determines the
position along the source beam from which the photon is
scattered, and the intensity (corrected for attenuation) at
that energy determines the electron density of the material
at that point. Farmer and Collins (1971) independently used
the same uncollimated detector technique in a medical appli-
. 137
cation. They used a collimated Cs source and an uncolli-
mated Ge(Li) detector to examine cross sectional structure.
Rather than move the patient or scan the beam, the energy
discrimination technique was used to determine origin of the
scattered photons. Problems with this method are attenua
tion of both the primary and scattered photons, and resolu
tion reduction caused by detection of multiply scattered
photons. Extensions of this method (Farmer and Collins,
1974) using two higher resolution Ge(Li) detectors, above
and below the patient, and focused to the plane of interest,
also suffered from attenuation and multiple scatter. Reiss
and Shuster (1972) and Dohring et al. (1974) used collimated
137
Cs sources and collimated detectors with patient motion
to determine lung function and measure lung density.
Problems with multiple scattering were again noted.


Figure VIII.27. Three-dimensional image diagram of the measured uncollimated
detector response to a 200 kVp source beam filtered by Pb for the TST mine at a depth
of burial of 2.54 cm. The response is sampled at a 2.54 cm increment.
307


211
TABLE VII.2
Mine to Soil Response Ratios
At Selected Beam Angles of Incidence
Detector Type
Mine
to Soil Fluence Ratio3
Angle of
Incidence
0
20
60
Number albedo
1.141
1.125
1.056
0.009
0.010
0.008
u
Uncollimated fluenceD
1.183
1.155
1.056
0.017
0.016
0.013
Collimated fluenceD
Acceptance angle
23.1
2.173
1.968
1.702
0.160
0.179
0.113
19.9
2.697
2.469
1.950
0.313
0.344
0.166
16.3
2.748
3.015
2.523
0.466
0.648
0.300
11.5
3.372
1.671
2.804
1.130
0.564
0.541
aThe calculation example is for a 100 keV photon beam of _
radius of 1 cm, incident on NSL soil of density 1.54 g/cm,
with the TST mine at a depth of burial of 2.5 cm. In each
case the beam is incident at the center top of the mine, and
the detector height is 34.6075 cm.
b
The detector consists of two 30 cm wide by 210 cm long
panels, separated by a raster gap of 30 cm, parallel to the
soil surface and centered on the beam/soil intercept posi
tion.


317
detector. The increase in response at the edge of the mine
nearest to the detector also is a result of the air.
Forward scattered photons from the mine which pass through
the near wall are now able to traverse great distances in
air before encountering soil. Many of these photons reach
the region viewed directly by the collimated detector (28.1
in this case). Forward scattered photons in soil with a
level surface, by contrast, are not nearly as likely to
reach this position because of soil attenuation.
Figures VIII.36 through VIII.41 are images of the TST
mine at a depth of burial of 2.54 cm with an array of
3
stones, each approximately 1 cm m volume, overlying a por
tion of the mine nearest to the detector. The series of
images examines the effect of varying the source beam
spectrum for the uncollimated detector, and then makes
comparisons with the collimated detector. The spectrum used
to produce the image in Figure VIII.36 has a beam energy of
100 kVp and is filtered by aluminum (see Figure F.4). As a
result, it contains a sizeable low energy component, which
is not efficient in penetrating the soil and scattering back
through it. The low energy source photons are sensitive to
the presence of the rock array, producing the deep response
depressions in the image at the rock positions. The
presence of the mine in the image is not obvious, although
filtration is capable of improving the portion of the image
not covered by rock to the point that detection is possible.
The image in Figure VIII.37 is produced with a 150 kVp beam


387
sounds in a head set, which have a tendency to make the op
erator tone deaf after a short period of time. The detector
is obviously not appropriate for maneuver by mechanized '
forces.
Microwave systems which have been investigated, but not
fielded have been based on the concepts using wave guide
beyond cutoff, depolarization, short-pulse radar, frequency
modulated-continuous wave (FM-CW) radar, and harmonic radar.
The wave guide beyond cutoff concept uses two dipoles,
one to transmit and the other to receive. The dipoles are
arranged in open cavities connected by a metal sheet. When
the metal sheet is less than one-half wavelength above the
ground, the direct coupled and surface reflection signals
are greatly reduced, improving the capability to detect the
signal from the mine. The major drawback of this system is
height sensitivity. When the metal plate is more than one-
half wavelength above the soil, false alarms are generated.
Accordingly, use of a system based on this concept is limit
ed to relatively level soil surface with little vegetation.
This concept was used to produce an unfielded vehicular
detection system for use on roads.
The depolarization scheme uses horizontally polarized
transmitted microwaves with an orthogonally arranged, hori
zontally polarized receiver. If the soil surface is level
and the soil isotropic, no signal will be detected. Linear
features of buried objects depolarize the microwaves and
produce a signal. Problems, in addition to soil


153
Complete absorption of the photon energy in a single event
in the material layers in front of the crystal is the
primary reason for the low response at low energy. It is
caused by photoelectric interactions. Partial absorption of
the photon energy in the material layers in front of the
crystal with subsequent scatter away from the crystal or
absorption in non-crystal layers also does not produce a
count. The initial interaction is a Compton scattering
event. This series of interactions occurs at all photon
energies, having its largest effect at higher energies and
large angles of incidence. Coherent interactions with any
part of the detector followed by transmission through the
crystal, scatter away from the crystal, or absorption in
non-crystal layers also produce a miss. This effect is more
likely at lower incident photon energies. Transmission
without interaction through the crystal is the primary cause
for the decrease in response at high energy.
Discriminator Level Setting Corresponding to Energies
Greater Than 0 MeV.
At first consideration, it might be thought that the
effect of any discriminator setting would be simply to
remove all energy deposition events below that setting from
contributing to the counts recorded. The effect, however,
extends beyond the energy corresponding to the discriminator
setting. Two manifestations of the extended effect are pos
sible, dependent upon whether the discriminator level cor
responds to an energy above or below the K edge of iodine.


338
spectra (Figures F.8 and F.3) is employed in these and the
remaining images discussed in this section. The strong
depression in the backscattered response over the iron disk
is due to the high probability of photoelectric absorption
compared to that of soil. Figure VIII.53 and VIII.54 show
the responses of the two detectors to a thin plastic con
tainer of water buried flush to the soil. The container has
a radius of 5 cm and a depth of 7 cm. Except for its size
in the x-y plane, the image resembles that of a mine.
Figure VIII.55 shows the collimated detector response to a
hole 15 cm in radius and 15 cm deep which has been refilled
with soil of lower density than that which surrounds it.
The depression in the response at the center of the image is
a result of the density differences. Photons striking the
higher density soil around the edges of the hole interact
relatively near the surface. Many travel long lateral
distances through the lower density soil before scattering
to the detector. Photons striking the low density soil
penetrate deeper into the soil. After scattering and
travelling laterally through soil, many reach the high
density region before scattering towards the detector.
Because of their relatively greater depth in the soil, fewer
photons are able to reach the detector. The low response at
the edge of the hole nearest the detector is caused by this
same effect. The result is a partial ring of high response.
When viewed by a detector consisting of two panels, the
image becomes a region of enhanced response with a central


165
plane detector response matrix. A full correction would
require a complete Monte Carlo calculation of the entire
process from source through detector system for each detec
tor position. Such calculations would be essentially im
possible to perform for the range of calculations required.
The small size of the detector being used merely increases
the problem by requiring large numbers of photon histories
to be followed to approach reasonable statistics. As will
be seen in comparisons of calculations and measurements in
Chapter VIII, the first order correction appears to be ade
quate for the problem. The DETCOR.PAS code models the full
detector and shield system in three dimensions. All layers,
including air spaces, are included (see Table III.l for
dimensions). Each energy/angle correction calculation en
tails a two-dimensional plane wave of photons, all of a
given energy and angle of incidence, impinging on the space
surrounding and occupied by the detector. Approximately
12000 photons with a spacing of 0.02 cm between adjacent
photons in the incident plane wave, are individually atten
uated through the three dimensional structure of the shield
and detector to determine each photon's probability of in
teraction within the Nal(Tl) crystal. This probability is
summed for all of the photons and compared to the same
quantity for a plane detector case with entrance restricted
to the size of the face of the detector. The ratio of these
two probabilities is the first order correction factor.
Mass attenuation coefficients for all the materials in the


92
TABLE IV. 3
Comparisons of Number and Energy
Albedo Calculations for Iron
Energy
(MeV)
Perpendicular Incidence
Number
Albedo
Berger and
Raso (1960)
Simple3
MCPHOT.PAS
0.10
0.042
0.042
0.003
0.002
0.20
0.106
0.105
0.004
0.003
0.50
0.149
0.146
0.005
0.004
1.00
0.141
0.135
0.005
0.003
Energy Albedo
Energy
(MeV)
Berger and
Raso (1960)
Simple3
MCPHOT.PAS
0.10
0.032
0.032
0.004
0.003
0.20
0.063
0.062
0.005
0.004
0.50
0.054
0.053
0.004
0.003
1.00
0.031
0.030
0.002
0.002
aSee text for description.


370


300
follow, specifics of the experimental conditions are
provided in the captions of the figures. In all figures,
the detector is located in the positive y-direction. With
only a few exceptions, where image details of importance
would be hidden, the detector is located to the left front
of the three-dimensional representation. The exceptions are
individually noted. In all cases, the detector is located
to the right of the two-dimensional representations.
Figures VIII.22 through VIII.30 provide images produced
by the uncollimated Bicron Nal(Tl) detector. Figures
VIII.22 and VIII.23 are three- and two-dimensional image
diagrams for the TST mine buried flush to the surface of the
soil. The source is 100 kVp and is filtered by lead (Figure
F.8). Edge effects at the near wall (depression in re
sponse) and far wall (enhancement of response) are seen.
The mine to soil detector response ratio for central por
tions of the mine is approximately 1.8, making detection and
imaging easy. Figure VIII.24 repeats the same image with
the source spectrum at 200 kVp, also filtered by lead
(Figure F.12). The images are similar in shape, but the
central mine to soil ratio is much lower (approximately
1.4). The existence of more low energy photons in the first
image spectrum is the cause of this difference. Figure
VIII.25 shows the results of the 100 kVp beam (Figure F.8)
incident on the TST mine at a depth of burial of 2.54 cm.
The resulting image is similar to the Monte Carlo large area
detector results in its noise content. Two-dimensional low


35
TABLE III.2
Sources Used in Determining Lower
Level Discriminator Setting
Source
Energy (keV)a
109
Cd (Ag K. x ray) 22.162
n? a
Bs (Cs K x ray) 30.970
137 ai
Cs (Ba K x ray) 32.191
i -5 -a
JJBa (gamma) 80.999
^^Cd (gamma from ^^mAg) 88.037
57Co (gamma) 122.06135
aPhoton energy data are from Lederer and Shirley (1978).


2
materials they irradiate. The general concepts for the mine
detection and imaging system are also introduced in this
chapter. Three related appendices (A, B and C) provide
background on the characteristics of landmines, a short
history of landmine warfare, and a description of other
technologies which have been applied to mine detection.
Chapter III describes the equipment and materials used
in the research. Included in this chapter are descriptions
of soil and mine materials used in the calculations and
measurements.
Chapter IV describes the photon interaction character
istics important to the mine detection problem. The single
scatter and Monte Carlo photon transport codes used in the
calculations are also described. Validation of the Monte
Carlo calculation method is presented.
Chapter V describes the method used to produce calcula
tions of the x-ray source spectrum and the validation of the
technique. Other source calculation methods are discussed.
A related appendix (D) provides a graphical display of one
of the validation methods. Appendix F provides graphs of
spectra used in experiments.
Chapter VI describes the method used to calculate the
response function of the sodium iodide scintillation crystal
used in the experiments. Validation of the calculated re
sponse function is provided. Response calculation for a
detector based on terbium activated gadolinium oxysulfide is
described in a related appendix (E). Detectors similar to


CHAPTER VIII
APPLICATION TO IMAGING
The production of images of buried nonmetallic antitank
mines is the primary focus of this research. This chapter
addresses the imaging process. Measurements using the
General Electric Maxitron 300 X-Ray Therapy Unit, the Bicron
Nal(Tl) detector, and the soil box with TST mine in locally
obtained soil are compared to calculations performed by the
MCPHOT.P code in conjunction with fluence spectra from the
XRSPEC.PAS code and the detector response function provided
by the DETNAI.P code. These comparisons are used to evalu
ate the capability of the calculation method to provide
accurate predictions. Environmental parameters are examined
using calculations to assess their impact on the imaging
process. The parameters investigated are detector height
variation, soil density, soil moisture content, and inhomo
geneities such as wood, water, steel, and aluminum, which
can be expected on the battlefield. These parameters are
investigated for each of the detector types introduced in
Chapter VII, except the segmented, uncollimated detector.
Results for such a detector closely parallel those for the
unsegmented, uncollimated detector. Images are produced
both by measurement and by Monte Carlo calculations.
Finally, the information derived from the calculations of
248


367
real (unarmed) mines, is the final step in determining the
feasibility of scatter radiation radiography to detect
nonmetallic antitank landmines.


Figure VIII.54. Three-dimensional image diagram of the measured collimated detector
response to a 200 kVp source beam filtered by Al for water contained in a thin plas
tic container buried flush to the soil surface. The response is sampled at a 1.27 cm
increment. The container is 5 cm in radius and 7 cm deep.
340


48
are placed in the beams of various spectra produced by the
GE Maxitron 300 X-Ray Therapy Unit. Before the materials
tests are conducted, each of the four energy spectra
utilized in the measurements is itself tested using exposure
attenuation by added aluminum filtration as described in
Chapter V. The conditions required for formal half value
layer measurements are observed in these measurements and in
the materials tests (Johns and Cunningham, 1983). The
transmission of exposure rate is also calculated using the
method described in Chapter V for NSL (three sets of data
for NSL at different density and moisture contents) and TNT.
TM
Seven thicknesses of the solidified Karo Light Corn
Syrup are each subjected to the four spectra: 80, 100, 150,
and 200 KVp, each filtered by 4.75 mm of beryllium inherent
filtration, 0.25 mm aluminum equivalent monitor chamber,
3.19 mm of aluminum added filtration, and an air path of
67.31 cm. Figure III.8 compares the measured exposure rate
transmissions with those calculated. Perfect agreement
would occur if the ratio for each sample of measurement to
calculation is 1.00 or, in terms of the figure, if the plot
ted points lie on the line of slope equal to 1.00.
Agreement is very good, and the explosive substitute is
deemed adequate.
For each of the four beam energies listed above, three
sets of five soil samples are prepared (60 samples in to
tal). Multiple samples are used because of the variability
in composition, density and moisture content characteristic


Energy (keV)
Figure F.l. X-ray fluence spectrum, 100 kVp, 1.01 mm Al. The x-ray fluence spectrum
at 100 kVp calculated by the XRSPEC.PAS code for the GE Maxitron 300 X-Ray Therapy
Unit with 4.75 mm beryllium inherent filtration, 1.01 mm aluminum added |iltration
and air path length of 60 cm is shown. Fluency units are photons per cm per keV.
Total fluence is normalized to 1 photon per cm .
471


182
energy albedos in the mine detection cases is always smaller
than the ratio of number albedos. This suggests that a
fluence detector, such as a scintillator, would provide
somewhat better discrimination between mine and soil than a
detector based on energy absorption, such as an ionization
chamber.
Spatial Distribution
Figures VII.7 and VII.8 show Monte Carlo calculations
of the spatial distribution of the backscattered fluence
intercepting a plane located 34.6075 cm (this height
corresponds to that used in the measurements portion of the
work) above the soil surface for the case of HTL soil alone
and soil with mine buried flush to the surface. The source
beam is composed of 100 keV photons (as shown later in this
chapter, approximately optimum for mine detection in HTL
soil) and is perpendicularly incident. Since the beam axis
intercepts the plane at its center, the figure indicates
that the greatest backscattering occurs directly along the
source direction. This is because the shortest attenuation
path out of each material is in that direction. Figure
VII.9 shows the quotient of spatial distribution of the mine
at 0.0 cm to that of soil. The dimensions of the display
have been reduced from those of the two preceding figures,
and symmetry considerations employed to eliminate large
variations in the quotient resulting from very small and
hence more uncertain responses. The ratio has a relative
minimum in the direction of greatest backscatter. While the


155
back to the response curve without discrimination is a
staircase because several different K fluorescent photons
are emitted by iodine. The transition energies are easily
calculated by simply adding the various K x ray energies to
the energy corresponding to the discriminator level setting.
In this example, the transition energies are 0.053318,
0.053613, 0.057276, and 0.058041 MeV.
At high energies, the detector response deviates
slightly, but noticeably from the no discrimination case.
This deviation is caused by Compton scattering events in the
crystal which deposit less than the energy required by the
discriminator level setting and then scatter out of the
crystal. These events are much more probable at higher
energies where the incoherent cross section is large rela
tive to the cross section for photoelectric interaction.
Figure VI.4 compares the response curve for perpendic
ular incidence on the plane detector with discriminator
settings of 0 and 0.035 MeV. A major difference from the
case with a discriminator setting corresponding to energies
less than the K edge energy of iodine is apparent: the low
energy edge of the "notch" is missing. This is because even
the lowest energy photon, capable of recording a count, is
also capable of emitting iodine K fluorescent x rays. The
transition energies back to (approximately) the response
curve without discrimination are now shifted to higher
energies: 0.063318, 0.063613, 0.067276, and 0.068041 MeV.


LIST OF FIGURES continued
FIGURES Page
VI.8 Detector response with edge and shield
correction 168
VII.1 Number albedos versus energy for HTL soil
and two TST mine cases 172
VII.2 Number albedo ratios versus energy for the
TST mine at 0.0 cm in three soils . 174
VII.3 Number albedo ratios versus energy for the
TST mine at 2.5 cm in three soils . 175
VII.4 Energy albedos versus energy for HTL soil
and two TST mine cases 177
VII.5 Multiple scatter fraction versus energy
for HTL soil and two TST mine cases . 179
VII.6 Ratio of number to energy albedo for HTL
soil and two TST mine cases 181
VII.7 Spatial distribution of backscattered
fluence from 100 keV photons per
pendicularly incident on HTL soil . 183
VII.8 Spatial distribution of backscattered
fluence from 100 keV photons per
pendicularly on the center of the TST
mine at 0.0 cm 184
VII.9 Spatial distribution of mine to soil
ratio of backscattered fluence from
perpendicularly incident 100 keV
photons 185
VII.10 Spatial distribution of the single
scattered mine to soil ratio from
perpendicularly incident 100 keV
photons 187
VII.11 Angular distribution of backscattered
fluence from 100 keV photons perpen
dicularly incident on HTL soil and
two TST mine cases 188
VII.12 Angular distribution of the multiple
scattered fluence from 100 keV photons
perpendicularly incident on HTL soil
and two TST mine cases 189
xviii


190
probability of such scatters in soil compared to that in the
lower atomic number explosive. Removing the single scat
tered component can be accomplished by collimation of de
tector segments located away from the beam axis.
Figures VII.13 and VII.14 show the results of
calculations for a plane of incidence parallel to the soil
surface at a height of 34.6075 cm from which a central 25 cm
radius about the beam axis has been removed. The results in
this figure are shown in terms of the integral angular spec
tra. Figure VII.13 compares the ratios of the integral
spectrum of the mine at 0.0 cm to that of soil for the full
plane and the plane missing the central disk. Figure VII.14
shows the same results at 2.5 cm depth of burial. The ra
tios achieved by this new configuration are large in both
cases. Figure VII.15 reveals the reason for the jump in the
ratios for collimators which admit photons at angles of in
cidence of approximately 0.65 (37 degrees) radians or less
(this angle is specific to this calculation). This colli
mator geometry achieves a significant exclusion of the
single scattered fluence. The large- ratios are a result of
the much greater lateral path distance a multiple scattered
photon must travel to reach the detector when it is highly
collimated. Long paths through soil produce a much greater
attenuation than paths through explosive. The total fluence
at the detector is much reduced from the uncollimated
detector calculations, as indicated by the large uncertain
ties associated with small acceptance angles in Figures
VII.13 and VII.14.


487
The same MCPHOT.PAS benchmark, converted to MCPHOT.P, was
run on the DSI-32. This comparison is no longer purely
between hardware, since two different compilers are now
being used. Results of this and other benchmark tests are
shown in Table G.l. The DSI-32 has been used for the
majority of the Monte Carlo calculations performed in this
research.
Comparison with the Cray X-MP/48 Supercomputer
As described in Chapter IV, one Monte Carlo photon
transport problem was run on a Cray X-MP-48 supercomputer to
test the MCPHOT.P code results against the MCNP transport
code (Briesmeister, 1986), a recognized standard mainframe
code, which, like the MCPHOT.P code, is capable of per
forming calculations with fully developed coherent and
incoherent scattering routines. While the purpose of that
comparison was to assess the accuracy of the MCPHOT.P code,
insights into the relative speed of calculations are also of
interest. The comparison is not completely fair to the Cray
computer, since its computation time is dominated by the
efficiency of the MCNP code, which is designed to do much
more than the relatively simple problems presented. The
Cray/MCNP combination was faster than the DSI-32/MCPHOT.P
combination by a factor of only 35.43. The Cray central
processing time, using the MCNP code, which would have been
required for Monte Carlo calculations of this research
effort is estimated to be on the order of 60 hours.


LIST OF TABLES
TABLES Title Page
111.1 Geometry of the Sodium Iodide Detector
and Shield 32
111.2 Sources Used in Determining Lower Level
Discriminator Setting 35
111.3 Composition of Soil Types 40
111.4 Characteristics of Common Warsaw Pact
Nonmetallic Antitank Mines 42
111.5 Ratios of the Linear Interaction
Coefficients of Sucrose to TNT 47
IV.1 Energy Mesh Structure for Mass
Interaction Coefficients 74
IV.2 Energy at Which Photoelectric and
Incoherent Scattering Mass Interaction
Coefficients Are Equal 76
IV.3 Comparison of Number and Energy Albedo
Calculations for Iron 92
IV.4 Comparison of Number Albedo
Calculations for Concrete 93
IV.5 Comparison of Energy Albedo
Calculations for Concrete 94
IV.6 Comparison of Number Albedo
Calculations for FTB Soil and
Buried DNB Mines 101
V.1 Energies of Tungsten K Characteristic
X Rays 110
V.2 Comparison of Exit Path Lengths from
Tungsten Anodes 115
VI.1 Energies of Iodine Fluorescent Emission
X Rays Used in the Detector Response
Calculations 143
xi


LIST OF FIGURES continued
FIGURES Page
D.14 Measured and calculated transmission of
exposure rate, 200 kVp, 3.00 mm Al. . 411
D.15 X-ray fluence spectrum, 200 kVp,
3.34 mm Al 412
D.16 Measured and calculated transmission of
exposure rate, 200 kVp, 3.34 mm Al. . 413
E.l Gadolinium oxysulfide based detector . 416
E.2 Active region of the detector 418
E.3 Spectrum and transmission curve at
115 kVp 421
E.4 Fraction of incident energy absorbed,
perpendicular incidence 430
E.5 Fraction of incident energy absorbed
in each screen, perpendicular
incidence 431
E.6 Fraction of incident energy reflected,
perpendicular incidence 432
E.7 Fraction of incident energy transmitted
perpendicular incidence 433
E.8 Fraction of incident energy absorbed,
45 degree incidence 437
E.9 Fraction of incident energy absorbed
in each screen, 45 degree incidence . 438
E.10 Fraction of incident energy reflected,
45 degree incidence 440
E.ll Fraction of incident energy transmitted,
45 degree incidence 441
E.12 Fraction of incident energy absorbed,
75 degree incidence 445
E.13 Fraction of incident energy absorbed in
each screen, 75 degree incidence. . 446
E.14 Fraction of incident energy reflected,
75 degree incidence 447
xxviii


Figure VIII.5. Three dimensional image diagram of measured detector response for the
lucite annulus experiment. The 100 kVp source spectrum is shown in Figure F.8.
260


Figure VII.9. Spatial distribution of of the mine to soil ratio of backscattered
fluence from perpendicularly incident 100 keV photons. This figure displays the
ratio of the two preceding figures. A minimum in the ratio occurs along the
direction of greatest backscatter.
185


TABLE IV. 1
Energy Mesh Structure for
Mass Interaction Coefficients
Energy Range
(MeV)
Energy Increment
(MeV)
0.001 to 0.050 0.001
0.050 to 0.300 0.005
0.300 to 1.000
0.010


LIST OF FIGURES
continued
FIGURES Page
VII.13 Mine to soil fluence ratio versus
collimator acceptance angle for 100
keV photons perpendicularly incident
on the TST mine at 0.0 cm in HTL soil 191
VII.14 Mine to soil fluence ratio versus
collimator acceptance angle for 100
keV photons perpendicularly incident
on the TST mine at 2.5 cm in HTL soil 192
VII.15 Multiple scatter fraction versus colli
mator acceptance angle for 100 keV
photons perpendicularly incident on
the TST mine at 0.0 cm in HTL soil. . 193
VII.16 Differential energy spectra for 100 keV
photons perpendicularly incident on HTL
soil and two TST mine cases 195
VII.17 Ratios of mine and soil integral energy
spectra for two TST mine cases in HTL
soil 197
VII.18 Edge effect geometries 199
VII.19 Spatial distribution of the single scat
tered fluence from a 100 keV photon
beam perpendicularly incident on the
inside edge of the TST mine 201
VII.20 Spatial distribution of the single scat
tered mine to soil fluence response
ratio for a 100 keV photon beam perpen
dicularly incident on the inside edge
of the TST mine 202
VII.21 Spatial distribution of the single scat
tered mine to soil fluence response
ratio for a 100 keV photon beam per
pendicularly incident on the outside
edge of the TST mine 203
VII.22 Nal(Tl) detector response and fluence
response versus source beam energy. . 206
VII.23 Ratio of Nal(Tl) detector response to
fluence response as a function of
source energy 207
xix


APPENDIX D
X-RAY TRANSMISSION CALCULATIONS
AND MEASUREMENTS
This appendix provides graphs of the results of calcu
lations and measurements of x-ray exposure rate transmis
sion. The measured transmission curves are the result of
experiments using the Maxitron 300 X-Ray Therapy Unit
(General Electric, 1962). Aluminum attenuators and an MDH
Industries 1015 X-Ray Monitor arranged in the geometry
recommended for half value layer measurements (Johns and
Cunningham, 1983) are used to determine the transmission of
exposure rate curves. Various combinations of peak kilo-
voltage and filtration are used. The calculated trans
mission curves derive from the XRSPEC.PAS code discussed in
Chapter V. These calculations are made for each of the
measured cases. The figures provided in this appendix show
the fluence spectrum computed and a comparison of the
measured and calculated exposure rate transmission curves.
397


0.40
o
XJ
0)
-Q
<
L_
Q)
jQ
E
rs
0.30 -
0.20 -
0.10
0.00 -)iiiiiiiiiii|iiiiiii|
20 60 100 140 180 220
Energy (keV)
Figure VII.1. Number albedos versus energy for HTL soil and two TST mine cases.
The number albedos displayed in this figure are for perpendicularly incident photons
beams. The depth of burial of 0.0 cm refers to the top surface of the mine being
flush with the soil surface.


and Development Center under contract, DAAK 70-86-K-0016. I
thank those individuals associated with the administration
of the contract for their active interest in the research.
Of those individuals, I particularly thank Edward Ostrosky
for his participation in the early measurements, and Dr.
Robert Moler for his reviews of the progress of the work.
IV


Figure VIII.41. Three-dimensional image diagram of the measured collimated detector
response to a 200 kVp source beam filtered by Al for the TST mine at a depth of
burial of 2.54 cm with overlying rock array. The response is sampled at a 2.54 cm
increment.
324


Figure VII.25. Spatial distribution of the fluence response from a 100 keV beam
incident at 60 degrees on the TST mine at 2.5 cm in NSL soil. The fluence response
(photons/(source photon-cin )) is shown at a height of 34.6075 cm above the soil
surface.
215


320
also filtered by aluminum (see Figure F.5). While this
spectrum still contains a significant low energy component,
the presence of higher energy photons increases the response
from the mine. The response depressions are still present.
The images shown in Figure VIII.38 and VIII.39 are produced,
respectively, with 150 and 200 kVp beams filtered by tin
(see Figures F.6 and F.7). The tin filter hardens the
spectra by preferentially removing the low energy components
present before beam filtration. The 150 kVp spectrum more
closely approximates the optimum energy for imaging in NSL
soil and produces the higher mine to soil detector responses
ratio near the center of the mine. Edge effects, not seen
in the previous images in this series are present in both
images. The edge effects at the wall of the mine nearest
the detector are obscured by the presence of the rock array.
The influence of the rock array is smallest in the 200 kVp
image. Figures VIII.40 and VIII.41 complete this series of
images by showing those produced by a collimated detector
with an acceptance angle of 21.6. The x-ray beams used are
150 and 200 kVp, both filtered by aluminum. The two fluence
spectra are shown in Figures F.2 and F.3. The presence of
the rock array is difficult to discern in either image.
These images are vastly superior to those produced by the
uncollimated detector. Between the two, the highest mine to
soil detector response ratio is given by the 150 kVp
spectrum. Spectral considerations play a much smaller role
in the collimated detection technique. Because low energy


Energy (keV)
Figure V.8. Spectrum comparison with Fewell and Shuping at 70 kVp. The measured
spectrum, from Fewell and Shuping (1977), is generated by a diagnositc x-ray unit
operated at 70 kVp with 0.7 mm aluminum equivalent inherent filtration, 2.00 mm
aluminum added2filtration and an air path length of 100 cm. Fluence units are
photons per cin per keV. The calculated spectrum is generated by the XRSPEC.PAS
code. Total fluence is normalized to 1 photon per cm .
127


Figure VIII.51. Three-dimensional image diagram of the measured uncollimated
detector response to a 100 kVp source beam filtered by Pb for a steel disk buried
flush to the soil surface. The response is sampled at 1.27 cm increment. The disk
is 5 cm in radius and 2 cm thick.
336


Figure VIII.47. Three-dimensional image diagram of the measured collimated detector
response to a 200 kVp source beam filtered by Al for the TST mine at a depth of
burial of 2.54 cm with irregular soil surface. The response is sampled at a 2.54 cm
increment.
332


362
TABLE VIII.15
Power and Signal to Noise Ratio Requirements
for Imaging and Mine Detection
with the Collimated Detector
Source Beam*3
2.5
Power0
(KW)
Depth of
cm .
SNRa
Burial3
7.5 cm .
Power0 SNR
(KW)
150 kVp
28.848
0.773
61.358 4.327
1.01 mm Al
200 kVp
17.162
0.941
33.951 5.571
2.67 mm Al
Calculations are for perpendicularly incident beams of the
indicated qualities originating from a diverging point
source 34.6075 cm above an HTL soil surface. The soil
contains 10% water by weight. Beam size at the soil surface
is 1.27 cm by 1.27 cm. The collimated detector consists of
two panels, each 30 cm wide, separated by a 30 cm raster
gap, and located 34.6075 cm above the soil surface. The
collimator acceptance angle is 23.1 degrees.
^Each includes 4.75 mm Be inherent filtration.
cThe power is that required to produce 10000 fluence counts
on the detector per pixel near the center of the mine.
^The minimum signal to noise ratio (SNR) required to allow
mine detection by a system transported on a vehicle moving
at 1.34 m/s, searching a path 3.05 m wide, while maintaining
a false alarm probability of 0.00075 and a detection proba
bility of 0.99. See text for details of calculation.


Figure VIII.21. Monte Carlo generated image for an iron disk buried flush to the
surface of NSL soil for the uncollimated fluence detector. The disk is 5 cm in
radius and 2 cm thick.
299


216
mine buried at 7.5 cm, demonstrating that the ratio at this
depth is similar to that of soil at this depth.
Raster Gap Size
The size of the raster gap is an important variable for
all of the detector types except the energy window detector.
In the energy window detector, removal of the central sec
tion preferentially removes higher energy single scattered
photons. Since the detector operates on differences in the
lower energies, there is no major influence on the mine to
soil ratio resulting from the gap. Calculations for a
series of raster gap and panel width combinations show no
statistically different results for gap sizes from 10 to 40
cm for the energy window detector. For the uncollimated
fluence detectors, both segmented and unsegmented, the gap
plays the role of removing the region of the central minimum
in the mine to soil response ratio. Finding the optimum gap
size involves maximizing the ratio between mine and soil
response, while maintaining a reasonable fluence on the
detector. Figure VII.26 shows a typical fluence response
versus distance from the beam axis. The example is for a
100 keV beam striking the center of the TST mine buried at a
depth of 2.5 cm in NSL soil. The rapid fall off in the
response, coupled with the general increase in the mine to
soil ratio with distance produce an optimization problem.
This problem is addressed in conjunction with determination
of the panel widths below.


Figure III.7. TST mine used in measurements. The TST mine is designed to simulate
nonmetallic antitank mines. The upper layer of the mine cylinder, whose thickness
can be varied, contains air. The lower portion contains the explosive substitute
material. A detailed description of the geometry and materials of the TST mine is
provided in the text.


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Figure III.2. Detector electronics, computer and x-ray source console. This
photograph shows, from left to right, the detector high voltage supply, scaler and
timer, amplifier and single channel analyzer, count rate meter, the IBM PC computer,
and the GE Maxitron 300 control console with remote TV picture of exposure room.


377
demoralize the enemy. Mines are used to supplement other
obstacles, especially natural terrain features. Whenever
possible, the effectiveness of minefields is enhanced by
direct and indirect fire weapon coverage. The density of
mines by type within a minefield is determined primarily by
the perceived enemy threat. Typical Soviet antitank mine
fields would contain 750 to 1000 mines per kilometer of
front, placed in multiple belts (Honeywell, 1981).


239
at the same intercept and at the mine center. The compari
son at mine center is appropriate because that is the loca
tion at which the unsegmented detector works best, while the
edges are where the segmented detector works best. The
segmented detector is seen to improve detectability over the
unsegmented detector only for beams incident on the inside
edge of the mine, and, even then, not dramatically.
The optimum source energy for the energy window detec
tor is found to be between 150 and 200 keV for depths of
burial of 2.5 cm and 200 keV or greater at 5.0 cm. These
conclusions are reached by comparing the mine to soil
fluence ratios produced by a detector in the standard con
figuration with 30 cm wide panels and a 10 cm wide raster
gap. Figure VII.32 shows a typical set of results. The
lower energy of the window is set to 35 keV in this and the
other comparison calculations. This value precludes count
ing only a very few photons and corresponds to the lower
level discriminator setting used in the measurements. The
spectra from which these results are derived are binned in 5
keV increments. Deviations in the mine to soil fluence
ratio, and that obtained using a real detector, may occur
because of the low energy of the source photons. As shown
in Figure VII.23, variation between fluence and detector
response at low energy can be large, even within a 5 keV
increment. In many detectors, the higher energies are not
attractive due to increased incoherent interactions which
result in partial energy depositions. These events will
mask the low energy scatter from the mine and soil.


0.90 i| i ri i ~r~i r~] i t~i | ~i i r | i 1 i | ~i i i | i i i |
40 60 80 100 120 140 160 180 200
Source Photon Energy (keV)
Figure VII.32. Source energy optimization curve for the energy window detector with
mine depth of burial of 5 cm in HTL soil. The ratio of mine to soil fluence response
at energies between 35 and 50 keV striking an uncollimated detector consisting of two
panels of 30 cm width and 210 cm length, separated by a raster gap of 10 cm, and
located 34.6075 cm above and parallel to the soil surface is shown as a function of
source energy for perpendicularly incident beams. The beam intercept is at the
center of the mine.
240


133
Figure E.22. Response versus distance for Ba. A comparison of the measured and
^lculated response of the terbium activated gadolinium oxysulfide detector for a
JBa point source as a function of distance from the detector plane is shown.
Uncertainties in measured data are too small to plot.
469


43
30.16 cm. The cylinder is 14.60 cm high and has two 0.635
cm thick covers for the top and bottom. An aluminum cylin
der with 0.24 cm thick walls, outside diameter of 28.89 cm
and height of 8.57 cm fits inside the lucite cylinder and
holds the explosive substitute material. Only the top 7.50
cm of the aluminum cylinder is filled with explosive mater
ial. Its lower portion is separated from this material by a
0.24 cm thick base plate. The 0.83 cm high curtain below
the aluminum base plate is drilled with three holes at 120
degree intervals. These holes align with five sets of three
holes in the lucite cylinder and are used to allow variable
setting of the air gap located between the top lucite cover
and the explosive substitute material. The aluminum con
tainer of the model provides structural support for the
heavy explosive substitute portion of the mine. Addition
ally, it served as the mold for the molten substitute
material when it was prepared. Aluminum is very similar to
soil in its photon scattering properties, and, as such, is
an acceptable wall material for the backscatter radiation
method of mine detection. Due to its metallic content, it
would be an unacceptable model for many other detection
methods. Figure III.7 shows the TST mine used in the
measurements.
Since actual explosive materials present safety and
administrative problems, a substitute material is required.
Since TNT is the most commonly used explosive in landmine,
it serves as the standard against which substitute materials


10 15 20 25 30 35 40 45 50
Distance from Source Axis (cm)
Figure VIII.2. Calculated and measured spatial distribution of detector response
from backscatter from sandy soil at 150 kVp. Responses are normalized to 1.00 at
19.775 cm from the beam axis. Geometry and source details are provided in Table
VIII.1. Uncertainties in measured results are too small to plot.
253


517
Bear, B. E. Chemistry of the Soil. New York: Reinhold,
1955.
Bell, G. E. "Spectral Distribution in the Continuous X-Ray
Spectrum and the Specification of X-Ray Quality." Brit.
J. Radiol. 9:680-688, 1936.
Berger, M. J., and Raso, D. "Monte Carlo Calculations of
Gamma-Ray Backscattering." Radiation Research 12:20-37,
1960.
Berger, M. J., and Seltzer, S. M. "Response Functions for
Sodium Iodide Scintillation Detectors." Nucl. Instr. and
Meth. 104:317-332, 1972.
Bloomquist, R. N., and Gelbard, E. M. "An Assessment of
Existing Klein-Nishina Monte Carlo Sampling Methods."
Nucl. Sci. Engr. 83:380-384, 1983.
Borland International. Turbo Pascal Reference Manual.
Scotts Valley, CA: Borland International, 1985.
Briesmeister, J. F. MCNP A General Monte Carlo Code for
Neutron and Photon Transport. Los Alamos, NM: Los Alamos
National Laboratory, 1986.
Buchanan, R. A.; Finkelstein, S. I.; and Wickersheim, K. A.
"X-Ray Exposure Reduction Using Rare-Earth Oxysulfide
Intensifying Screens." Radiol. 105:185-190, 1972.
Bulatov, B. P., and Andrushin, N. F. "Gamma-Ray Energy and
Number Albedos." Sov. J. At. Energy 22:307-308, 1967.
Caidin, M. The Tigers Are Burning. New York: Hawthorn,
1974.
Campbell, J. G., "Computer Code Listings for Backscatter
Radiation Radiography Applications to Landmine Detec
tion." Unpublished Report. University of Florida,
Gainesville, FL, 1987.
Carter, L. L., and Cashwell, E. D. Particle-Transport
Simulation with the Monte Carlo Method. Technical
Information Center Publication TID-26607. Oak Ridge, TN:
Energy Research and Development Administration, 1977.
Chan, H. P., and Doi, K. "Studies of X-Ray Absorption and
Quantum Noise Properties of X-Ray Screens by Use of Monte
Carlo Simulation." Med.Phys. 11:37-46, 1984.
Cheney, W., and Kincaid, D. Numerical Mathematics and
Computing. Monterey, CA: Brooks/Cole Publishing, T980.


position
333
y position
1 3 5 7 9 11 13 15 17
Figure VIII.48. Two-dimensional image diagram of the
measured collimated detector response to a 200 kVp source
beam filtered by Al for the TST mine at a depth of burial of
2.54 cm with irregular soil surface. The response is
sampled at a 2.54 cm increment.


Figure VII.20. Spatial distribution of the single scattered mine to soil fluence
response ratio for a 100 keV photon beam perpendicularly incident on the inside edge
of the TST mine. This figure shows the ratio of the spatial distribution of single
scattered fluence of Figure VII.19 with the TST mine at a depth of burial of 2.5 cm
in NSL soil to that produced without a mine present.
202


its shield are described in detail in Chapter III. This
chapter discusses the response function calculation for the
detector and its validation.
Considerable work has been performed by many research
ers on the detector response of Nal(Tl). The amount of
research on Nal(Tl) response at the low photon energies of
interest in the mine detection problem is considerably
smaller than that at high energies, but is still adequate to
provide checks of the computer code used in calculating the
response matrix for this research. The usual application
of a Nal(Tl) scintillation detector is to perform spectral
measurements rather than counting, which is done in this
effort. As a result, most of the validation checks avail
able involve features of the spectral response, that is,
peak ratios and shapes of energy spectra. Accordingly,
these features are examined in assessing the computer code.
The approach used in developing the detector response matrix
is to begin with an infinite plane detector consisting of
(from face towards photomultiplier) the outer aluminum can
thickness, the three materials between the can and sodium
iodide crystal (as explained in Chapter III, these mater
ials, thicknesses and densities were provided by the manu
facturer for the purpose of this calculation, but cannot be
published because of their proprietary nature), the sodium
iodide crystal, and the quartz light pipe (see Figure
III.4). The response of this detector is calculated for
a mesh of 24 energies, ranging from 10 to 300 keV, and 9


122
results are then compared to calculations for the same
transmission experiment simulated by the XRSPEC.PAS code.
Figure V.5 shows the results of such a comparison for the
spectrum shown in Figure V.2. Other comparisons are
provided in Appendix D. Figures in the appendix show the
calculated spectra, and the associated measured and calcu
lated transmission of exposure rate. Measurements are made
with an MDH Industries, Inc. 1015 X-Ray Monitor, which has a
flat energy response to below 20 keV. As can be seen by the
comparisons, the agreement between calculations and measure
ments is very good.
Comparisons with Published Spectra
Comparisons with published measurements of x-ray
spectra are also performed. Fewell and Shuping (1977) re
viewed published spectral measurements and recommend their
own work and that of Epp and Weiss (1966) as the best avail
able. In doing so, they indicate that serious discrepancies
exist in other published spectra. Accordingly, comparisons
are made with these two recommended sets of published
spectra.
Figures V.6 and V.7 show the comparison between the
XRSPEC.PAS fluence spectrum calculation and the measurements
of Epp and Weiss. The voltage waveform used in the Epp and
Weiss measurements is considerably different from that of
the GE Maxitron 300. The XRSPEC.PAS code is modified to
model this new waveform, which is a constant potential term
plus a 120 Hz component with a peak to peak amplitude equal


APPENDIX A
CHARACTERISTICS OF LANDMINES
A landmine is an explosive device placed in or on soil.
While it is designed to destroy or damage vehicles, or to
kill or incapacitate personnel, the primary purpose of mines
is to reduce the mobility of enemy forces (U.S. Department
of the Army, 1979a). Landmines are produced by dozens of
countries. Their characteristics are extremely varied.
Variables include size, geometry, composition, fuzing, and
method of use. Mine sizes range from about that of a tennis
ball to disks of diameters on the order of a meter. Two
shapes predominate, the right circular cylinder and the
rectangular parallelepiped, though other shapes, including
irregular, exist. A typical landmine is shown in Figure
A. 1.
Mine Classifications
A number of different schemes can be used to classify
mines. Mine cases may be metallic or nonmetallic. The
explosive is usually trinitrotoluene (TNT), but other ex
plosives are also employed (U.S. Department of the Army,
1979b, 1986). Mine construction ranges from very sophisti
cated industrial manufacture to crude, but often very
368


TABLE OF CONTENTS
continued
CHAPTERS Page
Imaging 287
Monte Carlo Generated Images 287
Measured Images 296
Dual Energy Subtraction Technique . 342
Power Requirements 347
Variables 348
Fraction of Source Photons Reaching
the Detector 350
Source Flux 350
Pixel Dwell Time 353
Calculation Technique 353
Power Calculations 357
IX CONCLUSIONS 363
APPENDICES
A CHARACTERISTICS OF LANDMINES 368
Mine Classification 368
Metallic or Nonmetallic 371
Antitank or Antipersonnel 372
Conventional or Scatterable 372
Surface or Buried 373
Fuzing Type 375
Employment of Landmines 376
B HISTORICAL EXAMPLES OF MINE WARFARE .... 378
Mine Development 378
Forerunners of Modern Mines 378
Mines of World War II 379
Countermine Warfare in World War II . 380
Mine Employment 380
North Africa 380
Eastern Front 382
Korea and Vietnam 383
C OTHER MINE DETECTION AND NEUTRALIZATION
METHODS 385
Detector Technololgies 385
General Considerations 385
Microwaves 386
Neutrons 388
Magnetic Resonance Techniques 390
Trace Gases 391
Animals 392
Biochemical Methods 392
Infrared Methods 393
viii


173
dependent on atomic number, and the density of soil and
explosive are similar, once the energy region of significant
photoelectric interaction is exceeded, the backscattered
fluences become similar. Figure VII.2 shows the ratios of
the number albedos for the mine at the surface to those of
the three major soils used in the research. The higher the
ratio between the mine and soil cases, the greater the
difference in the backscattered characteristics, and, in
general, the greater the ease of mine detection. The great
est ratio occurs at low energy because the greatest differ
ence between the photoelectric interaction cross sections of
soil and explosive also occurs here. The higher atomic num
ber soil absorbs the incident photons much more efficiently
than the explosive. MCL soil with the highest atomic number
of the three soils shows the greatest contrast. Figure
VII.3 shows this same ratio for the three soils with the
mine buried at 2.5 cm. Apparent in this figure is the exis
tence of optimum energies for mine detection. For the rea
sons discussed above, the backscattered responses for the
buried mine and soil cases are more similar at both low and
high energy. Somewhere in between, an optimum source energy
exists. This optimum energy is dependent upon the atomic
number of the soil material. In NSL soil, it is about 80
keV; in HTL soil, about 100 keV; and in MCL soil, about 150
keV. This variation with soil type is simply a result of
the extent of the energy region in which photoelectric in
teractions are important. Beyond this region the incoherent


390
the radiological hazard represented by battlefield destruc
tion of the source.
Magnetic Resonance Techniques
In 1965/ Southwest Research Institute attempted to
apply electron paramagnetic resonance to mine detection.
To produce the free electron densities necessary for signal
production, the explosive of the mine was irradiated. On
the basis of extrapolation from experiments at liquid
nitrogen temperature using 60Co as the irradiation source,
. 12
it was estimated that an exposure rate on 10 R/hr would be
required. Accordingly, the program was terminated.
In 1972, Southwest Research Institute proposed to use
nuclear magnetic resonance for mine detection. Differentia
tion between hydrogen in explosives and water in soil was
demonstrated in laboratory experiments. An electromagnet
was constructed which was capable of producing a homogeneous
magnetic field at a distance of 10 cm from its coils. A
detector system based on this technique was built in 1974.
Problems included a 20 second time period to obtain a single
measurement, and the inability to detect anything beyond 10
cm range of the field. This 10 cm limit included the dis
tance from the coils in air to the soil surface, severely
limiting the depth of detection in soil. These problems and
failure of the device to operate properly during field tests
caused termination of the effort.


178
interactions before reflection, resulting in greater energy
loss, than in the higher atomic number cases. Figure VII.5
displays this fact by showing the fraction of backscattered
photons which have undergone multiple scatter for each case.
The ratio of the energy albedo of a given atomic number
material to a higher atomic number material can be shown to
be always less than the corresponding number albedo ratio.
Bulatov and Andrushin (1967) use the calculated albedos of
Berger and Raso (1960) to show that the ratio of number to
energy albedo versus energy is a linear relationship in the
energy range above 200 keV. The slope of the line is found
to be greatest in lower atomic number materials. Table
VII.1 compares the results of Bulatov and Andrushin to cal
culations performed by the MCPHOT codes, and recalculation
from the original Berger and Raso data. Figure VII.6 shows
this linear relationship below 200 keV for the three mine
detection related cases. Algebraic manipulation provides
b(soil) + m(soil) E
b(TNT) + m(TNT) E '
where Ag is an energy albedo,
An is a number albedo,
b is an intercept, and
m is a slope.
Since the slope for a lower atomic number material is larger
and the intercepts are nearly equal, the bracketed quantity
is a number less than 1.00. Accordingly, the ratio of
Ae(TNT) A^(TNT)
Ag (soil) AN(soil)


374
is quite restricted. This fact, combined with the presence
of smoke, employed to assist movement of armored vehicles
through open areas which may be covered by enemy fire,
severely degrades the capability to detect mines (U.S.
Department of the Army, 1979a). Moreover, there are many
cases when mine detection is desired. A synergism exists
when a minefield is covered by fire and the force attempting
to breach the minefield is aware of its presence. The
breaching vehicles are forced to slow their movement, drama
tically increasing their vulnerability to direct covering
fires. Even when a minefield is not covered by fire, the
knowledge of the presence of mines may provide the necessary
delay required to disrupt a coordinated attack.
Depths of burial of antitank mines may range down to
approximately 15 cm in soil. In general, however, the depth
of burial is much closer to the surface. Buried antiper
sonnel mines are always placed close to the surface. U.S.
pressure fuzed antitank mines are generally buried flush
with the soil surface and covered with a layer of soil for
camouflage. The recommended depth of this layer ranges from
0 to a maximum of 5 cm depending on the source (U.S. Depart
ment of the Army, 1969, 1973, 1979a). For burial in sod,
the turf is cut and rolled back for mine emplacement, and
then replaced. In snow of less than 10 cm depth, mines are
buried so that the pressure plate remains above the ground.
For snow depths of 10 to 28 cm, mines are laid on the soil
surface. For snow depths greater than 28 cm, mines are


Energy (keV)
Figure F.ll. X-ray fluence spectrum, 200 kVp, 0.75 mm Pb. The x-ray fluence spectrum
at 200 kVp calculated by the XRSPEC.PAS code for the GE Maxitron 300 X-Ray Therapy
Unit with 4.75 mm beryllium inherent filtration, 0.75 mm lead added |iltration and
air path length of 60 cm is shown. Fluence units are photons per cin per keV. Total
fluence is normalized to 1 photon per cm .
481


Figure VIII.43. Three-dimensional image diagram of the measured uncollimated de
tector response to a 200 kVp source beam filtered by Pb for the TST mine at a depth
of burial of 2.54 cm with irregular soil surface. The response is sampled at a 2.54
cm increment.
327


Figure E.8. Fraction of incident energy absorbed, 45 degree incidence. The fraction
of incident x-ray photon absorbed in the two phosphor layers of the detector system
constructed from two halves of 3M Trimax 12 screen B 184048 as a function of incident
x-ray photon energy (MeV) for the case of 45 degree incidence is shown.
437


17
Improvements on Previous X-Ray Backscatter Efforts
The shortcomings of the Texas Nuclear Corporation re
search effort, described above, provide the basis for
improvements in the x-ray backscatter technique. The
concepts investigated in this dissertation differ from the
previous efforts in a number of areas. The major difference
is the examination of the formation of images of buried
objects, rather than detection based upon a single differ
ence between soil and soil with buried object. Creating an
image requires capabilities that were unavailable in the
past. X-ray sources capable of long linear scans and the
image processing technology to allow real time analysis of
data have been developed since the Texas Nuclear Corporation
efforts. An image provides the important capability to
discriminate between buried mines and other buried objects
which have photon interaction characteristics similar to
mine materials. Coupling the scanning x-ray beam with a
detector large enough to assure coverage of width of the
largest vehicle which must traverse a mined area eliminates
another shortcoming of the previous effort. A diagram of a
conceptual detector is shown in Figure II.1.
Research Goals
The goals of this research effort are to optimize
the design parameters of a large area, x-ray backscatter
imaging system and to examine the effect of environmental
parameters on the detection and imaging process. The design
parameters available for optimization are the energies of


Figure VIII.22. Three-dimensional image diagram of the measured uncollimated
detector response to a 100 kVp source beam filtered by Pb for the TST mine buried
flush to the soil surface. The response is sampled at a 2.54 cm increment.
301


5
Previous Uses of Scattered Radiation
The first suggested use of Compton (incoherent) scat
tering to determine characteristics of a material was by
Odeblad and Norhagen (1956). They showed that the intensity
of the scattered radiation for a fixed source energy and
scattering angle depends on the electron density of the
scattering medium. In a small volume of uniform composi
tion, the electron density is proportional to the material
6 0
density. Using a collimated Co gamma-ray source and a
collimated scintillation detector, they were able to measure
the relative electron densities of materials in the small
volume defined by the intersection of the fields of view of
the detector and source collimators.
19 2
Lale (1959) used a collimated Ir source and a col
limated detector positioned to receive forward scattered
Compton photons to measure electron density within trans
verse cross sections in rabbits and guinea pigs. The sub
jects were moved with respect to the beam to produce an
image of density variation. The process was very slow, and
subject to considerable quantum noise and attenuation of the
incident and scattered beams, but demonstrated that air in
organs would provide a large change in measured electron
density in images. In an extension of this work, Lale
(1968) used 5.6 MV x rays to reduce attenuation losses.
A patient platform was lowered through the beam. Forward
scattered photons were detected with a liquid scintillator.


142
Carter and Cashwell (1977). Secondary L fluorescence fol
lowing or Ka2 emission is also allowed. Table VI.1
provides the energies of these fluorescent x rays.
The response function calculation for the gadolinium
oxysulfide detector (Appendix E) is primarily concerned with
the gross amount of energy deposited in the phosphor layer
by x-ray photon interactions in the phosphor, which is then
converted to light photons. Because of the faster response
time of Nal(Tl), it is the sum of the energies of all the
interactions of a single x-ray photon and its progeny, which
are deposited in the crystal, that is of importance. For
each photon, this sum is compared to the energy correspond
ing to the lower level discriminator setting of the counting
system. Only if the energy deposited in the Nal(Tl) exceeds
the discriminator energy is a count recorded. The response
is the number of counts per incident photon at a given
energy and angle of incidence as opposed to the amount of
energy deposited per incident photon at a given energy and
angle of incidence in the case of the gadolinium oxysulfide
based detector. The DETNAI.P code calculates this response
for nine discriminator settings ranging from 0 to 45 keV. A
derivative of the DETNAI.P code, NAISPEC.PAS, computes the
spectrum of energies deposited in the Nal(Tl) crystal.


Energy (keV)
Figure D.13. X-ray fluence spectrum, 200 kVp, 3.00 mm Al. The x-ray spectrum at 200
kVp calculated by the XRSPEC.PAS code for the GE Maxitron 300 X-Ray Therapy Unit with
4.75 mm beryllium inherent filtration, 3.00 mm aluminum added filtration (includes
0.25 mm aluminum equivalent monitor ionization2chamber) and air path length of 90.07
cm is shown. Fluence units are photons per cin per keV. Total fluence is normalized ^
to 1 photon per cm. h
o


135
(any material can be used as the attenuator in the tech
nique) were numerically differentiated to provide the deri
vative required to support the calculation. Algorithms used
for computing the gamma function and modified Bessel func
tion are from Press et al. (1986). Figure V. 12 compares the
results of fluence spectra calculations at 80 kVp by the
modified Kramers' formula method and by the Archer-Wagner
method. While some differences exist due to the minor
characteristic x-ray contribution, the agreement is seen to
be good. Figure V.13 shows the same comparison at 150 kVp
where the characteristic contribution is large. The com
parison is now poor, highlighting the reason for rejection
of this otherwise excellent technique.
Rubio and Mainardi (1984) have attempted to extend the
Archer-Wagner method to include characteristic x rays. The
extension involves adding exponential terms with parameter
coefficients to the fitting function, resulting in delta
functions in the inverse Laplace transform. In their paper,
Rubio and Mainardi use published measured fluence spectra to
calculate exposure transmission data. These calculated data
are then applied to a fitting function, which allows for
only two K x rays in the inverse transform. Calculated
spectra are produced which predict the characteristic
components to between 10 and 15% of the measured values. No
demonstration of spectral reconstruction from actual trans
mission data, subject to random error found in any actual
experimental measurement, is made. Attempts to apply this


1200 -i
1000:
O
c
o
o
0
en
i_
0
CL
(n
c
rj
o
O
800-
600 :
400 :
200 :
calculated
* measured
0
'i i i i i i i i i l i i i i i i i "r i | i n i i i r i i | r i i i i r~n i |
6 8 10 12
Distance from First Screen (cm)
4
137
Figure E.21. Response versus distance for Cs. A comparison of the measured and
^l^culated response of the terbium activated gadolinium oxysulfide detector for a
Cs point source as a function of distance from the detector plane is shown.


LANDMINE DETECTION BY
SCATTER RADIATION RADIOGRAPHY
by
JOHN G. CAMPBELL
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1987

ACKNOWLEDGMENTS
A number of individuals and organizations have played
an important role in my research. First and foremost, I
thank my wife, Becky, for her support, understanding, and
patience.
Dr. Alan Jacobs, who was my research advisor, was
always willing to help, whether the assistance required
discussion of new ideas or manual labor. The basic concept
of the project, using imaging techniques for mine detection,
was his. The generous amount of time he took from a very
busy schedule is greatly appreciated. I thank the other
members of my committee, Dr. Edward Carroll, Dr. Edward
Dugan, Dr. John Staudhammer, and Dr. Mark Yang, for their
time and guidance.
Two graduate students, who worked on other aspects of
the research problem, also contributed to my efforts.
Captain Dale Moss designed the soil box positioning system
and its computer control. Linda Hipp was an equal partner
in the assembly of the positioning system and spent many
long hours performing measurements.
I thank Bill Coughlin of the Radiation Control
Department for the loan of an ionization chamber for the
exposure rate transmission experiments, and Harvey Norton,
11

of the same organization, for the use of a calibration set
of radionuclide sources. Dr. William Ellis provided the
filter sets used in the measurements.
The electronics skills and untiring efforts of Ken
Fawcett were solely responsible for keeping an old x-ray
machine in operation for the measurements. His expertise
was crucial to this research.
I thank Lois Carroll, who typed this manuscript, for
her professional and always cheerful assistance.
Gary Melocik of Bicron Corporation provided details on
the composition and geometry of the Nal(Tl) detector used in
the experiment. Dr. William Frank, 3M Corporation, provided
information on the composition of the Trimax 12 rare earth
intensifying screens. Without their assistance, the detec
tor response calculations could not have been performed.
Andrew Lickly of Applied Reasoning Corporation, and
David Hampton of Seattle Telecom and Data, Inc., ran bench
mark versions of the Monte Carlo code on their accelerator
boards. Two graduate students of the Nuclear Engineering
Sciences Department also helped test the code. Samer Kahook
ran a benchmark on the IBM PC/AT. Kiratadas Kutikkad ran a
mine detection problem on the Cray X-MP/48 using the MCNP
code.
I thank the United States Army for allowing me the op
portunity to continue my education and for financial support
during the research effort. The measurements portion of
this work was supported by the U.S. Army Belvoir Research
iii

and Development Center under contract, DAAK 70-86-K-0016. I
thank those individuals associated with the administration
of the contract for their active interest in the research.
Of those individuals, I particularly thank Edward Ostrosky
for his participation in the early measurements, and Dr.
Robert Moler for his reviews of the progress of the work.
IV

TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ii
LIST OF TABLES xi
LIST OF FIGURES XV
ABSTRACT xxxi
CHAPTERS
I INTRODUCTION 1
II BACKSCATTER MINE DETECTION AND IMAGING . 4
Previous Uses of Scattered Radiation ... 5
Backscattered Photon Mine Detection. ... 8
Fluorescence Emission 8
Rayleigh Scattering 9
Compton Scattering 10
Backscatter Radiation Radiography 13
Genesis of Current Research Effort. . 13
Improvements on Previous X-Ray
Backscatter Efforts 17
Research Goals 17
III EQUIPMENT AND MATERIALS 20
Equipment 20
X-Ray Source 20
Soil Box and Positioning System .... 27
Detector and Related Electronics. ... 30
Computer Control System . 36
Materials. 38
Soils 38
Nonmetallic Antitank Mine Model .... 39
Materials Tests 46
IV RADIATION TRANSPORT 52
Photon Interactions 52
Coherent Scattering 52
Incoherent Scattering 59
Photoelectric Effect 67
Mass Interaction Coefficients 71
v

TABLE OF CONTENTS continued
CHAPTERS Page
Single Scatter Model 73
Computation Scheme 73
Interaction Modeling 78
Monte Carlo Model 78
Problem Parameters and Data 80
Random Number Generators 81
Computation Scheme 83
Modelling Scattering Interactions ... 87
Russian Roulette 89
Code Output 89
Validation of the Monte Carlo Codes. ... 90
Number and Energy Albedo Calculations 91
Energy Spectra Comparisons 91
Comparison with Buried Mine
Calculations 91
Testing the Scattering Routines .... 99
V X-RAY SOURCE 105
Kramers' Formula Method 105
Kramers' Formula 106
Time Dependent Accelerating Potential 107
Characteristic X-Ray Production. . 108
Attenuation by Materials in the Beam
Path 109
Anode Self-Attenuation Ill
Effects Neglected in Model 116
General Features of the Calculated
Spectra 117
Testing the Modified Kramers' Formula
Model 119
Exposure Rate Transmission
Measurements 119
Comparisons with Published Spectra. . 122
Other Methods to Determine X-Ray Spectra 126
Measurement 126
Monte Carlo Calculation 130
Laplace Transform Pair Method 130
VI DETECTOR RESPONSE 139
Plane Detector Code 141
Assumptions in the Plane Detector
Response Calculation 144
Energy Deposition 146
Case of Zero Degree Incidence 146
Case of Large Angle Incidence 149
Counts Per Incident Photon 151
vi

TABLE OF CONTENTS
continued
CHAPTERS Page
Discriminator Setting Corresponding
to 0 MeV 151
Discriminator Setting Corresponding
to Energies Greater Than 0 MeV 153
Validation of the Plane Detector Response
Calculations 157
Iodine Escape Ratio 157
Measured Energy Spectra 163
Shield and Edge Effects 163
Calculation of the Correction Factor. 163
Results of the Correction Factor
Calculation 166
VII MINE DETECTION MECHANISMS 169
Backscattered Photon Signal Differences. 169
Fluence 170
Energy Fluence 176
Spatial Distribution 182
Angular Distribution 186
Energy Spectra 194
Edge Effects 198
Conclusions Based on Signal
Differences 204
Irradiation Geometry and Optimum Energy. 208
Height of Detector 208
Angle of Incidence 209
Raster Gap Size 216
Detector Collimator Length 222
Detector Panel Dimensions 223
Segmented Detector Geometry 227
Source Beam Collimation 229
Source Energy Optimization 232
Depth of Burial 241
Polyenergetic Sources 244
Conclusions Based on Optimizations. . 246
VIII APPLICATION TO IMAGING 248
Comparisons with Measurements. ...... 249
Spatial Distribution of Detector
Response 249
Detector Response with Mine Present . 251
Edge Effects 258
Energy Window Detector 262
Environmental Parameters 266
Height Sensitivity 266
Soil Density Variation 272
Soil Moisture Content 277
Inhomogeneities 283

TABLE OF CONTENTS
continued
CHAPTERS Page
Imaging 287
Monte Carlo Generated Images 287
Measured Images 296
Dual Energy Subtraction Technique . 342
Power Requirements 347
Variables 348
Fraction of Source Photons Reaching
the Detector 350
Source Flux 350
Pixel Dwell Time 353
Calculation Technique 353
Power Calculations 357
IX CONCLUSIONS 363
APPENDICES
A CHARACTERISTICS OF LANDMINES 368
Mine Classification 368
Metallic or Nonmetallic 371
Antitank or Antipersonnel 372
Conventional or Scatterable 372
Surface or Buried 373
Fuzing Type 375
Employment of Landmines 376
B HISTORICAL EXAMPLES OF MINE WARFARE .... 378
Mine Development 378
Forerunners of Modern Mines 378
Mines of World War II 379
Countermine Warfare in World War II . 380
Mine Employment 380
North Africa 380
Eastern Front 382
Korea and Vietnam 383
C OTHER MINE DETECTION AND NEUTRALIZATION
METHODS 385
Detector Technololgies 385
General Considerations 385
Microwaves 386
Neutrons 388
Magnetic Resonance Techniques 390
Trace Gases 391
Animals 392
Biochemical Methods 392
Infrared Methods 393
viii

TABLE OF CONTENTS continued
APPENDICES Page
Neutralization 394
Mechanical Systems 394
Explosive Methods 395
Magnetic Signature Duplication 396
D X-RAY TRANSMISSION MEASUREMENTS 397
E GADOLINIUM OXYSULFIDE DETECTOR 414
Detector Description 414
Detector Design 414
Screen Composition 417
Detector Response Matrix Calculation . 422
Calculation Technique 422
General Results of Calculations .... 425
Description of the Detector Response
Matrix 428
Perpendicular Incidence 429
45 Degree Incidence 436
75 Degree Incidence 444
Comparison with Published Results . 449
Response Matrix Relationship to
Detector Electronics 450
Shortcomings of the Detector 455
Sensitivity 456
Fluorescence Decay Constant 460
Corrective Actions 463
Comparison of Measured and Calculated
Responses 464
Calculation Technique 464
Measurements 465
F X-RAY SPECTRA USED IN MEASUREMENTS .... 470
G COMPUTER CODES 484
Computer Hardware 484
Personal Computers and Monte
Carlo Calculations 484
Computer Selection 485
Comparison with Cray X-MP/48
Supercomputer 487
Computer Software 489
Computer Languages 489
Radiation Transport Codes 489
X-Ray Spectra Codes 491
Detector Response Codes 492
Imaging Codes 493
Utility Codes 494
Photon Interaction Data Files 496
Commercial Software 497
IX

TABLE OF CONTENTS
continued
APPENDICES Page
H MONTE CARLO TECHNIQUES 501
Angular Scattering Distributions 501
Momentum Transfer Variable 501
Incoherent Scattering 502
Sampling the Klein-Nishina
Distribution 504
Coherent Scattering 506
Random Number Generators 509
MCPHOT.PAS Generator 509
MCPHOT.P Generator 509
Fluorescent Emission 510
Application to Polyenergetic Sources . 512
Available Methods 512
Application of the Fit Method 513
LIST OF REFERENCES 516
BIOGRAPHICAL SKETCH 527
x

LIST OF TABLES
TABLES Title Page
111.1 Geometry of the Sodium Iodide Detector
and Shield 32
111.2 Sources Used in Determining Lower Level
Discriminator Setting 35
111.3 Composition of Soil Types 40
111.4 Characteristics of Common Warsaw Pact
Nonmetallic Antitank Mines 42
111.5 Ratios of the Linear Interaction
Coefficients of Sucrose to TNT 47
IV.1 Energy Mesh Structure for Mass
Interaction Coefficients 74
IV.2 Energy at Which Photoelectric and
Incoherent Scattering Mass Interaction
Coefficients Are Equal 76
IV.3 Comparison of Number and Energy Albedo
Calculations for Iron 92
IV.4 Comparison of Number Albedo
Calculations for Concrete 93
IV.5 Comparison of Energy Albedo
Calculations for Concrete 94
IV.6 Comparison of Number Albedo
Calculations for FTB Soil and
Buried DNB Mines 101
V.1 Energies of Tungsten K Characteristic
X Rays 110
V.2 Comparison of Exit Path Lengths from
Tungsten Anodes 115
VI.1 Energies of Iodine Fluorescent Emission
X Rays Used in the Detector Response
Calculations 143
xi

LIST OF TABLES continued
TABLES Page
VII.1 Comparison of the Linear Relationship
Between the Ratio of Number to Energy
Albedo and Source Energy at
Perpendicular Incidence 180
VII.2 Mine to Soil Response Ratios at Selected
Beam Angles of Incidence 211
VII.3 Front to Back Panel Fluence Ratios of
the Collimated Detector for 100 keV
Photon Beams Incident at 60 Degrees . 214
VII.4 Results of Calculations for the Geometric
Parameters of the Collimated Fluence
Detector 220
VII.5 Mine to Soil Fluence Ratio Dependence on
Panel Width and Raster Gap Size for an
Uncollimated Detector 226
VII.6 Optimum Source Energies for the Uncolli
mated Fluence Detector 235
VII.7 Comparison of the Segmented and Unseg
mented Uncollimated Fluence Detectors 238
VII.8 Mine to Soil Fluence Ratio at Selected
Depths of Burial of the TST Mine. . 242
VII.9 Mine to Soil Fluence Ratios Versus Depth
of Mine Burial for the Energy Window
Detector with Source Energy of 100 keV. 245
VIII.1 Parameters for Spatial Distribution
Comparison 250
VIII.2 Comparison of Calculated and Measured Mine
to Soil Detector Response/Ratio with the
TST Mine at 0.0 cm 257
VIII.3 Energy Window Measurements for the TST
Mine at 2.54 cm Depth of Burial .... 265
VIII.4 Mine to Soil Fluence Ratio from the
Collimated Detector with Recently
Buried Mines 276
VIII.5 Mine to Soil Fluence Ratio from the
Energy Window Detector with Recently
Buried Mines 278
Xll

LIST OF TABLES
continued
TABLES Page
VIII.6 Mine to Soil Fluence Ratio of the
Uncollimated Fluence Detector for
Three Water Contents of HTL Soil
with the TST Mine at 2.5 cm Depth
of Burial 280
VIII.7 Mine to Soil Fluence Ratio of the
Collimated Fluence Detector for
Two Water Contents of HTL Soil
with the TST Mine at 2.5 cm Depth
of Burial 281
VIII.8 Mine, to Soil Fluence Ratio of the
Energy Window Detector for Three
Water Contents of HTL Soil with
the TST Mine at 2.5 cm Depth of
Burial 282
VIII.9 Object to Soil Fluence Ratio from
the Collimated Detector for
Selected Inhomogeneities 286
VIII.10 Object to Soil Fluence Ratio from
the Energy Window Detector for
Selected Inhomogeneities 288
VIII.11 Operational Requirements for a Vehicle-
Mounted Antitank Mine Detection
System 349
VIII.12 Photon Output of the GE Maxitron 300
X-Ray Therapy Unit 352
VIII.13 Imaging Quantities Necessary to Fulfill
Operational Requirements 354
VIII.14 Power and Signal to Noise Ratio Require
ments for Imaging and Mine Detection
with the Uncollimated Detector 358
VIII.15 Power and Signal to Noise Ratio Require
ments for Imaging and Mine Detection
with the Collimated Detector 362
E.l Gadolinium Oxysulfide Screen Model .... 423
E.2 Energies of Fluorescent Photons Used
in the DETECT. PAS Code 426
E.3 Calculated Ratios of Radiation Field
Quantities, 133Ba to 137Cs 466
xiii

LIST OF TABLES continued
TABLES Page
G.l Benchmarks for Monte Carlo Transport
Codes 488
G.2 Photon Interaction Data Files 498
H.l Fluorescent Emission Probabilities .... 511
xiv

LIST OF FIGURES
FIGURES Title Page
II.1Conceptual large area backscatter detector
system 18
111.1 X-ray source, soil box and positioning
system and detector 22
111.2 Detector electronics, computer and x-ray
source console 24
111.3 Lead shield for tube head and detector . 29
111.4 Geometry of sodium iodide detector and
shield 31
III. 5 Components of the counting system 37
III.6 Soil mass attenuation coefficients .... 41
III. 7 TST mine used in measurements 45
111.8 Transmission comparison for TNT and
substitute 49
111.9 Transmission comparison for NSL and
local soil 51
IV.1 Atomic form factor versus momentum
transfer variable 55
IV.2 Solid angle differential coherent
scattering cross section versus
scattering angle 57
IV. 3 Coherent cross section versus photon
energy 58
IV.4 Fractional energy of Compton scattered
photons versus incident photon energy 60
IV.5 Solid angle differential Klein-Nishina
cross section versus scattering angle 62
xv

LIST OF FIGURES continued
FIGURES Page
IV.6 Incoherent scattering function versus
momentum transfer variable 64
IV.7 Comparison of the solid angle differential
Klein-Nishina and incoherent scattering
cross sections 65
IV.8 Incoherent scattering cross section versus
photon energy 66
IV.9 Photoelectric interaction cross section
versus photon energy 69
IV.10 Probability of K shell fluorescence
versus atomic number 70
IV.11 Energies of K fluorescent photons versus
atomic number 72
IV.12 Mass interaction coefficients of aluminum
versus photon energy 75
IV.13 Boundaries and materials of Monte Carlo
calculations 84
IV.14 Number albedo versus energy for concrete 95
IV. 15 Backscattered energy spectrum, 0.200 MeV
on aluminum 96
IV. 16 Backscattered energy spectrum, 0.6616 MeV
on aluminum 97
IV. 17 Backscattered energy spectrum, 0.6616 MeV
on iron 98
IV.18 Comparison of calculations of the solid
angle differential coherent cross
section 101
IV.19 Comparison of calculations of the solid
angle differential incoherent cross
section 102
V.l Transmission curve without anode self-
attenuation 112
V. 2 Typical x-ray spectrum calculation .... 118
xvi

LIST OF FIGURES continued
FIGURES Page
V.3 Heel effect displayed by spectra 120
V.4 Heel effect displayed by half value
thickness 121
V.5 Typical transmission curve comparison. . 123
V.6 Spectrum comparison with Epp and Weiss
at 80 kVp 124
V.7 Spectrum comparison with Epp and Weiss
at 105 kVp 125
V.8 Spectrum comparison with Fewell and
Shuping at 70 kVp 127
V.9 Spectrum comparison with Fewell and
Shuping at 80 kVp 128
V.10 Spectrum comparison with Fewell and
Shuping at 90 kVp 129
V.ll Archer-Wagner method fit to measured
transmission data 134
V.12 Comparison of modified Kramers' method
and the Archer-Wagner method at
80 kVp 136
V.13 Comparison of modified Kramers' method
and the Archer-Wagner method at
150 kVp 137
VI.1 Fraction of incident energy absorbed
perpendicular incidence 147
VI.2 Fraction of incident energy absorbed
75 degree incidence 150
VI.3 Plane detector response, discrimination
less than 0.03317 MeV 152
VI.4 Plane detector response, discrimination
greater than 0.03317 MeV 156
VI.5 Iodine escape peak ratio versus energy . 158
VI.6 Measured and calculated Nal(Tl) spectra. 164
VI. 7 Plane detector response 167
xvii

LIST OF FIGURES continued
FIGURES Page
VI.8 Detector response with edge and shield
correction 168
VII.1 Number albedos versus energy for HTL soil
and two TST mine cases 172
VII.2 Number albedo ratios versus energy for the
TST mine at 0.0 cm in three soils . 174
VII.3 Number albedo ratios versus energy for the
TST mine at 2.5 cm in three soils . 175
VII.4 Energy albedos versus energy for HTL soil
and two TST mine cases 177
VII.5 Multiple scatter fraction versus energy
for HTL soil and two TST mine cases . 179
VII.6 Ratio of number to energy albedo for HTL
soil and two TST mine cases 181
VII.7 Spatial distribution of backscattered
fluence from 100 keV photons per
pendicularly incident on HTL soil . 183
VII.8 Spatial distribution of backscattered
fluence from 100 keV photons per
pendicularly on the center of the TST
mine at 0.0 cm 184
VII.9 Spatial distribution of mine to soil
ratio of backscattered fluence from
perpendicularly incident 100 keV
photons 185
VII.10 Spatial distribution of the single
scattered mine to soil ratio from
perpendicularly incident 100 keV
photons 187
VII.11 Angular distribution of backscattered
fluence from 100 keV photons perpen
dicularly incident on HTL soil and
two TST mine cases 188
VII.12 Angular distribution of the multiple
scattered fluence from 100 keV photons
perpendicularly incident on HTL soil
and two TST mine cases 189
xviii

LIST OF FIGURES
continued
FIGURES Page
VII.13 Mine to soil fluence ratio versus
collimator acceptance angle for 100
keV photons perpendicularly incident
on the TST mine at 0.0 cm in HTL soil 191
VII.14 Mine to soil fluence ratio versus
collimator acceptance angle for 100
keV photons perpendicularly incident
on the TST mine at 2.5 cm in HTL soil 192
VII.15 Multiple scatter fraction versus colli
mator acceptance angle for 100 keV
photons perpendicularly incident on
the TST mine at 0.0 cm in HTL soil. . 193
VII.16 Differential energy spectra for 100 keV
photons perpendicularly incident on HTL
soil and two TST mine cases 195
VII.17 Ratios of mine and soil integral energy
spectra for two TST mine cases in HTL
soil 197
VII.18 Edge effect geometries 199
VII.19 Spatial distribution of the single scat
tered fluence from a 100 keV photon
beam perpendicularly incident on the
inside edge of the TST mine 201
VII.20 Spatial distribution of the single scat
tered mine to soil fluence response
ratio for a 100 keV photon beam perpen
dicularly incident on the inside edge
of the TST mine 202
VII.21 Spatial distribution of the single scat
tered mine to soil fluence response
ratio for a 100 keV photon beam per
pendicularly incident on the outside
edge of the TST mine 203
VII.22 Nal(Tl) detector response and fluence
response versus source beam energy. . 206
VII.23 Ratio of Nal(Tl) detector response to
fluence response as a function of
source energy 207
xix

LIST OF FIGURES
continued
FIGURES Page
VII.24 Ratios of integral energy spectra for
100 keV photons incident on the TST
mine at 2.5 cm in NSL soil for the
cases of 0 to 60 degree incidence . 212
VII.25 Spatial distribution of the fluence
response from a 100 keV beam inci
dent at 60 degrees on the TST mine
at 2.5 cm in NSL soil 215
VII.26 Fluence response versus distance from
beam axis for 100 keV photons perpen
dicularly incident on the TST mine at
2.5 cm in NSL soil 217
VII.27 Relationship between the raster gap size,
the length of the collimator, and the
spacing of the first collimator element
required to exclude single scattered
Photons from the detector 224
VII.28 Geometry of the segmented fluence
detector 228
VII.29 Fluence response ratio matrices for the
segmented detector for perpendicularly
incident 150 keV photon beams on the
TST mine at 2.5 cm in HTL soil 231
VII.30 Source energy optimization curve for the
uncollimated fluence detector with mine
depth of burial of 5 cm in NSL soil . 234
VII.31 Source energy optimization curve for the
segmented fluence detector with mine
depth of burial of 2.5 cm in NSL soil 237
VII.32 Source energy optimization curve for the
energy window detector with mine
depth of burial of 5 cm in NSL soil . 240
VIII.1 Calculated and measured spatial distribu
tion of detector response from back-
scatter from sandy soil at 100 kVp. . 252
VIII.2 Calculated and measured spatial distribu
tion of detector response from back-
scatter from sandy soil at 150 kVp. . 253
xx

LIST OF FIGURES
continued
FIGURES Page
VIII.3 Calculated and measured spatial distribu
tion of detector response from back-
scatter from sandy soil at 200 kVp. . 254
VIII.4 Comparison of the number albedos of
sucrose and TNT 256
VIII.5 Three dimensional image diagram of
measured detector response for the
lucite annulus experiment 260
VIII.6 Two dimensional image diagram of
measured detector response for the
lucite annulus experiment 261
VIII.7 Three dimensional image diagram of
measured detector response for the
steel annulus experiment 263
VIII.8 Two dimensional image diagram of
measured detector response for the
steel annulus experiment 264
VIII.9 Fluence response as a function of
height above the soil surface for
selected panel widths of the
uncollimated detector 268
VIII.10 Fluence response as a function of
height above the soil surface for
selected acceptance angles of the
collimated detector 270
VIII.11 Fluence response as a function of
height above the soil surface for
the energy window detector 273
VIII.12 Ratio of fluence responses for two
densities of HTL soil with the TST
mine at selected depths of burial
as a function of source energy for
the uncollimated detector 274
VIII.13 Object to soil fluence response ratio
for selected materials as a function
of source energy for the uncolli
mated detector 284
xxi

LIST OF FIGURES
continued
FIGURES Page
VIII.14 Monte Carlo generated image for the TST
mine buried flush to an NSL soil
surface for the uncollimated fluence
detector 290
VIII.15 Monte Carlo generated image for the TST
mine buried flush to an HTL soil
surface for the uncollimated fluence
detector 291
VIII.16 Monte Carlo generated image for the TST
mine buried flush to an MCL soil
surface for the uncollimated fluence
detector 292
VIII.17 Monte Carlo generated image for the TST
at 2.5 cm depth of burial in NSL soil
for the uncollimated fluence detector 294
VIII.18 Low pass filtered Monte Carlo image for
the TST mine at 2.5 cm depth of burial
in NSL soil for the uncollimated
fluence detector 295
VIII.19 Monte Carlo generated image for the TST
mine at 5.0 cm depth of burial in NSL
soil for the uncollimated fluence
detector 297
VIII.20 Monte Carlo generated image for a simu
lated water puddle on HTL soil with
20% water content by weight for the
uncollimated fluence detector 298
VIII.21 Monte Carlo generated image for an iron
disk buried flush to the surface of
NSL soil for the uncollimated fluence
detector 299
VIII.22 Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine buried flush to
the soil surface 301
VIII.23 Two dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine buried flush to
the soil surface 302
xxii

LIST OF FIGURES continued
FIGURES
VIII.24
VIII.25
VIII.26
VIII.27
VIII .28
VIII.29
VIII.30
VIII.31
Page
Three dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine buried flush to
the soil surface 303
Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm 304
Low pass filtered image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm 306
Three dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm 307
Low pass filtered image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm 308
Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine laid on the soil
surface 309
Two dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for the TST mine laid on the soil
surface 310
Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm 311
xxm

LIST OF FIGURES
continued
FIGURES
VIII.32
VIII.33
VIII.34
VIII.35
VIII.36
VIII.37
VIII.38
VIII.39
Page
Two dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
A1 for the TST mine at a depth of
burial of 2.54 cm 312
Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 7.62 cm 314
Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine laid on the soil
surface 315
Two dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine laid on the soil
surface 316
Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array 318
Three dimensional image diagram of the
measured uncollimated detector response
to a 150 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array 319
Three dimensional image diagram of the
measured uncollimated detector response
to a 150 kVp source beam filtered by
Sn for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array 321
Three dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Sn for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array 322
xxiv

LIST OF FIGURES
continued
FIGURES
VIII.40
VIII.41
VIII.42
VIII.43
VIII.44
VIII.45
VIII.46
VIII.47
Page
Three dimensional image diagram of the
measured collimated detector response
to a 150 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array 323
Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with overlying rock
array 324
Irregular soil surface used in measure
ments 326
Three dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface 327
Two dimensional image diagram of the
measured uncollimated detector response
to a 200 kVp source beam filtered by
Pb for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface 328
Three dimensional image diagram of the
measured collimated detector response
to a 100 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface 330
Three dimensional image diagram of the
measured collimated detector response
to a 150 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface 331
Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface 332
xxv

LIST OF FIGURES
continued
FIGURES
VIII.48
VIII.49
VIII.50
VIII.51
VIII.52
VIII.53
VIII.54
VIII.55
Page
Two dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for the TST mine at a depth of
burial of 2.54 cm with irregular soil
surface 333
Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for a wood disk buried flush to the
soil surface 334
Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for a wood disk buried flush to the
soil surface 335
Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for a steel disk buried flush to the
soil surface 336
Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for a steel disk buried flush to the
soil surface 337
Three dimensional image diagram of the
measured uncollimated detector response
to a 100 kVp source beam filtered by
Pb for water contained in a thin plastic
container buried flush to the soil
surface 339
Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for water contained in a thin
plastic container buried flush to the
soil surface 340
Three dimensional image diagram of the
measured collimated detector response
to a 200 kVp source beam filtered by
Al for a hole filled with loose soil. 341
xxvi

LIST OF FIGURES
continued
FIGURES Page
VIII.56 Failure of the dual energy subtraction
technique 345
VIII.57 Two dimensional image diagram of the
measured uncollimated detector
response to a 100 kVp source beam
filtered by Pb for the TST mine at
a depth of burial of 2.54 cm with
irregular soil surface 346
A.l Typical antitank mine 370
D.l X-ray fluence spectrum, 80 kVp,
2.00 mm A1 398
D.2 Measured and calculated transmission of
exposure rate, 80 kVp, 2.00 mm Al.. . 399
D.3 X-ray fluence spectrum, 80 kVp,
2.24 mm Al 400
D.4 Measured and calculated transmission of
exposure rate, 80 kVp, 2.24 mm Al . 401
D.5 X-ray fluence spectrum, 100 kVp,
2.0 0 mm Al 402
D.6 Measured and calculated transmission
of exposure rate, 100 kVp, 2.00 mm Al 403
D.7 X-ray fluence spectrum, 100 kVp,
2.24 mnt Al 404
D.8 Measured and calculated transmission of
exposure rate, 100 kVp, 2.24 mm Al. . 405
D.9 X-ray fluence spectrum, 150 kVp,
3.00 mm Al 406
D.10 Measured and calculated transmission of
exposure rate, 150 kVp, 3.00 mm Al. . 407
D.ll X-ray fluence spectrum, 150 kVp,
3.34 mm Al 408
D.12 Measured and calculated transmission of
exposure rate, 150 kVp, 3.34 mm Al. . 409
D.13 X-ray fluence spectrum, 200 kVp,
3.00 mm Al 410
xxvii

LIST OF FIGURES continued
FIGURES Page
D.14 Measured and calculated transmission of
exposure rate, 200 kVp, 3.00 mm Al. . 411
D.15 X-ray fluence spectrum, 200 kVp,
3.34 mm Al 412
D.16 Measured and calculated transmission of
exposure rate, 200 kVp, 3.34 mm Al. . 413
E.l Gadolinium oxysulfide based detector . 416
E.2 Active region of the detector 418
E.3 Spectrum and transmission curve at
115 kVp 421
E.4 Fraction of incident energy absorbed,
perpendicular incidence 430
E.5 Fraction of incident energy absorbed
in each screen, perpendicular
incidence 431
E.6 Fraction of incident energy reflected,
perpendicular incidence 432
E.7 Fraction of incident energy transmitted
perpendicular incidence 433
E.8 Fraction of incident energy absorbed,
45 degree incidence 437
E.9 Fraction of incident energy absorbed
in each screen, 45 degree incidence . 438
E.10 Fraction of incident energy reflected,
45 degree incidence 440
E.ll Fraction of incident energy transmitted,
45 degree incidence 441
E.12 Fraction of incident energy absorbed,
75 degree incidence 445
E.13 Fraction of incident energy absorbed in
each screen, 75 degree incidence. . 446
E.14 Fraction of incident energy reflected,
75 degree incidence 447
xxviii

LIST OF FIGURES continued
FIGURES Page
E.15 Fraction of incident energy transmitted,
75 degree incidence 448
E.16 Emission spectrum of gadolinium
oxysulfide with 0.3 atom % terbium. . 452
E.17 Emission spectrum of 3M Trimax
12 screens 453
E.18 Average number of visible photons
produced per incident x-ray photon. . 454
E.19 Dark pulse count rate versus time 459
E.20 Measured pulse height spectra 462
137
E.21 Response versus distance for Cs . . 468
133
E.22 Response versus distance for Ba . . 469
F.l X-ray fluence spectrum, 100 kVp,
1.01 mm A1 471
F.2 X-ray fluence spectrum, 150 kVp,
1.01 mm A1 472
F.3 X-ray fluence spectrum, 200 kVp,
2.67 mm Al 473
F.4 X-ray fluence spectrum, 100 kVp,
9.52 mm Al 474
F.5 X-ray fluence spectrum, 150 kVp,
9.52 mm Al 475
F.6 X-ray fluence spectrum, 150 kVp,
1.85 mm Sn 476
F.7 X-ray fluence spectrum, 200 kVp,
1.8 5 mm Sn 477
F.8 X-ray fluence spectrum, 100 kVp,
0.25 mm Al, 0.24 mm Pb. 478
F.9 X-ray fluence spectrum, 100 kVp,
0.7 5 mm Pb 479
F.10 X-ray fluence spectrum, 150 kVp,
0.25 mm Al, 0.75 mm Pb 480
xxxx

LIST OF FIGURES continued
FIGURES Page
F.ll X-ray fluence spectrum, 200 kVp,
0.75 mm Pb 481
F.12 X-ray fluence spectrum, 200 kVp,
0.25 mm Al, 0.75 mm Pb 482
F.13 X-ray fluence spectrum, 200 kVp,
0.25 mm Al, 1.35 mm Pb 483
H.l The fit technique 514
xxx

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
LANDMINE DETECTION BY SCATTER
RADIATION RADIOGRAPHY
By
John G. Campbell
August 1987
Chairman: Alan M. Jacobs
Major Department: Nuclear Engineering Sciences
The application of scatter radiation radiography to
the detection of buried nonmetallic antitank landmines is
examined. A combination of calculations and measurements
is used to address the problem. The primary calculation
tool is a Monte Carlo photon transport code. Measurements
are made with an x-ray source, sodium iodide detector, and
soil box positioning system. The soil box containing a
model of a nonmetallic antitank mine is moved beneath the
x-ray source to simulate both the forward motion of a
vehicle transporting the detection system and raster of the
beam to search a path of sufficient width to allow safe
passage. Calculations are used to suggest mine detection
mechanisms and to optimize geometric parameters and x-ray
beam quality. Measurements are used to validate the
calculation results for a small detector and produce images
of buried mines. The calculations are extended to large
xxxi

area detectors which are required to provide path searches
of approximately three meter widths. Environmental para
meters, such as height sensitivity, soil density and mois
ture content, and inhomogeneities are examined in both
calculations and measurements. Power requirements are also
addressed.
A system based upon detector collimation to emphasize
differences in the multiple scattered components, character
istic of soil and the explosive found in mines, is found to
be capable of mine detection at depths of burial of at least
7.5 cm at power levels compatible with portability, and at
speeds, path widths, detection probabilities and false alarm
probabilities consistent with operational requirements. De
tection at greater depths is possible in soil recently dis
turbed by mine burial.
Images of holes refilled with loose soil can be dis
tinguished from those of buried mines by their character
istic features. However, the refilled hole images bear some
resemblance to those of mines laid on the soil surface. A
compound detector, consisting of both collimated and un
collimated regions, can be used to overcome this problem and
increase the probability of detection of mines buried at
shallow depths.
XXXI1

CHAPTER I
INTRODUCTION
This research studies the use of backscattered x rays
to detect and image buried nonmetallic antitank mines. A
source of x-ray photons is directed at the soil surface.
After interacting with soil or a buried object, backscat
tered photons strike a detector located above the soil
surface producing a response. Detection of a buried object
depends upon differences between the photon interaction
characteristics of soil and the object. The x-ray source is
rastered over the soil surface producing an array of respon
ses, each of which carries information related to the mater
ials through which photons passed before reaching the detec
tor. This array of detector responses is manipulated to
produce an image characteristic of those materials. Calcu
lations are performed to optimize the detection and imaging
process. A variety of detector geometries and types are
examined by these calculations. Measurements are made with
a small sodium iodide scintillation detector to examine the
predictions of the calculations and to produce images of
buried objects.
Chapter II provides a summary of the use of scattered
x-ray and gamma-ray photons to provide information about
1

2
materials they irradiate. The general concepts for the mine
detection and imaging system are also introduced in this
chapter. Three related appendices (A, B and C) provide
background on the characteristics of landmines, a short
history of landmine warfare, and a description of other
technologies which have been applied to mine detection.
Chapter III describes the equipment and materials used
in the research. Included in this chapter are descriptions
of soil and mine materials used in the calculations and
measurements.
Chapter IV describes the photon interaction character
istics important to the mine detection problem. The single
scatter and Monte Carlo photon transport codes used in the
calculations are also described. Validation of the Monte
Carlo calculation method is presented.
Chapter V describes the method used to produce calcula
tions of the x-ray source spectrum and the validation of the
technique. Other source calculation methods are discussed.
A related appendix (D) provides a graphical display of one
of the validation methods. Appendix F provides graphs of
spectra used in experiments.
Chapter VI describes the method used to calculate the
response function of the sodium iodide scintillation crystal
used in the experiments. Validation of the calculated re
sponse function is provided. Response calculation for a
detector based on terbium activated gadolinium oxysulfide is
described in a related appendix (E). Detectors similar to

3
this could prove useful for covering the large areas neces
sary to find vehicle paths through minefields.
In Chapter VII, results of the application of the Monte
Carlo transport code to the physics and geometry of mine
detection employing backscattered radiation are provided.
Based on these calculations, several detector types are
selected for further investigation. Optimization of the
geometry and source energy is made for each type of detector
selected.
Chapter VIII applies the results of the previous chap
ter to producing images of mines. Calculated and measured
images are examined. The effects of environmental para
meters on images are discussed, and power requirements are
estimated.
Chapter IX presents conclusions derived from this re
search effort along with recommendations for directions for
future work.

CHAPTER II
BACKSCATTER MINE DETECTION AND IMAGING
Conventional radiography uses the transmission of
photons through an irradiated object to produce an image.
The image depends upon the photon attenuation properties of
the internal structure of the object. Conventional radi
ography cannot be used to examine objects buried in soil,
such as mines, because of the obvious inability to locate
the detector below the object. Backscatter radiography,
which depends upon differences in the photon scattering
properties of irradiated objects to produce an image, is
suited to the geometry of mine detection. Photons can
originate and be detected above the soil surface. Scattered
radiation has been used in medical and engineering applica
tions to determine properties and form images of irradiated
objects. Nonmetallic mine detectors using backscattered
radiation have been constructed and tested, but have not
been considered useful enough for actual field use. The
detection and imaging principles investigated in this re
search are designed to overcome problems inherent in the
previous work.
4

5
Previous Uses of Scattered Radiation
The first suggested use of Compton (incoherent) scat
tering to determine characteristics of a material was by
Odeblad and Norhagen (1956). They showed that the intensity
of the scattered radiation for a fixed source energy and
scattering angle depends on the electron density of the
scattering medium. In a small volume of uniform composi
tion, the electron density is proportional to the material
6 0
density. Using a collimated Co gamma-ray source and a
collimated scintillation detector, they were able to measure
the relative electron densities of materials in the small
volume defined by the intersection of the fields of view of
the detector and source collimators.
19 2
Lale (1959) used a collimated Ir source and a col
limated detector positioned to receive forward scattered
Compton photons to measure electron density within trans
verse cross sections in rabbits and guinea pigs. The sub
jects were moved with respect to the beam to produce an
image of density variation. The process was very slow, and
subject to considerable quantum noise and attenuation of the
incident and scattered beams, but demonstrated that air in
organs would provide a large change in measured electron
density in images. In an extension of this work, Lale
(1968) used 5.6 MV x rays to reduce attenuation losses.
A patient platform was lowered through the beam. Forward
scattered photons were detected with a liquid scintillator.

6
Kondic and Hahn (1970) suggested the use of Compton
scattering to measure density variations in two-phase flow.
They examined collimated sources used with both collimated
and uncollimated detectors. With the uncollimated detector,
energy discrimination was used to determine the path taken
by a scattered photon. The relationship between energy and
angle in a Compton single scattering event determines the
position along the source beam from which the photon is
scattered, and the intensity (corrected for attenuation) at
that energy determines the electron density of the material
at that point. Farmer and Collins (1971) independently used
the same uncollimated detector technique in a medical appli-
. 137
cation. They used a collimated Cs source and an uncolli-
mated Ge(Li) detector to examine cross sectional structure.
Rather than move the patient or scan the beam, the energy
discrimination technique was used to determine origin of the
scattered photons. Problems with this method are attenua
tion of both the primary and scattered photons, and resolu
tion reduction caused by detection of multiply scattered
photons. Extensions of this method (Farmer and Collins,
1974) using two higher resolution Ge(Li) detectors, above
and below the patient, and focused to the plane of interest,
also suffered from attenuation and multiple scatter. Reiss
and Shuster (1972) and Dohring et al. (1974) used collimated
137
Cs sources and collimated detectors with patient motion
to determine lung function and measure lung density.
Problems with multiple scattering were again noted.

Clarke and Van Dyke (1973) and Garnett et al. (1973)
developed a two-source method to determine bone density.
The two source technique is used to eliminate the problem of
attenuation by tissue above the bone. The second source is
of the same energy as the single scattered beam of the first
for a selected scattering angle. Measurements of both
transmitted and scattered beams are made in two orientations
to allow correction for attenuation.
Battista et al. (1977) examined the physics of scatter
imaging and described the two major limitations to be atten
uation of the single scattered photon fluence and contamina
tion by multiply scattered photons. They provide methods
for obtaining a correction for the multiple scattering prob
lem. Battista and Bronskill (1978) extended this investiga
tion and concluded that multiple scatter is an inherent
limitation whose effect can be reduced, but not eliminated,
by improving the energy resolution of the detector. They
also showed that the use of forward scattered components
both reduces dose to patients and the effects of multiple
scatter. Anghaie (1982) showed that predictions of the
multiple scattered component could be used to improve image
resolution by subtracting it from the total signal.
Hanson et al. (1983) successfully used heavily filtered
x-ray beams in the two source densitometry method, taking
advantages of the high intensities and well-defined beams
available from x-ray machines. Errors from contamination by
multiple scattering were found to exceed those due to the
polychromatic nature of the source.

8
Jacobs et al. (1979) proposed an imaging scheme much
different than those discussed thus far. A collimated
scanning x-ray source with an uncollimated detector was used
to view large angle backscattered photons. Energy modula
tion of the source was used to produce two images. The
image at the lower source energy is characteristic of the
overlying materials. When subtracted from the higher energy
image (after multiplication by an appropriate factor), the
result is an image characteristic of deeper layers within
the irradiated object. The technique was found to be sensi
tive to regions of air within the object. This dual energy
approach was shown to allow irregular surface features to be
removed from the final image.
Backscattered Photon Mine Detection
A number of attempts have been made to use backscat
tered photons to detect buried nonmetallic mines. With only
one exception, the published descriptions are from efforts
sponsored by the United States military. Detailed accounts
of these mine detection systems are contained in classified
documents. The descriptions provided here are from unclas
sified summaries (Roder, 1975; Nolan et al., 1980). The
wide range of other technologies which have been examined as
possible mine detection methods are described in Appendix C.
Fluorescence Emission
Although fluorescent emission is not a backscatter
technique, attempts to use it as a mine detection mechanism
are similar. Between 1954 and 1957, the Armour Research

9
Foundation used a 150 kVp x-ray source to attempt to produce
fluorescent emission from the lead or mercury contained in
mine fuzes. These elements are found in approximately one
gram quantities of lead azide, lead styphnate or mercury
fulminate (U.S. Department of the Army, 1986). High resolu
tion detectors were used to look for the energies of the
characteristic x rays of lead or mercury. The Compton scat
tered fluence was found to completely obscure any fluores
cent emission signal which might be present. Additional
efforts using more modern detectors produced this same re
sult, and the technique was deemed infeasible.
Rayleigh Scattering
From 1958 to 1961, Tracerlab, Inc. attempted to use
Rayleigh (coherent) scattering from these same high atomic
number components of the mine fuze as a detection mechanism.
Because the probability of Rayleigh scattering decreases and
the direction of scattering becomes more forward peaked as
incident energy increases, the technique is limited to shal
low depths of burial. A 120 kVp x-ray source was employed,
in an attempt to produce Rayleigh scattered photons when the
beam struck the high atomic number materials in the fuze.
Because the incident beam was polyenergetic, the Rayleigh
scattered photons were also produced in a spectrum of ener
gies. Compton scattering was again the dominant source of
the detected signal. Two rastering detectors were tightly
collimated to focus on a very small volume which might con
tain the mine fuze. Detection was signaled by a small shift

10
in the backscattered spectrum to higher energies. The very
small sampled volume, which led to scans on the order of
hours per square foot, was the cause for termination of this
effort. Unfortunately, this detection system was not tested
with a real mine. Had it been employed in such a fashion, a
large difference between cases of irradiation of soil only
and of soil containing a buried mine would have resulted.
The mine detection mechanism would have been the difference
between the photoelectric cross sections of soil and mine.
The higher photoelectric absorption of photons striking soil
results in fewer photons capable of being backscattered than
in the mine present case.
Compton Scattering
The first attempt to examine the contrast mechanism
afforded by the difference photoelectric cross sections of
soil and mine materials was made by the Naval Ordnance
Laboratory in 1960 to 1961. Unfortunately, 2 and 10 MV
bremsstrahlung sources were selected for the experiments.
At these energies the photoelectric cross sections of soil
and mine materials are both very small. The dominant inter
action is Compton scattering, and the respective material
cross sections for this interaction at these energies are
nearly the same. Additionally, the material densities of
soil and explosive are similar. As a result no contrast
mechanism existed and only negative results were obtained.

11
Beginning in 1967 and extending until 1973, Texas
Nuclear Corporation conducted experiments to produce non-
metallic mine detection systems using backscatter of gamma
or x rays. These experiments culminated in a nonmetallic
antitank mine detector. A less successful nonmetallic anti
personnel mine detector was also produced. Both systems
used vertically collimated sources and vertically collimated
detectors. Low energy x-ray sources were used to enhance
the photoelectric contrast between mine and soil. The
antitank mine detector used a 130 kVp x-ray source mounted
on the front of a 1/4-ton truck and four CsI(Tl) scintilla
tion detectors. It was capable of operation at several
miles per hour. Field tests were conducted at a variety of
military installations with U.S. and Soviet mines filled
with dinitrobenzene (a nonexplosive substitute for trini
trotoluene) Although depths of detection of up to 10 cm
were achieved, a number of conditions of the test were
optimized to enhance the mine detection process. The tests
were conducted in areas free of buried organic material,
such as tree roots, whose response was known to produce
false alarms in the detector. The areas of the tests were
also fairly level, minimizing sensitivity to irregular
surfaces. Deep ruts or depressions comparable to the size
of a mine were also capable of producing false alarms. The
test areas were free of vegetation, which if present would
have lowered the contrast between soil and soil with mine,
and if nonuniform, could have produced false alarms. The

12
extent of coverage was also a problem; mines located midway
between two detectors were missed unless they were on the
surface. A final objection to the system involved soil
density. It was found that the detector was sensitive to
density changes whether a mine was present or not. Concern
was expressed that dummy minefields could be produced by
simply digging and refilling holes. The act of emplacing a
mine significantly alters the soil density, reducing it, on
the average, to 75% of the undistrubed value (Roder, 1975).
After weathering had returned the soil to its normal
density, detection was no longer possible at 10 cm, and the
response difference at 7.5 cm was much reduced. Further
work on this detection system was terminated primarily as a
result of the apparent superiority of a competing techno
logy, and secondarily as a result of the inadequacies de
scribed (Nolan et al., 1980).
Coleman (1971) performed Monte Carlo calculations for
several cases in support of this effort. They are discussed
in Chapter IV. These calculations and the majority of Texas
Nuclear experiments were conducted with solid blocks of di
nitrobenzene. The mines used in the field tests were filled
with dinitrobenzene, but it is unclear whether any air
space, characteristic of real mines (described in Appendix
A), was provided.
Preiss and Livnat (1973), working in Israel, provide
the only non-U.S. military publication of research on the
detection of nonmetallic mines by the backscatter of

13
ionizing radiation. The system consisted of an uncollimated
75
Se source with a Nal(Tl) detector collimated to view a
10 cm diameter circle at the soil surface at a fixed detec
tor height. The system was placed on a cart and pushed by
the operator over dirt road surfaces. The electronic com
ponents of the detector were carried by backpack. This
research effort was the first to consider the effect of the
air space which exists at the top of mines. Experiments
with solid explosive filling the mine and with an actual
mine, containing an air space, revealed completely different
effects. In the case of the solid mine, the ratio of the
detector response with mine present to mine absent (soil
only) was found to be greater than 1.00. In the case of the
mine with air space, the ratio was less than 1.00. Mine
detection was accomplished by selecting an energy range in
the backscattered spectrum which enhanced the reduction in
response with the mine present.
Backscatter Radiation Radiography
Genesis of Current Research Effort
A high priority has been placed on research into the
detection of landmines (West et al., 1985; U.S. Department
of the Army, 1986). The increased interest in this research
is based upon a combination of factors, driven by the imple
mentation of a new dynamic operational concept by the U.S.
Army. This new concept, termed the AirLand Battle, is
oriented primarily to the threat of a Warsaw Pact attack
into Western Europe. The superseded defensive concept,

14
termed the Active Defense, concerned itself with attrition
of numerically superior attacking forces by use of defensive
positions prepared in depth on the battlefield (DePuy, 1984;
Holder, 1985). Simulations indicated that this concept
would be successful against the first echelon of a Warsaw
Pact attack, but without extensive, rapid reinforcement
would be of doubtful utility against the following echelons.
The AirLand battle concept emphasizes the use of aggressive
engagement of the attacking force using both fire and man
euver at varying depths on the battlefield. Counterattacks
into the flanks of the attacking force and into rear supply
and transport areas are encouraged to disrupt the rigid
plans and time tables characteristic of Soviet military
operations. These maneuvers are also designed to enhance
one of the few perceived advantages of Western military
forces in conventional combat with Soviet forces; the
capability of Western leaders of virtually any size unit to
use their initiative in fluid situations compared to the
discouragement (at least until recently) of any deviation
from detailed plans, regardless of tactical situation,
applied to Soviet leaders, especially of smaller sized units
(Suvorov, 1984? Walker, 1986; Baxter, 1986). Another key
factor in the development of the AirLand Battle concept is
the advent of a series of technological advances and equip
ment modernizations which make rapid maneuver feasible
(RisCassi, 1986).

15
The landmine represents a serious challenge to rapid
maneuver. The employment of mines by the attacking force to
protect its flanks and rear areas could do much to neutral
ize the new operational concepts. The effectiveness of
landmines is high. More than 20% of Allied tank casualties
in World War II were caused by mines. United Nations tank
casualties in the Korean conflict were as high as 70% in
offensive operations. In Vietnam (through 1970) 70% of all
U.S. vehicle losses were due to mines (U.S. Department of
the Army, 1973). The keystone manual of the U.S. Army, FM
100-5, Operations (U.S. Department of the Army, 1982),
emphasizes synchronized execution. Clearly, the capability
of mines to produce delays and disruptions is inconsistent
with the new maneuver oriented operational concepts.
Adding to this concern is the mine warfare capability
and experience of the Soviet Army, which is unsurpassed by
any army in history (Honeywell, 1981). Appendix B provides
examples of the Soviet experience with mines. The primary
mission assigned to Soviet engineer units is to insure the
momentum of maneuver mobility by rapidly overcoming natural
and manmade obstacles, while at the same time hindering
enemy force movement (Sidorenko, 1973). The second portion
of this mission, directly affecting the new U.S. Army oper
ational concepts, is accomplished by Mobile Obstacle Detach
ments, which provide countermobility support by laying mine
fields and establishing other expedient obstacles along
enemy avenues of approach (Plyaskin et al., 1973; Uli,

16
1986). In short, the Soviet Army is aware of its vulner
abilities on its flanks and in its rear areas, and is
organized to address the threat, in part, by employing
mines. Soviet doctrine has long included the rapid
emplacement of mines on the surface without burial (U.S.
Department of the Army, 1979a). In the 1970's, mechanical
minelayers and mine dispensing chutes for vehicles and
helicopters were fielded to allow rapid minefield emplace
ment. More recently fielded scatterable mine systems fur
ther enhance the capability to respond to the new U.S. op
erational concepts (West et al., 1985).
Aside from manual probing, a hand-held nonmetallic mine
detector of questionable capability (the hand-held metallic
detector works well), and actual mine detonation in an
adverse encounter, the U.S. Army has no method for detecting
buried nonmetallic mines (U.S. Department of the Army,
1986). These slow or adverse detection mechanisms are
incompatible with the advent of new operational concepts
which rely upon maneuver mobility. Accordingly, reviews of
all previous detection technologies have been conducted by
the U.S. Army in an attempt to find systems which might be
made to work. One such review (Moler, 1985) examined the
range of nuclear techniques (x-ray backscatter is included
within this category, even though it is actually an atomic
technique). This review recommended imaging using x-ray
backscatter as the highest priority nuclear technique for
additional research.

17
Improvements on Previous X-Ray Backscatter Efforts
The shortcomings of the Texas Nuclear Corporation re
search effort, described above, provide the basis for
improvements in the x-ray backscatter technique. The
concepts investigated in this dissertation differ from the
previous efforts in a number of areas. The major difference
is the examination of the formation of images of buried
objects, rather than detection based upon a single differ
ence between soil and soil with buried object. Creating an
image requires capabilities that were unavailable in the
past. X-ray sources capable of long linear scans and the
image processing technology to allow real time analysis of
data have been developed since the Texas Nuclear Corporation
efforts. An image provides the important capability to
discriminate between buried mines and other buried objects
which have photon interaction characteristics similar to
mine materials. Coupling the scanning x-ray beam with a
detector large enough to assure coverage of width of the
largest vehicle which must traverse a mined area eliminates
another shortcoming of the previous effort. A diagram of a
conceptual detector is shown in Figure II.1.
Research Goals
The goals of this research effort are to optimize
the design parameters of a large area, x-ray backscatter
imaging system and to examine the effect of environmental
parameters on the detection and imaging process. The design
parameters available for optimization are the energies of

18
Source
surface. The beam is scattered as it penetrates the soil
and mine. Some of the photons scattering within the mine
reach the panels of the detector after single or multiple
scatters. Distances indicated on the diagram are the height
of the detector above the soil, h; the depth of burial of
the mine, d; the size of the gap between the two panels, d ;
and the width of a panel, d ^

19
the x-ray beams, beam angle of incidence, beam size, beam
collimation, detector geometry, and detector collimation.
Environmental parameters are soil type, soil density, soil
moisture content, inhomogeneities with the soil, surface
irregularities, mine geometry, and mine depth of burial.
The method for examining parameters is a combination of
calculations and measurements. The primary calculation tool
is a Monte Carlo photon transport code written specifically
for the mine detection problem. Measurements are made with
a small Nal(Tl) detector to validate the Monte Carlo pre
dictions, allowing extension of the code to large area
detector configurations.

CHAPTER III
EQUIPMENT AND MATERIALS
The apparatus used to perform measurements is designed
to simulate the raster of the x-ray beam across a soil sur
face which may contain buried objects. This raster simula
tion is accomplished by moving a soil box under a fixed
x-ray beam. The complete simulation system consists of the
x-ray machine, the soil box and its positioning system, the
detector and its related electronics, and the computer con
trol devices. Figure III.l shows the x-ray source, soil box
and positioning system, and detector. Figure III.2 shows
the detector electronics, computer control and x-ray source
control systems. Materials used for soil and buried objects
are selected to simulate those items found under field con
ditions .
Equipment
X-Ray Source
An x-ray machine is selected as the source of the pho
tons for backscatter imaging applications because of its
capability to produce intense photon beams which can be
rastered. Extremely high activity radionuclide sources
would be required to produce similar intensities in the
collimated beams necessary for the imaging process. Such
20

Figure III.l X-ray source, soil box and positioning system, and detector. The GE
Maxitron 300 x-ray generator (top center) is held in a fixed position while the soil
box (center) is moved in raster mode by drive screws powered by DC motors with
controlled clutch/brakes. The positioning interface to the controlling computer is
on the right side of the photograph.

N>
ro

Figure III.2. Detector electronics, computer and x-ray source console. This
photograph shows, from left to right, the detector high voltage supply, scaler and
timer, amplifier and single channel analyzer, count rate meter, the IBM PC computer,
and the GE Maxitron 300 control console with remote TV picture of exposure room.



25
sources require heavy shielding at all times and pose a
constant radiological safety concern. An x-ray machine
poses the same hazard only when in operation. Since the
mine detection problem requires a minimum path width equal
to the widths of following vehicles (on the order of 3
meters), rastering of the beam is required. Mechanical
systems are not practical for rastering a radionuclide
source at the speeds required for the imaging problem (on
3
the order of 10 m/s), or alternatively, moving a collimator
along a line source at those speeds. The electron beam of
an x-ray machine can be scanned along an extended anode at
very high speeds to provide the raster required. An addi
tional advantage of an x-ray machine is the capability to
alter intensities by varying beam current and to alter beam
quality by varying tube voltage or filtration. Separate
radionuclide sources would be required to accomplish such
alterations.
The source of the photons used in the backscatter imag
ing experiments is a General Electric Maxitron 300 X-Ray
Therapy Unit (General Electric, 1962). The unit is capable
of producing continuous beams of 70 to 300 kVp at beam cur
rents between 5 and 20 mA. The primary voltage waveform
accelerating the electrons to the anode is single phase,
self-rectified at approximately 1200 Hz. The accelerated
electrons strike a 45 degree angle tungsten anode. If the
electron energy exceeds that of the K shell binding energy
of tungsten, K characteristic x rays are produced in

26
addition to the continuous x rays produced at all energies.
All beams pass through a 4.75 mm thick beryllium window.
Additional filtration can be provided both within and out
side the head of the unit. Adjustable internal, rectangular
collimators are employed to shape the beam. When an ex
ternal filter is used, an additional external collimator is
employed to prevent the majority of scattered or fluorescent
photons produced within the external filter from reaching
the soil plane.
The shielding of the head of the x-ray unit is supple
mented by a 0.16 cm (1/16 inch) thick layer of lead. This
additional shielding was found to be required when measure
ments were performed using an uncollimated detector with a
heavily filtered beam at higher accelerating potentials.
The higher accelerating potentials produce photons more
likely to penetrate the standard shielding of the unit.
This fact, combined with low intensity fields produced by
heavily filtered beams, results in a significant fraction of
the detector response being caused by head leakage scatter.
The lead shielding reduces the probability of head leakage
photons reaching the soil and subsequently scattering into
the detector. The shielding employed does not entirely
eliminate the problem, requiring two sets of measurements
to be made at high energies when an uncollimated detector is
used. The first image scan is made with the desired beam
filtration. A second scan is then made with a very thick
lead external filter which prevents beam photons from

27
reaching the soil. This second image scan is, therefore,
the result of the head leakage scatter. Subtraction of the
second scan from the first corrects the imaging data for the
head leakage scatter. Structural constraints caused by the
weight of the shield prevent thicker layers from being used.
Figure III.3 shows lead shielding covering the head of the
x-ray machine.
Soil Box Positioning System
The soil box positioning system was constructed accord
ing to a design by Moss (1986). The control system was con
structed by Moss. The soil box is positioned in the x-y
plane (the plane parallel to the floor of the exposure room)
beneath the source by a two level linear bearing system
driven by ball screws which are powered by DC motors with
controlled clutch/brakes. The scan motion is boustrophe-
donic. Both local and remote control of the positioning
system are available. Local control is used to provide the
initial beam-soil intercept position prior to irradiation.
Remote control of the soil box motion is through an RS-232
serial interface bus. It is used in the imaging process to
move the soil box through the array of measurement posi
tions. Two soil boxes of dimensions of 66 cm by 66 cm by 45
cm deep and 122 cm by 91 cm by 45 cm deep are used. The
larger box is required for measurements with a collimated
detector. Both are filled with locally obtained sandy soil
typical of North Central Florida.

Figure III.3. Lead shield for tube head and detector. The detector within its
shield and the shielding of the head of the x-ray generator are viewed from below.
The shielding is required to attenuate x-ray leakage from the generator head in
directions other than that of the beam. The filter holder with filter and external
collimator is also shown.

29

30
Detector and Related Electronics
Two types of detectors have been used in the imaging
measurements. The x-ray sensing portion of the first de
tector is based on terbium activated gadolinium oxysulfide
rare earth intensifying screens. This device was construct
ed to provide an inexpensive, sensitive, large area detec
tor. For reasons detailed in Appendix E, this detector is
found to be unsuitable for the detection and imaging tasks.
It is replaced by Bicron Model .5M.390/.5L-X, sodium iodide
detectors. This detector type is used in all imaging
measurements. The geometry of this detector is shown in
Figure III.4. Also included in this diagram is a composite
shield designed to allow the detector, when operated in an
uncollimated mode, to simulate small regions of a large area
plane detector by permitting photons to enter only through
the exposed face. Several regions of the detector (labeled
3, 4, 5 and 6 in Figure III.4) are not identified in the
diagram. Bicron Corporation, the manufacturer of the detec
tor, provided the compositions and densities for these
materials with the understanding that they would not be
published due to their proprietary nature (Melocik, 1986).
They are included in the Monte Carlo calculations performed
to determine the detector response function (described in
Chapter VI). Table III.l provides the dimensions of the
materials shown in Figure III.4.
Because a large area, plane detector is a possible can
didate for an actual fielded system (Chapter II), it is

Figure III.4. Geometry of the sodium iodide detector and shield. A cross section of
the Bicron Model .5M.39Q/.5L-X Nal(Tl) detector (Melocik, 1986), and locally fabri
cated shield is shown (not to scale). Numbers in detector and shield regions
correspond to materials and dimensions provided in Table III.l.

32
TABLE III.l
Geometry of the Sodium Iodide
Detector and Shield
#
Material
Diameter
Width
or Thickness
(cm)
1
Nal(Tl) crystal
1.2700
0.9906
2
Quartz light pipe
1.2700
1.2700
3
Bicron proprietary
0.1588
a
4
Bicron proprietary
1.5875
a
5
Bicron proprietary
1.5875
a
6
Bicron proprietary
1.5875
a
7
Aluminum housing (face)
1.6383
0.0254
8 inner
Air space
0.04
1.0643
9 inner
Tin
0.07
1.0643
8 mid
Air space
0.06
1.0643
9 mid
Tin
0.07
1.0643
10 inner
Lead
0.1588
15.0343
8 outer
Air space
0.08
2.3343
9 outer
Tin
0.07
2.3343
10 outer
Lead
0.3175
2.3343
Dimensions of the Bicron Model .5M.390/.5L-X Nal(Tl) detec
tor and locally fabricated shield used in measurements and
calculations. Numbers (#) in the table are keyed to Figure
III.4.
aMaterials and thicknesses are proprietary information of
Bicron Corporation.

33
desirable to retain as much similarity to such a configura
tion as possible. The shield is employed to assist in re
taining this similarity in the small sodium iodide detector
by preventing large numbers of photons from striking the
sides of the crystal. The responses of a small detector,
taken at a number of positions, can then be used to simulate
a large detector. Additionally, considerably greater detail
is available with a small detector than with a large detec
tor which averages detailed response information over its
greater area. The purpose of the tin inner layer of the
shield is to prevent K fluorescent x rays produced in the
lead of the shield from entering the sides of the detector.
If this layer were not present and a lead layer was adjacent
to the detector, lead K fluorescent x rays from the lip of
the layer would enter through the side of the detector. The
high photoelectric cross section of tin at these energies
(72.794 to 87.343 keV) makes it an attractive material for
shielding lead x rays. The lower level discriminator of the
counting system is set high enough to preclude counting of
tin K fluorescent x rays (25.042 to 29.106 keV) (Storm and
Israel, 1970). The face of the Nal(Tl) crystal and the
bottom of the shield are at the same level to preclude
collimation of the detector. Collimators are attached to
the detector shield when such a configuration is desired. A
detailed description of the modeling of the detector
response function, including correction for edge effects and
the shield, is provided in Chapter VI.

34
The usual purpose of the lower level discriminator
setting of the counting system is to preclude pulse height
events corresponding to electronic noise. As described
above, an additional purpose in this detector system is to
prevent tin K fluorescent x rays, which could enter through
the sides of the detector, from being counted. A set of
radioactive sources is used to determine the relationship
between photon energy and lower level discriminator setting
(in combination with a fixed detector high voltage supply,
and amplifier and preamplifier settings). Sources and ener
gies used for this calibration are given in Table III.2. A
discriminator setting corresponding to 35 keV was selected
to prevent counting of spillover of the tin K ray peak as a
result of the resolution of the detector. Based upon the
Monte Carlo spectral and number albedo calculations (Chapter
IV provides examples), this setting results in only a small
reduction of the total detector response compared to the
case when no discrimination is used. The fluence spectral
calculations show that only when the source energy is small
is there any significant contribution below 35 keV. The
number albedo (the fraction of incident photons which are
reflected from a surface) calculations show that low energy
source photons produce significantly less backscatter than
high energy photons (this is true up to about 300 keV).
Additionally, results of the detector response calculation,
provided and described in Chapter VI show that low energy
photons produce a much lower response than all others except

35
TABLE III.2
Sources Used in Determining Lower
Level Discriminator Setting
Source
Energy (keV)a
109
Cd (Ag K. x ray) 22.162
n? a
Bs (Cs K x ray) 30.970
137 ai
Cs (Ba K x ray) 32.191
i -5 -a
JJBa (gamma) 80.999
^^Cd (gamma from ^^mAg) 88.037
57Co (gamma) 122.06135
aPhoton energy data are from Lederer and Shirley (1978).

36
very high energy photons (which pass through the detector
without significant interaction). The 35 keV value also
provides some safeguard for the lower level discriminator
setting determination from non-linearities observed in the
low energy response of Nal(Tl) (Aitken et al., 1967). The
light output and hence pulse height is not proportional to
the amount of energy deposited in the Nal(Tl) crystal for
low photon energies. Figure III.3 shows the detector and
shield. The slotted wooden structure supporting the
detector allows the distance between the beam axis and the
detector to be varied.
The detector is operated in a pulse counting mode. The
detector high voltage is supplied at -900 volts. Figure
III.5 provides a diagram of the components of the counting
system. Remote control of the counting system is by an
IEEE-488 General Purpose Interface Bus (GPIB).
Computer Control System
An IBM PC personal computer controls both the RS-232
serial interface bus, which operates the soil box position
ing system, and the IEEE-488 GPIB, which operates the
counting system. Software for these two functions was
provided by Moss (1986). The RS-232 serial interface bus
transmits the direction, distance and axis of motion to the
motor controllers. The GPIB controls the counting channel
and time through the counter/timer. The two systems are
integrated by the computer to allow complete automation of
the scanning and counting tasks required to produce an

Figure III.5. Components of the counting system

38
image. Independent operation of the positioning and count
ing systems is also possible.
Simple graphical display programs, written in Turbo
Pascal (Borland, 1985), are used to rapidly analyze the
image data. These programs accept the data files produced
by the counting system control program.
Materials
Soils
Three soil types are selected for calculations to
represent a range of soil properties. Norfolk sandy loam
(Jaeger, 1975) has a high silicon dioxide content and is
similar to the North Central Florida sandy soil used in the
measurements. Hagerstown loam (Bear, 1955) is close to the
average of all soil types examined in elemental composition.
Malatula clay loam is a lateritic soil with high iron con
tent. Lateritic soils are produced under conditions of high
rainfall and high temperatures. These conditions, over geo
logic periods of time, lead to the decomposition of organic
materials and selected minerals. The result is a soil low
in silicon dioxide and high in hydrated oxides of iron and
aluminum (Bear, 1955). A global average soil constructed
from the average elemental composition of the crust of the
earth is also used in some calculations (Jaeger, 1975).
This global average soil is very similar in its photon in
teraction properties to Hagerstown loam. Hereafter, these
soils will be referred to as NSL (Norfolk sandy loam), HTL
(Hagerstown loam), MCL (Malatula clay loam) and GAD (global

39
average). The elemental compositions, densities and weight
percentages of water of these soils are given in Table
III.3. A comparison of the mass attenuation coefficients of
the NSL, HTL and MCL soils is given in Figure III.6. The
coefficients are calculated from Hubbell's data (1982).
Nonmetallic Antitank Mine Model
Nonmetallic antitank mines of the Warsaw Pact are the
subject of the mine detection effort. Nonmetallic mines are
important subjects for study because of the difficult prob
lem they present to all current mine detector types and
because their implications to changes in U.S. operational
doctrine. Metallic mines are not considered since other
techniques are more applicable to their detection. While
nonmetallic antipersonnel mines are also very difficult to
detect, they are a secondary concern for mounted armor
combat operations. Also, while buried, surface laid, and
scatterable mines would be employed in any large scale
conflict in Europe, this study concerns itself primarily
with the buried mine, the more difficult detection problem.
Table III.4 provides characteristics of several common
conventional Warsaw pact nonmetallic landmines. The TST
mine, listed in the table for the purpose of comparison, is
the model used in experiments and calculations. As indi
cated by the table, it is representative of common Warsaw
pack nonmetallic antitank mines.
The TST model consists of a lucite, right circular
cylinder, with 0.635 cm thick walls and outside diameter of

40
TABLE III.3
Composition of Soil Types
Element
Weight
NSL
Percentage of
HTL
Elements
GAD
in Dry Soils3
MCL
H
0.070
0.185
-

C
0.502
1.320
-
-
0
52.627
49.637
47.330
38.702
Na
0.082
0.629
2.840
0.052
Mg
0.054
0.674
2.110
0.784
Al
1.095
6.236
8.240
18.955
Si
44.142
34.330
28.100
1.730
P
0.026
0.086
-
0.493
S
0.028
0.162
-
-
K
0.083
2.327
2.640
0.075
Ca
0.278
0.688
3.650
0.129
Ti
0.425
0.626
-
8.035
Mn
0.008
0.040
-
0.504
Fe
0.580
3.061
5.090
30.578
aData for NSL and GAD are from Jaeger
and MCL are from Bear (1955).
Density and Moisture
(1975)
Ranges
. Data for HTL
Soil Type
Density Range*3
(q/cm )
Moisture
(%)
_ b
Range
NSL
1.40 -
1.96
5 -
25
HTL
0.96 -
2.17
8 -
25
GAD
0.96 -
2.17
10 -
30
MCL
0.080 -
1.80
15 -
30
^Data from Hough (1957) and Chilton et al. (1984).

Figure III.6. Soil mass attenuation coefficients. The mass attenuation coefficients
(cm /g) of the three soils used in the majority of the calculations, Malatula clay
loam (MCL), Hagerstown loam (HTL), and Norfolk sandy loam (NSL) are displayed. The
mass attenuation coefficients for trinitrotoluene (TNT), the explosive contained in
most mines, are also shown for comparison.

42
TABLE III.4
Characteristics of Common
Nonmetallic Antitank
Warsaw Pact
Mines
Mine
Country
Mass
(kg)
Diameter
(cm)
Height
(cm)
Expl.
Type
Expl.
Mass (kg)
PM-60
GDR
11.3
32
12
TNT
8.6
TM-60
USSR
11.3
32
11.7
TNT
7.5
TMB-2
USSR
7.0
27.4
15.5
TNT or
AMATOL
5.0
PT-Mi-
Ba-III
CZECH
9.9
32.2
10.2
TNT
5.6
TST
N/A
10.3
30.2
variable
sucrose
7.5
Table adapted from U.S. Department of the Army, TRADOC
Threat Monograph, Comparison of Selected NATO and Warsaw
Pact Engineer Organizations and Equipment (U.S. Army
Training and Doctrine Command, Fort Monroe, VA, 1979b),
p. 88.

43
30.16 cm. The cylinder is 14.60 cm high and has two 0.635
cm thick covers for the top and bottom. An aluminum cylin
der with 0.24 cm thick walls, outside diameter of 28.89 cm
and height of 8.57 cm fits inside the lucite cylinder and
holds the explosive substitute material. Only the top 7.50
cm of the aluminum cylinder is filled with explosive mater
ial. Its lower portion is separated from this material by a
0.24 cm thick base plate. The 0.83 cm high curtain below
the aluminum base plate is drilled with three holes at 120
degree intervals. These holes align with five sets of three
holes in the lucite cylinder and are used to allow variable
setting of the air gap located between the top lucite cover
and the explosive substitute material. The aluminum con
tainer of the model provides structural support for the
heavy explosive substitute portion of the mine. Addition
ally, it served as the mold for the molten substitute
material when it was prepared. Aluminum is very similar to
soil in its photon scattering properties, and, as such, is
an acceptable wall material for the backscatter radiation
method of mine detection. Due to its metallic content, it
would be an unacceptable model for many other detection
methods. Figure III.7 shows the TST mine used in the
measurements.
Since actual explosive materials present safety and
administrative problems, a substitute material is required.
Since TNT is the most commonly used explosive in landmine,
it serves as the standard against which substitute materials

Figure III.7. TST mine used in measurements. The TST mine is designed to simulate
nonmetallic antitank mines. The upper layer of the mine cylinder, whose thickness
can be varied, contains air. The lower portion contains the explosive substitute
material. A detailed description of the geometry and materials of the TST mine is
provided in the text.

UT

46
are compared. Previous studies made use of dinitrobenzene
as a TNT substitute. Unfortunately, this material is toxic.
Evaluation of a number of common nontoxic materials is made
by comparing linear interaction coefficients with those of
TNT. Sucrose is selected as the substitute. Table III.5
shows the comparison of the interaction coefficients of TNT
and sucrose.
TM
The explosive substitute is solidified Karo Light
Corn Syrup. While this material is not sucrose, it has
similar elemental composition and photon interaction
characteristics. Upon heating, a portion of the fructose
contained in the syrup is converted to sucrose. A number of
test batches of the substitute are made by removing water
from the syrup by heating. When the capability to consis-
tently obtain the same material density (1.56 g/cm ) is
achieved, samples are used in the tests described below and
found to be an acceptable substitute for TNT.
Materials Tests
Tests of photon interaction characteristics of the
explosive substitute and soil materials are conducted to
insure that the cross section sets used in the Monte Carlo
photon transport calculations are adequate. As described
TM
above, the TNT substitute is solidified Karo Light Corn
3
Syrup with a density of 1.56 g/cm The soil used in the
experiments is obtained locally. Its high sand content
suggests that it is similar to the Norfolk Sandy Loam (NSL)
soil described above. Samples of each of these materials

47
TABLE III.5
Ratios of the Linear Interaction
Coefficients of Sucrose to TNT
Energy
(MeV)
Coherent
Interaction Coefficient Ratios3
Incoherent Photoelectric
Total
0.010
0.9379
1.0257
0.9505
0.9524
0.015
0.9346
1.0171
0.9520
0.9581
0.020
0.9336
1.0117
0.9528
0.9652
0.030
0.9335
1.0062
0.9540
0.9789
0.040
0.9334
1.0037
0.9545
0.9873
0.050
0.9334
1.0024
0.9547
0.9919
0.060
0.9334
1.0017
0.9559
0.9944
0.080
0.9334
1.0008
0.9548
0.9967
0.100
0.9335
1.0004
0.9571
0.9978
0.150
0.9333
1.0000
0.9571
0.9987
0.200
0.9338
0.9998
0.9572
0.9991
0.300
0.9338
0.9997
0.9572
0.9994
0.400
0.9339
0.9996
0.9572
0.9994
0.500
0.9339
0.9996
0.9583
0.9995
0.600
0.9339
0.9996
0.9586
0.9995
0.800
0.9340
0.9996
0.9581
0.9995
1.000
0.9339
0.9996
0.9583
0.9996
aSucrose density: 1.588 g/cm3; TNT density: 1.654 g/cm3
(Weast, 1967). For the purpose of backscatter radiation
effects, the two interaction coefficient ratios of the most
importance in evaluating a substitute material are the
incoherent and total coefficients. Coefficient data are
from Hubbell et al. (1975) and Hubbell (1982).

48
are placed in the beams of various spectra produced by the
GE Maxitron 300 X-Ray Therapy Unit. Before the materials
tests are conducted, each of the four energy spectra
utilized in the measurements is itself tested using exposure
attenuation by added aluminum filtration as described in
Chapter V. The conditions required for formal half value
layer measurements are observed in these measurements and in
the materials tests (Johns and Cunningham, 1983). The
transmission of exposure rate is also calculated using the
method described in Chapter V for NSL (three sets of data
for NSL at different density and moisture contents) and TNT.
TM
Seven thicknesses of the solidified Karo Light Corn
Syrup are each subjected to the four spectra: 80, 100, 150,
and 200 KVp, each filtered by 4.75 mm of beryllium inherent
filtration, 0.25 mm aluminum equivalent monitor chamber,
3.19 mm of aluminum added filtration, and an air path of
67.31 cm. Figure III.8 compares the measured exposure rate
transmissions with those calculated. Perfect agreement
would occur if the ratio for each sample of measurement to
calculation is 1.00 or, in terms of the figure, if the plot
ted points lie on the line of slope equal to 1.00.
Agreement is very good, and the explosive substitute is
deemed adequate.
For each of the four beam energies listed above, three
sets of five soil samples are prepared (60 samples in to
tal). Multiple samples are used because of the variability
in composition, density and moisture content characteristic

Figure III.8. Transmission comparison for TNT and substitute. A comparison of the
measured transmission of exposure rates produced by samples of the explosive sub
stitute material, and the calculated attenuation of exposure rates of TNT for the
same thicknesses as the substitute samples is shown. Calculations were performed by
the XRSPEC.PAS code (described in Chapter V).
VO

50
of the soil. Two of the sets of samples differed only in
density; the compacted set density is measured to be 1.579
3 3
g/cm and the loose soil set, 1.450 g/cm Both have an
average moisture content of 3.26%. The third set differs
both in moisture content and density. It is prepared by
heating the soil to remove all moisture. The density of
3
this soil is 1.62 g/cm The increase in density with loss
of water is a result of combustion of low density organic
matter in the soil during heating. All samples are of the
same thickness. Exposure transmission measurements and
calculations are compared in Figure III.9. Agreement is
very good, indicating that the local soil is, as suspected,
close to NSL soil in its photon interaction properties.

Figure III.9. Transmission comparison for NSL and local soil. A comparison of the
measured transmission of exposure rates produced by sets of samples of the locally
available soil, and the calculated attenuation of exposure rates of NSL soil for the
same thicknesses as the local soil samples is shown. Calculations were performed by
the XRSPEC.PAS code (described in Chapter V).
cn

CHAPTER IV
RADIATION TRANSPORT
In the mine detection system, photons, originating from
an x-ray source, travel through air, and strike the soil.
The photons then undergo interactions with the soil and
objects buried within it. Some photons are scattered back
through the soil surface and strike the detector. This
chapter describes the fundamental photon interactions of
importance to the mine detection problem, the radiation
transport models used to simulate those interactions, and
their validation.
Photon Interactions
Photons interact with matter through a variety of
mechanisms. The energy range of interest for mine detection
and imaging (described in Chapter VII) results in only three
photon interactions of importance: coherent scattering,
incoherent scattering and the photoelectric effect. A brief
description of each of these interaction types is provided.
Coherent Scattering
Thomson gave the first description of the interaction
of an electromagnetic wave with a free electron (jammer,
1966). Applying purely classical physics to the interac
tion, he showed that the time varying electric field
52

53
associated with the electromagnetic wave would cause the
electron to oscillate with the same frequency as the field.
The resulting accelerated charged particle would then radi
ate an electromagnetic wave of this same frequency. Since
the frequency of the photon is unchanged, there is no change
in photon energy as a result of the coherent scattering
interaction. This elastic scattering process is known as
Thomson scattering. The solid angle differential cross
section (the probability of scatter into a unit solid angle
per electron per unit fluence incident on the electron) for
Thomson scattering is given by
where
daT
d fi
(1 +
2 v
cos eg)
F
da
^ is the solid angle differential Thomson
scattering cross section,
re is the classical radius of the electron,
0g is the scattering angle.
When the photon energy is such that its associated
wavelength is comparable in size to the atoms in the mater
ial in which it scatters, the interaction can no longer be
considered to be with a single free electron. The inter
action is now collectively with all the electrons of an
atom. These atomic electrons oscillate and radiate in
phase. The process is called coherent or Rayleigh scatter
ing. In this case the solid angle differential cross
section becomes

54
where is the solid angle differential coherent
scattering cross section,
F(x,Z) is the atomic form factor, which depends
upon the atomic number, Z, of the material
and the momentum transfer variable, x, given
by
x
where X is the wavelength of the photon.
The integral of the solid angle differential coherent
cross section gives the probability of coherent scattering
per atom per unit incident fluence,
2
(1 + cos20_)sin F2(x,Z)d6
s s s
e
b
where a ^ is the total coherent scattering cross section
per atom. Coherent scattering cross sections and atomic
form factors are provided in tabular form for all elements
by Hubbell et al. (1975). The square of the atomic form
factor represents the probability that the electrons of an
atom take up the recoil momentum of the interaction without
absorbing any of the incident photon's energy. Figure IV. 1
shows a graph of the atomic form factors of aluminum (Z=13)

F(x.Z)
Figure IV.1. Atomic form factor versus momentum transfer variable. Atomic form
factors for aluminum and iron are shown as a function of the momentum transfer
variable. Data are from Hubbell et al. (1975).

56
and iron (Z=26) as a function of x. At large values of x,
the atomic form factor and, hence, the probability of coher
ent interaction, is small. Large values of x correspond to
small photon wavelengths or high photon energies. The high
er the atomic number of the material, the larger the atomic
form factor at a given energy and scattering angle. Hence,
at a given energy, coherent scattering is more probable in
high Z materials than in low Z materials. The effect of the
atomic form factor term is to strongly peak the coherent
scattered photons in the forward direction. This forward
peaking is largest in low Z materials and at high energies.
Figure IV.2 displays these effects. Because of the forward
peaking and lack of change in energy, the typical coherently
scattered photon closely resembles the incident photon, and
many calculations ignore this interaction mechanism ./'in
terms of the mine detection problem, coherent backscatter
will be important only at relatively low energies, and will
have a larger effect in the soils containing the highest
portion of high Z elements^X Figure IV.3 shows the coherent
cross section of aluminum and iron as a function of photon
energy.
It should be noted that atomic form factors are avail
able only for individual atoms and a very few compounds.
Since coherent scattering is a cooperative process involving
all the electrons of an atom and the spatial distribution of
the electron density about an atom in a molecule is altered
relative to the free atom, the use of the available atomic

Figure IV.2. Solid angle differential coherent scattering cross section versus
scattering angle. The graph shows that for a given material, coherent scattering is
more forward peaked at higher energy, and for a given energy, coherent scattering in
any direction is greatest in the material with the higher atomic number.

Figure IV.3. Coherent cross section versus photon energy. The coherent scattering
cross section of aluminum and iron are shown. The material having the higher atomic
number has the higher coherent scattering cross section at all energies. Data for
the graph are from Hubbell et al. (1975).
<_n
00

59
form factors for compounds is only an approximation to
physical reality.
Incoherent Scattering
Compton (1923) first described photon inelastic scat
tering from a free electron. In his model of this inter
action, the photon strikes a free, stationary electron pro
ducing a new, lower energy, scattered photon and a recoil
electron. This free electron case will be approximately
correct if the energy of the incident photon is very large
in comparison with the binding energy of the electron to its
atom. Compton's formula for the dependence of the scattered
photon's energy on the energy of the incident photon and the
scattering angle is
E' =
E
l+a(l-cose ) '
S
where E' is the energy of the scattered photon,
E is the energy of the incident photon,
0g is the scattering angle, and
2 2
a = E/m c where me is the rest mass energy of the

electron (0.511 MeV).
This relationship plays a very important role in the
mine detection problem^ Figure IV.4 shows the fractional
energy (E'/E) in a Compton interaction as a function of in
cident photon energy for several scattering angles. The
fractional loss is greatest at high energies, and at a fixed
energy, for large scattering angles (backscattering). Since

Fraction of Incident Energy
Figure IV.4. Fractional energy of Compton scattered photons versus incident photon
energy. The graph shows that the fraction of energy retained by the scattered photon
is greatest for small scattering angles, and for low incident photon energies.

61
/high photon energies are required for deep penetration,
these two factors combine to make backscatter from signifi
cant depths in the soil difficulty/
The Klein-Nishina formula (Evans, 1955) gives the solid
angle differential scattering cross section for the inelas
tic scattering of an unpolarized photon from a free elec
tron ,
da
KN
1+cos 0
[l+a(1-cose )]
O
a2(1-cose )2
o
[l+a(l-cos0 )]
s
da
In this equation
KN
d fl
is the solid angle differential
Klein-Nishina cross section per electron. Figure IV.5 shows
the differential Klein-Nishina cross section as a function
of scattering angle for three energies. At low energies
forward scatter and backscatter are approximately equally
probable. As energy increases, scattering becomes more
forward peakedy/This fact increases the difficulty of the
backscatter detection of mines/ The use of higher energy
photons, which are capable of penetrating to great depths in
soil, will eventually lead to a lower backscattered fluence
due to this forward peaking and the two factors discussed
above with respect to Compton's energy/angle relationship^
In reality, photons are bound, and inelastic events at
energies at which the incident photon energy is not very

Figure IV.5. Solid angle differential Klein-Nishina cross section versus scattering
angle. The variation of the cross section with scattering angle is shown for three
incident photon energies. As the incident energy increases, backscattering becomes
less probable.
cr*
NJ

63
large compared to the atomic binding energy are not cor
rectly accounted for by the Klein-Nishina formula. The
Klein-Nishina formula is corrected by multiplication by the
incoherent scattering function, S(x,Z),
da
inc
dfi
da
KN
d fi
S(x,Z)
/
where
doinc
dft
is the solid angle differential incoherent
scattering cross section.
The incoherent scattering function represents the
probability that an atomic electron struck by a photon will
absorb energy and be excited or removed from the atom.
Figure IV. 6 shows the incoherent scattering function for
aluminum and iron as a function of the momentum transfer
variable. The function has the effect of decreasing the
Klein-Nishina cross section (per electron) with the re
duction being greatest at low energies and in high Z mater
ials. Figure IV.7 displays these effects. The incoherent
scattering cross section is given by the integral over solid
angle of the differential cross section
'2ir
ainc
"o
IT
da
KN
dft
S(x,Z)sin0 d0 d ,
s s
where a. is the total incoherent scattering cross section
xnc
per atom.
Tabulated values of the incoherent scattering cross
section are provided by Hubbell et al. (1975). Figure IV.8

x (Reciprocal Angstroms)
Figure IV.6. Incoherent scattering function versus momentum transfer variable. To
account for incoherent scattering from bound electrons/ the Klein-Nishina cross
section is multipled by the incoherent scattering function. Data are from Hubbell et
al. (1975).
a\

65
Figure IV.7. Comparison of the solid angle differential
Klein-Nishina and incoherent scattering cross sections. The
solid angle differential Klein-Nishina and incoherent scat
tering cross sections per electron (in units of barns per
steradian per electron) of aluminum and iron are compared at
20 keV (a) and 100 keV (b).

Figure IV.8 Incoherent scattering cross section versus photon energy. The inco
herent scattering cross section per electron of aluminum and iron are compared to the
Klein-Nishina cross section. The reduction from the Klein-Nishina cross section is
greatest at low energy and in the material with the higher atomic number. Data are
from Hubbell et al. (1975).

67
shows the incoherent scattering cross section per electron
of aluminum and iron, and that calculated from the integral
of the unmodified Klein-Nishina formula. /The Klein-Nishina
cross section overestimates the true incoherent cross sec
tion at low energy. The error in the Klein-Nishina cross
section is larger in high Z materials. Because the effect
of the incoherent scattering function is important only at
low energies, it is often neglected in calculations^" The
same caveat described in the discussion of the atomic form
factor, regarding atomic and molecular electron density
configurations, applies to the incoherent scattering func
tion.
Photoelectric Effect
In the photoelectric effect, an incident photon strikes
an atomic electron and is completely absorbed. The electron
is emitted from the atom with kinetic energy equal to the
difference in the incident photon energy and the binding
energy of the electron to the atom. If the interaction is
with an inner shell electron, the vacancy remaining after
the interaction will be filled, either producing a fluor
escent emission photon(s) or Auger electrons. In the energy
region of interest to the mine detection problem, the cross
section per atom for the photoelectric interaction varies
approximately as
Zn/E3
where n varies between 4.0 and 5.0 depending on photon
energy (Anderson, 1984). This approximation indicates the

68
photoelectric cross section will be large at low energies
and in high atomic number materials. Figure IV.9 shows the
variation of the photoelectric cross section of iodine
(Z=53), gadolinium (Z=64) and lead (Z=82) as a function of
photon energy (each of these materials plays a role in this
research). Superimposed on the variation with atomic number
and energy, discussed above, are edges. These sharp discon
tinuities in the cross sections are the result of the dis
crete binding energies of electrons in their atomic shells.
Below an edge energy, the incident photon does not possess
sufficient energy to overcome the binding energy of the
electrons in a particular shell. As photon energy increases
to just above the edge energy, this is no longer the case
and the cross section increases dramatically as a result of
the capability to remove the newly available electrons. As
a result of these edges, a lower atomic number material may
have a higher cross section for the photoelectric inter
action in an energy range below the edge energy of a higher
atomic number material.
Figure IV.10 shows the probability of K shell fluores
cent emission following the filling of a vacancy in the
inner atomic shell. /In low atomic number materials, this
probability is small; the alternate radiationless emission
of Auger electrons dominates (Evans, 1955). Since soil
and explosive materials contain generally low atomic number
elements, fluorescent emission from these materials is not
very probable./ Even in those few instances in which

Figure IV.9. Photoelectric interaction cross section versus photon energy. The
photoelectric interaction cross sections of iodine, gadolinium and lead are shown.
K, L and M edges of gadolinium and lead, and K and L edges of iodine occur within the
energy range of the graph. Data are from Storm and Israel (1970).

O 20 40 60 80 100
Atomic Number (Z)
Figure IV.10. Probability of K shell fluorescence versus atomic number. Data for
this graph are taken from reviews of measurements of the K fluorescent yield by Fink
et al. (1966) and Bambynek et al. (1972). The solid line is an empirical fit to the
data Bambynek et al. consider most reliable.

71
fluorescent emission does occur, the emitted photons will be
very low in energy due to the small binding energy of K
shell electrons in low Z materials. Figure IV.11 shows this
effect. These very low energy photons will be rapidly ab
sorbed near their point of origin and produce a negligible
contribution to the backscattered fluence. In materials
such as those of Figure IV.9, fluorescent emission plays an
important role and cannot be neglected. These materials are
associated with the detection of the scattered photons and
are discussed in Chapter VI and Appendix E. Emission of
fluorescent photons is isotropic.
Mass Interaction Coefficients
The interaction cross sections described above are
converted into mass interaction coefficients for use in the
transport models. For compounds and mixtures, the cross
section data from Hubbell et al. (1975) and elemental weight
fractions are used to construct the mass interaction co
efficients. In cases where edge effects are important,
the photoelectric data of Storm and Israel (1970) are also
used. These sets of mass interaction data are then expanded
by cubic spline interpolation into fine energy mesh tables
for use in the models. In cases where edge effects are
important, the cubic spline interpolations are performed
separately above and below the edges and then merged. The
mass interaction coefficient tables cover an energy range
from 1 keV to 1 MeV. The mesh structure used is given in

Figure IV.11. Energies of Ka^ fluorescent photons versus atomic number. The Ka. x
ray is the most probable fluorescent photon to be emitted. Data are from Storm and
Israel (1970).
to

Table IV.1. Supplementing this structure are table entries
for energies just above and just below edges.
73
> Figure IV.12 shows the mass interaction coefficients of
aluminum as a function of photon energy. The energy ranges
of dominance of the interactions are dependent on the atomic
number of the absorber. /The photoelectric effect dominates
at low energies; incoherent scattering, at higher energies.
In no case does coherent scattering dominate. Table IV.2
gives the approximate energy at which the photoelectric and
incoherent mass interaction coefficients are equal for
materials of interest to the mine detection problem^/
Single Scatter Model
A single scatter photon transport computer code,
SGLMIN.PAS, written in Turbo Pascal (Borland, 1985) provides
a simple introduction to the variables associated with the
mine detection problem. While multiple scatter plays a very
important role, this simple model has been used to provide
insights into many aspects of the mine detection problem.
Computation Scheme
The code computes the single scattered fluence to an
array of detector positions located above and parallel to
the soil surface. The parameters which can be varied in
calculations are energy of the incident photon beam, angle
of incidence of the beam, height of the detector plane above
the soil, soil type and density, depth of burial of the
mine, and the beam/soil/mine intercept position. For each
position in the array in the detector plane, the code

TABLE IV. 1
Energy Mesh Structure for
Mass Interaction Coefficients
Energy Range
(MeV)
Energy Increment
(MeV)
0.001 to 0.050 0.001
0.050 to 0.300 0.005
0.300 to 1.000
0.010

Figure IV.12. Mass interaction coefficients of aluminum versus photon energy. Mass
interaction coefficients (in units of cm /g) for coherent scattering (coh), incoher
ent scattering (inc), and photoelectric interaction (pe) of aluminum are shown. The
sum of these coefficients is the mass scatter coefficient total).

TABLE IV.2
Energy at Which Photoelectric
and Incoherent Scattering Mass Interaction
Coefficients Are Equal
Material
Effective Z
Energy (MeV)
Wood
6.525
0.025
Sucrose
6.704
0.026
TNT
6.919
0.026
Air
7.374
0.029
Quartz
10.805
0.046
NSL soil
10.905
0.048
HTL soil
11.381
0.053
Concrete
11.576
0.055
GAD soil
11.912
0.055
Aluminum
13.000
0.052
MCL soil
15.856
0.080
Iron
26.000
0.115
Sodium iodide
46.558
0. 260
Lead
82.000
0.550

77
computes the fluence per incident photon. This quantity is
obtained by calculating a series of probabilities. These
probabilities are of survival while passing through air from
the source to the soil plane, of survival while passing
through soil or mine to a scattering point, of undergoing an
incoherent scattering interaction in a small incremental
volume about a scattering point, of scattering into an in
cremental solid angle about a point in the detector array,
of survival while passing from the scattering point through
the soil or mine towards a point in the detector plane, and
of survival while passing through air from the soil plane to
a point in the detector plane. The product of these prob
abilities gives the desired fluence per incident photon at a
single point in the detector plane from a single incremental
scattering volume. The summation of such results from in
crements along the photon's path to a depth where the incre
mental response is negligible gives the total single scat
tered fluence per incident photon at a single point in the
detector array. This process is carried out for all points
in the detector array. Typically, the array consists of 421
points at a 10 cm increment within a 200 cm by 200 cm de
tector plane. A geometry routine calculates the distances
along the photon path through the various materials en
countered. A full three dimensional representation of the
TST mine with air and explosive layers is included in the
geometry routine. Output of results of calculations is

78
optionally to the computer terminal screen, hardcopy, disk
file and three-dimensional graphical display.
Interaction Modelling
The code uses the fine energy mesh mass interaction
coefficient data described previously in this chapter.
Log-log interpolation is used to determine values of the
coefficients at energies not provided within the fine mesh
tables. Coherent scattering is not included in the model.
Incoherent scattering includes modification of the Klein-
Nishina distribution by the incoherent scattering function.
Contributions due to fluorescent emission from soils or mine
following photoelectric interactions are neglected based
upon their low probability of occurrence in low Z materials,
and the very low energies (and, therefore, high attenuation)
characteristic of such photons when an infrequent emission
occurs. For example, the probability of K fluorescent emis
sion following a photoelectric interaction of a photon,
whose energy exceeds the K edge energy, with an aluminum
atom in soil is less than 2%. If a fluorescent photon were
produced (part of the less than 2%), its energy would be
1.486 keV (Storm and Israel, 1970) and would have a mean
-4
free path of about 2 x 10 cm in soil.
Monte Carlo Model
The majority of the calculations supporting this
research have been made with Monte Carlo computer codes.
Two versions of the radiation transport code have been used.
MCPHOT.PAS is written in Turbo Pascal (Borland, 1985) for

79
use on personal computers. MCPHOT.P is written in Green
Hills Pascal (Green Hills, 1984) for use with the Definicon
DSI-32 coprocessor (Marshall et al., 1985) which provides
increased speed of calculation. Appendix G provides addi
tional information about this device. The two codes are
essentially identical in most respects, although calcula
tions of angular spectra are included in the MCPHOT.P code
to support computations for collimated detectors.
The Monte Carlo transport codes follow the histories of
monoenergetic photons from their source to the detector
plane. The detector response function, described in detail
in Chapter VI, which is also the result of a Monte Carlo
calculation, couples directly to the energies and angles of
incidence of the photons striking the detector plane. The
results of the calculation of the x-ray spectrum, described
in Chapter V, are used to weight the monoenergetic Monte
Carlo transport calculations to account for polychromatic
sources. This technique allows the monoenergetic calcula
tions to be used with any x-ray source spectrum, producing a
considerable reduction in computation time from the alter
native of sampling of a spectrum within the transport
calculation.
Appendix H provides details for the techniques used to
sample the more complex probability density functions
encountered in the Monte Carlo code. Also included in this
appendix are details concerning the random number generators
used in the Monte Carlo codes and the technique for applying
the monoenergetic source results to polychromatic sources.

80
Problem Parameters and Data
Each of the Monte Carlo codes begins with the input of
problem data. These inputs are the photon interaction data
of air, soil and explosive, material densities, mine ge
ometry, and problem parameters. The photon interaction data
are the mass interaction coefficient files for coherent
scattering, incoherent scattering and the photoelectric
effect, the atomic form factors, incoherent scattering
functions and an integral used for sampling the coherent
scattering distribution (described in Appendix H). The mass
interaction data are read from files constructed using the
fine energy mesh described previously. The atomic form
factors and incoherent scattering functions are read from
files constructed in the same 45 value format as the tables
which appear in Hubbell et al. (1975). The integral asso
ciated with coherent scattering is also read from files
arranged in a 45 value format. Interactive input provides
the parameters for the particular problem. The parameters
available are initial photon energy, angle of incidence,
source height, beam geometry, soil type, height and extent
of detector plane, mine type, explosive type, depth of
burial of mine, beam/soil/mine intercept position, and
number of photon histories to be followed. Three beam
geometries are allowed: parallel beam, diverging circular
beam and diverging rectangular beam.

81
Random Number Generators
The Monte Carlo codes are prolific users of random
numbers uniformly distributed on an interval between 0 and
1. For example, tests at 150 keV with the TST mine at 1.5
cm depth of burial in HTL soil showed that an average of 80
random number calls were made per photon. Since calcula
tions employing 200,000 photons are not unusual, it is
apparent that the period of the random number generator used
should be long. Random number generators are not actually
random; all follow fixed rules for producing a sequence of
numbers with a cycle length characteristic of the technique
used. The period of the generator refers to how many random
numbers can be generated before the sequence repeats. Prob
lems with short periods of random number generators employed
on personal computers are common (Whitney, 1984; Wichmann
and Hill, 1987). In the interest of speed of computation,
multiplicative and linear congruential random number gener
ators are used. Implementations of these types of random
number generators, which use integer arithmetic, are effi
cient and fast, but subject to machine dependent period
constraints. The general form of these generators is
Ij+-^ = [alj + c] mod m ,
where m is the modulus, a is the multiplier and c is the
increment. The modulus operator (mod) requires division of
the bracketed quantity by m and retention of the remainder.

82
To obtain a random number between 0 and 1, the result of the
above operation is divided by m + 1. In a multiplicative
congruential generator, c is equal to zero. Unless care is
taken to avoid improper selection of the values of the con
stants, seriously flawed generators can be produced (Press
et al., 1986). The constants used in the random number
generators (detailed in Appendix H) in the MCPHOT.PAS and
MCPHOT.P codes are well established and recommended.
The Compaq Deskpro (Compaq, 1984a) used for the MCPHOT.
PAS calculations is based upon the Intel 8086 computer chip.
The 16 bit words of this machine allow only 65,535 distinct
integer values. Employment of a linear congruential method
on such a machine results in a maximum period of the same
size, provided optimum values of a, c, and m are chosen.
This is clearly unacceptable for the problem at hand. The
method selected for use in the MCPHOT.PAS code is a multi
plicative congruential form, which uses real numbers, sug
gested by Cheney and Kincaid (1980). An 8087 math coproces
sor (8087-2 for the Compaq Deskpro) and the 8087 supported
version of Turbo Pascal must be employed with this method to
obtain 16 digit real precision (Borland, 1985) required by
the algorithm. The maximum period of this generator is on
30
the order of one billion (2 ) random numbers (Cheney and
Kincaid, 1980). The penalty paid for this long period is
reduced speed due to real number arithmetic (Norton, 1986) .
The Definicon DSI-32 coprocessor used with the MCPHOT.P code
is based upon the National Semiconductor 32032 computer chip

83
(Definicon Systems/ 1986). This machine allows for more
. . 32
than four billion distinct integers (2 -1), and makes the
use of fast, integer based random number generators with
long periods possible. The algorithm selected is a linear
congruential method suggested by Dyck et al. (1984). The
maximum period of this generator is approximately one-half
billion (Forsythe et al./ 1977).
Computation Scheme
Based upon selection of a particular beam geometry and
angle of incidence/ photons are individually started from
the source position. Random numbers are used to determine
the position, and in the case of diverging beams, the direc
tion of the photon within the beam. Each photon begins its
history with the initial energy assigned in the input, a
weight of 1.00, and series of integer codes which indicate
that it has not yet been involved in a scattering event,
that it is initially traveling in air, and that it is not at
any of the material boundaries of the problem.
Based upon the photon's position and direction of
travel, the distance to the next material boundary is com
puted. In the case of the photon just emitted from the
source, this first boundary is the soil, but thereafter any
of seven boundaries are possible. Figure IV.13 shows the
boundaries and material indices used in the calculation. A
series of geometry routines determine which of the boundar
ies the photon will intercept if it continues on its path

84
A
A


Figure IV.13. Boundaries and materials of Monte Carlo
calculations. Triangles indicate boundaries; circles/
materials. The boundaries are the detector plane (1)/ the
soil surface (2), the top of the mine (3), the air-explosive
interface in the mine (4), the bottom of the mine (5), the
cylinder wall in the air region of the mine (6), and the
cylinder wall in the explosive region of the mine (7). The
materials are air above the soil (1)/ soil (2), air within
the mine (3), and explosive (4). The detector plane boun
dary exists only for photons travelling upward/ away from
the soil plane.

85
without interaction, and then, which of those boundaries is
closest and its distance.
Based upon the material in which the photon is travel
ing, a calculation of the distance to interaction is made.
While the distance any single photon travels before inter
acting is not predictable, the distribution of the distances
for a large number of photons is
p(x) = yexp(-yx),
where p(x) is the probability density function describing
the distribution of distances travelled to an
interaction,
y is the linear attenuation coefficient for the
material in which the photon travels at the
photon's energy,
x is the distance to first interaction.
This distance- distribution is sampled using random numbers
by the relationship
x = -(1.0/y) ln(rn),
where rn is a random number uniformly distributed between 0
and 1. The linear attenuation coefficient is obtained by
summing the mass interaction coefficients at the photon
energy for the appropriate material and then multiplying by
the material density.
The distances to the next boundary and to interaction
are then compared. If the boundary distance is smaller, the
photon is placed at the boundary and allowed to continue in

86
the same direction of travel in the new material. A routine
in the code determines the new material index by examining
the position and direction of travel of the photon. This is
true unless the boundary is that of the detector plane. In
this case the photon is scored. A number of pieces of in
formation are extracted during the scoring process. They
include the weight and energy of the photon, the detector
response produced by the photon, the number of scattering
events the photon has undergone, the position in the
detector plane of the photon intercept, and the angle of
incidence of the photon on the detector plane.
If the interaction distance is smaller, the position of
interaction is calculated, and the type of interaction is
determined. Because photoelectric effect interactions
cannot contribute to the scattered fluence at the detector,
and fluorescent emission is not important, a weighting
technique is used to force all photons to scatter, greatly
increasing the efficiency of the calculation. The weighting
factor applied at each scattering event is given by
^coh + ^inc
t
u
where each of the interaction coefficients is found by
table look-up at the photon energy in the material of the
interaction. This weighting factor represents the proba
bility that the interaction is a scattering event and is,
therefore, a number less than one. Since incoherent scat
tering events lower the energy of the resulting photon and

87
since the cross section for the photoelectric effect becomes
larger as energy decreases, the weighting factor decreases
with each incoherent scattering interaction. The type of
interaction is forced by this weighting procedure to either
be a coherent or incoherent scattering event. The type of
interaction is determined by finding the ratio,
^coh
and comparing it to a random number. In this ratio, y is
the linear photoelectric interaction coefficient. This
ratio is the probability that the scattering event is co
herent. If the random number is less than the ratio, the
interaction is a coherent scattering event; otherwise, it is
an incoherent scattering event.
Modeling Scattering Interactions
If the interaction is determined to be a coherent scat
tering event, the probability density function,
p(^)
da
coh
d?r
coh
f
must be sampled to determine the direction of the scattered
photon. Conventional rejection techniques are inefficient
for sampling this distribution (Williamson, 1983a). The
technique used is a combination of inversion and rejection
sampling (Carter and Cashwell, 1977; Williamson and Morin,
1983a). It is described in detail in Appendix H.

88
If the interaction is determined to be an incoherent
scattering event, a rejection method described by Carter and
Cashwell (1977) is used to sample the direction of scatter.
The probability density function to be sampled is given by
the ratio of the differential incoherent scattering cross
section to the total incoherent scattering cross section,
p( fl) =
da-
me
dQ
a.
me
As described in Appendix H, this technique requires that the
Klein-Nishina distribution be sampled for scattering direc
tion as a first step in the method. The Kahn method (Kahn,
1956) for performing this sampling is selected based upon
efficiency and calculation speed comparisons by Bloomquist
and Gelbard (1983).
Regardless of the type of scattering event which oc
curs, the routines in the codes return a scattering angle
(in terms of the cosine of the scattering angle) with re
spect to the initial direction of the photon. The energy of
a coherently scattered photon is unchanged; that of an
incoherently scattered photon is altered by the Compton
energy/scattering angle relationship. The scattering angle
specifies the polar angle with respect to the initial photon
direction. The azimuthal angle is uniformly distributed and
is sampled by selecting a random number and multiplying by
2tt. Given these two angles, the direction cosines with re
spect to the initial photon direction are defined. A

89
routine in the Monte Carlo codes then uses the precollision
direction cosines and the scatter direction cosines with
respect to the initial direction to calculate the new
direction cosines with respect to the coordinate system of
the problem. An algorithm given by Carter and Cashwell
(1977) is used for this pupose.
Russian Roulette
Before allowing a scattered photon to recycle through
the scheme described, the photon is examined to determine if
Russian roulette should be played. The criteria for
subjecting the photon to Russian roulette are that the
photon be located well outside or below the mine and be
moving away from the mine, or that the photon be at least 1
cm below the soil surface and have an energy of 20 keV or
less, or that the photon has a weight of 0.05 or less. The
Russian roulette method used in the code selects a random
number and compares it to 0.5. If the random number is less
than 0.5, the photon's weight is increased by a factor of
two, and it is allowed to travel to the next boundary or
interaction. If the random number is greater than 0.5, the
photon is terminated and a new photon is started. The
Russian roulette routine is used to save computation time
from being applied to photons which are not likely to
contribute significantly to the backscattered fluence.
Code Output
Code output is to terminal screen, printer, and dis
kette files. The hardcopy output includes a recapitulation

90
of the problem parameters, summary statistics, energy
spectrum of the backscattered fluence, and angular spectral
information to support calculations for collimated detector
geometries (MCPHOT.P only). The diskette file output is the
spatial distribution of the backscattered fluence and
detector response.
Validation of the Monte Carlo Codes
The MCPHOT.PAS and MCPHOT.P codes include detailed
consideration of coherent and incoherent scattering because
of the importance of low energy photons to the backscatter
mine detection problem. Published literature on backscatter
effects is rarely concerned with the low energy regime of
interest in this research. When such results at low energy
are published, these detailed effects are ignored. In order
to allow comparison with published results, the more sophis
ticated coherent and incoherent scattering routines must be
replaced by routines which neglect coherent scatter entirely
and use the Klein-Nishina distribution for incoherent scat
ter. Two separate comparisons are made with published re
sults. One is made at the simplified level; a second, with
the fully developed scattering routines employed. This dual
comparison also provides information on the range of appli
cability of the simplified approach. The fully developed
scattering routines are validated separately from the Monte
Carlo transport codes, and by comparison with a general
purpose, mainframe computer code.

91
Number and Energy Albedo Calculations
Number and energy albedos are the fractions of the num
ber and energy of source photons which are reflected from a
surface. Berger and Raso (1960) and Raso (1963) provide re
sults of Monte Carlo calculations for number and energy
albedos. Table IV.3 compares the results of their calcula
tions for iron with those of the MCPHOT.PAS code without the
full coherent and incoherent scattering routines. Tables
IV.4 and IV.5 compare the same published data for concrete
(Chilton et al., 1984) with those of the MCPHOT.PAS code,
both with and without the fully developed scattering rou
tines. As is apparent from the tables, comparisons are ex
cellent for the simplified codes. Figure IV.14 compares the
number albedo calculations for concrete by the MCPHOT.PAS
code with and without the fully developed scattering rou
tines. The differences are significant only at low energies.
Energy Spectra Comparisons
Minato (1973) provides energy spectra of the back-
scattered fluence from aluminum and iron at several ener
gies. Figures IV.15 through IV.17 show comparisons of
Minato's spectra with calculations by the MCPHOT.PAS code.
Agreement is very good.
Comparison with Buried Mine Calculations
Coleman (1971) provides results of Monte Carlo calcula
tions at three energies for buried mines. The mine model
used in these calculations is a right circular cylinder with
a radius of 11.43 cm and a thickness of 8.636 cm (Coleman,

92
TABLE IV. 3
Comparisons of Number and Energy
Albedo Calculations for Iron
Energy
(MeV)
Perpendicular Incidence
Number
Albedo
Berger and
Raso (1960)
Simple3
MCPHOT.PAS
0.10
0.042
0.042
0.003
0.002
0.20
0.106
0.105
0.004
0.003
0.50
0.149
0.146
0.005
0.004
1.00
0.141
0.135
0.005
0.003
Energy Albedo
Energy
(MeV)
Berger and
Raso (1960)
Simple3
MCPHOT.PAS
0.10
0.032
0.032
0.004
0.003
0.20
0.063
0.062
0.005
0.004
0.50
0.054
0.053
0.004
0.003
1.00
0.031
0.030
0.002
0.002
aSee text for description.

93
TABLE IV.4
Comparisons of Number
Albedo Calculations for Concrete
Perpendicular
Incidence
Number Albedo
Energy
(MeV)
Berger and
Raso (1960)
Raso
(1963)
Simple3
MCPHOT.PAS
Full3
MCPHOT.PAS
0.01
-
-
0.0018
0.0002
0.0039
0.0003
0.015
-
-
0.0047
0.0004
0.0074
0.0005
0.020
0.008
0.002
-
0.0084
0.0003
0.0119
0.0004
0.03
-
-
0.0225
0.0015
0.0285
0.0015
0.04
-
-
0.0457
0.0013
0.0529
0.0012
0.05
0.076
0.004
-
0.0761
0.0011
0.0808
0.0012
0.07
-
-
0.1386
0.0024
0.1419
0.0025
0.10
0.213
0.006
-
0.2098
0.0022
0.2243
0.0034
0.15
-
-
0.2647
0.0010
0.2638
0.0032
0.20
0.285
0.006
0.285
0.006
0.2873
0.0026
0.2891
0.0032
0.25
-
-
0.2901
0.0032
0.2992
0.0046
0.50
0.268
0.006
0.275
0.006
0.2810
0.0040
-
1.00
0.221
0.006
0.207
0.006
0.2140
0.0040
aSee text for description.

94
TABLE IV. 5
Comparisons of Energy
Albedo Calculations for Concrete
Perpendicular Incidence
Energy Albedo
Energy
(MeV)
Berger and
Raso (1960)
Raso
(1963)
Simple3
MCPHOT.PAS
Full3
MCPHOT.PAS
0.01
-
-
0.0018
0.0004
0.0038
0.0006
0.015
-
-
0.0045
0.0008
0.0072
0.0010
0.02
0.008
0.004
-
0.0078
0.0006
0.0113
0.0007
0.03
-
-
0.0204
0.0027
0.0261
0.0019
0.04
-
-
0.0403
0.0023
0.0469
0.0025
0.05
0.065
0.006
-
0.0650
0.0018
0.0692
0.0021
0.07
-
-
0.1105
0.0039
0.1133
0.0040
0.10
0.153
0.008
-
0.1515
0.0031
0.1630
0.0050
0.15
-
-
0.1640
0.0013
0.1633
0.0032
0.20
0.154
0.007
-
0.1556
0.0028
0.1564
0.0022
0.25
-
-
0.1406
0.0031
0.1429
0.0044
0.50
0.085
0.004
0.087
0.004
0.0880
0.0030
-
1.00
0.041
0.002
0.038
0.002
0.0410
0.0020
a
See text for description.

Figure IV.14. Number albedo versus energy for concrete. Calculated values of the
number albedo for the case of perpendicular incidence as a function of incident
photon energy are compared. The Berger and Raso (1960) values agree well with the
simple MCPHOT code calculations. Both neglect coherent scattering, and use only the
Klein-Nishina scattering distribution. The full MCPHOT code calculation includes
coherent scattering and incoherent scattering from bound electrons.
U1

Figure IV.15. Backscattered energy spectrum, 0.200 MeV on aluminum. Calculations
are for perpendicular incidence of 0.200 MeV photons on aluminum by Minato (1973) and
the simple MCPHOT are compared.

Photons/MeV/Incident Photon
Figure IV.16. Backscattered energy spectrum, 0.6616 MeV on aluminum. Calculations
are for perpendicular incidence of 0.6616 MeV photons on aluminum by Minato (1973)
and the simple MCPHOT are compared.

Photons/MeV/Incident Photon
Figure IV.17. Backscattered energy spectrum, 0.6616 MeV on iron. Calculations are
for perpendicular incidence of 0.6616 MeV photons on iron by Minato (1973) and the
simple MCPHOT are compared.

99
1971) or 8.890 cm (Roder and Van Konyenburg, 1975). The
mine is composed entirely of dinitrobenzene (DNB) at a
3
density of 1.44 g/cm ; no air space is considered. The soil
(hereafter identified as FTB) composition used in the cal
culations is from samples taken at Fort Belvoir, Virginia.
3
The soil density used is 1.30 g/cm The code used for the
calculations does not consider coherent scattering and uses
the Klein-Nishina distribution without modification by the
incoherent scattering factor. Photon interaction data sets
were constructed for FTB soil and DNB to allow calculations
using the MCPHOT.P code. Coleman's values of the number
albedo from soil only and with mine present are compared
with calculations by the MCPHOT.P code in Table IV.6. The
comparisons are very good.
Testing the Scattering Routines
The sampling techniques used for coherent and incoher
ent scattering are tested by comparison with analytical cal
culations of the respective solid angle differential scat
tering cross section as a function of the cosine of the
scattering angle. The same routines employed in the MCPHOT.
PAS and MCPHOT.P codes are used to sample the cosine of the
scattering angle for coherent and incoherent scattering.
These codes are run for 100,000 samples with the cosines of
the scattering angles binned in increments of 0.02. Figures
IV.18 and IV.19 compare the analytical and Monte Carlo cal
culations of the solid angle differential scattering cross
section as a function of the cosine of the scattering angle

100
TABLE IV.6
Comparisons of Number Albedo
Calculations for FTB Soil and Buried DNB Mines
Energy
Depth of
Number
Albedo
(MeV)
Burial (cm)
Coleman
(1971)
MCPHOT.P
0.070
Soil only
0.117
+
0. 002
0.1162

0.0110
0.120
Soil only
0.2094
+
0.0014
0.215
+
0.003
0.130
Soil only
0.2204
0.0015
0.200
Soil only
0.256
+
0.004
0.2634

0.0016
0.070
5.08
0.119

0.002
0.1196
+
0.0011
0.120
5.08
0.227
+
0.003a
0.2257

0.0015
0.130
5.08
0.2380

0.0009
0.200
10.16
0.259
+
0.004
0.2627
+
0.0016
aColeman
provides a calculation
for
a range
between
0
.120
and 0.130 MeV with uniform distribution of source energies.

*
Figure IV.18. Comparison of calculations of the solid angle differential coherent
cross section. Analytical and Monte Carlo calculations of the solid angle coherent
scattering cross section are compared for 20 keV photons on aluminum. The Monte
Carlo sampling technique used here is also employed in the MCPHOT codes. 100,000
photon histories are used in the Monte Carlo calculation.
101

Figure IV.19. Comparison of calculations of the solid angle differential incoherent
cross section. Analytical and Monte Carlo calculations of the solid angle incoherent
scattering cross section are compared for 50 keV photons on aluminum. The Monte
Carlo sampling technique used here is also employed in the MCPHOT codes. 100,000
photon histories are used in the Monte Carlo calculation.
102

103
for coherent and incoherent scattering. The comparisons are
very good.
An additional test of the scattering routines and the
entire code was made by comparing MCPHOT.P results with
those of the MCNP code (Briesmesiter, 1986). MCNP is a
general purpose Monte Carlo code developed at Los Alamos
National Laboratory for neutron and photon transport. It is
a widely accepted standard code for mainframe computer use
in nuclear engineering and weapons applications. An option
in the MCNP code allows full treatment of photon scattering
using atomic form factors and the incoherent scattering
function. A buried mine problem was run using the MCNP code
on a Cray X-MP/48 computer and compared to the same calcula
tion using the MCPHOT.P code on the Definicon DSI-32. In
order to conserve central processing unit time on the Cray
computer, the problem was limited to a cylinder of 50 cm
radius about the beam axis. The MCPHOT.P code was modified
for this same constraint. The only difference between the
two calculations was to allow the MCNP code to model photo
electric interactions with subsequent fluorescent emissions.
This was done to test the assumption in the MCPHOT.P code
that fluorescent emission from soil and mine materials could
be ignored. Comparisons were made with the number of pho
tons striking a 50 cm radius disk above the soil, the total
energy of those photons and their energy spectrum. In each
case the comparison was excellent. Differences in the
number and energy of photons striking the disk are less than

104
1.5%. With the exception of one low energy bin, all energy
spectra results are within expected statistical variation.
The fractional contribution of fluorescent emission photons
to the fluence at the disk was found to be 0.00027, justify
ing their neglect in the MCPHOT.P code. Further, since
these photons appeared in the 5 to 10 keV bin of the energy
spectrum, and most real detectors employ some type of dis
crimination against low energy noise, these photons would
not be detected.

CHAPTER V
X-RAY SOURCE
A number of techniques are available for determining or
modelling the spectra produced by x-ray machines. The
method selected for use in the mine detection calculations
is presented and other techniques are discussed.
Kramers1 Formula Method
The technique selected for calculating the x-ray spec
tra of the GE Maxitron 300 Therapy Unit is based upon a
modification of Kramers' formula (Kramers, 1923). The model
is implemented by an interactive computer code, XRSPEC.PAS,
written in Turbo Pascal (Borland, 1985) for use on personal
computers. The code calculates 1 keV increment spectra for
fluence, energy fluence and exposure, and the integrals of
these quantities. The relative values of integral quantities
calculated by varying the amount of attenuating material in
the beam can be used to simulate transmission experiments,
which can then be checked against actual measurements. Since
the values are relative, it is equally valid to consider the
calculated quantities to be fluence rate, energy fluence rate
and exposure rate. Fluence files created for use with the
photon transport calculations of the mine detection problem
are normalized so that the integrated fluence is 1.00 pho-
2
tons/(source photon cm ).
105

106
Kramers' Formula
Kramers' formula is a simple relationship between the
energy associated with an electron accelerating potential and
the intensity or energy fluence spectrum of the x rays
produced when the electrons strike a target, in this case the
anode of an x-ray machine. The formula is based upon the
nonrelativistic, semiclassical physics of electron energy
loss, neglecting electron scattering. It applies only to the
continuous portion of the x-ray spectrum produced by the
bremsstrahlung process. Despite these simplifying assump
tions, its use in calculations of x-ray spectra is well es
tablished. The International Commission on Radiological
Units and Measurements (1964) finds the method to perform
well over a wide range of energies, provided that modifica
tions for self-absorption in the anode and attenuation by
other materials in the path of the beam are made.
One form of Kramers' formula is
1(E) = k (Eq E),
where I is the intensity or energy fluence of x-ray photons
of energy, E,
k is a constant of proportionality dependent on the
anode material,
Eq is the energy of the electrons striking the anode,
and
E is the energy of an x-ray photon within the
spectrum.

107
Since electron energy is related to accelerating potential
by the relation
E = e V/
where e is the charge of the electron, and
V is the accelerating potential,
Kramers' formula is alternatively written as
I(V) = k"* (VQ V),
where k" is k/e.
Application of this formula results in an unattenuated
bremsstrahlung spectrum which declines linearly from a maxi
mum of k'V^^ at V equal to zero, to a value of zero when V is
equal to V In order to apply Kramers' formula to the case
of the GE Maxitron 300 Therapy Unit, a number of modifica
tions are necessary. These modifications are described in
the following paragraphs.
Time Dependent Accelerating Potential
Since the accelerating potential of the GE Maxitron 300
is self-rectified, single phase, it varies in time. As a
result, the VQ term in Kramers' formula must be replaced
with an expression which accounts for the time dependence of
the accelerating potential. This time dependence is model
led as a sinusoid based upon waveforms associated with the
GE Maxitron 300 (General Electric, 1962). The expression
used to model the single phase nature of the accelerating
voltage is
V = v cosTr(t/200), t =-100,... ,100,
O ill cl X

108
where VQ is the time dependent accelerating potential of
electrons striking the anode, and
Vmax t^te max;*-muin accelerating potential of
electrons striking the anode or the peak tube
potential.
To account for the self-rectified nature of the potential,
the value of the cosine is permitted to take on only posi
tive values by constraining its argument to -tt/2 to tt/2.
The resulting 201 values of the intensity are summed in 1
keV intervals. Negative values of the quantity, VQ V,
result in no contribution to the intensity.
Characteristic X-Ray Production
If the energy of the accelerated electrons exceeds the
binding energy of electrons of the anode material, charac
teristic x rays may be produced. Only K characteristic
photon emission from the tungsten anode is modelled by the
XRSPEC.PAS code; that is, only interactions with the K or
inner shell atomic electrons of tungsten are considered.
This presents no problem as long as sufficient filtration of
the beam is applied to remove the low energy L characteris
tic radiation. For the mine detection application, even
this filtration requirement is unnecessary, since virtually
no L x rays survive interaction with the soil to contribute
to the scattered fluence. The filtration is important,
however, in tests of the code which rely on transmission
measurements of the uncollided beam in which thin layers of
attenuating material are employed.

109
The ratio of the intensity (or energy fluence) of K
characteristic radiation to the intensity of the continuous
spectrum as a function of electron energy, and the relative
intensities of the various K x rays are provided by Dyson
(1975). Because the characteristic to continuous ratio is a
function of electron energy, and because that energy is
changing in time for the GE Maxitron 300, characteristic
x-ray production is time dependent. The sinusoidal model of
the accelerating potential described for the time dependent
continuous x-ray production is again employed. Table V.l
provides a listing of the energies of the K characteristic x
rays used in the computer code. Because the and x
rays are stored in the same energy interval in the 1 keV
increment scheme of the code, only four distinct K x ray
energy channels appear in code output. Additionally, since
the Ka^ and Kctj x rays are in adjacent energy intervals,
graphs of spectra appear to show only three K rays.
Attenuation by Materials in the Beam Path
All calculated spectra for the GE Maxitron 300 normally
include a minimum of four materials in the path of the beam.
These are the beryllium window of the x-ray tube, a monitor
ionization chamber, the filter required to remove L x rays
of tungsten, and air. Sets of mass attenuation coefficients
for these materials and others used in experiments are cal
culated by cubic spline fits of the data of Hubbell (1982).
Attenuation coefficients include the effect of coherent
scattering. In cases where detailed information concerning

110
TABLE V.l
Energies of Tungsten K Characteristic X Rays
X Ray
Actual Energy3
(keV)
Code Energy Bin
(keV)
Kcd
59.321
59
Ka2
57.984
58
KB1
67.244
67
KS2
69.081
69
K63
66.950
67
aActual energies of K characteristic x rays are from
Storm and Israel (1970).

Ill
the L and K edges is required, the cross section data of
Storm and Israel (1970) are used. The mass attenuation data
are constructed for energies between 1 and 300 keV with a 1
keV increment. These data sets have been constructed for
the following materials: tungsten, beryllium, aluminum,
copper, iron, lead, lucite, air, gadolinium oxysulfide,
sucrose, TNT and a soil type (Norfolk sandy loam) similar to
that used in the mine detection and imaging experiments.
Anode Self-Attenuation
Since x-ray photons are produced by electron interac
tions within the anode, they are subjected to attenuation by
tungsten as they exit. Correction for anode attenuation is
accomplished using the method suggested by Soole (1971).
Soole compares calculations using Kramers' formula without
correction for anode self-attenuation to published exposure
transmission data. He finds the resulting calculated expo
sure transmission curves to indicate a softer (lower energy)
spectrum than the measured values implied. Figure V.l shows
a typical calculation by the XRSPEC.PAS code without anode
self-attenuation. The figure shows measured and calculated
exposure rate transmission produced by placing varying
thicknesses of aluminum in the x-ray beam. The geometry of
the measurements conforms to the requirements for formal
half value layer determination (Johns and Cunningham, 1983).
The discrepancy between the calculation and measurement is
the same as is observed by Soole. The steeper slope of the
calculated curve implies a softer beam, that is, one which

c
o
* en
E
w
c
o
f-
Figure V.l. Transmission curve without anode self-attenuation. A typical measured
transmission of exposure rate is compared to a calculation by the XRSPEC.PAS code
without anode self-attenuation. The source spectrum was produced by the GE Maxitron
300 X-Ray Therapy Unit operated at 100 kVp with 4.75 mm beryllium inherent filtra
tion, 2.00 mm aluminum added filtration (includes 0.25 mm aluminum equivalent monitor
ionization chamber), and air path length of 91.44 cm.
112

113
is more strongly attenuated. Soole shows that uncertainties
in the amount of characteristic radiation produced cannot
account for the discrepancy, and concludes that self-attenu
ation in the anode is the cause. The high photoelectric
interaction cross section of tungsten preferentially removes
the lower energy components resulting in the harder spec
trum. Soole makes use of the concept of mean effective
depth of production of x rays, originally presented by
Hanson and Salem (1961). While x rays are not produced at a
single point at depth within the anode, Hanson and Salem
show that for the purpose of calculations, a mean effective
depth can be defined. This depth is very small, on the
order of microns for tungsten. Soole independently deter
mines this depth using Kramers' formula by iteratively
adding small amounts of tungsten to materials through which
the beam passes. The mean effective depth is that which
provides the least squares deviation between calculated and
measured transmission data. His tungsten depths, derived in
this manner, are somewhat higher than published mean effec-
2
tive depths (in mg/cm of any target material). The pub
lished data are for a variety of smooth surface metal tar
gets, but do not include tungsten. The surface of a
tungsten anode, especially one which has been in operation
for an extended period of time, is far from smooth at the
micron level, so the differences are not surprising.
The least squares fitting technique employed by Soole
and described above, is used with exposure transmission

114
measurements on the GE Maxitron 300 and calculations using
Kramers' formula with the modifications described to deter
mine the mean effective depths of x-ray production associ
ated with the unit. Because the source of Soole's exposure
transmission data used a constant potential machine, it was
expected that the effective depths calculated for the single
phase GE Maxitron 300 would be smaller for the same kVp and
filtration. The opposite is found to be the case. While
this may be due to differences in wear on the surfaces of
the respective anodes (the GE Maxitron 300 is approximately
25 years old), a somewhat different point of view provides
results which are more compatible. Since the hardening of
the beam is due to preferential removal of softer components
as they pass through the tungsten anode, it is not actually
the depth of penetration which is paramount, but rather, the
length of the exit path the photons must traverse. Calcula
tions of this exit path distance from Soole's work (19 de
gree anode angle) and that of the GE Maxitron 300 (45 degree
anode angle) are compared in Table V.2. The values are
similar. It should be noted that this correction technique
may account for other factors which affect beam hardness,
such as variation of the shape of the primary waveform with
peak kilovoltage.
To use the exit path data within the XRSPEC.PAS compu
ter code, a least squares fit of the tungsten exit thickness
versus maximum energy of the beam is made. The resulting
energy dependent thickness is then included in the materials
through which the beam passes.

115
TABLE V. 2
Comparison of Exit Path Lengths Through Tungsten
Anodes Which Provide the Best Fit to Measured
Exposure Rate Transmission Data as Calculated
Using Kramers' Formula.
Beam Energy
(kVp)
Filtration
(mm of Al)
Exit Path
Soole (1971)
Length (microns)
GE Maxitron 300
80
2.00
6.99
5.63
80
2.24
-
5.86
80
3.00
6.01
-
100
2.00
6.99
5.81
100
2.24
-
5.75
100
3.00
4.04
-
150
3.00
-
5.20
150
3.34
-
5.32
150
3.44
-
5.79
200
3.00
-
4.07
200
3.34

4.90

116
Effects Neglected in the Model
In addition to the simplifying assumptions inherent in
Kramers' formula, several other effects are neglected.
These include the effect of the filter in producing secon
dary photons in the beam, and the effect of the external
collimator in preferentially hardening the outer portions of
the beam.
When a photon interacts in the filter, a number of out
comes are possible. The XRSPEC.PAS model, by its use of
simple attenuation coefficients, assumes that any interact
ing photon is removed from the beam. In reality, coherent
scatter, incoherent scatter and fluorescent emission photons
can be produced and may contribute to the beam. The exter
nal collimator exists to remove these photons, but it cannot
fulfill this function if the photons pass through the col
limator opening.
Since the walls of the collimator are parallel to the
centerline of the beam, and the beam is diverging, a higher
fraction of photons striking the lower walls will penetrate
the collimator. This results in an unwanted penumbra about
the defined beam, which will be spectrally harder than the
center.
These effects are highly dependent upon the geometry
and materials involved. Detailed calculations made for the
actual geometry and materials used in the mine detection
experiments show the effects to be negligible, producing a
maximum shift in the average energy of a spectral distribu
tion of 20 eV.

117
General Features of the Calculated Spectra
Figure V. 2 shows a typical spectrum calculation. The
low energy components are removed by aluminum filtration,
producing the maximum in the continuous portion of the
spectrum. K characteristic x-ray peaks are present since
the maximum accelerating potential exceeds 69.508 keV, the
binding energy of the inner shell electrons of tungsten
(Storm and Israel, 1970). A less obvious feature in the
spectrum also occurs at this energy. A close examination of
the continuous portion of the spectrum reveals a discontinu
ity at the tungsten K edge energy. This discontinuity is
somewhat obscured by the nearby characteristic x rays. The
drop in the fluence is due to the discontinuous increase in
the photoelectric cross section of tungsten at its K edge
energy. Photons having energies just below that of the edge
and exiting the anode are less attenuated than those of
energies just above the edge energy. Examples of this
feature also occur in published spectra (Sundararaman et
al., 1973; Stanton et al., 1979).
Another well known feature of x-ray measurements, the
heel effect, is demonstrated by the XRSPEC.PAS code. The
heel effect refers to the spectral hardening of portions of
the beam which pass through greater thicknesses of the
anode, and thus suffer greater self-attenuation. Portions
of the beam located closest to the anode are, therefore, the
hardest. Since increased attenuation is largest for low
energy photons, the result is a variation of hardness within

Figure V.2. Topical x-ray spectrum calculation. The fluence spectrum (in units of
photons per cm per keV) at 150 kVp calculated by the XRSPEC.PAS code for the GE
Maxitron 300 X-Ray Therapy Unit with 4.75 mm beryllium inherent filtration, 3.44 mm
aluminum added filtration (includes 0.25 mm aluminum equivalent monitor ionization
chamber) and air path length of 90.07 cm is shown. Total fluence is normalized to 1
photon per cm .
00

119
the beam. Calculations using the XRSPEC.PAS code show this
feature. Figure V.3 shows the results of calculations of
the fluence spectra for three portions of an x-ray beam
generated at 80 kVp. The spectrum associated with the por
tion of the beam nearest the anode is reduced in magnitude
and shifted to higher energies by the heel effect. Figure
V. 4 displays the effect in a form often found in medical
physics texts (Hendee, 1984). Here the effect is shown in
the variation of half value thickness, the thickness of
material (aluminum in this case) required to reduce the
exposure rate of the x-ray beam by a factor of two. The
calculation of this figure uses the geometry required for
formal half value measurements (Johns and Cunningham, 1983).
As shown in the figure, greater thicknesses of aluminum are
required for portions of the beam nearest the anode.
Testing the Modified Kramers' Formula Model
The validity of the modified Kramers' formula method
for calculating x-ray spectra is tested by comparisons with
exposure rate transmission measurements and published
measurements of spectra.
Exposure Rate Transmission Measurements
The transmission of exposure rate of x-ray beams pro
duced by the GE Maxitron 300 is measured for a variety of
combinations of maximum accelerating potentials and filia
tions Beams produced by these energy and filtration com
binations are transmitted through varying thicknesses of
aluminum to develop transmission curves. These measured

Figure V.3. Heel effect displayed by spectra. A comparison of x-ray spectra for
three beam angles generated at 80 kVp calculated by the XRSPEC.PAS code for the GE
Ma^itron 300 X-Ray Therapy Unit. Fluence units are relative number of photons per
cni per keV.
120

2.5
Beam Angle from Center Line (degrees)
Figure V.4. Heel effect displayed by half value thickness. A comparison of first
half value layers (mm of aluminum) of 80 kVp beams as a function of beam angle is
shown. Values were calculated by the XRSPEC.PAS code for the GE Maxitron 300 X-Ray
Therapy Unit.
121

122
results are then compared to calculations for the same
transmission experiment simulated by the XRSPEC.PAS code.
Figure V.5 shows the results of such a comparison for the
spectrum shown in Figure V.2. Other comparisons are
provided in Appendix D. Figures in the appendix show the
calculated spectra, and the associated measured and calcu
lated transmission of exposure rate. Measurements are made
with an MDH Industries, Inc. 1015 X-Ray Monitor, which has a
flat energy response to below 20 keV. As can be seen by the
comparisons, the agreement between calculations and measure
ments is very good.
Comparisons with Published Spectra
Comparisons with published measurements of x-ray
spectra are also performed. Fewell and Shuping (1977) re
viewed published spectral measurements and recommend their
own work and that of Epp and Weiss (1966) as the best avail
able. In doing so, they indicate that serious discrepancies
exist in other published spectra. Accordingly, comparisons
are made with these two recommended sets of published
spectra.
Figures V.6 and V.7 show the comparison between the
XRSPEC.PAS fluence spectrum calculation and the measurements
of Epp and Weiss. The voltage waveform used in the Epp and
Weiss measurements is considerably different from that of
the GE Maxitron 300. The XRSPEC.PAS code is modified to
model this new waveform, which is a constant potential term
plus a 120 Hz component with a peak to peak amplitude equal

c
o
en
en
£
en
c
a
i
I
Figure V.5. Typical transmission curve comparison. A comparison of measured and
calculated transmission of exposure rate of a 150 kVp beam produced by the XRSPEC.PAS
code for the GE Maxitron 300 X-Ray Therapy Unit with 4.75 mm beryllium inherent fil
tration, 3.44 mm aluminum added filtration (includes 0.25 mm aluminum equivalent
monitor ionization chamber) and air path length of 91.44 cm.
123

Energy (keV)
Figure V.6. Spectrum comparison with Epp and Weiss at 80 kVp. The measured spec
trum, from Epp and Weiss (1966), is generated by a diagnositc x-ray unit operated at
80 kVp with 0.5 mm inherent aluminum filtration, 2.00 mm aluminum a^ded filtration
and an air path length of 2.13 m. Fluence units are photons per cin per keV. The
calculated spectrum is generated by the XRSPEC.PAS code. Total fluence is normalized
to 1 photon per cm.
124

Energy (keV)
Figure V.7. Spectrum comparison with Epp and Weiss at 105 kVp. The measured spec
trum, from Epp and Weiss (1966), is generated by a diagnositc x-ray unit operated at
105 kVp with 0.5 mm inherent aluminum filtration, 2.00 mm aluminum added filtration
and an air path length of 2.13 m. Fluence units are photons per cin per keV. The
calculated spectrunj is generated by the XRSPEC.PAS code. Total fluence is normalized
to 1 photon per cm.
125

126
to 25% of the constant potential term. This waveform would
be expected to produce a harder spectrum than the single
phase waveform of the GE Maxitron 300 when operated at the
same peak kilovoltage. Comparisons at 80 and 105 kVp are
shown. The lack of characteristic x rays in the measured 80
kVp spectrum casts some doubt on the quality of these mea
surements. The characteristic x rays should be more intense
in this spectrum than in the corresponding GE Maxitron 300
spectrum as a result of the waveform. Overall, however, the
comparisons are generally good.
Figures V.8, V.9 and V.10 show the comparison with the
measurements of Fewell and Shuping (1977). The voltage
waveform of the x-ray machine used in these measurements is
single phase, as is the GE Maxitron 300. Comparisons are
made at 70, 80 and 90 kVp. The comparisons in all three
cases are excellent. The presence of characteristic x rays
in the measured 80 kVp spectrum reinforces the lack of
confidence in the Epp and Weiss measurements described
above.
Other Methods to Determine X-Ray Spectra
Several other methods are frequently applied to the
problem of determining x-ray spectra.
Measurement
The most direct method for determining x-ray spectra is
measurement. Unfortunately, this method is an extremely
difficult, expensive, and time consuming endeavor requiring
highly specialized equipment and detailed corrections for

Energy (keV)
Figure V.8. Spectrum comparison with Fewell and Shuping at 70 kVp. The measured
spectrum, from Fewell and Shuping (1977), is generated by a diagnositc x-ray unit
operated at 70 kVp with 0.7 mm aluminum equivalent inherent filtration, 2.00 mm
aluminum added2filtration and an air path length of 100 cm. Fluence units are
photons per cin per keV. The calculated spectrum is generated by the XRSPEC.PAS
code. Total fluence is normalized to 1 photon per cm .
127

Energy (keV)
Figure V.9. Spectrum comparison with Fewell and Shuping at 80 kVp. The measured
spectrum, from Fewell and Shuping (1977), is generated by a diagnositc x-ray unit
operated at 80 kVp with 0.7 mm aluminum equivalent inherent filtration, 3.00 mm
aluminum added2filtration and an air path length of 100 cm. Fluence units are
photons per cin per keV. The calculated spdectrum is2generated by the XRSPEC.PAS
code. Total fluence is normalized to 1 photon per cm.
128

Energy (keV)
Figure V.10. Spectrum comparison with Fewell and Shuping at 90 kVp. The measured
spectrum, from Fewell and Shuping (1977), is generated by a diagnositc x-ray unit
operated at 90 kVp with 0.7 mm aluminum equivalent inherent filtration, 4.00 mm
aluminum added2filtration and an air path length of 100 cm. Fluence units are
photons per cni per keV. The calculated spectrum is generated by the XRSPEC.PAS
code. Total fluence is normalized to 1 photon per cm.
129

130
the response of the detector employed in the measurement
(Baird, 1981). As noted above, serious discrepancies in
published measurements of x-ray spectra are noted in the
literature (Fewell and Shuping, 1977), indicating that the
relative difficulty of the technique is high. For these
reasons, a measurement technique is not selected. However,
as described above, comparisons of calculated results with
published measurements of spectra, which have been deter
mined by reviewers to be reliable, have been useful in
testing the modified Kramers' formula method.
Monte Carlo Calculation
Implementation of a Monte Carlo code to calculate x-ray
spectra requires a good understanding of the bremsstrahlung
interaction cross sections for thick targets. Unfortunate
ly, these cross sections are not well known for the diagnos
tic and therapeutic x-ray energy ranges which are of in
terest in the mine detection problem (Koch and Motz, 1959).
Results of Monte Carlo calculations of x-ray spectra are
generally considered inferior to other techniques (Huang et
al., 1981). As a result this method is not selected.
Laplace Transform Pair Method
This technique was first introduced by Silberstein
(1932, 1933). It requires that exposure transmission meas
urements be made by placing varying thicknesses of materials
in the path of the beam (usually aluminum or copper). The
resulting exposure rate transmission versus thickness data
is then fit to a function of the attenuation coefficient of

131
the material which has a known inverse Laplace transform.
This inverse transform function, multiplied by the deriva
tive of the attenuation coefficient with respect to energy
to transform variables from attenuation coefficient to
energy, constitutes the x-ray spectrum. Silberstein pro
vided the first such Laplace transform pair.
Significant improvements to Silberstein's original
transform pair were made by Bell (1936) and Jones (1940) to
account for the known physics of x-ray spectra and photon
attenuation. Greening (1947) provided an approximation
technique for accounting for the characteristic portion of
the x-ray spectrum and also produced the first definition of
the general properties required of other Laplace transform
pairs for use in spectral reconstruction (Greening, 1950).
The original Silberstein pair, though modified by additional
parameters, continued to be used even though its fits to
transmission data were often not particularly good. Better
Laplace transform pairs were identified (Saylor, 1969;
Huang et al., 1981? Archer and Wagner, 1982), but with their
use, the capability to approximate the characteristic por
tion of the spectrum was lost. Baird (1981) provides a
theoretical analysis of the general Laplace transform pair
technique. Ahuja et al. (1986), provide a summary of the
Laplace transform pair models which have been used up to
1986. The International Commission on Radiological Units
and Measurements (1964) cautions that the usefulness of this
technique depends upon the accuracy of measurement of the

132
transmission curve and the number of parameters used in
fitting the curve.
The Archer-Wagner method (Archer and Wagner, 1982) is
generally accepted as the most accurate transform pair
available today (Rubio and Mainardi, 1984; Archer, 1985,
Ahuja et al., 1986). Joseph (1975) establishes the physical
basis for the form used in the Archer-Wagner fitting func
tion, accounting for its accuracy in approximating trans
mission data. The Archer-Wagner method does not include
characteristic x-ray contributions, but can be used to check
spectral calculations for cases in which the characteristic
x-ray component is negligible or absent. Mathematically, it
is the most complex of the sets of transform pairs that have
been used. The function used in fitting the exposure rate
transmission measurements is of the form
x(£) =
where X(£) is the ratio of exposure (or exposure rate)
2
after passing through E, g/cm of attenuating
material to the exposure (or rate) without any
attenuating material,
y is the mass attenuation coefficient of the
attenuating material at the maximum energy in
the spectrum, and
are the fitting parameters to be determined.
V
ab
U+a) (£+b)
exp(-uo£)
a ,b, v

133
The associated fluence spectrum is given by
F(E) 7T'L;/2(at,)V
F(E) r(v)
y -yo
a-b
v-l/2
[-
(a+b) ,
exp | 2 ~
v-l/2
where F(E)
V
r
i
2 (a-b)(y-yQ)
_ L
dE
is the fluence as a function of energy,
is the mass attenuation coefficient of the
attenuating material at energy, E,
is the gamma function,
is the modified Bessel function, and
dy is the derivative of the mass attenuation
dE
coefficient with respect to energy at
energy, E.
In order to implement the Archer-Wagner method, a
nonlinear parameter fitting computer program was written
using the Levenberg-Marquardt method (Press et al., 1986).
Figure V.ll shows an example of the excellent capability of
the Archer-Wagner formula to fit measured transmission data.
For spectra generated at 100 kVp and below (where character
istic radiation does not play a major role), the worst fit
data point in four cases examined was less than 0.8%. Once
the parameters are determined, a second program computes the
fluence spectrum at a 1 keV increment. The previously
assembled mass attenuation coefficient data for aluminum

1
c
o
ot
(n
E
cn
c
a
L_
I-
10
T "I1 | I I T | I 1 I | H I | I I I | l I
0.2 0.4 0.6 0.8 1.0
~i r i i t I r i | i rr | i i i |
1.2 1.4 1.6 1.8 2.0
g/cm2 Of Aluminum
Figure V.11. Archer-Wagner method fit to measured transmission data. The excellent
capability of the Archer-Wagner fitting equation (Archer and Wagner, 1982) is
demonstrated.
M
OJ

135
(any material can be used as the attenuator in the tech
nique) were numerically differentiated to provide the deri
vative required to support the calculation. Algorithms used
for computing the gamma function and modified Bessel func
tion are from Press et al. (1986). Figure V. 12 compares the
results of fluence spectra calculations at 80 kVp by the
modified Kramers' formula method and by the Archer-Wagner
method. While some differences exist due to the minor
characteristic x-ray contribution, the agreement is seen to
be good. Figure V.13 shows the same comparison at 150 kVp
where the characteristic contribution is large. The com
parison is now poor, highlighting the reason for rejection
of this otherwise excellent technique.
Rubio and Mainardi (1984) have attempted to extend the
Archer-Wagner method to include characteristic x rays. The
extension involves adding exponential terms with parameter
coefficients to the fitting function, resulting in delta
functions in the inverse Laplace transform. In their paper,
Rubio and Mainardi use published measured fluence spectra to
calculate exposure transmission data. These calculated data
are then applied to a fitting function, which allows for
only two K x rays in the inverse transform. Calculated
spectra are produced which predict the characteristic
components to between 10 and 15% of the measured values. No
demonstration of spectral reconstruction from actual trans
mission data, subject to random error found in any actual
experimental measurement, is made. Attempts to apply this

Figure V.12. Comparison of modified Kramers' method and the Archer-Wagner method at
80 kVp. A comparison of two calculated x-ray spectra for an 80 kVp beam generated by
the GE Maxitron 300 X-Ray Therapy Unit with 4.75 mm beryllium inherent filtration,
2.00 mm aluminum added filtration (includes 0.25 mm aluminum equivalent monitor ioni
zation chamber^, and an air path length of 90.17 cm is shown. Fluence u^its are
photons per cni per keV. Total fluence is normalized to 1 photon per cm.
136

Energy (keV)
Figure V.13. Comparison of modified Kramers' method and the Archer-Wagner method at
150 kVp. A comparison of two calculated x-ray spectra for a 150 kVp beam generated
by the GE Maxitron 300 X-Ray Therapy Unit with 4.75 mm beryllium inherent filtration,
3.44 mm aluminum added filtration (includes 0.25 mm aluminum equivalent monitor
ionization chamber), and an air path length of 90.17 cm is shown. Fluen^e units are
photons per cin per keV. Total fluence is normalized to 1 photon per cm .
137

138
technique as a part of this dissertation research effort
with four K characteristic x rays failed when applied to
real data. Values of the fluence for a characteristic x-ray
energy are as likely to be negative (without physical
meaning) as not. Conclusions regarding the limitation of
the usefulness of the Archer-Wagner method to cases of
little or no characteristic radiation are unchanged by the
extension proposed by Rubio and Mainardi.

CHAPTER VI
DETECTOR RESPONSE
Several types of detectors have been used in the mine
detection calculations. Early in the course of the work, a
detector based on terbium activated gadolinium oxysulfide
was constructed for measurements. For a variety of reasons
described in Appendix E, this detector is judged to be un
suitable for the mine detection effort. Nevertheless, this
general type of detector has some very positive features for
specific detection techniques. Appendix E provides a de
scription of this detector, its response function, and its
shortcomings.
Several configurations of large area detectors similar
to those envisioned in a working system have also been used
in calculations. In these cases, since a detector material
has not been selected, fluence response is used. These de
tectors are discussed in Chapter VII.
The detector employed in imaging and detection experi
ments is a small sodium iodide scintillation crystal. This
small detector allows detailed examination of response fea
tures, which would be lost by integration in a large area
detector. As a result, it also provides rigorous tests of
analytical predictions. The structure of the detector and
139

its shield are described in detail in Chapter III. This
chapter discusses the response function calculation for the
detector and its validation.
Considerable work has been performed by many research
ers on the detector response of Nal(Tl). The amount of
research on Nal(Tl) response at the low photon energies of
interest in the mine detection problem is considerably
smaller than that at high energies, but is still adequate to
provide checks of the computer code used in calculating the
response matrix for this research. The usual application
of a Nal(Tl) scintillation detector is to perform spectral
measurements rather than counting, which is done in this
effort. As a result, most of the validation checks avail
able involve features of the spectral response, that is,
peak ratios and shapes of energy spectra. Accordingly,
these features are examined in assessing the computer code.
The approach used in developing the detector response matrix
is to begin with an infinite plane detector consisting of
(from face towards photomultiplier) the outer aluminum can
thickness, the three materials between the can and sodium
iodide crystal (as explained in Chapter III, these mater
ials, thicknesses and densities were provided by the manu
facturer for the purpose of this calculation, but cannot be
published because of their proprietary nature), the sodium
iodide crystal, and the quartz light pipe (see Figure
III.4). The response of this detector is calculated for
a mesh of 24 energies, ranging from 10 to 300 keV, and 9

141
angles of incidence, ranging from 0 to 89.9 degrees. Ten
thousand photon histories are followed for each energy/angle
mesh point. A correction to this response matrix is then
calculated for the effect of the shield and edge leakage for
the same energy/angle mesh.
Plane Detector Code
The plane detector response is calculated by the
DETNAI.P code, written in Green Hills Pascal (Green Hills
Software, 1984) and implemented on the DSI-32 coprocessor
(Marshall et al., 1985). Cross sections for all materials
are calculated for a fine energy mesh by cubic spline
interpolation of data by Hubbell et al. (1975), Hubbell
(1982), and Storm and Israel (1970) when detailed informa
tion concerning photoelectric edge effects is required.
Full coherent, incoherent and photoelectric interactions,
including fluorescent emission from iodine are included.
The atomic form factors and incoherent scattering factors
are from Hubbell (1975). Implementation of the coherent
scattering routine is based on the techniques of Carter and
Cashwell (1977), and Williamson and Morin (1983a, 1983b).
Implementation of the incoherent scattering routine is also
based on the recommendations of Carter and Cashwell (1977),
utilizing the Kahn method (1956) for sampling the Klein-
Nishina relationship as a first step in the technique. The
atomic fluorescent yield of iodine is from Bambynek et al.
(1972). Four iodine fluorescent emission K x rays and one L
x ray are allowed, in accordance with the recommendations of

142
Carter and Cashwell (1977). Secondary L fluorescence fol
lowing or Ka2 emission is also allowed. Table VI.1
provides the energies of these fluorescent x rays.
The response function calculation for the gadolinium
oxysulfide detector (Appendix E) is primarily concerned with
the gross amount of energy deposited in the phosphor layer
by x-ray photon interactions in the phosphor, which is then
converted to light photons. Because of the faster response
time of Nal(Tl), it is the sum of the energies of all the
interactions of a single x-ray photon and its progeny, which
are deposited in the crystal, that is of importance. For
each photon, this sum is compared to the energy correspond
ing to the lower level discriminator setting of the counting
system. Only if the energy deposited in the Nal(Tl) exceeds
the discriminator energy is a count recorded. The response
is the number of counts per incident photon at a given
energy and angle of incidence as opposed to the amount of
energy deposited per incident photon at a given energy and
angle of incidence in the case of the gadolinium oxysulfide
based detector. The DETNAI.P code calculates this response
for nine discriminator settings ranging from 0 to 45 keV. A
derivative of the DETNAI.P code, NAISPEC.PAS, computes the
spectrum of energies deposited in the Nal(Tl) crystal.

143
TABLE VI. 1
Energies of Iodine Fluorescent Emission X Rays
Used in the Detector Response Calculations
X Ray
Weighted average of 3 L x rays
K.
kal
K
a2
KBl'
K
32
weighted average of M2,
M4 to K transitions
weighted average of N2,
to K transitions
Energy (keV)
4.206
28.613
28.318
M3,
32.276
N3
33.041

Assumptions in the Plane Detector
Response Calculation
144
Knoll (1979) addresses a number of complications in
calculations of response functions for Nal(Tl) detectors.
These complications are described below, along with the
assumptions used for handling them in this research and
their rationale.
In any energy deposition event, photon energy is
converted to kinetic energy of electrons (and the energy
required to overcome electron binding, which is generally
negligible for x-ray photons). It is the kinetic energy of
electrons which ultimately produces the visible light pho
tons which strike the photocathode of the photomultiplier
tube and begin the process of producing a voltage pulse.
If the ranges of these secondary electrons are large with
respect to the crystal dimensions, a significant fraction
would leak out of the crystal without having their energies
absorbed. This effect is ignored in the DETNAI.P calcula
tions because of the very short ranges of secondary elec
trons produced by low energy photons. The effect is impor
tant only for high energy gamma rays which produce high
energy secondary electrons. The effect of electron escape
at these energies is unimportant (Berger and Seltzer, 1972).
Bremsstrahlung radiation is produced when charged
particles are accelerated in an electric field (the same
process producing the continuous portion of the x-ray
spectrum in an anode of the x-ray tube). In the Nal(Tl)

145
crystal, the charged particles of interest are again the
secondary electrons described above, and the electric field
is primarily that of the nuclei of iodine atoms. In the
energy range of interest in the mine detection problem, the
probability of producing bremsstrahlung photons is small.
Any bremsstrahlung produced would be of very low energy
resulting in rapid local reabsorption. For these reasons,
bremsstrahlung escape is not considered in the detector
response calculations of the DETNAI.P code.
Fluorescent emissions following photoelectric interac
tions near the surface of the Nal(Tl) crystal may escape the
crystal. This effect is included in the DETNAI.P code (and
in NAISPEC.PAS). It plays an important role in the shape of
the response function and serves as a method for checking
the response calculations against published values of the
iodine escape ratio (described below). This effect is more
important for low energy photons (above the K edge of io
dine) because high photoelectric cross sections make inter
actions near the surface of the crystal and the subsequent
fluorescent escape more probable.
Scatter of source photons from surrounding materials
will obviously effect the detector response if not accounted
for. Shielding the head of the x-ray machine and the sides
of the detector reduces this effect. The DETNAI.P code
assumes no scatter off of surrounding materials. As is de
scribed in Chapter VIII, the initial problem in reconciling
measured and calculated response was determined to be caused

146
by scatter of head leakage photons. The detector response
calculation played the key role in identifying this
previously unnoticed scatter path.
If two pulses arrive during the resolving time of the
detector, the sum of the pulses will be detected, resulting
in a single count at an incorrect energy. This is avoided
by measuring at count rates where such sum events are im
probable. One of the criteria for selection of the energy/
filtration combinations being used is to avoid high count
rate situations.
Energy Deposition
As explained above, gross energy deposition is not the
primary quantity of interest in Nal(Tl) response. It is,
however, instructive to examine the energy absorption
process to obtain a better physical feel for the nature of
the interactions occurring in the detection process.
Case of Zero Degree Incidence
Figure VI.1 shows the fraction of the incident photon
energy absorbed in the Nal(Tl) crystal as a function of
incident photon energy for the case of 0 degree incidence on
the outer aluminum layer of the detector. The shape of the
curve is explained by examining the photon interaction
characteristics of the crystal.
At low energy the fraction of incident energy absorbed
is low due to absorption of photons in the material layers
in front of the crystal. As incident energy increases, more
photons are capable of penetrating the front layers and

Figure VI.1. Fraction of incident energy absorbed, perpendicular incidence. The
calculated fraction of incident photon energy absorbed in the Nal(Tl) crystal of a
plane model of a Bicron Model .5M.39Q/.5L-X detector for the case of zero degree
incidence is shown. Calculations were performed by the DETNAI.P Monte Carlo code.
147

148
reaching the Nal(Tl) crystal, resulting in an increase in
the fraction of energy absorbed in the crystal.
At the K edge of iodine (0.03317 MeV), there is a dis
continuous decrease in the fraction of energy absorbed in
the Nal(Tl) crystal. Below this energy, incident photons
are unable to remove K shell electrons in iodine; above it,
they are. The removal of a K shell electron is frequently
followed by emission of a K fluorescent x ray (radiationless
Auger electron emission is also possible). The decrease in
the fraction of energy absorbed in the crystal at the K edge
energy is caused by the escape of these iodine K fluorescent
x rays from front surface of the crystal.
Above the K edge, the absorbed fraction increases to a
maximum at about 0.100 MeV. This increase is due primarily
to the increasing depth of penetration of the incident pho
tons. The deeper into the Nal(Tl) crystal that photons
interact, the more difficult it is for the K fluorescent x
rays to escape the crystal. As depth of penetration in
creases, they are reabsorbed in the crystal with increasing
efficiency. A secondary mechanism for the increase in ab
sorbed fraction is the enhanced capability for penetration
of the material layers in front of the crystal.
As incident energy increases above the peak at approxi
mately 0.100 MeV, there is a decrease in the absorbed frac
tion. This is primarily a result of transmission of photons
through the crystal without interaction and small angle
(forward) Compton scattering events in which the scattered

149
photon escapes the rear of the crystal, depositing only a
small fraction of its original energy. These transmission
losses are moderated somewhat by backscatter into the crys
tal from the quartz light pipe located on the back side of
the crystal.
Case of Large Angle Incidence.
The Figure VI.2 shows the fraction of incident energy
absorbed within the Nal(Tl) crystal for photons incident at
75 degrees. The general shape of the curve remains similar
to that of the zero degree incidence case. Differences
between the cases are again explained by examining the
physical processes occurring within the detector. In the
low energy region, the fraction absorbed in the crystal is
much reduced as compared to the zero degree incidence case.
This is primarily caused by the much higher absorption of
energy in the material layers in front of the crystal, which
is a result of the long slant paths through these materials.
A secondary cause is a greater fraction of the incident
photons being backscattered from these layers without
reaching the Nal(Tl) crystal.
The effect at the iodine K edge has the same explana
tion as in the zero degree incidence case. Above the K
edge, the two factors discussed in the zero degree incidence
case are both again present, although the increased penetra
tion of the layer in front of the crystal plays a much
larger role for the large angle of incidence case.

Figure VI.2. Fraction of incident energy absorbed, 75 degree incidence. The
calculated fraction of incident photon energy absorbed in the Nal(Tl) crystal of a
plane model of a Bicron Model .5M.39Q/.5L-X detector for the case of 75 degree
incidence is shown. Calculations were performed by the DETNAI.P Monte Carlo code.
150

151
At high energies, the decrease in fraction absorbed is
much less than in the zero degree incidence case. This is a
result of the much thicker Nal(Tl) layer seen by an uncol
lided photon (long slant path through the crystal). Few, if
any, photons are transmitted through the crystal without
interaction. The primary transmission mechanism becomes
Compton scatter.
Counts Per Incident Photon
As described above, it is not the gross energy absorbed
which determines the number of counts recorded, but the
total energy absorbed in the crystal as a result of all
interactions of each individual incident photon and its
progeny. A further modification to the number of counts
recorded is the setting of the lower level discriminator.
Figure VI.3 shows the response of the plane detector in
counts per incident photon striking the outer case of the
detector for two discriminator level settings corresponding
to 0 and 0.025 MeV.
Discriminator Setting Corresponding to 0 MeV
This discriminator setting results in a count being
recorded for any energy depositing photon event occurring in
the crystal. The effect of the iodine K edge, so prominent
in the energy deposition curves, is removed by this criter
ion. Any deviation from a value of 1.00 counts per incident
photon is a result of photons completely missing the crystal
or undergoing only coherent interactions in the crystal.
Several mechanisms are responsible for such misses.

Figure VI.3. Plane detector response, discrimination less than 0.03317 MeV. The
calculated detector response (number of counts per incident photon striking the
detector) for the case of perpendicular incidence on a plane model of a Bicron Model
.5M.39Q/.5L-X detector is shown. The calculation was performed by the DETNAI.P Monte
Carlo code for the cases of lower level discriminator settings corresponding to 0.000
and 0.025 MeV.
152

153
Complete absorption of the photon energy in a single event
in the material layers in front of the crystal is the
primary reason for the low response at low energy. It is
caused by photoelectric interactions. Partial absorption of
the photon energy in the material layers in front of the
crystal with subsequent scatter away from the crystal or
absorption in non-crystal layers also does not produce a
count. The initial interaction is a Compton scattering
event. This series of interactions occurs at all photon
energies, having its largest effect at higher energies and
large angles of incidence. Coherent interactions with any
part of the detector followed by transmission through the
crystal, scatter away from the crystal, or absorption in
non-crystal layers also produce a miss. This effect is more
likely at lower incident photon energies. Transmission
without interaction through the crystal is the primary cause
for the decrease in response at high energy.
Discriminator Level Setting Corresponding to Energies
Greater Than 0 MeV.
At first consideration, it might be thought that the
effect of any discriminator setting would be simply to
remove all energy deposition events below that setting from
contributing to the counts recorded. The effect, however,
extends beyond the energy corresponding to the discriminator
setting. Two manifestations of the extended effect are pos
sible, dependent upon whether the discriminator level cor
responds to an energy above or below the K edge of iodine.

154
Figure VI.3 also displays the detector response versus
incident energy for a discriminator setting (0.025 MeV)
below the iodine K edge (0.03317 MeV). Below the energy
corresponding to the discriminator level setting (0.025 MeV,
in this example), there is no response as would be expected
by the definition of the purpose of the discrimination
process. Between the discriminator setting and the K edge,
the response closely resembles that of the no discrimination
case. It is actually very slightly smaller as a result of
Compton interactions which deposit less than 0.025 MeV in
the crystal and then scatter out of the crystal. The in
coherent cross section is low at these energies in compari
son with the cross section for photoelectric interaction, so
these events are relatively rare.
Above the K edge energy, there is a "notch" in the
response curve. This "notch" is a result of photoelectric
events in the crystal which are followed by the emission and
escape of iodine K fluorescent x rays. In this region of
the curve, for such events, the total energy deposited by an
incident photon in the Nal(Tl) crystal is less than that
required by the discriminator setting and no count is re
corded. Eventually, an incident photon energy is reached at
which the energy deposited in the crystal exceeds that re
quired by the discriminator setting regardless of whether a
fluorescent photon escapes or not. When this occurs the
response curve once again becomes very similar to that of
the case of no discrimination. In actuality, the transition

155
back to the response curve without discrimination is a
staircase because several different K fluorescent photons
are emitted by iodine. The transition energies are easily
calculated by simply adding the various K x ray energies to
the energy corresponding to the discriminator level setting.
In this example, the transition energies are 0.053318,
0.053613, 0.057276, and 0.058041 MeV.
At high energies, the detector response deviates
slightly, but noticeably from the no discrimination case.
This deviation is caused by Compton scattering events in the
crystal which deposit less than the energy required by the
discriminator level setting and then scatter out of the
crystal. These events are much more probable at higher
energies where the incoherent cross section is large rela
tive to the cross section for photoelectric interaction.
Figure VI.4 compares the response curve for perpendic
ular incidence on the plane detector with discriminator
settings of 0 and 0.035 MeV. A major difference from the
case with a discriminator setting corresponding to energies
less than the K edge energy of iodine is apparent: the low
energy edge of the "notch" is missing. This is because even
the lowest energy photon, capable of recording a count, is
also capable of emitting iodine K fluorescent x rays. The
transition energies back to (approximately) the response
curve without discrimination are now shifted to higher
energies: 0.063318, 0.063613, 0.067276, and 0.068041 MeV.

Figure VI.4. Plane detector response, discrimination greater than 0.03317 MeV. The
calculated detector response (number of counts per incident photon striking the
detector) for the case of perpendicular incidence on a plane model of a Bicron Model
.5M.39Q/.5L-X detector is shown. Calculations were performed by the DETNAI.P Monte
Carlo code for the cases of lower level discriminator settings corresponding to 0.000
and 0.035 MeV.
156

157
Validation of the Plane Detector
Response Calculations
Published measurements and calculations are used to
verify the detector response calculations.
Iodine Escape Ratio
A number of researchers have made calculations and
measurements of the iodine escape ratio for Nal(Tl). In a
Nal(Tl) energy spectrum, this is the ratio of the area under
the iodine K fluorescent x ray escape peak to that of the
full energy deposition peak (often referred to as the photo
peak). Counts falling within the iodine escape peak are a
result of photons having photoelectric interactions within
the Nal(Tl) crystal after which iodine K fluorescent photons
escape the crystal. The iodine escape peak is actually com
posed of the several peaks because several different energy
iodine K x rays are emitted and can escape. The energies of
these peaks are simply the energy of the incident photon
(which is equal to the energy of the full energy deposition
peak) minus the energy of the escaping x rays. Because of
the relatively poor resolution of Nal(Tl), these individual
escape peaks are smeared into a single peak in any real
energy spectrum measurement.
Figure VI.5 compares calculations of the NAISPEC.PAS
code to two other sets of Monte Carlo calculations of the
iodine escape peak ratio (Dell and Ebert, 1969; Sharma et
al., 1972). Those two sets of calculations have been shown
to compare well to measurements of the iodine escape peak

Figure VI.5. Iodine escape peak ratio versus energy. A comparison of Monte Carlo
calculations of the iodine escape peak ratio for perpendicular incidence on Nal(Tl)
as a function of incident photon energy is shown. The results of Dell and Ebert
(1969), Sharma et al. (1972), and the NAISPEC.PAS codes are compared.
158

159
ratio. Calculations performed for this comparison modelled
the detector used by Dell and Ebert (1969) in the experimen
tal portion of their work. This detector consisted of a 2.5
cm (diameter) by 2.5 cm (thickness) Nal(Tl) crystal with a
0.013 cm beryllium window. All photon beams were tightly
collimated, small in diameter and incident perpendicularly
on the center of the face of the detector. These condi
tions, combined with the low energies of the photons used
(40 to 100 keV), make scatter out of the crystal negligible.
Therefore, a plane detector approximation for calculation
purposes is acceptable. As shown in Figure VI.5, the
NAISPEC.PAS calculations agree well with these other
efforts. The discrepancies which exist are a result of
differences in the basic data, assumptions, and techniques
used in the calculations. The Sharma paper provides an
excellent discussion of the calculation techniques they
used; the Dell and Ebert calculations are poorly docu
mented, but are probably very similar in nature to those of
Sharma et al. The effect of the various differences are in
some instances to increase, and others to decrease the
iodine escape ratio.
Sharma et al. assume a bare Nal(Tl) crystal suspended
in vacuum. The NAISPEC.PAS code models the beryllium wall
suspended in air. The effect of the presence of a low
atomic number material wall is to produce incoherent scat
ters which alter photon directions producing interactions,
on the average, closer to the surface of the Nal(Tl) crystal

160
(if the photons reach the crystal) and result in a greater
probability of escape of K fluorescent x rays. Actually,
the situation is more complicated since multiple incoherent
scatters can reduce the photon energy below the K edge
energy and thereby prevent the possibility of fluorescent
photon emission. This effect is more important for photon
energies not much greater than the iodine K edge energy.
Coherent scattering is not modelled in the Sharma cal
culations. Full coherent scattering with angular distribu
tions based on the atomic form factors of Hubbell et al.
(1975) is included in the NAISPEC.PAS model. Full coherent
scattering will alter directions of the interacting photons,
and for the reasons discussed in the paragraph above will
increase the escape ratio.
The calculations of Sharma et al. use only the Klein-
Nishina relationship to model the angular distribution of
the scatter after a Compton event. Full incoherent
scattering with angular distributions of the scattered
photons modified by the incoherent scattering functions of
Hubbell et al. (1975) is included in the NAISPEC.PAS code.
Lower incoherent interaction rates are the result of lower
cross sections. This will lower the escape ratio for the
reasons discussed above.
The K fluorescent yield is the total probability of
fluorescent emission following electron transition to a
vacancy in the K shell. Sharma et al. use a value of 0.91
from Fink et al. (1966). The most current value, which is

161
used in the NAISPEC.PAS and DETNAI.PAS codes is 0.882
(Bambynek et al., 1972; Lederer and Shirley, 1978). For the
NAISPEC.PAS code, this results in a larger full energy
deposition peak, and, hence, a lower iodine escape ratio.
The model of Sharma et al. lumps all K fluorescent pho
tons into a single energy (that of the most probable photon,
the K ^) and does not model L x ray emission (it follows
that no secondary emission after or emission is
modelled either). The NAISPEC.PAS code allows for four
individual K x ray energies, and L x ray emission, including
secondary L emission after K emission. The second most
probable K x ray photon is the which is lower in energy
than the K The average K x ray is less capable of es
caping the crystal and will result in a lower escape ratio.
The calculations of Sharma et al. assume any inter
action of a K x ray photon is an absorption. (Dell and
Ebert do not make this assumption). The NAISPEC.PAS makes
no assumption about how a K x ray will interact; its history
is followed until it is absorbed. This means that a photon
arising from a Compton scatter of a K x ray could escape the
crystal, increasing the escape ratio.
In the calculations of Sharma et al. any history of a
photon whose energy falls below 10 keV is terminated. There
is no termination of any history in the NAISPEC.PAS code
based on an energy cutoff. The lack of a cutoff allows
additional chances for very low energy photons to escape the
crystal, increasing the escape ratio.

162
Sharma et al. use the mass interaction coefficient data
of Grodstein (1957). The NAISPEC.PAS code uses the most
current published interaction data (Hubbell et al., 1975;
Hubbell, 1982; Storm and Israel, 1970). The incoherent
interaction coefficients in the Grodstein data are simply
calculated from the Klein-Nishina relationship. As a result
they are too high at low energies. Additionally, below 40
kev, the photoelectric data of Grodstein is very poor (15 to
20% low). The correct (lower) incoherent data will reduce
the escape ratio. The correct photoelectric data (higher)
will increase the escape ratio.
The model of Sharma et al. uses the broad energy mesh
of the Grodstein tables (14 energies between 10 and 300 keV)
and employs linear interpolation to obtain other values.
The NAISPEC.PAS code uses a fine mesh table constructed from
a cubic spline interpolation of the more modern data (183
energies between 1 and 300 keV), and uses log-log interpola
tion to obtain other values. Linear interpolation over
estimates the photoelectric interaction data in a coarse
mesh table leading to interactions nearer the crystal sur
face. The more accurate procedure of the NAISPEC.PAS code
will, therefore, lower the escape ratio.
The calculations of Sharma et al. are based on 10000
photon histories; the NAISPEC.PAS calculations are based on
50000 photon histories. The number of histories by itself
has no effect on the value of the escape ratio, but on how
precisely it is calculated.

163
Measured Energy Spectra
Figure VI.6 compares an energy spectrum measurement
made by Dell and Ebert (1969) as part of their iodine escape
work. The calculated energy spectrum is from the NAISPEC.
PAS code and employs a gaussian distribution to smear the
discrete energies calculated into the resolution of the
Nal(Tl) crystal employed in the measurements. Assumptions
on the variation of resolution with energy are from Berger
and Seltzer (1972). Agreement between the measured and
calculated spectra is seen to be good.
Shield and Edge Effects
The plane detector response described above is adjusted
for two types of photon events, which occur in the real de
tector, but not in the plane model. These effects are
caused by photons which penetrate the detector shield, enter
the side wall, and deposit energy in the Nal(Tl) crystal,
increasing the observed count rate above that which is
predicted by the plane detector response calculations; and
photons, which enter the bottom face of the detector and
exit the side wall of the detector without depositing
sufficient energy to produce a count, decreasing the ob
served count rate predicted by the plane detector response
calculations.
Calculation of the Correction Factor
A computer code DETCOR.PAS was written in Turbo Pascal
(Borland, 1985) to make a first order approximation of the
correction factor at each energy/angle mesh point in the

Figure VI.6. Measured and calculated Nal(Tl) spectra. A comparison of calculated
Nal(Tl) spectra due to perpendicularly incident Ka x rays of erbium on a 2.5 cm thick
crystal with a 0.013 cm thick beryllium window is shown. Measured values from Dell
and Ebert (1969) and calculated values from the NAISPEC.PAS code are normalized at
the maximum value of the full energy deposition peak (photopeak) .
164

165
plane detector response matrix. A full correction would
require a complete Monte Carlo calculation of the entire
process from source through detector system for each detec
tor position. Such calculations would be essentially im
possible to perform for the range of calculations required.
The small size of the detector being used merely increases
the problem by requiring large numbers of photon histories
to be followed to approach reasonable statistics. As will
be seen in comparisons of calculations and measurements in
Chapter VIII, the first order correction appears to be ade
quate for the problem. The DETCOR.PAS code models the full
detector and shield system in three dimensions. All layers,
including air spaces, are included (see Table III.l for
dimensions). Each energy/angle correction calculation en
tails a two-dimensional plane wave of photons, all of a
given energy and angle of incidence, impinging on the space
surrounding and occupied by the detector. Approximately
12000 photons with a spacing of 0.02 cm between adjacent
photons in the incident plane wave, are individually atten
uated through the three dimensional structure of the shield
and detector to determine each photon's probability of in
teraction within the Nal(Tl) crystal. This probability is
summed for all of the photons and compared to the same
quantity for a plane detector case with entrance restricted
to the size of the face of the detector. The ratio of these
two probabilities is the first order correction factor.
Mass attenuation coefficients for all the materials in the

166
calculation do not include coherent scattering, since these
events do not deposit energy and, generally, do not greatly
change the direction of travel of a photon. The model
implicitly assumes that the variation in fluence over the
size of the detector is small, which is a good approximation
for the small detector being used.
Results of the Correction Factor Calculations
Results of the calculations show that except at high
energies (200 keV or greater), the effect of photons pene
trating the shield into the side of the crystal outweighs
that of photons leaking through the side wall of the crys
tal, making the correction factor a number greater than
1.00. The reason for this phenomenon is twofold. Photons
in the low energy range under consideration are very rapidly
attenuated by the Nal(Tl) crystal, reducing the impact of
leakage to only those photons which strike very close to the
bottom edge of the crystal. The protrusion (see Figure
III.l) of the detector face below the shield (to avoid col-
limation), combined with the layer of low atomic number
material, which is packed around the sides of the crystal
within the aluminum housing (proprietary material), plays a
significant role. This side region is relatively poorly
shielded and allows significant numbers of photons to
penetrate into Nal(Tl) crystal through the side wall.
Figure VI.7 and VI.8 display, respectively, the plane
detector response function and the result of correcting it
for shield and edge effects.

Figure VI.7. Plane
Model .5M.39Q/.5L-X
angle of incidence.
detector response. The response of the plane model of a Bicron
Nal(Tl) detector is displayed as a function of photon energy and
167

Figure VI.8. Detector response with edge and shield correction. The response of the
plane model of a Bicron Model .5M.39Q/.5L-X Nal(Tl) detector, corrected for edge and
shield effects, is displayed as a function of photon energy and angle of incidence.
168

CHAPTER VII
MINE DETECTION MECHANISMS
The detection of a buried, nonmetallic antitank mine
using backscattered ionizing radiation depends upon dif
ferences between the characteristics of the reflected
photons for the cases of mine present and absent. These
differences derive from the simple physical characteristics
of the two cases. The mine represents a low atomic number
inclusion within the higher atomic number soil. Addition
ally, the mine has a definite geometric shape and includes a
region of air near its upper surface. While soil and ex
plosive densities are similar, the soil and air densities
are very dissimilar. This chapter describes the implica
tions of these physical differences in producing dissimilar
ities in the backscattered photon signals and provides the
basis for mine detection mechanisms to exploit them. Re
sults provided are from calculations using the SGLMIN.PAS
and MCPHOT.P codes.
Backscattered Photon Signal Differences
The physical differences discussed above lead to dissi
milarities in the fluence, energy fluence, spatial distri
bution, angular distribution, and energy spectra of the
backscattered photon signals. Additionally, the geometry of
169

170
the mine and its air layer produce edge effects and signal
variation with beam/mine intercept. Single scatter and
Monte Carlo calculations are used in this section to intro
duce the basic detection mechanisms resulting from the
physics and geometry of mine/soil system. Except for exami
nation of angle of incidence, all calculations in this sec
tion use a perpendicularly incident source beam; and, except
for the examination of edge effects, a beam intercept at the
center of the mine. Justification for concentration on per
pendicular incidence is provided later in the chapter.
Monte Carlo generated images, which examine multiple inter
cepts, are described Chapter VIII.
Fluence
Because the principal scatterer in the mine, the explo
sive material, has a lower atomic number than the soil which
surrounds it, the photon interaction characteristics in the
two materials are considerably different. The lower atomic
number of the explosive, at any given energy, results in a
lower photoelectric interaction probability and higher in
coherent scattering probability within the mine. This
produces a lower rate of photoelectric absorption and a
corresponding higher probability for photon backscatter.
Differences will be significant only for the energy region
in which the photoelectric interaction cross section of soil
is also significant. Above this energy region, incoherent
scattering is dominant in both materials, and is much less
capable of distinguishing between soil and explosive.

171
Figure VII.1 shows number albedos as a function of source
beam energy for perpendicular incidence on HTL soil, and the
centers of TST mines buried in HTL soil with their top sur
faces 0.0 (flush to the surface) and 2.5 cm below the
ground. The number albedo, representing the fraction of all
incident photons which are reflected, is directly propor
tional to the backscattered fluence. In all three cases,
the shapes of the number albedo curves are similar. The
number albedo is low at low energies because photoelectric
interactions are dominant. At these energies, photons are
much more likely to be absorbed than scattered. As source
photon energy increases, the probability of incoherent
scattering increases, accounting for the rise in the number
albedo. At higher energies the rate of increase slows and
the curves level off. This is a result of the preference in
incoherent scattering for forward scatter as energy in
creases. The case of the mine buried flush with the surface
shows the greatest difference from the soil alone. This is
expected since it presents the low atomic number explosive
directly to the beam. The difference for the case of the
mine buried at 2.5 cm is much smaller. At low energy there
is little difference from the soil only case. This is a
result of the inability of the low energy photons to pene
trate the soil layer in both entrance and exit directions.
As energy increases, photons are able to penetrate, but soil
attenuation reduces the backscattered signal. Since the
incoherent cross section per electron is only weakly

0.40
o
XJ
0)
-Q
<
L_
Q)
jQ
E
rs
0.30 -
0.20 -
0.10
0.00 -)iiiiiiiiiii|iiiiiii|
20 60 100 140 180 220
Energy (keV)
Figure VII.1. Number albedos versus energy for HTL soil and two TST mine cases.
The number albedos displayed in this figure are for perpendicularly incident photons
beams. The depth of burial of 0.0 cm refers to the top surface of the mine being
flush with the soil surface.

173
dependent on atomic number, and the density of soil and
explosive are similar, once the energy region of significant
photoelectric interaction is exceeded, the backscattered
fluences become similar. Figure VII.2 shows the ratios of
the number albedos for the mine at the surface to those of
the three major soils used in the research. The higher the
ratio between the mine and soil cases, the greater the
difference in the backscattered characteristics, and, in
general, the greater the ease of mine detection. The great
est ratio occurs at low energy because the greatest differ
ence between the photoelectric interaction cross sections of
soil and explosive also occurs here. The higher atomic num
ber soil absorbs the incident photons much more efficiently
than the explosive. MCL soil with the highest atomic number
of the three soils shows the greatest contrast. Figure
VII.3 shows this same ratio for the three soils with the
mine buried at 2.5 cm. Apparent in this figure is the exis
tence of optimum energies for mine detection. For the rea
sons discussed above, the backscattered responses for the
buried mine and soil cases are more similar at both low and
high energy. Somewhere in between, an optimum source energy
exists. This optimum energy is dependent upon the atomic
number of the soil material. In NSL soil, it is about 80
keV; in HTL soil, about 100 keV; and in MCL soil, about 150
keV. This variation with soil type is simply a result of
the extent of the energy region in which photoelectric in
teractions are important. Beyond this region the incoherent

o
D
tu
O
"O
0
J3
<
L_
0
jQ
E
n
20 60 100 140 180 220
Energy (keV)
Figure VII.2. Number albedo ratios versus energy for the TST mine at 0.0 cm in three
soils. The ratio of the number albedos of mine present to soil only are shown for
three soil types for perpendicularly incident photon beams striking the center of the
TST mine buried flush with the soil surface.
174

o
o
o
O
0
.o
<
L-
0
JD
E
rj
Energy (keV)
Figure VII.3. Number albedo ratios versus energy for the TST mine at 2.5 cm in three
soils. The ratio of the number albedos of mine present to soil only are shown for
three soil types for perpendicularly incident photon beams striking the center of the
TST mine at a depth of burial of 2.5 cm.
175

176
interaction dominates and fails to significantly differen
tiate between soil and explosive. This region of photo
electric importance extends furthest in higher atomic number
materials. Similar conclusions are reached later in this
chapter for more realistic detector configurations in which
energy requirements for the source are established. It is
apparent that the use of high energy sources is not produc
tive. Optimum source energies for an uncollimated fluence
detector lie below 200 keV. As discussed below, this is
also true for collimated detectors.
Energy Fluence
The energy albedo represents the fraction of incident
photon energy reflected from a surface. It is, therefore,
directly proportional to the backscattered energy fluence.
Figure VII.4 shows the energy albedo as a function of source
energy for the same cases examined in the preceding section.
Comparison with Figure VII.1 indicates that the energy
albedos are smaller in each case than the number albedos.
This is a result of the loss of energy which occurs with
each incoherent scattering event. The energy albedo curves
also exhibit maxima in the energy region of consideration.
This is a result of the nature of the energy loss phenome
non; the fractional loss in energy is greater at higher
incident energy in incoherent scattering interactions. The
maximum is most apparent in the lowest atomic number case,
the mine buried flush to the surface. This is because the
average photon undergoes more incoherent scattering

Energy Albedo
0.00 -jiii|iii|iii|iiiiiii|
20 60 100 140 180 220
Energy (keV)
Figure VII.4. Energy albedos versus energy for HTL soil and two TST mine cases,
energy albedos displayed in this figure are for perpendicularly incident photon
beams.
The
177

178
interactions before reflection, resulting in greater energy
loss, than in the higher atomic number cases. Figure VII.5
displays this fact by showing the fraction of backscattered
photons which have undergone multiple scatter for each case.
The ratio of the energy albedo of a given atomic number
material to a higher atomic number material can be shown to
be always less than the corresponding number albedo ratio.
Bulatov and Andrushin (1967) use the calculated albedos of
Berger and Raso (1960) to show that the ratio of number to
energy albedo versus energy is a linear relationship in the
energy range above 200 keV. The slope of the line is found
to be greatest in lower atomic number materials. Table
VII.1 compares the results of Bulatov and Andrushin to cal
culations performed by the MCPHOT codes, and recalculation
from the original Berger and Raso data. Figure VII.6 shows
this linear relationship below 200 keV for the three mine
detection related cases. Algebraic manipulation provides
b(soil) + m(soil) E
b(TNT) + m(TNT) E '
where Ag is an energy albedo,
An is a number albedo,
b is an intercept, and
m is a slope.
Since the slope for a lower atomic number material is larger
and the intercepts are nearly equal, the bracketed quantity
is a number less than 1.00. Accordingly, the ratio of
Ae(TNT) A^(TNT)
Ag (soil) AN(soil)

Figure VII.5. Multiple scatter fraction versus energy for HTL soil and two TST mine
cases. The fraction of all backscattered photons reaching the detector, which have
been multiply scattered, is compared for three scattering cases as a function of
source energy.
179

180
TABLE VII.1
Comparison of the Linear Relationship
Between the Ratio of Number to Energy Albedo
and Source Energy at Perpendicular Incidence
Bulatov and Berger and MCPHOT.P
Andrushin (1967) Raso (1960)
Concrete
slope (MeV 1)
4.28
4.45
4.47
intercept
1.00
0.94
0.95
Iron .
slope (MeV-1)
3.55
3.59
3.53
intercept
1.00
0.96
0.98
HTL soil ,
slope (MeV-1)
-
-
4.58
intercept


0.93
HTL soil with TST
mine flush with
surface slope (MeV j
-
-
5.27
intercept


0.98
HTL soil with TST
mine at 2.5 cm depth_^
of burial slope (MeV x)
_
4.78
intercept
-
-
0.94

Number Albedo/Energy Albedo
Energy (keV)
Figure VII.6. Ratio of number to energy albedo for HTL soil and two TST mine cases.
The relationship between the number to energy albedo ratio as a function of energy is
linear.
181

182
energy albedos in the mine detection cases is always smaller
than the ratio of number albedos. This suggests that a
fluence detector, such as a scintillator, would provide
somewhat better discrimination between mine and soil than a
detector based on energy absorption, such as an ionization
chamber.
Spatial Distribution
Figures VII.7 and VII.8 show Monte Carlo calculations
of the spatial distribution of the backscattered fluence
intercepting a plane located 34.6075 cm (this height
corresponds to that used in the measurements portion of the
work) above the soil surface for the case of HTL soil alone
and soil with mine buried flush to the surface. The source
beam is composed of 100 keV photons (as shown later in this
chapter, approximately optimum for mine detection in HTL
soil) and is perpendicularly incident. Since the beam axis
intercepts the plane at its center, the figure indicates
that the greatest backscattering occurs directly along the
source direction. This is because the shortest attenuation
path out of each material is in that direction. Figure
VII.9 shows the quotient of spatial distribution of the mine
at 0.0 cm to that of soil. The dimensions of the display
have been reduced from those of the two preceding figures,
and symmetry considerations employed to eliminate large
variations in the quotient resulting from very small and
hence more uncertain responses. The ratio has a relative
minimum in the direction of greatest backscatter. While the

Figure VII.7. Spatial distribution of backscattered fluence from 100 keV photons
perpendicularly incident on HTL soil. The fluence (photons/(incident photon-cin ))
striking a plane located 34.6075 cm above and parallel to the soil surface is shown.
The source beam is incident at the origin of the x-y plane at the soil surface.
183

Figure VII.8. Spatial distribution of backscattered fluence from 100 keV photons
perpendicularly on the centeij of the TST mine at 0.0 cm. The fluence
(photons/( incident photon-cin )) striking a plane located 34.6075 cm above and
parallel to the soil surface is shown. The source beam is incident at the origin of
the x-y plane at the soil surface, which is also the center of the top face of the
mine cylinder in this example.
184

Figure VII.9. Spatial distribution of of the mine to soil ratio of backscattered
fluence from perpendicularly incident 100 keV photons. This figure displays the
ratio of the two preceding figures. A minimum in the ratio occurs along the
direction of greatest backscatter.
185

186
ratio is greater than 1.00 everywhere, it is higher at posi
tions further from the beam axis because, for equal slant
paths through their respective materials, photons traveling
through explosive are less attenuated than those travelling
through soil. The existence of the central minimum is es
sentially due to the single scattered component. Figure
VII.10 shows the same quotient for the single scattered
component only, more clearly revealing its origin. This
result implies that a detector will be better able to detect
mines if the regions corresponding to the central minimum
are not included within it. As a practical matter, part of
the central region must be removed to allow raster of the
beam.
Angular Distribution
The angular distribution referred to in this section is
that of the photons striking a plane above the soil surface
after backscatter from soil or mine. Figure VII.11 shows
the differential angular spectra for the cases under discus
sion for a perpendicularly incident 100 keV beam. Zero
radians or 0 degrees is equivalent to perpendicular inci
dence on the plane. Figure VII.12 shows the same spectra
for the multiply scattered photons only. Greater differ
ences in ratios between the soil and mine cases in the
multiple scatter spectra suggests that a detector which is
capable of removing the single scatter component would be
more sensitive to mine detection. The differences in the
multiple scattered spectra are a result of the much lower

Figure VII.10. Spatial distribution of th<
perpendicularly incident 100 keV photons,
to soil fluence ratio intercepting a plane
the soil surface is shown.
single scattered mine to soil ratio from
The single scatterer component of the mine
located 34.6075 cm above and parallel to
187

Photons/Radian/Source Photon
Figure VII.11. Angular distribution of backscattered fluence from 100 keV photons
perpendicularly incident on HTL soil and two TST mine cases.
188

Photons/Radian/Source Photon
Figure VII.12. Angular distribution of the multiple scattered fluence from 100 keV
photons perpendicularly incident on the HTL soil and two TST mine cases.
189

190
probability of such scatters in soil compared to that in the
lower atomic number explosive. Removing the single scat
tered component can be accomplished by collimation of de
tector segments located away from the beam axis.
Figures VII.13 and VII.14 show the results of
calculations for a plane of incidence parallel to the soil
surface at a height of 34.6075 cm from which a central 25 cm
radius about the beam axis has been removed. The results in
this figure are shown in terms of the integral angular spec
tra. Figure VII.13 compares the ratios of the integral
spectrum of the mine at 0.0 cm to that of soil for the full
plane and the plane missing the central disk. Figure VII.14
shows the same results at 2.5 cm depth of burial. The ra
tios achieved by this new configuration are large in both
cases. Figure VII.15 reveals the reason for the jump in the
ratios for collimators which admit photons at angles of in
cidence of approximately 0.65 (37 degrees) radians or less
(this angle is specific to this calculation). This colli
mator geometry achieves a significant exclusion of the
single scattered fluence. The large- ratios are a result of
the much greater lateral path distance a multiple scattered
photon must travel to reach the detector when it is highly
collimated. Long paths through soil produce a much greater
attenuation than paths through explosive. The total fluence
at the detector is much reduced from the uncollimated
detector calculations, as indicated by the large uncertain
ties associated with small acceptance angles in Figures
VII.13 and VII.14.

0.0 ~|~i ~T'i"T~r r~r~f 1 1 r |~r~r~i rrn"l i t rr T~r~r ~i r r >
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40
Collimator Acceptance Angle (radians)
Figure VII.13. Mine to soil fluence ratio versus collimator acceptance angle for 100
keV photons perpendicularly incident on the TST mine at 0.0 cm in HTL soil. A 25 cm
radius central section of the detection plane has been removed. The plane is located
34.6075 cm above and parallel to the soil surface.
191

4.0
0.0 iiiiir~i| iii|mr~|mi|r-1i|r~ii|r~ir
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40
Collimator Acceptance Angle (radians)
Figure VII.14. Mine to soil fluence ratio versus collimator acceptance angle for 100
keV photons perpendicularly incident on the TST mine at 2.5 cm in HTL soil. A 25 cm
radius central section of the detection plane has been removed. The plane is located
34.6075 cm above and parallel to the soil surface.
192

0.5 i "i" | i i i | r~r r | i i i [ rrn'T rr i i r r \ r i r
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40
Collimator Acceptance Angle (radians)
Figure VII.15. Multiple scatter fraction versus collimator acceptance angle for 100
keV photons perpendicularly incident on the TST mine at 0.0 cm in HTL soil. The
fraction of backscattered photons which are multiply scattered intercepting a plane
with its central 25 cm radius section missing at a height of 34.6075 cm above the
soil surface is shown.
193

194
It is significant that an optimum collimation angle may
occur for a particular combination of photon energy, detec
tor height, and mine geometry. If the collimator acceptance
angle is too large, single scattered photons are admitted,
making the ratio low. As noted in Chapter II, many early
applications of scatter imaging made use of the fact that
the single scattered fluence is very nearly independent of
all variables except density. Since the mine and soil
densities are similar, the single scattered fluences are
roughly alike. If the collimator acceptance angle is too
small, the area viewed by the collimated region of the
detection plane shrinks. When the geometry is such that the
area viewed is at the edge of the mine, the ratio drops.
This edge effect is caused by the air layer in the mine.
The photons scattering in the explosive enter the soil at
depths which prevent them from reaching the surface. The
average photon scattering in the soil, which eventually
reaches the collimated plane, is always close to the
surface. In extreme cases, the ratio may fall below unity.
Energy Spectra
Figure VII.16 shows the differential energy spectra for
100 keV photons perpendicularly incident on the problem
cases. The major difference in the spectral shapes with the
mine present occurs in the lower energy region and is due to
the increased multiple scatter in the lower atomic number
materials. The break in the smoothness of the spectral
curves at high energy is due to coherent backscatter. The

Photons/MeV/lncident Photon
20 40 60 80 100
Scattered Photon Energy (keV)
Figure VII.16. Differential energy spectra for 100 keV photons perpendicularly in
cident on HTL soil and two TST mine cases. Differential energy spectra (photons/
(source photon MeV)), calculated for the soil and mine present cases. The major
difference between soil and mine is at low energy.
195

196
low energy differences suggest energy discrimination which
removes high energy components might be useful in mine
detection. Figure VII.17 shows the ratio of the integral
spectra for the mine present cases to that of the soil only
case. This figure emphasizes the desirability of removing
the higher energy scatter components. At low energy the
ratio is large; at high energy, it becomes equal to the
number albedo ratio. Three significant problems exist for a
detector based on this concept. First, the number of low
energy backscattered photons is small, as indicated by the
large uncertainties at low energy in Figure VII.17. Second,
if the source contains low energy photons, as most x-ray
spectra do, the backscattered spectra will also contain many
low energy photons. This is because the fractional energy
lost by a low energy photon in an incoherent interaction is
small. X-ray spectra without low energy components can be
produced by heavy filtration by high atomic number mater
ials, but this further reduces the magnitude of an already
small signal at a fixed power level of the x-ray generator,
and may make source shielding leakage radiation the origin
of a significant contributor to the signal. Third, if a
radiation detector based on scintillation is employed and
produces a significant Compton continuum, the low energy
responses will be masked. Large area scintillation detec
tors, containing high atomic number materials would reduce
this problem.

Figure VII.17. Ratios of mine and soil integral energy spectra for two TST mine
cases in HTL soil. The energy value appearing in the graph is that of the upper end
of the energy window with the lower end set at zero.
197

198
Edge Effects
An example of an edge effect has been discussed in the
section concerning angular distributions of the backscat-
tered fluence. The presence of the air layer in the mine is
the principal cause for the edge effects. As first noted by
Preiss and Livnat (1973), the air layer reduces the back-
scattered fluence from that produced by a mine composed of
solid explosive. Preiss and Livnat used an uncollimated,
high energy radionuclide source with a collimated asymmetri
cally located detector to enhance this reduction in re
sponse. Other edge effects are produced by the air layer
when the source beam strikes just inside or outside the edge
of a mine. The edge effects can be described most simply in
terms of a single scatter model. Figure VII.18 shows the
geometry of the edge effect phenomena. The top portion of
the figure shows two photons scattering at the same polar
angle, 0 but at azimuthal angles which differ by 180 de
grees. These scattered photons are produced by a beam
striking near the inside edge of the mine. The two detector
positions, which are symmetric with respect to the beam, but
not with respect to the mine center, lie in the paths of the
two photons. The paths taken by the two photons are through
different materials. The path on the left includes con
siderably more air than the path on the right. The trans
mission probability along the left path will be much greater
than that of the right path which traverses more soil.
Extension of this argument to all scattering paths for a

199
left source right
left source right
detector detector
Figure VII.18. Edge effect geometries. (a) Edge effect
produced by a beam intercept just inside the mine wall.
(b) Edge effect produced by a beam intercept just outside
the mine wall.

200
large number of incident photons results in the response of
the detector on the left being higher than that on the
right. The lower half of the figure shows the analogous
basis for the edge effect of a beam striking just outside
the mine. Here, the path on the left includes air, while
the path on the right is entirely through soil.
Figure VII.19 shows the single scatter spatial distri
bution resulting from a perpendicularly incident, 100 keV
photon beam striking just inside of the edge of the mine
buried at 2.5 cm. Examination of this figure reveals an
asymmetric spatial distribution of the backscattered fluence
response. Fewer photons are backscattered into the positive
y half of the plane than into the negative y portion.
Figures VII.20 and VII.21 more clearly display this type of
asymmetry by showing the spatial distribution of the single
scatter mine to soil fluence ratios for this inside inter
cept, and an intercept just outside the edge. A detector
occupying the left front portion of the plane of Figure
VII.20 will record a response less than that of soil alone.
This is a result of the air layer allowing photons to reach
depths normally not attainable. These deeply located pho
tons are then unable to reach the detector through the long
slant paths through soil. The reduction in response occurs
because these photons produce essentially no contribution to
the backscattered fluence as they traverse the low density
air.

Figure VII.19. Spatial distribution of the single scattered fluence from a 100 keV
photon beam perpendicularly incident on the inside edge of the TST mine. The single
scattered fluence (photons/(incident photon-cnr )) striking a plane located 34.6075 cm
above and parallel to the soil surface is shown. The mine is buried at a depth of
2.5 cm in NSL soil.
201

Figure VII.20. Spatial distribution of the single scattered mine to soil fluence
response ratio for a 100 keV photon beam perpendicularly incident on the inside edge
of the TST mine. This figure shows the ratio of the spatial distribution of single
scattered fluence of Figure VII.19 with the TST mine at a depth of burial of 2.5 cm
in NSL soil to that produced without a mine present.
202

Q)
<0
O
&
$
cP
Figure VII.21. Spatial distribution of the single scattered mine to soil fluence
response ratio for a 100 keV photon beam perpendicularly incident outside the edge of
the TST mine. The TST mine is buried at a depth of 2.5 cm in NSL soil. The ratio is
shown at a height of 34.6075 cm above the soil plane.
203

204
Conclusions Based on Signal Differences
The differences in the backscattered signals for mine
present and absent suggest the examination of four detector
types. These detector types are a simple, uncollimated
detector to exploit differences in fluence; a collimated
detector to exploit differences in the angular distribution
of the fluence; an energy window detector to exploit the
differences in the low energy spectra; and a segmented
fluence detector to exploit differences caused by edge
effects. Each of these detector types must be capable of
rapidly detecting mines over a path wide enough to allow
passage of an armored vehicle. This requirement results in
detector configurations similar to that shown in Figure
II.1, that is, large area detectors which allow rastering of
an x-ray source beam. The existence of the raster gap and
practical considerations of reasonable size result in
configurations different than those employed in the simple
physical arguments described above. The geometry of these
more realistic configurations is examined later in this
chapter. Despite the increase in geometric complexity,
calculations for the more realistic configurations are shown
to closely follow the general results presented above. Each
of the more realistic detector types is modelled as two
panels of detecting material located above and parallel to
the soil surface, and separated by a gap to allow raster of
the source beam. The collimated detector adds the capabil
ity to limit the acceptance angle of photons incident on the

205
detector. The energy window detector selects and accepts
for counting, only those photons within a specific energy
range striking the uncollimated panels. The segmented
detector divides the panels into regions for comparisons of
asymmetric fluence responses.
Except in the case of the small Nal(Tl) detector, used
in the measurements to obtain images and to verify calcu
lated predictions, only fluence response is considered. As
long as the detector employed is capable of efficiently
sensing photons in the energy range below 200 keV, the error
introduced by considering only the fluence response is not
major. Figure VII.22 displays the Nal(Tl) and fluence
responses for the case of the TST mine buried at 2.5 cm in
HTL soil as a function of source beam energy. The shapes of
the response curves are very similar and results expressed
in terms of ratios of fluence responses can be expected to
closely follow detector response ratios. Differences will
exist at low source energies. As an example, Figure VII.23
displays the ratio of the detector response to the fluence
response for the case just discussed. The ratio is small at
low energies because of the detector materials in front of
the scintillation crystal and due to the lower level energy
discrimination (35 keV in this example). The photons
striking the detector are lower in energy than the source
photons due to the incoherent scattering process, so that
the figure is really a nonlinearly, energy-shifted version
of the detector response versus energy curves, integrated

Source Photon Energy (keV)
Figure VII.22. Nal(Tl) detector response and fluence response versus source beam
energy. The responses (counts/source photon) are for perpendicular incidence of
photon beams on the center of the TST mine buried at a depth of 2.5 cm in HTL soil.
Both responses are for an infinite plane at a height of 34.6075 cm above the soil
surface.
206

Source Photon Energy (keV)
Figure VII.23. Ratio of Nal(Tl) detector response to fluence response as a function
of source energy. This figure shows the ratio of the two responses displayed in
Figure VII.22.

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over all angles of incidence, presented in Chapter VI (com
pare this figure with Figure VI.4). The low ratio at low
source energies is not of major consequence because such
source photons do not contribute strongly to either of the
responses. The energy window detector, which uses low
energy photons as its detection mechanism, is a possible
exception to these comments. If significant differences in
the energy distributions of the mine and soil cases exist
within energy bin widths (5 keV) used in the calculations,
errors will be introduced as a result of the rapid variation
in the detector to fluence response ratio at low energy.
Irradiation Geometry and
Optimum Energy Considerations
A combination of practical concerns, and the physics of
the backscatter problem limit the geometric relationship
between detector and soil surface. With the large area,
panel detector configuration as a basis, the irradiation
geometry is examined. Optimum source energies are also
discussed.
Height of Detector
The height of the detector above the soil surface must
allow for operation over rough terrain. From a purely
theoretical standpoint the optimum height would be deter
mined as that which maximizes the ratio of mine present to
mine absent response while providing the largest possible
fluence striking the detector. This height depends on the

209
energy of the source beam and the panel geometry. Such
considerations lead to optimum heights on the order of 15 to
25 cm for uncollimated detectors, dependent upon the width
of the panels employed. As a practical concern, the height
is determined by the rough terrain operation requirement.
Heights of approximately 30 cm above the soil surface are
probably the minimum acceptable to preclude damage to the
detector. Even this may not be enough if large collimators
are employed. With the exception of calculations to
determine the effect of height variation, computations in
this study have been performed for a detector height of
34.6075 cm. This height corresponds to that used in
measurements and is near the minimum acceptable, and hence
close to the practical optimum. A description of sensi
tivity to height variation of the detectors is provided in
Chapter VIII.
Angle of Incidence
The optimum angle of incidence for the source beam on
the soil is zero degrees (perpendicular). This angle pro
vides the maximum penetration depth into the soil. All
other angles effectively increase the apparent depth of
burial of the mine, making detection more difficult. An
objection to perpendicular incidence is that the maximum
backscattered response is located on line with the source
beam (see Figures VII.7 and VII.8), where a detector cannot
be placed. However, the existence of the central minimum in
the mine to soil response ratio, discussed above, makes

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inclusion of this region unattractive. Table VII.2 shows an
example of the effect of angles of incidence other than zero
degrees on the mine to soil ratio for collimated and uncol
limated fluence detectors. A number albedo detector is
inclu