DATA ACQUISITION AND REDUCTION OF

HIGH RESOLUTION GAMMA-RAY SPECTRA

,By

DAVID BALDWIN COTTRELL

A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF

THE UNIVERSITY OF FLORIDA IN PARTIAL

FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

1973

TO MY WIFE

FOR HER PATIENCE

AND ENCOURAGEMENT

ACKNOWLEDGEMENTS

The author wishes to express his gratitude to the miny people

who contributed to the success of this project. First and foremost

is his research director, Dr. Stuart P. Cram, whose continued guid-

ance, encouragement, and enthusiastic support made this work possible.

The author is also grateful to the other members of his committee,

Dr. Roger G. Bates, Dr. James D. Winefordner, Dr. William H. Ellis,

and Dr. Frank G. Martin, for their help and cooperation during the

course of this study. Finally, the helpful discussions with fellow

members of the research group are gratefully acknowledged.

Special thanks go to Jack E. Leitner for his unselfish coopera-

tion and time during the early months of this work. His many helpful

discussions concerning computer operation contributed greatly to the

success of this project.

The design of the electronic components used in this work was

contributed by Mr. Bob Dugan and his able staff in the electronics

lab of the Chemistry Department.

The author wishes to acknowledge the financial support which he

has received. This research was supported in part by NSF Research

Grant No. GP-14754, and in part by a Traineeship from the National

Science Foundation.

The author's deep appreciation goes to Mrs. Edna Roberts, his

typist, for her expert work.

Finally, the author wishes to express his gratitude to his

parents, Mr. and Mrs. R. E. Cottrell, for their faith and encourage-

ment, and to his wife, Liz, for her pn.. nc anid understanding through-

out the duration of this work.

TABLE OF CO:TE~N'S

Page

ACK NO-,LEDGE ENTS ...... ......... ..... iii

LIST OF TABLES . . . . . . ... . . . . vii

LIST OF FIGU ES . . . . . . . . . . viii

ABSTRACT . . . . . . . . . . . . xiv

INTRODUCTION . . . . . . . . .. ... . 1

Research Objectives . . . . . . . . .. .

Historical Review . . . . . . . . . 2

TIEORETICAL . . . . . .. . . . . . 8

Data Smoothing . . . . . . . . . . 8

Peak Detection . . . . . . . . . . 9

Peak Quantitation . . . . . . . . . 14

Curve Fitting ..................... 18

Curve Fitting . . . . . . . . . . 18

Method of Standard Addition . . . . . ... 27

EXPERIMENTAL . . . . . . . . ... . . . 30

Hardware . . . . . . . . .. . . . 33

Interface . . . . . . . . ... . 33

Timing System . . . . . . . . . 36

Software . . . . . . . . .. . . . 39

Data Acquisition . . . . . . .. . 40

Data Printout . . . . . . . . . 46

Display . . . . . . . . ... . . 46

Data Smoothing. . . . . . . . . . 53

Page

. . . . . . . 5

Peak Detection .

Preparation of FOCAL Compatible Data . . . 69

RESULTS AND DISCUSSION . . . .

System Evaluation . . . .

Data Smoothing . . . . .

Peak Detection . . . . .

Curve Fitting . . . . .

Peak Areas . . . . . .

Liver Analysis . . . . .

APPENDICES . . . . . .

APPENDIX I. CORE RESIDENT SOFTWARE .

APPENDIX II. FOCAL PROGRAMS . .

1. Photopeak Fitting Routine

2. Baseline Fitting Routine .

3. Calculation of the Total Fit

4. Numerical Integration by the

5. Linear Least Squares . .

BIBLIOGRAPHY . . . . . .

BIOGRAPHICAL SKETCH . . . . .

ted Curve

Trapezoid

. .

. .

. .

. . . .

. . .

. .

. . .

. . .

. .

thod

75

75

88

94

109

194

198

227

228

287

288

291

294

296

298

300

305

LIST OF TABLES

TABLE

I EXPERIMENTAL CONDITIONS FOR THE SAMPLE SPECTRA . .

II COMBINED RESULTS OF THE AUTOMATED PEAK SEARCHES .

III NUMBER OF PEAKS FOUND BY THE AUTOMATED PEAK SEARCHES

IV PERCENT CHANGE IN THE RESIDUAL OF THE CURVE

FITTING FUNCTION . . . . . . . .

V DESCRIPTION OF PEAKS SELECTED FOR CURVE FITTING .

VI INITIAL AND FINAL VALUES FROM THE CURVE

FITTING CALCULATIONS . . . . . . . .

VII INITIAL AND FINAL VALUES FROM THE CURVE

FITTING CALCULATIONS . . . . . . . .

VIII CURVE FITTING RESULTS . . . . . . . .

IX CURVE FITTING RESULTS . . . . . . . .

X CURVE FITTING RESULTS . . . . . . . .

XI SIGNIFICANT PEAKS IN AN IRRADIATED LIVER SAMPLE .

XII EXPERIMENTAL CONDITIONS FOR THE LIVER ANALYSIS . .

XIII RESULTS OF THE LIVER ANALYSIS . . . . . .

XIV RESULTS OF THE LIVER ANALYSIS . . . . . .

XV EXPERIMENTAL AND NATIONAL BUREAU OF STANDARDS

RESULTS OF THE ANALYSIS OF STANDARD REFERENCE

MATERIAL 1577 (BOVINE LIVER) . . . . . .

vii

Page

76

96

102

. . 115

. . 116

. . 117

. . 120

. . 196

. . 197

. . 199

. . 205

. . 207

. . 209

. . 210

. . 223

LIST OF FIGURES

Figure

1. Two possible peak shapes in a digital, gamma-

ray spectrum . . . . . . . . .

2. Quantitative peak areas from three different

methods . . . . . . . . . .

3. Physical interpretations of the eight parameters

in a photopeak fitting function . . . .

4. Block diagram of the experimental system . .

5. Interface between an analog to digital converter

and a PDP-8/L computer . . . . . .

6. Timing system for accurate and precise timing

control of the data acquisition software. A

push button switch is engaged from time T to

T The timing pulse is generated from time

T to T and corresponds in length to the time

B+ 0

preset on the thumbwheel switch . . . .

7. Flowchart of the data acquisition software . .

8. Timing relations between the computer and

analog to digital converter . . . . .

9. Flowchart of the data printout software . .

10. Sample page from the computer printout of

a stored spectrum . . . . . . .

11. Flowchart of the display software . . . .

12. Flowchart of the data smoothing software . .

15. Flowchart of the peak detection (method one)

software . . . . . . .

14. Flowchart of the software which tests for peak

validity and permanently stores valid peak

locations and boundaries . . . . . .

viii

Page

. . 11

. . 17

. . 22

. . 31

. . 35

. . 37

. . 42

. . 45

. . 48

. . 50

. . 52

. . 54

. . 57

. . 59

Figure

15. Flowchart of the peak detection (method two)

software . . . . . . . . . .

16. Flowchart of the software which determines

the first differences and prints the

final results of the peak searches ..

17. Flowchart of the software which .calculates the

average height of the noise over 1:0 channels

18. Flowchart of the software which calculates and

prints the peak areas by the total peak

area and Wasson methods . . . . . .

19. Flowchart of the software which converts the

integer data to floating point and stores the

results in core locations accessible by the

FOCAL subroutine FNEW . . . . . .

20. Plot of spectrum 6, attenuated by a factor of

(x 8). The full energy range of the spectrum

is 0-1.578 MeV (0.624 KeV/channel) . . .

21. Plot of spectrum 6, unattenuated. The full

energy range of the spectrum is 0-1.578

MeV (0.624 KeV/channel) . . . . . .

22. Plot of spectrum 6, attenuated by a factor of

(x 1/2). The full energy range of the

spectrum is 0-1.578 MeV (0.624 KeV/channel)

25. Plot of channel number vs. photopeak energy

for the full energy range used in the

research (data obtained from spectrum 6). .

24. Plot of channel number vs. photopeak energy

for the low energy region (data obtained

from spectrum 10) . . . . . . .

25. Plot of the resolution of the experimental

system vs. photopeak energy for the full

energy range used in the research (data

obtained from all eleven sample spectra)

26. Effects of the statistical scatter on the

total peak area, resulting in too large

(peak A) or too small (peak B) a quanti-

tative area . . . . . . . .

. .. 66

S . 71

. 75

S. 78

S. 80

82

Page

Figure

27.

Page

Plot of spectrum 9, unattenuated. The full

energy range of the spectrum is 0- KeV

(0.471 KeV/channel) . . . . . .

28. Plot of spectrum 7, unattenuatea. The full

energy range of the spectrum is 0-;j7 KeV

(0.165 KeV/channel) . . . . . .

29. Plot of spectrum 11, attenuated by a factor

of (x 1/2). The full energy range of the

spectrum is 477-955 KeV (0.2553 KeV/channel.

50. Plot of spectrum 4, unattenuated. The full

energy range of the spectrum is 0.1.578 MeV

(0.624 KeV/channel) . . . . . .

31. Plot of the percent change in the resiLu-l

sum of squares vs. the number of iterations

performed in the curve fitting process .

32. Raw data and fitted curve (offset) for the

1115.51 KeV Zn 65 peak taken from

spectrum 2 . . . . . . . .

55. Raw data and fitted curve (offset) for the

884.5 KeV Ag 110m peak taken from

spectrum 1 . . . . . . . .

34. Raw data and fitted curve (offset) for the

884.5 KeV Ag 110m peak taken from

spectrum 9 . . . . . . . .

35. Raw data and fitted curve (offset) for the

937.5 KeV Ag 110m peak taken from

spectrum 1 . . . . . . . .

36. Raw data and fitted curve (offset) for the

937.5 KeV Ag 110m peak taken from

spectrum 9 . . . . . . . .

37. Raw data and fitted curve (offset) for the

884.5 KeV Ag-ll0m peak taken from

spectrum 11 . . . . . . . .

38. Raw data and fitted curve (offset) for the

320.08 KeV Cr 51 peak taken from

spectrum 7 . . . . . . . .

39. Raw data and fitted curve (offset) for the

1099.27 KeV Fe 59 peak taken from

spectrum 3 . . . . .

S . 01

105

108

122

. . . 128

. . . 150

. . . 152

. . . 157

40. Raw data and fitted curve (offset) for

the 937.5 KeV Ag 110m peak taken

from spectrum 4 . . . . . . . . 159

41. Raw data and fitted curve (offset) for

the 884.5 KeV Ag 110m peak taken

from spectrum 4 . . . . . . . .... .. 141

42. Raw data and fitted curve (offset) for

the 121.13 KeV Se 75 peak taken

from spectrum 7 . . . . . . . .... .. 143

45. Raw data and fitted curve (offset) for

the 511 KeV annihilation peak taken

from spectrum 8 . . . . . . . .... .. 145

44. Raw data and fitted curve (offset) for

the 817.9 KeV Ag 110m peak taken

from spectrum 1 . . . . . . . .... . 147

45. Raw data and fitted curve (offset) for

the 817.9 KeV Ag 110m peak taken

from spectrum 9 . . . . . . . .... . 149

46. Raw data and fitted curve (offset) for

the 446.2 KeV Ag 110m peak taken

from spectrum 1 . . . . . . . .... .. 151

47. Raw data and fitted curve (offset) for

the 400.64 KeV Se 75 peak taken

from spectrum 10 . . . . . . . ... 155

48. Raw data and fitted curve (offset) for the

817.9 KeV Ag 110m peak taken from

spectrum 4 . . . . . . . . ... . 155

49. Raw data and fitted curve (offset) for the

446.2 KeV Ag 110m peak taken from

spectrum 10 . .. . . . . . . . . . 157

50. Raw data and fitted curve (offset) for the

620.1 KeV Ag 110m peak taken from

spectrum 9 . . . . . . . . .. . . 159

51. Raw data and fitted curve (offset) for the

96.75 KeV Se 75 peak taken from

spectrum 7 . . . . . . .. .. . . . 162

52. Raw data and fitted curve (offset) for the

96.75 KeV Se 75 peak taken from

spectrum 10 . . . . . . .. . . . . 164

Figure

Page

53. Raw data and fitted curve (offset) for the

817.9 KeV Ag 110m peak taken from

spectrum 11 . . . . . . . .... . 167

54. Raw data and fitted curve (offset) for the

620.1 KeV Ag 110m peak taken from

spectrum 11 . . . . . . . .... . 169

55. Raw data and fitted curve (offset) for the

505.89 KeV Se 75 peak taken from

spectrum 7 . . . . . . . . . . 171

56. Raw data and fitted curve (offset) for the

505.89 KeV Se 75 peak taken from

spectrum 10 .. . . . . . . . . . 173

57. Raw data and fitted curve (offset) for the

1173.2 KeV Co 60 peak taken from

spectrum 6 . . . . . . . . . . 175

58. Raw data and fitted curve (offset) for the

1173.2 KeV Co 60 peak taken from

spectrum 5 . .. . . . . . . . 177

59. Raw data and fitted curve (offset) for the

744.2 KeV Ag 110m peak taken from

spectrum 11 . . . . . . . . . . 179

60. Raw data and fitted curve (offset) for the

657.6 KeV Ag 110m peak taken from

spectrum 6 . . .... . . . . . . 181

61. Raw data and fitted curve (offset) for the

1173.2 KeV Co 60 peak taken from

spectrum 5 ...... . . . .* * * * 185

62. Raw data and fitted curve (offset) for the

1173.2 KeV Co 60 peak taken from

spectrum 3. The data was smoothed before

the fit was obtained . . . . . . . 185

65. Raw data and fitted curve (offset) for the

657.6 KeV Ag 110m peak taken from

spectrum 8. The data was smoothed before

the fit was obtained. .... .. . . . . 188

64. Raw data and fitted curve (offset) for the

884.5 KeV Ag 110m peak taken from

spectrum 6. The data was smoothed before

the fit was obtained. . . . . . . .. 190

Figure

Page

Figure

65. Raw data and fitted curve (offset) for the

677.5 and 686.8 KeV Ag 110m peaks taken

from spectrum 1 . . . . . . . . .

66. Plot of an irradiated liver spectrum,

unattenuated. The full energy range of the

spectrum is 2.583 MeV (1.164 KeV/channel) . .

67. Plot of an irradiated liver spectrum,

attenuated by a factor of (x 0.208). The

full energy range of the spectrum is

2.383 MeV (1.164 KeV/channel) . . . . .

68. Plot of the total peak area (open circles)

and Wasson area (closed circles) vs. the

amount of standard added to the liver samples

for the analysis of chlorine. The peak areas

were obtained from the 1.643 MeV Cl 58 peak

69. Plot of the total peak area (open circles)

and Wasson area (closed circles) vs. the

amount of standard added to the liver samples

for the analysis of chlorine. The peak areas

were obtained from the 2.168 MeV Cl 38 peak

70. Plot of the total peak area (open circles) and

Wasson area (closed circles) vs. the amount

of standard added to the liver samples for

the analysis of manganese. The peak areas

were obtained from the 0.847 MeV Mn 56 peak

71. Plot of the total peak area (open circles) and

Wasson area (closed circles) vs. the amount

of standard added to the liver samples for the

analysis of manganese. The peak areas were

obtained from the 1.811 MeV Mn 56 peak . .

72. Plot of the total peak area (open circles) and

Wasson area (closed circles) vs. the amount of

standard added to the liver samples for the

analysis of potassium. The peak areas were

obtained from the 1.525 MeV K 42 peak . .

73. Plot of the total peak area (open circles) and

Wasson area (closed circles) vs. the amount of

standard added to the liver samples for the

analysis of sodium. The peak areas were

obtained from the 1.368 MeV Na 24 peak .

xiii

193

202

204

212

214

216

. . 218

. . 220

. . 222

Page

Abstract of Dissertation Presented to the Graduate Council

of the University of Florida in Partial Fulfillment of the

Requirements for the Degree of Doctor of Philosophy

DATA ACQUISITION AND REDUCTION OF

HIGH RESOLUTION GAkMMI-RiAY SPECTRA

By

David Baldwin Cottrell

March, 197-

Chairman: Dr. Stuart P. Cram

Major Department: Chemistry

A versatile, mini-computer based laboratory system was developed

for the collection and reduction of high resolution gamma-ray spectra.

A dedicated mini-computer served as both a control and memory for the

data acquisition, and a central processing unit for the automated

data reduction.

An interface and timing system were designed and constructed to

allow computer control of the data acquisition. A complete software

package was written to perform all aspects of the data acquisition and

reduction. The application of the total analytical system to the

analysis of a complex biological material was studied.

A new peak detection algorithm, sensitive to small signal-to-noise

peaks, was developed to automatically search the digital data and de-

termine the locations and boundaries of photopeaks in a gamma-ray spec-

tra. A technique was devised to perform curve fitting by the method of

nonlinear least squares on a mini-computer. A new function, which de-

fines the shape of a photopeak in a Ge(Li) spectrum, was developed and

tested. Photopeak areas calculated from the fitted functions were

compared to the peak areas determined by conventional methods directly

from the digital data.

xiv

INTRODUCTION

The principles of activation analysis, which have been reviewed by

Lynn (1), were first introduced by Hevesy and Levi (2,3) in 1956 and

Seaborg and Livingood (4) in 1958. Little was done with this technique,

however, until the dawn of the nuclear age, following World War II,

brought about an increasing availability of nuclear reactors. Since then

the development of sophisticated radiation detectors and additional

sources of nuclear particles has contributed to the remarkable growth of

this technique. The sensitivity and accuracy of activation analysis

have made it an extremely useful method of trace element determination

in almost every scientific field.

Neutron activation analysis has proven to be an extremely sensitive

analytical technique for most elements in a diversity of matrices, from

distilled water to biological tissues. The development of high resolu-

tion, lithium-drifted germanium detectors has made possible the instru-

mental analysis of complex samples by gamma-ray spectrometry. The

digital computer has proven essential to the rapid, accurate reduction

of the large volume of data required by this technique.

Research Objectives

This research was directed toward the development of a versatile,

mini-computer based laboratory system for the collection and reduction

of high resolution gamma-ray spectra. A real time system for collecting

2

data under the control of a dedicated mini-computer was developed to main-

tain the high resolution of the detector and the integrity of the pulse-

height. New concepts in direct data reduction by the laboratory computer

were developed and compared to existing methods, with special emphasis

placed upon small signal-to-noise peaks in the pulse-height spectrum

from Ge(Li) detectors. The application of such a system to the analysis

of biological materials was examined.

Historical Review

Early researchers in neutron activation analysis could measure only

total activity and were forced to use some form of chemical separation

to isolate the radioactive element of interest. Development of the early

pulse-height discriminators and the sodium iodide scintillation detector,

however, contributed to the increasing popularity of instrumental activa-

tion analysis by gamma-ray spectrometry. Connally and Leboeuf (5) were

among the first to demonstrate the value of this new analytical tech-

nique. Morrison and Cosgrove (6,7) demonstrated the usefulness of gamma-

ray spectrometry in the determination of trace impurities in a bulk com-

ponent, and several researchers proved the practicality of totally instru-

mental neutron activation analysis (8-10). With the development of the

Ge(Li) detector (11), high resolution gamma-ray spectrometry is today the

accepted method of data collection in neutron activation analysis.

By the early sixties many scientists realized that the method of

data reduction was equally as important as that of data collection. The

volume of data required in gamma-ray spectrometry was more than could be

handled by manual reduction. Covell (12) attempted to solve this problem

by developing a new, simplified method of data reduction. His new

technique used only the data from a fixed number of channels immediately

to the left and right of the peak center. Most laboratories, however,

realized that a better solution was to take advantage of the computa-

tional power and speed of the digital computer.

Guinn and Lasch (13) noted that comparison of photopeak areas with

those in standard spectra was still the easiest and most practical quan-

titative approach. Computer routines were written to obtain this infor-

mation by fitting a mathematical function to the experimental data (14,

15), or by simply analyzing the raw digital data (16-18). Often, how-

ever, the limited resolution of the NaI(Tl) scintillation detector

failed to produce resolved photopeaks. Heath (19) discussed the value

of the computer for the analysis of these complicated spectra.

Lee (20) reported on the instrumental technique of complement sub-

traction. The theory of spectrum stripping was quickly expanded and

computerized (13,21-25). Standard spectra of pure elements were collec-

ted and stored in the computer memory. Sequential subtraction of the

spectra corresponding to the highest energy photopeak was then performed

until only the background remained.

This method was often unsuccessful for low energy peaks uncovered

after several subtractions. A more complex approach, based on the

theory of least squares, sought to overcome this problem (9,24-28). An

assumption was made that contributions from the various elements in any

channel were independent and additive. By the method of least squares,

standard spectra were combined until the best fit to the entire experi-

mental spectrum was obtained. Another approach, based on the same

4

assumptions, attempted to solve a set of simultaneous linear equations

using data from only selected channels of the standard and experimental

spectra (29-52).

Other special methods were reported (35,54), but the above were by

far the most commonly used methods for the analysis of complex scintil-

lation gamma-ray spectra. Because of resolution problems, most of these

.computerized techniques required some form of qualitative input before

accurate quantitative calculations could be performed.

The development of the high resolution, semiconductor Ge(Li) de-

tector (35) caused a rapid change in the field of activation analysis.

The superior resolution required bigger and better pulse-height analyzers

and resulted in a tremendous increase in the volume of digital data to

be reduced. It also produced a distinctly different form of gamma-ray

spectra, with photopeaks more numerous but now resolved and available

for direct quantitation. Prussin and co-workers (36,37) quickly demon-

strated the value of this new detector for instrumental analysis of

complex mixtures. The fully resolved photopeaks easily furnished both

qualitative and quantitative information.

The increased resolution also increased the problem of statistical

scatter of the digital data. Several methods were proposed to smooth the

spectra, to remove the undesired scatter without destroying the analyt-

ical information lying underneath (38-40). A least squares technique

particularly suited for computer adaptation was reported by Savitsky and

Golay (41). Yule (16,42) successfully applied this technique to gamma-

ray spectra and determined that the number of points in the smoothing

should be as large as possible without exceeding the full width at half

maximum of the photopeaks. Tominaga and co-workers (45) studied the

5

effects of smoothing on peak area determinations and reported that smoothing

was often unnecessary for curve fitting methods but beneficial for other

quantitative techniques. Yule (44) showed that one smoothing by the

Savitsky and Golay method did not distort the analytical information con-

tained in the spectra, as long as the correct smoothing interval was used.

Several methods were developed for automatically locating peaks in a

Ge(Li) gamma-ray spectrum. Connelly and Black (45,46) described the

technique of cross-correlation for both peak detection and area deter-

mination. Dooley and co-workers (47) looked for significant count in-

creases in adjacent channel groups to indicate the presence of a peak.

Gunnink and Niday (48) examined the changes in slope between data points.

Ralston and Wilcox (49) developed a special method for defining the base-

line from which to begin and end peak integration.

An automated peak detection method particularly suitable for effi-

cient software execution involved the numerical approximation of the

derivatives of the digital spectrum. Morrey (50) described in detail the

utilization of the second, third, and fourth derivatives to locate peaks.

Yule (16,51) applied the convolution technique of Savitsky and Golay (41)

to obtain the smoothed derivatives in one rapid, efficient, computational

operation. He demonstrated the use of both the first derivative alone

(51), and of higher derivatives (52), to locate peaks. Barnes (53) re-

ported a slightly different form of calculating the smoothed derivatives,

but obtained essentially the same results as the Savitsky and Golay method.

Several authors (54-56) chose to use the second differences, similar

to the second derivatives, to locate peaks. Mills (54) pointed out that

the smoothed spectra gave better estimates of the initial parameters

for peak fitting. Subtraction of adjacent data points then gave a good

approximation of the smoothed derivative.

Once the photopeaks were located, some measure of their area was

necessary to obtain quantitative information about the contributing

element. The area could be calculated either directly from the digital

data or from the integration of an analytical function which was fitted

to the peak.

Several methods were developed to obtain quantitative information

directly from the digital data. The most commonly used technique was

the total peak area (TPA) method, successfully employed by several

workers (335,8,31,57). This method assumed a linear baseline beneath

the peak and subtracted a trapezoid background correction from the summed

total area to obtain the quantitative area.

The previously mentioned method of Covell (12) was also utilized

(43). In this method a linear baseline was again assumed, but only the

data from a fixed number of channels immediately to the left and right

of the peak center were used in the area computation. Sterlinski (58,59)

modified Covell's method to give increasingly greater weight to those

channels nearer to the peak center.

Quittner (60,61) proposed a method for estimating the actual base-

line contribution to the total peak area. He first fitted a second or

third degree polynomial to several channels on either side of the peak.

He then constructed a baseline beneath the peak in such a way that, at

the peak boundaries, it had the same magnitudes and slopes as the fitted

polynomials.

Baedecker (62) described a modification of the TPA method suggested

by Wasson in a private communication. This technique combined the prin-

ciples of the TPA and Covell methods in that it constructed the same

baseline as the TPA method but only used data from a fixed number of

7

channels immediately surrounding the peak center. The author then ex-

amined the precision obtainable by the methods described above.

Baedecker's experiments showed that the more complex methods did

not provide a significantly greater precision than the simple ones.

Hle thercfor-. recommended the Wasson technique, except for cases where

there were large deadtime differences between samples or where changes

in resolution created a problem. For these latter cases he recommended

the TPA method.

More complex approaches to photopeak quantitation, such as curve

fitting, were also reported. The least squares technique for fitting a

function to a set of data points, discussed by Roberts, Wilkinson, and

Walker (65), w:as the usual method of choice, although Ciampi and co-

workers (34) used a maximum probability technique.

Early authors (55,64,65) used a pure Gaussian fitting function to

approximate the photopeak shape in Ge(Li) spectra. However it soon be-

came clear that this function did not give a satisfactory fit to the

peak shape. Routti and Prussin (56) discussed the physical properties

of a Ge(Li) detector system which gave rise to the basic photopeak

shape and noted that there was often severe tailing of the basic Gaussian

on the low energy side. Additional tailing was also observed under con-

ditions of high counting rates.

Many functional forms were suggested to account for the tailing of

the main Gaussian shape. Sanders and Holm (66) pointed out that the

only criterion for the selection of the analytical fitting function was

an adequate representation of the data points. They, among others (56,

67,68), used a functional form which combined a Gaussian with an expon-

ential contribution for tailing. Kern (69) and Pratt and Luther (70)

suggested methods of skewing the Gaussian with a polynomial. Robinson

(71) combined two offset Gaussians and an arctangent to represent the

photopeak shape. The background slope was usually represented by either

a polynomial or an exponential.

On-line computer control of data acquisition was reported by a few

workers (72-76). DerMateosian (77) described an experimental system

which interfaced a laboratory computer to a pulse-height analyzer. He

then described the advantages of direct data reduction by the small

computer. Norbeck and Mancusi (78) described the more common approach,

which involved the transfer of the digital data to a large computer

for reduction.

Neutron activation analysis has been used for the analysis of

biological materials since shortly after its introduction to the scien-

tific world. Much of this work involved the chemical separation and

isolation of the desired element (79,80) or the removal of large inter-

ferences, such as sodium (81). Recently, however, instrumental analysis,

using Ge(Li) detectors, was used for the multielement analysis of bio-

logical materials (82). Linekin and co-workers (83), however, indicated

that the majority of this research used data reduction techniques de-

veloped by researchers in other fields. Therefore, it is the purpose of

this research to demonstrate the applicability of the dedicated laboratory

computer to both the acquisition and reduction of gamma-ray spectra of

complex biological samples.

THEORETICAL

Modern activation analysis experiments usually involve the acquisi-

tion of large amounts of digital data. The computer can therefore relieve

the analyst of many hours of tedious, time-consuming data reduction.

Correctly programmed the computer can quickly search the data, locate

valid peaks, and determine their energies and peak areas.

Data reduction is easily done on a large computer, where the programs

may be complex, lengthy, and written in a conversational language such as

FORTRAN, without significantly increasing the computation time. On a

mini-computer, however, the data reduction methods should be programmed

in assembly language and decoded into machine language to conserve core

space and keep the turn around time compatible with laboratory operation.

Data Smoothing

Due to the statistical nature of the spectra obtained in gamma-ray

spectrometry, it is often desirable to smooth the digital data before

attempting automated data reduction. This is done to remove much of the

random noise without unduely degrading the underlying analytical informa-

tion.

The smoothing technique used in this research was described by

Savitsky and Golay (41). This method uses a data convolution process to

obtain the least squares fit of a polynomial function to the center point

of a block of raw data. The convoluting integers are the same for either

a cubic or a quadratic function.

With the correct set of convoluting integers and normalization

factor the smoothed data value is calculated from

i=+m

Y = CiYi)/N (i)

J i=-m i

where Y. = smoothed data value, in counts

3

i = running index for the data block

m = (number of points in the block 1)/2

C. = convoluting integer for the ith point

1

in the block

Y. .= raw data for the ith point in the block,

j+i

in counts

j = index for the channel number

N = normalization factor, a scaler

Yule (42,44) has shown that a single smoothing does not degrade

the analytical information if the number of points in the smoothing in-

terval does not exceed the average peak width at half maximum. It will

be shown in a later section, however, that the smoothed data produce

more accurate results from the automated data reduction routines.

Peak Detection

Figure 1 illustrates the two possible peak shapes found in digital

spectra. The first has a positive first derivative from the left bound-

ary minimum to the peak maximum, and a negative first derivative from

the maximum to the right boundary minimum. The second peak, however,

11

2

to

cu

U,

co4

C,'

4-i

M

co

0)

a)

4

0

C-

o,

a)

-'-

has several minima superimposed on the basic peak shape. This problem

is common in spectra which cover a narrow energy range, resulting in a

greater number of channels within the peak boundaries. It is also

common to peaks with small peak-to-noise ratios. The first derivative

will change signs several times within the true peak boundaries.

In order to limit the size and complexity of the peak detection

software, and still locate both types of valid peak shapes, two detec-

tion routines are used. Together they occupy less than 12% of the

available 4K of core and require only two to eight minutes to search a

2048 channel spectrum and print all qualitative and quantitative infor-

mation.

Both of the peak detection routines use the sign change of the

first derivative to locate minima and maxima. However, since neither

routine requires the absolute value of the derivative, the sign changes

may be determined from the first differences.

The first routine searches for a minimum to maximum height which is

greater than a multiple (usually one) of the baseline noise. The noise

is determined by averaging the minimum to maximum heights over the forty

channels immediately preceding the height in question. If two peaks are

separated by less than forty channels, as illustrated by Figure 1, the

same value of the noise is used to test both peaks. Each time a satis-

factory height is detected, the integral channel location of the minimum

is stored as a possible left peak boundary.

The right peak boundary is determined by the channel location of the

next minimum whose height, relative to the left boundary minimum, is less

than the average noise value. As shown by Figure 1, one or more maxima

13

may be detected within the boundary minima. The peak maximum is determined

by the channel location of the highest maxima.

Valid peaks must exceed a minimum width, which is determined by the

resolution of the system. The peak height, relative to both boundaries,

must also exceed a minimum peak-to-noise ratio, which may be assigned a

value as low as two. If any of these requirements are not satisfied,

the region defined by the boundary channels is assumed to be a noise spike.

The second peak detection routine assumes that all valid peaks have

only one maximum, located at the channel where the sign of the first

derivative changes from positive to negative. The left and right bound-

aries are then located at the first minimum to either side of the peak

maximum.

Valid peaks must also have a minimum number of channels between

each boundary minimum and the peak maximum. This number is determined

from the resolution of the system and may be as small as two. The peak

height, relative to both boundaries, must also exceed the minimum peak-

to-noise ratio.

The two peak detection routines are complementary to each other.

While both methods will locate the first peak in Figure 1, method two is

faster and less sensitive to changes in the slope of the baseline. Only

method one will detect the second peak in Figure 1, but, as will be shown

in a later section, this method of detection may select erroneous bound-

ary channels. A complete search of the spectrum by both routines is

therefore necessary to insure a complete and accurate analysis.

Peak Quantitation

Once the peak boundaries are deter-lined, a quantitative measure

of the peak area, and thus of the activity of the decaying isotope, is

calculated. Several techniques have been suggested for obtaining this

area directly from the digital data. Two of these, the total peak area

(TPA) method and a modification of this, devised by Wasson and cited

by Baedecker (62), are used in this research.

The total peak area method yields the largest value for the peak

area within the selected boundaries. The area is calculated from

i=R

TA E C- (CL + C)(R L + 1)/2 (2)

i=L

where

AT = total peak area, in counts

TPA

C. = number of counts in channel i, LisR

L = channel number of the left boundary

R = channel number of the right boundary

An alternative method, devised by Covell (12), uses only a portion of

this total peak area. The usable area is calculated from

i= M+N

AC = E C (N + 1/2)(C+N + CM-N) (

i = M-N

where

AC = Covell's peak area in counts

M = the channel number of the peak maximum

N = the number of channels included to the"

left and right of the peak maximum

The Wasson modification is a combination of the above two methods. The

usable Wasson area is calculated from

i=M+N

AW = Ci (N + 2)(BM+N + BMN) (4)

i=M-N

where

AW = Wasson's peak area in counts

B = the background in channel j determined from

a straight line between channels L and R

These three methods are graphically illustrated in Figure 2.

Baedecker (62) has shown that the Wasson area yields a more pre-

cise measure of the peak area. The total peak area includes contribu-

tions from the extremities of the peak, where the statistical fluctua-

tions are greater. The Covell method excludes these regions but yields

a much smaller absolute area than the Wasson method. This research in-

cludes both the TPA and the Wasson methods in an attempt to obtain the

best results in all cases.

CO

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Curve Fitting

The method of curve fitting is used to obtain an estimate of the

total peak area not obtainable directly from the digital data. The

final functional parameter estimates can be used to calculate the area

beneath the fitted curve by integration. This method is independent of

peak boundaries and yields an excellent estimate of the true area of

the peak.

The method of least squares, which has been successfully applied

to chromatographic data by Roberts, Wilkinson, and Walker (65) and

Chesler and Cram (84), is used to fit a suitable function to the digital

data. If

X = the independent variable, i = 1,2,...,N

Y = the experimentally observed data, i = 1,2,...,N

P = the parameters in the theoretical function F.,

j = 1,2,...,m

k

P. = the estimated value of P. for the kth iteration

k k

AP = the correction to the estimate P.

J J

W. = a weighting factor, a scaler, i = 1,2,...,N

F. = F(P,,P2,...,Pm,X.) = the theoretical function

evaluated at point X.

N = the number of experimental data points

m = the number of parameters in the function

then the nonlinear least squares technique is an iterative process that

fits the function F to a set of N data points.

The residual sum of squares

N

S = W(Fi Y.) (5)

i=l

is minimized through the choice of values of the m parameters.

This leads to equation (6), a set of m equations in the m unknowns

k k k

API, LP2, '...P m. For the kth iteration the function F. is given by F

and new estimates of the parameters are calculated from

k+l k k

P = P + AP j = 1,2,...,m (7)

The process converges when

lim P j = 1,2,...,m (8)

k-o J

In this research all values of W. are set equal to one.

1

The full energy peak in a Ge(Li) spectrum may be estimated by a

basic Gaussian shape which has a low energy tail. The width of the

Gaussian is determined by both the electronic noise of the system and

by statistical processes connected with energy absorption in the detec-

tor. The tail on the leading edge of the Gaussian is caused by the in-

complete charge collection of hole-electron pairs, due to recombination

and trapping. Several researchers, including Routti and Prussin (56),

Varnell and Trischuk (67), and Head (68), have shown that the basic peak

shape may be accurately approximated by a Gaussian function which has

been joined to some form of leading exponential edge.

The fitting function used in this research is a modification of

the empirical function successfully used by Chesler and Cram (84) to

'41-4 -41 U4

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-4 1-4-4

d cu

z wjz 1-

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CX4 L4 r4 a4I a:

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ni n:4:r"

-4 -4 -4

zw H wd

"4 "4 4

21

fit chromatographic peaks. It is composed of a leading exponential edge,

a hyperbolic tangent joining function, and a central Gaussian. The

functional form is

-(Xi-P 4)2

Fi = P(exp[ 2P5 ] + 0.5 (1-Tanh[P2(Xi-P)]) x

(9)

2 1/2

x [P6exp(-P7[((P8-X i) 12 + (P -XiJ)]

where PI = the height of the Gaussian, in counts

P2 = the rate of change of the joining function

P = the center of change of the joining function,

in sigma units

P4 = the center of the Gaussian, in sigma units

2

P = 0 of the Gaussian

P6 = the initial height of the exponential, in counts

P7 = the rate of decrease of the exponential

P8 = the position of the start of the exponential, in

sigma units

X = the independent variable, in sigma units

The physical interpretations of these parameters are graphically illus-

trated in Figure 3.

Several constraints should be placed on the parameter estimates to

aid in the correct convergence of the fitting process. These constraints

are suggested by the physical interpretation of the emperical fitting

function. The heights of both the Gaussian and the exponential tail

should always remain positive. The change of the joining function and the

0

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u

11

IfIf

C:

0

,$,4

.iJ

.4

0

Go

0K

-4

l^ .- o

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exponential should proceed in only one direction. The value of a

should always be positive. The positions of the joining function and the

start of the exponential should always be to the left of the peak maximum.

k k k k k

Therefore the signs of P P 2 P, and P should always be positive,

1' 2' 35 6' 7

k k k

while those of P and P should remain negative. Only the sign of P

5 8 C 4

should be allowed to vary.

The signs of the parameter estimates are checked following the solu-

tions of equation (7) but before the beginning of the next iteration.

If any sign is found to be incorrect the value of the parameter estimate

is changed to one-half of the last accepted value.

To simplify the partial derivatives let

-(X -P )2

A. = exp[ ] (10)

12P5

B. = 0.5 (l-Tanh[P (X -P3)]) (11)

C = P6exp(-P7[ (P-X 1/2 + P8-Xil) (12)

and therefore

F= P (Ai + B.C.) (15)

The partial derivatives may then be calculated from

6F.

= A. + BC (14)

P i i

1

F (1B.

ap2 IC (- ~P (15)

3F i B

2 2

-P 1i -P ) (16)

S1-

ap P1 ( (17)

4 4

ap 1 B (a) (18)

5 5

8F. bC

P 1 p B. ( ) (19)

6 6

8F. P c.

8?p 1 B i
8 8

where

_A -(4-Xi )Ai (X -P )Ai

p i 4 i (22)

P4 P5 P5

Ai (Xi-P4) 2Ai

ap 2 (25)

5 2P

5

B i

2

-2(X.-P )

(exp[P (X -P5)] + exp[-P2 (XiP)12

6B. 2P

-2 2

P5 (exp[P2(Xi-P5)] + exp[-P2(Xi-P )]2

ac c.

i 6 1

6 6

8c

Ci =

p57 -C.

[(X2 1/2 (PX

[(Ps-X.) ] + (P8-X.))

(24)

(25)

(26)

(27)

ac (P -X )

p CiP7 1/2 + 1 ) (28)

S8 (P -X 21

The baseline on either side of the peak is approximated by the polynomial

D. = P+ P + P X + P X (29)

1 9 10 i 11 i 12 i

where X. is expressed in channel units. The same nonlinear least

1

squares process is used to fit this four parameter function. The

partial derivatives are calculated from

6D.

ap 1 (30)

9

6D.

p0 X (51)

10

6 2

aP (32)

11

6D.

6 = x535)

12

The total fitting function which approximates the combined peak

and baseline shape is therefore

T. = Fi + Di i = 1,2,...,N (34)

The solution of this total function, however, requires the filling of

a twelve by twelve matrix, and the solving of twelve equations in

twelve unknowns. The computation time for each iteration can be greatly

reduced by fitting the polynomial baseline separately. Equation (29)

is then evaluated for all points and subtracted from the experimental

data. The resulting corrected data are then fitted with the eight

parameter function F..

1

The success of the curve fitting process depends greatly on the

accuracy of the initial parameter estimates. The digital data are

often used to obtain these estimates. The initial value of P is deter-

9

mined from the value of the baseline at the left peak boundary. The

1 1i 1

initial values of P, P and P are set to zero. The values of the

10 11 12

eight peak parameters may be estimated from the corrected digital data,

1

following the baseline subtraction. The estimate of P is obtained

1 1 1 1

directly from the corrected data. The values of P P P P, and

P are usually estimated by 3.0, -1.5, 0, 1.0, and -1.5 respectively.

8

1 1

The initial estimates of P' and P depend upon the actual shape of the

leading edge of the peak, but are usually between zero and one.

leading edge of the peak, but are usually between zero and one.

27

To obtain the X. values in the fitting interval, expressed in sigma

units, the right side of the peak is assumed to be pure Gaussian. The

number of abscissa points from the peak maximum to the right boundary

is therefore assumed to be equal to three sigma units. From this

assumption the values of the increment and the initial abscissa point

in the fitting interval are determined. It will be shown later that

the peak function can be successfully fitted to as few as ten data

points.

Method of Standard Addition

In the method of standard addition quantitative peak areas are

determined for samples to which known amounts of standard have been

added. This gives

Ai = k(Wi + Si) (55)

where

Ai = peak area for sample i, in counts

k = a constant

W. = the amount of element in sample i, in grams

i

S = the amount of element added to sample i, in micrograms

and

A = k(Wp) (56)

where

A = peak area of a pure sample, in counts

W = the amount of element in a pure sample, in grams

P

Before they can be compared, however, all results must be normalized

to a standard sample weight. The normalization factor is given by

CF. desired standard weight

i sample weight in grams

1.00 grams

sample weight in grams

After normalization, equations (35) and (56) become

A.CF. = k(W CF + S.CF.)

1 1. i i

and

A CF = k(W CF )

Since

W.CFi = W CF

then subtraction of equation (39) from equation (38) yields

then subtraction of equation (59) from equation (58) yields

A.CF. = k(S CF ) + A CF

S1 i i pp

The X-intercept of a plot of A.CF. as a function of S CF. is therefore

2.2. ii

-A CF

X-intercept = -PE = -W CF

k p p

which is the negative of the desired experimental value.

The method of standard addition is used to insure a constant

matrix effect from the complex sample. The data points are fitted by

the method of linear least squares, which assumes that all of the error

is in the calculated peak areas, and the measured amounts of standard

(37)

(58)

(39)

(40)

(41)

(42)

29

solution added to the samples are exact. The resulting mean square

deviation (MSD), calculated by the least squares method, is used to

estimate the error in the X-intercept from

+ Error = + MSD/k (45)

EXPERIMENTAL

The hardware and software developed for this research were designed

and constructed to yield a completely flexible multichannel pulse-height

spectrometer. The experimental system, shown in Figure 4, was capable

of both high resolution, high precision data acquisition, and rapid,

comprehensive data reduction. The central, dedicated computer served

as both a control and memory for the collection process, and a central

processing unit for the data reduction.

The elements up to and including the analog to digital converter

(ADC) are common to all pulse-height analyzer systems. They include a

detector, a pre-amplifier, a linear pulse-height amplifier, and an ADC.

The experimental system developed for this research utilized a 50

cc lithium-drifted germanium detector made by Nuclear Diodes. The de-

tector was a wrap-around coaxial design which was rated at 8% efficiency,

relative to a 3x3 NaI(TI) detector. The resolution of the Ge(Li) de-

tector was rated at 2.5 KeV, measured at the 1.35 MeV cobalt peak, and

the peak-to-compton ratio was rated at 23:1.

The detector was biased at 2500 volts by an Ortec Model 456 high-

voltage power supply. A Nuclear Diodes Model 105 pre-amplifier was

connected to an Ortec Model 451 spectroscopy amplifier. An Ortec Model

444 biased amplifier was available as an option.

The 0-10V output of the linear amplifier was digitized by a North-

ern Scientific Model NS-629 analog to digital converter. The Wilkinson

type ADC was capable of 8192 channels of resolution and used a 50 MHz

5'

F- I

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32

clock rate for the digitization process. The dead time of the ADC was

rated at 5 + 0.02N psec per event, where N is the channel address of

the converted signal. The maximum dead time of the system was therefore

167 psec.

All signals necessary for the transfer of the digital data and the

control of the ADC operation were 0-5V positive logic, and were access-

ible through pins at the back panel of the ADC. Thirteen bits of

address data were available for parallel transfer, as well as a ready

signal, a clear line, and a dead time signal. The ADC performed most

of the functions of a biased amplifier and, when desired, allowed a full

8192 channels of resolution to be used with the 2048 channels of avail-

able memory.

The non-flexible nature of most commercially available pulse-height

analyzers was overcome by the use of a programmable mini-computer as the

basic control and memory unit. The versatile nature of the software

allowed complete flexibility in all functions, including data acquisi-

tion, printout, display,and data reduction. The computer was a PDP-8/L

from Digital Equipment Corporation. With 8K of available core, 4K was

used for memory storage and 4K was allotted for core resident software.

The PDP-8/L used 12-bit words, had a cycle time of 1.6 psec, contained

one common bus, and had one level of program interrupt.

All major input and output was achieved through a Model ASR 33

Teletype, which typed ten characters a second. The spectra were dis-

played on an ITT Model 1935D fifteen-inch display oscilloscope, and

were plotted on a Model 7127A strip chart recorder from Hewlett-

Packard. A Tri-Data Model 4096 magnetic tape unit, capable of trans-

fering 462 12-bit words a second, was used for all bulk storage.

The computer based

required the design and

ents. An interface was

acquisition by the ADC,

digital address data to

was built to accurately

are discussed in detail

Hardware

pulse-height analyzer system, described above,

construction of two critical hardware compon-

built to allow computer control of the data

and to provide a means for transferring the

the computer. A high precision digital clock

control all count times. These two components

below.

Interface

The logic interface shown in Figure 5 was designed and developed

to allow computer control of the ADC, and to provide a means for paral-

lel transfer of digital data from the 15-bit ADC output register to

the 12-bit accumulator register of the computer. Since only 2048

channels of memory storage were available, the twelve least significant

bits of the ADC output were connected to the computer.

Since all computer peripherals were connected to one common bus,

individual devices were controlled by means of a 6-bit binary code

generated through the memory buffer register (MBR). The execution of

an input-output transfer (IOT), software command (6XXY8), caused a

logical "1" to be generated for 4.25 u.sec on the six memory buffer

lines indicated by the two octal digits XX (56 for the ADC interface).

Therefore, by connecting a sik-input nand gate to the appropriate MBR

lines, a specific device, such as the interface, was individually

controlled.

4J

Q)

C-

0

Q

0-4

to

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0

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0

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LLL

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moo

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wrw 0

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OOOO000000--

0 "

< _

L= ,________________

' -1

The same 6XXY command caused the computer to generate any com-

8

bination of three input-output pulses (lOP's), each 600 nsec in dura-

tion. The octal digit Y designated which combination of IOP's were

generated. If more than one IOP was designated by the software command,

the order of generation was IOP1, IOP2, and IOP4, with each pulse

separated by a 100 nsec delay. As shown in Figure 5, only when the

correct device code (XX) was called were the IOP's passed through the

logic of the device selector. This prevented the IOP's intended for

other peripherals from activating the ADC interface.

Each of the three IOP's performed a specific function in the ADC

interface. The IOPI was used to check the status of the ready flag

of the ADC. When the flag was set to a logical "1", indicating that

the current gamma-ray pulse had been digitized and the address data

were available at the output register, the IOP1 was passed to the

input-output skip gate of the computer. This pulse caused the computer

to skip execution of the next software command, and is discussed in

more detail in the software section. The IOP2 was used to open a 12-

bit bus driver network, which allowed a parallel transfer of the

address data from the output register of the ADC to the accumulator

register of the computer. The IOP4 was used to send a pulse to the

clear input of the ADC. This pulse caused the ADC to clear the out-

put register, reset the ready flag to a logical "0", and accept a

new input signal for digitization. The timing of these signals will

be discussed more thoroughly in the software section.

Timing System

The timing system shown in Figure 6 was designed and constructed

dU 0 x.

ojg ou

4-4 -a 4

0 4-

0 C

C4 a) 3s

o-

o to .

cu c

4-1 S

43 u

S0

Ea

O E

0

4--c

41

C E-4

io

a m

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00 c

00 4-

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rei

4-)

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58

to allow the highly precise and accurate control of experimental count

times required by this research. A 1 MHz crystal clock, accurate to

three parts in 10 was passed through a series of logic networks to

yield a 1 Hz output. The 1 Hz clock rate was passed through the divide-

by-six network shown in Figure 6 to yield a 1/6 Hz input to the four

decade, presettable down counter. The 1/6 Hz pulse train clocked the

counter every tenth of a minute.

When the counter was at zero, the gated output from the four de-

cades was a logical "1", which held the input nand gate closed to the

clock pulses. A push button switch, connected to the contact bounce

eliminating network shown in Figure 6, produced a short logic pulse

from time TA to time T This enabled the contents of a four decade

thumbwheel switch to be transferred to the four decades of the down

counter. The contents of the counter were continuously shown on a

four digit, LED, decimal display.

The gated output of the four decades caused the input nand gate

to open at time TB, which allowed the passage of the 1/6 Hz clock

pulses. The leading edge of the first pulse through the input gate

(at time TB+) caused the Q output of the control flip-flop to go from

a logical "0" to a logical "1". This output was connected to both the

interrupt facility of the computer and the remaining input nand gate.

The logical "1" therefore served to both initiate the computer in-

terrupt and to open the input nand gates and allow the clock pulses

to drive the counter.

As the 1/6 Hz clock pulses triggered the counter, the time remain-

ing for data acquisition was constantly shown on the lighted display.

When the counter reached zero, at time TO, the gated output of the

39

four decades reset the control flip-flop, causing the Q output to return

to a logical "O". The input nand gate was also closed, preventing any

more clock pulses from reaching the counter.

In this manner a logical pulse, extending from time T+ to time

TO, was transferred to the interrupt facility of the computer, as

illustrated in Figure 6. Since this pulse was initiated by the leading

edge of a clock pulse, the length of the logical pulse corresponded to

the time period originally set on the thumbwheel switch. The effect of

this timing pulse is discussed further in the software section.

A single pole, double throw switch allowed a choice between count-

ing in live time or clock time. When the live time position was chosen,

the 1 MHz clock rate, directly out of the crystal, was gated with the

dead time signal of the ADC. Clock pulses were therefore allowed to

pass to the counter only when the ADC was clear to accept an input

pulse from the linear amplifier. When the clock time position was

chosen all clock pulses were passed to the counter.

Software

The complex mathematical calculations required by the curve fit-

ting and linear least squares processes were performed using the con-

versational computer language FOCAL, developed by Digital Equipment

Corporation. The FOCAL programs written to perform these mathema-

tical calculations are listed in Appendix II.

All other software used in this research was written in assembly

language and decoded into machine language. The final software

package was completely resident in the 4K of core allotted for that

purpose, and included all routines necessary for the operation of the

experimental system and all data reduction routines except those in-

volving curve fitting. Also present in core was Digital Equipment

Corporation's floating point package, DEC-08-YQ2B-PB, designed to per-

form basic mathematical operations and to provide a means for obtaining

formatted digital input and output through a Teletype. A complete pro-

gram listing, excluding the floating point package, is found in Appendix

I. The following section discusses the methods of operation of this

software.

Data Acquisition

In order to maintain the resolution of the detector and ADC, a

pulse-height analyzer system must be capable of high speed data acquisi-

tion and have an adequate memory. To satisfy these requirements with a

PDP-8/L computer, the data were stored as 24-bit, double precision words

in one 4K block of core, and the computer was devoted full time to the

data collection process. This yielded the shortest possible software

execution time and created a 2048 channel analyzer, with a memory storage

capacity of over 16 million counts per channel.

Figure 7 illustrates the software sequence for the data collection

process, and Figure 8 shows the timing relations between the computer

and the ADC. The software was written to interact with the ADC inter-

face and timer described earlier in the hardware section. The following

discussion uses ideas introduced in this earlier section.

The software routine first cleared the entire 4K of memory. Then,

using Teletype interaction, a pointer was set to allow an exit to

either a printout routine or a program halt. If a printout was desired,

the specific parameters (first and last desired channels) were entered

Figure 7. Flowchart of the data acquisition software

YES

CLEAR

ADC o

CHECK I

FLAG FROM

DEVICE o I

SELECTOR

II I

ADC I I

DEADTIME I I

I I

SET ADC

FLAG o

I

INPUT-

OUTPUT o

TRANSFER

STORE

DATA o I

I

CLEAR

ADC 9

0 5 10 15 20 25 30 35 40

TIME, /jsec.

Figure 8. Timing relations between the computer and analog

to digital converter

through the Teletype. The link, a 1-bit register also used as a

pointer, was then set to one, to indicate that no data collection had

occurred.

The heart of the data acquisition routine consisted of two soft-

ware loops. The outer loop was a service routine for the interrupt

facility of the PDP-8/L. When the interrupt was on, the computer con-

tinually monitored the Q output of the control flip-flop of the timer.

If the output of the timer was ever a logical "O", indicating that the

timer was off, the computer immediately transferred software execution

to location zero'and turned the interrupt off. The software sequence

beginning at location zero checked the link and, if no data had been

collected, turned the interrupt on again. Thus the computer waited

in a software loop until the timer was initiated, indicating the start

of a count. When the timer output went to a logical "1" the computer

set the link to zero and entered the inner, data acquisition loop.

An input-output transfer (IOT) command, 65618, called the ADC

interface and generated an IOP1 to check the status of the ADC ready

flag. If the flag was not set, a repeat command caused the sequence

to be repeated every 5.85 psec, as illustrated in Figure 8. Once the

flag was set, however, the next IOP1 was passed to the input-output

skip facility of the computer, and the repeat command was skipped. The

skipped instruction allowed the execution of another lOT, 65668, which

again called the ADC interface, and generated an IOP2 and an IOP4.

As Figure 8 illustrates, the IOP2 was generated first and caused the

twelve bits of address data to be parallel transferred from the ADC to

the accumulator register of the computer. The IOP4, 100 nsec later,

cleared the ADC output register and ready flag, which allowed the ADC

to accept a new signal for conversion.

While the ADC was converting the new signal, the computer performed

the proper data storage by incrementing the memory location designated

by the contents of the accumulator. Only the lower 12-bit word of the

channel address was incremented, unless the incrementation caused an

overflow into the second twelve bits. The storage process required

11.2 psec, and the overflow, which occurred only once every 4096 counts

in any given channel, required an additional 8 psec. This time period

constituted the entire dead time of the computer and was independent

of the ADC dead time. When the data storage was completed, the computer

returned to the flag checking sequence.

During the entire data collection process the interrupt remained

on. When the count time expired, and the timer output returned to a

logical "0", the computer immediately transferred control from the

data acquisition loop back to the interrupt service loop. Since the

link had been set to zero, the software execution sequence followed

the exit pointer to either the data printout routine or a program halt.

For the general case of incrementation of only the lower 12-bit

word, there was an 11.2 psec computer dead time between the clearing

of the ADC and the generation of the first IOP1 to check the ready

flag. The conversion time for the ADC was rated at 5 + 0.02N psec,

where N was the channel number. Therefore, during the computer dead

time the ADC could complete conversion only on pulses which occurred

in the first 410 channels. For these lower energy pulses the flag

was set before the first IOP1 was generated. For all channels above

410, however, the computer had to wait in a 5.85 1sec loop until the

ADC conversion was completed.

46

In Figure 8 the latter case is illustrated. A sequence of IOT's,

each 4.25 psec in length, generated the IOPl's to check the ADC ready

flag. These pulses were separated by a 1.6 psec repeat command until

the flag was set, at which time a second IOT immediately followed the

first. This IOT generated both the IOP2 and the IOP4, which initiated

the storage process and cleared the ADC respectively. The only variable

time in the sequence was the length of the ADC dead time, which depend-

ed upon the channel address of the digitized signal.

Data Printout

Figure 9 shows the flow chart for the data printout process. The

printout software was entered either directly from the data acquisition

routine (point A) or as an individual routine (point B). Using the print-

out parameters (first and last desired channels), obtained by direct in-

put through the Teletype, the computer initialized all necessary coun-

ters and variables. Then the desired block of data was printed by the

Teletype in a format shown in Figure 10. The printout was terminated

whenever channel 2047, or the last desired channel was passed.

As Figure 10 illustrates, the first number in each line of data

was the channel address of the first data point in the line. The re-

maining five numbers were the contents of the five channels designated

by the line number. The number of digits in the output was variable,

and all leading zeroes were replaced by spaces. The page header in-

cluded the spectrum number, the magnetic tape number, and the date of

the data collection. Each page of the printout was eleven inches in

length and contained 50 lines of data.

Display

Another requirement of a pulse-height analyzer system, a means of

Figure 9. Flowchart of the data printout software

48

INPUT PRINTOUT

A A PARAMETERS

THROUGH TTYP

INITIALIZE

COUNTERS AND

VARIABLES

PRINT NEW

PAGE HEADER

RE-INITIALIZE

COUNTERS FOR

NEW LINE

PRINT LINE 8

PRINT DATA

PASSED YES

2047?

NO

PASS)D YES

LAST DESIRED

CHANNEL?

LINE?

Y2S

YES FINISHED NO

PAGE?

Figure 10. Sample page from the computer printout of a stored

spectrum

5 TAPE = 2 DATE : 6/ 4/ 72

15.J3

1505

lbl

1515

1523

1533

1535

15453

1 545

1550

1555

1560

1565

1570

1575

15t03

1 5b5

1535

1600

160b

16103

1615

1623

1625

1633

1635

1643

1645

1650

1655

1660

1665

1670

1675

1680

1665

1693

16-15

1703

1705

1710

1715

1720

1725

1730

1735

1740

1745

446

418

454

453

471

47

45=

501

448

476

441

475

458

517

476

487

473

475

499

475

430

433

438

5vb

1436

5714

450

511

1471

6319-

4057

229

191

183

146

160

144

124

129

145

124

101

113

126

114

lou

177

450

424

466

477

432

463

460

455

472

443

502

455

511

523

477

537

584

502

427

397

366

45,

630

1821

7479

41;3

368

651

2054

7735

2216

201

167

167

162

145

162

136

152

139

129

113

123

102

123

143

214

139

477

476

431

406

414

444

425

477

456

435

458

533

487

513

514

502

467

489

479

459

385

36sa

401

443

757

2419

9018

2252

431

763

2660

8789

1009

194

181

165

134

148

157

131

141

126

135

119

141

114

119

121

216

96

444

457

456

477

444

466

474

442

466

462

474

47 ~

485

4b8

430

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503

511

531

440

413

376

434

510

611

3147

7 14

104

461

914

3606

407

172

182

170

163

142

145

142

133

135

140

116

109

107

95

15b

269

87

3)7

395

461

46d

445

400

445

411

469

463

479

471

469

509

517

537

52)

522

488

469

406

3Be

433

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1124

4240

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5)1

494

11-6

4733

6583

274

155

169

144

148

157

145

149

120

125

127

100

105

111

122

171

224

88

Sp-.EC i.;1 =

visual display of the data contained in memory, was achieved through

the software illustrated in Figure 11. The digital data were converted

to analog voltages by a 10-bit digital to analog converter (DAC). The

analog output of the DAC was fed to either an oscilloscope or a strip

chart recorder. The method of display was selected by setting bit two

on the PDP-8/L switch register to a one for a plotter and to a zero for

a scope.

Since the DAC converted only the ten most significant bits of the

low order word of each channel, the spectrum had to first be treated

to yield a meaningful display. This was achieved in two ways. If the

initialization routine was entered at the start, the spectrum was

searched for any data greater than 409510 (larger than twelve bits).

If any were found, the entire spectrum was rotated to the right one bit

(divided by two). This process was repeated until all data had been

fully rotated into the lower twelve bits of each channel address. The

second method of display set the low order word of each channel whose

contents exceeded twelve bits to 409510 (to yield a full scale display).

The initialization routine was then entered at point C. When all data

were ready for display, the first and last desired channels were enter-

ed directly through the Teletype, and the display subroutine (beginning

at point E) was called.

The subroutine first checked the switch register to determine the

desired display device. When a scope was indicated, the subroutine

was returned, if necessary, to its basic form. After initializing all

counters, the data were sequentially displayed through the DAC. Each

point was retained by the DAC for as short a time as possible (18.65 sec).

At the end of the desired data block the subroutine checked bit

Figure 11. Flowchart of the display software

one of the switch register. The display sequence was repeated until

this bit was set to 1, at which time it was terminated.

When a plotter display was desired several changes were made in

the subroutine. A delay loop of approximately 64 msec was executed

between the display of each data point to allow the plotter pen time to

respond to the signal. At the end of the desired data block the display

was terminated. Once terminated, however, the identical display could

be repeated by entering the routine at point D.

Data Smoothing

The software shown in Figure 12 used the method of Savitsky and

Golay (41) to smooth the digital data stored in the computer memory.

The original spectrum of raw data was replaced in core by the smoothed

data. The concepts and equations for this method were discussed earlier

in the theory section.

All values required by equation (1) were entered directly through

the Teletype. This input included the number of points in the smooth

and all smoothing constants. Then the required number of raw data

points were stacked in a string in lower core. Each point in the

string was multiplied by appropriate smoothing constant and added to a

subtotal. The smoothed data value was obtained by dividing the final

subtotal by the appropriate normalization factor. The smoothed value

was then stored in upper core in place of the original raw value. The

raw string was advanced, the next raw data point was added to the end

of the string, and the process was repeated. This sequence was re-

peated until the entire spectrum had been replaced by smoothed data.

Peak Detection

The two peak detection routines were discussed earlier in the

Figure 12. Flowchart of the data smoothing software

55

theory section. Together the two routines were designed to locate and

determine boundaries for the two peak shapes illustrated in Figure 1.

The first method of detection, described in Figures 15 and 14, was

specifically developed to locate the second peak shape in Figure 1.

This peak shape, which has several statistical minima superimposed on

the peak, was commonly found in spectra which had not been previously

smoothed, and with peaks which had a small peak-to-noise ratio. Peaks

of third type were also commonly found in spectra which covered a narrow

energy range, even after these spectra had been smoothed.

After setting the printout pointer to the second detection routine,

and initializing the required pointers, counters, and variables, the

first detection method began the search for a positive first derivative,

which indicated the location of a statistical minimum in the digital

data. After saving the integral channel location of the minimum as a

possible left peak boundary, the routine located the next maximum by

the derivative sign change from positive to negative. A subroutine,

which was entered at point N and will be discussed later, was then called

to calculate the average minimum to maximum height of the noise over the

40 channels immediately preceding the possible left boundary. The height

from the boundary minimum to the maximum was then compared to a multiple

(designated by the variable MINHT, usually one) of the average noise.

Unless the height exceeded this noise value, the routine began the search

for a new left boundary. If the minimum to maximum height was larger

than the noise, the possibility of a peak was recognized and the routine

continued the search for a right peak boundary.

As Figure 1 illustrates, however, more than one statistical minima

Figure 15. Flowchart of the peak detection (method one) software

57

START

SET PEATRK ( L

PRINTOUT

POINTER TO

2ND SEARCH

POSITIVE NC

INITIALIZE DERIVATIVE?

POINTERS,

COUNTERS, AND

VARIABLES YES

SAVE POSSIBLE

RIGHT BOUNDARY

COMPARE HEIGHT

BETWEEN RIGHT

NO POSITIVE AND LEFT BOUNDARY

DZR.elA.T IVE ? TO MIN,'HT*NOISE

F ES

-YYES

NO NEGATIVE

DERIVATIVE? NO NEGATIVE

DERIVATIVE?

YES YES

SAVE POSSIBLE

PEAK MAXIMUM SAVE NEW

POSSIBLE

PEAK MAXIMUM

CALCULATE

AVERAGE

PEAX-TO-PEAX COMPARE ABSOLUTE

NOISE (N) HEIGHTS OF

TWO MAXIMA

COMPARE PEAK

HEIGHT (RELATIVE

TO LEFT BOUNDARY) YES ,

TO MINHT*NOISE OLD > NEW?

NO

HEIGHT > NOISE? NO SETN

I OLD NEW

W0)

-44

U, -

0

"41

ci '

41

CC3

00

Da0

V.Li -

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44

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were often detected within the true peak boundaries. The routine

located the next minimum and saved the channel location as a possible

right boundary. The height of this minimum, relative to the left

boundary minimum, was then compared to the value of the average noise

times the variable MINHT. If the height exceeded the noise value, the

right boundary was rejected, and the routine determined the location

of the next maximum. The absolute heights of the maxima were then com-

pared, and the channel location of the higher was saved as the peak

maximum. The search was then continued for a right boundary minimum

whose height, relative to the left boundary minimum, was less than the

noise value. When this boundary was found, the routine jumped to point

G, shown in Figure 14, to test for peak validity.

Beginning at point G the routine calculated the number of channels

between the two boundary minima. If the number of channels was less

than the required peak width, designated by the variable NCH and de-

termined by the resolution of the system, the peak was rejected as a

noise spike. The routine then returned to point F, where the channel

location of the last minimum was saved as a possible left boundary and

the search was continued. If the peak was wide enough, however, the

subroutine beginning at point H was called to test the peak height,

relative to both the left and right boundaries. If either height was

less than the required peak-to-noise value, designated by the variable

N, the routine rejected the peak by returning to point F in the peak

detection routine. If all peak criteria were satisfied, however, the

subroutine beginning at point I was called to permanently store the

peak parameters in a string. A counter for the number of peaks was

also incremented, and the routine returned to point F to search for the

next peak.

The second peak detection method, described in Figure 15, was

designed to locate major peaks in a spectrum and assumed that all

valid peaks contained only one maximum. After setting the printout

pointer to a program halt and initializing all required pointers,

counters, and variables, the routine began the search for a positive

first derivative. If the positive derivative was the first in a series,

indicating the location of a statistical minimum, the channel location

of the minimum was saved as a possible left peak boundary. The routine

then continued the search until the required number of consecutive

positive derivatives, designated by the variable MNUM and determined

by the resolution of the system, had been detected.

If the required number was reached the channel location of the

next negative derivative was saved as the location of the peak maximum.

The routine then searched for the next minimum, indicated by the channel

location of the next positive derivative. If the required number of con-

secutive negative derivatives, again designated by the variable MNUM,

were detected, the location of the minumum was saved as a possible

right peak boundary. If either series of derivatives were too small,

the peak was rejected as noise.

Once the boundary channels were located, the routine called the

noise evaluation subroutine to calculate the average noise height over

the 40 channels immediately preceding the left peak boundary. The same

subroutine used by the first peak detection routine, beginning at

point H, was then called to validate the peak height. If the peak-to-

noise ratio exceeded the value designated by the variable N, the sub-

routine beginning at point I was called to permanently store the peak

Figure 15. Flowchart of the peak detection (method two) software

63

SET PEAK PRINTOUT L

POINTER TO HALT

INITIALIZE POSITIVE NO

POINTERS

COUNTERS, AND DERIVATIVE?

COUNTERS, AND

VARIABLES

YES

L MINIMUM NO

NEG. SERIES

COMPLETED?

YES

POSITIVE ( N)

DERIVATIVE? 1

SAVE POSSIBLE

RIGHT BOUNDARY

YES

YES FIRST CALCULATE

IN POSITIVE > AVERAGE

SAVE POSSIBLE

LEFT BOUNDARY

HO

MINIMUM E0 TI

POS. SERIES

COMPLETED?

VALID NO

YES PEAK?

YES

NO NEGATIVE

DERIVATIVE?

SAVE POSSIBLE

LEFT BOUNDARY

YES

SAVE POSSIBLE

PEAK .rAXIMUM CLEAR IST IN

SERIES FLAG

64

parameters. The routiic then saved the location of the last minimum

as a possible left boundary and began the search for the next peak at

point K.

Whenever the sign of the first derivative was requested by the

peak search routines, the derivative subroutine, entered at point L

and described in Figure 16, was called to calculate the sign of the

first difference. When channel 2047 was reached, however, the peak

search was terminated, and the peak printout routine, described in

Figure 16, was entered at point K. This routine printed the number

of peaks located by the search and typed a header for the remaining

printout. Then, for each peak, the peak parameters were printed and

a subroutine, which was entered at point Q and is discussed later,

was called to calculate and print the peak areas. When all peaks were

completed the peak printout pointer was followed to either the second

peak detection routine or to a program halt.

Whenever the value of the average noise was required, the sub-

routine entered at point N and described in Figure 17 was called by

the peak search routines. First the channel counter was moved back

40 channels from the left boundary of the peak in question. If this

starting channel address was less than the right boundary of the last

valid peak, as illustrated by the second peak in Figure 1, the sub-

routine restored the channel counter and exited with the last noise

value. If not, the subroutine preceded to locate minima and maxima

by the sign changes in the first derivative. After locating each ex-

tremity, the minimum to maximum height was calculated and added to a

subtotal, and a counter was incremented for a divisor. When the 40

channels were evaluated, the average noise was calculated by dividing

Figure 16. Flowchart of the software which determines the

first differences and prints the final

results of the peak searches

SUBTRACT DATA IN

CURRENT CHANNEL

FROM DATA IN

CURRENT CHANNEL+1

PRINT LEFT

BOUNDARY, PEAK

MAXIMUM, AND

PIGHT BOUNDARY

Figure 17. Flowchart of the software which calculates the

average height of the noise over 40 channels

'f .-C

69

the subtotal by the divisor. The subroutine then restored the channel

counter and exited with the new noise value.

The software required to calculate and print the peak areas is

described in Figure 18. The subroutine, which was called by the peak

printout routine and was entered at point Q, first used the peak par-

ameters to calculate a total, trapezoid, and quantitative area accord-

ing to equation (2). The areas were then printed as total peak area

values. The peak parameters were then altered according to the Wasson

peak area method. The nur.ber of channels to the left and right of the

peak maximum included in the Wasson calculation were designated by the

variable NWASON. If either of the original peak boundaries were inside

the Wasson boundaries, the subroutine was exited without further print-

out. If the peak was wide enough, however, the slope of the total peak

baseline was calculated and used to determine the absolute heights of

the Wasson peak boundaries. These new boundary values were then used

to calculate new total, trapezoid, and quantitative areas, which were

printed as Wasson area values.

Preparation of FOCAL Compatible Data

All curve fitting calculations were performed using the FOCAL

programs listed in Appendix II. These programs required that the

digital data be converted to floating point and stored in core loca-

tions accessible by the FOCAL subroutine FNEW. The software described

in Figure 19 was written to perform the conversion and relocation of

the digital data.

The first and last channels of the desired data block were en-

tered directly through the Teletype. After initializing the required

counters and variables, the data block was relocated in integer form

Figure 18. Flowchart of the software which calculates and

prints the peak areas by the total peak area

and Wasson methods

SET:

XI = LEFT BOUNDARY

MAX = PEAK MAXIMUM

X4 RIGHT BOUNDARY

-a

Figure 19. Flowchart of the software which converts the

integer data to floating point and stores

the results in core locations accessible

by the FOCAL subroutine FNEW

o

74

to begin in location zero. The data relocation insured that the

final converted data were not stored in core locations occupied by the

data block. The data were then sequentially converted to a three-word

floating point form and relocated in the core locations corresponding

to the even FNEW locations. The odd FNEW locations were cleared for

later use as storage locations for the fitted data.

RESULTS AND DISCUSSION

System Evaluation

In order to thoroughly test the performance of the analytical data

system, eleven different sample spectra were collected and stored on

51 59 65 75 86,

magnetic tape. Pure isotopes of Cr Fe Zn Se Rb

24 '26 50 54 37

and Ag obtained from New England Nuclear, were used to prepare

47

the radioactive samples, thus insuring that spectra of known composition

were experimentally generated. Table I lists the experimental condi-

tions under which the spectra were collected. The same isotopic samples

were used to generate spectra 6-8 and spectra 9-11.

Figures 20-22 illustrate the display capability of a strip chart

recorder under control of the display software. The output to the re-

corder was generated by a 10-bit digital to analog converter. The dis-

play routine easily rotated the stored spectrum to the left or right

one bit at a time, thereby multiplying or dividing the contents by two.

This allowed the operator to display the spectrum completely on scale

(Figure 20) or to highlight the regions of interest (Figures 21,22).

Data from spectra 6 and 10 were used to measure the linearity of

the data acquisition system. Figure 25 illustrates the linearity be-

tween gamma-ray energy and photopeak location over the total energy

range used in these studies. The data were obtained from spectra 6,

and the method of linear least squares was used to obtain the slope of

1.48 channel/KeV, the zero energy intercept of 0.37, and the standard

deviation of 0.72 channel. The peak locations were determined by the

TABLE I

EXPERIMENTAL CONDITIONS FOR THE SAMPLE SPECTRA

SPECTRUM ISOTOPIC HALF-LIFE SPECTRUM ENERGY

NUMBER CONTENTS (DAYS) RANGE (KeV)

1 Ag 110m 255 0 1578

2 Zn 65 245 0 1578

5 Fe 59 45.6 0 1578

4 Zn 65 245 0 1578

Ag 110m 255

5 Fe 59 45.6 0 1578

Zn- 65 245

6 Cr 51 27.8 0 1578

Fe 59 45.6

Zn- 65 245

Se 75 120

Rb 86 18.7

Ag 110m 255

7 Cr 51 27.8 0 357

Fe 59 45.6

Zn- 65 245

Se 75 120

Rb 86 18.7

Ag 110m 255

8 Cr 51 27.8 357 672

Fe 59 45.6

Zn- 65 245

Se 75 120

Rb 86 18.7

Ag 110m 255

9 Se 75 120 0 965

Ag 110m 255

10 Se 75 120 0 477

Ag 110m 255

11 Se 75 120 477 955

Ag 110m 255

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peak detection software and were given by the integral channel loca-

tion of the peak maxima. The possible error in these values was there-

fore on the order of + 1 channel. For this reason the standard devia-

tion of 0.72 channel represented an excellent verification of the

linearity of the data acquisition system over the total energy range,

while channel zero was well within the error limits of the zero energy

intercept, 0.57 + 0.72.

Figure 24 shows that this linearity was retained even when the

spectrum energy range was decreased and the resolution of the ADC was

increased by a factor of two. The least squares slope, zero energy in-

tercept, and standard deviation were 4.30 channel/KeV, -5.47, and 1.27

channels respectively. The increased standard deviation was expected

since the number of channels per unit of energy was increased by a

factor of almost three. Therefore the measured error of only + 1.27

channels again demonstrated the excellent linearity of the system. The

non-zero value of the zero energy intercept was not significant since

it represented only a relative point from which the ADC measured the

pulse-height. The zero intercept setting of the ADC was adjustable

electronically and was set as close to zero as possible. Once set, how-

ever, further adjustment proved unnecessary, even when the resolution

was changed, as shown by the results above.

The system stability was demonstrated by comparing the slopes of

the linearity curves calculated from the first six spectra. These

spectra were collected on six different days, but under identical ex-

perimental conditions. The six spectra had a mean slope of 1.48 channel/

KeV and a standard deviation of 0.001 channel/KeV, only + 0.07 of the mean.

The resolution of the Ge(Li) detector was shown to be a linear

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