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Data acquisition and reduction of high resolution gamma-ray spectra

Material Information

Title:
Data acquisition and reduction of high resolution gamma-ray spectra
Creator:
Cottrell, David Baldwin, 1946-
Publication Date:
Copyright Date:
1973
Language:
English
Physical Description:
xiv, 305 leaves. : illus. ; 28 cm.

Subjects

Subjects / Keywords:
Data smoothing ( jstor )
Gamma ray spectrum ( jstor )
Mathematical independent variables ( jstor )
Noise spectra ( jstor )
Photopeaks ( jstor )
Point estimators ( jstor )
Software ( jstor )
Spectral index ( jstor )
Spectral methods ( jstor )
Spectral resolution ( jstor )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Gamma ray spectrometry -- Computer programs ( lcsh )
Nuclear activation analysis ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis -- University of Florida.
Bibliography:
Bibliography: leaves 300-304.
Additional Physical Form:
Also available on World Wide Web
General Note:
Typescript.
General Note:
Vita.

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Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. 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:
022835400 ( alephbibnum )
14120744 ( oclc )
ADB0911 ( notis )

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Full Text











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.

















































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"0



E


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4-4










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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

* I I -



>4 "4-4















-4 1-4-4
d cu
































z wjz 1-




"'-



-,41 -4-,41 ~CU







-4



"41 ,1 r l -4 OL -4
CX4 L4 r4 a4I a:
/l /D / /D l
I I 1 1
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










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.iJ








.4
0







Go









0K
-4
l^ .- o
\ \ 0







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




CL -41a



cr-



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0 0



0 c0

w






CL.




7M Aj
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4-4
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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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4.J


0
,4



Dr









4JJ
'-4




0






















-4

r4-
s.J



li-

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35




LLL
U.
ULLJ

moo




OOOOOOOO-O-- --
















0000000000--.
wrw 0





















O -Nr--------------
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
u oa
00 c


00 4-

4









rei
4-)








co~


o0G
ua










U +





E-4 4.)










c
E44
rlr




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3l






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
47
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
553
1124
4240
b844
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 -


'44
I-'

















'41
44 -









-4r

44






to
4~
ry-4






59


m


z z

-E
0 .4 4 u

0














ZZ E-

_ __ zc.E
"~M: 0 w







< r" z L










F- E4X
U U E-U
2Z1-4





































M E-)






A0




uz
E- U)
ZZ







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
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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.

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Full Text

PAGE 1

DATA ACQUISITION AND REDUCTION OF HIGH RESOLUTION GaM1<1A-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. TH_E DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1973

PAGE 2

TO MY WIFE FOR HER PATIENCE AND ENCOURAGEMENT

PAGE 3

AC KNOWLE DGE MENTS The author wishes to express his gratitude to tlie many people who contributed to the success of this project. First and foreaost is his research director, Dr. Stuart P. Cram, vjhose continued guidance, encouragement, and enthusiastic support made this work possible. The author is also grateful to the other members of his commitcee, 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 fellov; members of the research group are gratefully acknowledged. Special thanks go to Jack E. Leitner for his unselfish cooperation and time during the early months of this vjork. 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 V7as 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 v;hich he has received. This research was supported in part by NSF Research Grant No. G?-lkl5k, 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 113.

PAGE 4

parents, Mr. and Mrs. R. E. Cottrell, for their faith and encouragement, and to his wife, Li?:, for her pa fiance and understanding throughout the duration of this v.'ork. IV

PAGE 5

TABLE OF CONTENTS Page ACKNOVJLEDGEIENTS iii LIST OF TABLES vii LIST OF FIGU;IES viii ABSTRACT xiv INTRODUCTION i Research Objectives i Historical Review 2 THEORETICAL 3 Data Smoothing g Peak Detection ^ ^ 9 Peak Quantitation m Curve Fitting ig Method of Standard Addition 27 EXPERU-ENTAL jq Hardware zx Interface ^5 Timing System 55 Software 59 Data Acquisition ^4-0 Data Printout I4.6 Display ^5 Data Smoothing 53 V

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Page Peak Detection r. Preparation of FOCAL Compatible Data ^5 RESULTS AND DISCUSSION 75 System Evaluation yi^ Data Smoothing 88 Peak Detection 9)1 Curve Fitting 109 Peak Areas iglj. Liver Analysis 198 APPENDICES 227 APPENDIX I. CORE RESIDENT SOra.'ARE 228 APPENDIX 11. FOCAL PROGRAMS 287 1. Photopeak Fitting Routine 288 2. Baseline Fitting Routine 291 5. Calculation of the Total Fitted Curve 29U k. Numerical Integration by the Trapszoid Method . . 296 5. Linear Least Squares 298 BIBLIOGP^APHY 500 BIOGRAPHICAL SKETCH 305 VI

PAGE 7

LIST OF TABLES TABLE Page I EXPERIMENTAL CONDITIONS FOR THE SAMl^LE SPECTRi\ 76 II COMBINED RESULTS OF THE AUTOMATED PEAK SEARCHES 96 III NUMBER OF PEAKS FOUND BY THE AUTOM\TED PEAK SEARCHES ... 102 IV PERCENT CH/iNGE IN THE RESIDUAL OF THE CURVE FITTING FUNCTION 115 V DESCRIPTION OF PEAKS SELECTED FOR CURVE FITTING 116 VI INITIAL AND FINAL VALUES FROM THE CURVE FITTING CALCULATIONS 117 VII INITIAL AND FINAL VxVLUES FROM THE CURVE FITTING CALCULATIONS 120 VIII CURVE FITTING RESULTS 196 IX CURVE FITTING RESULTS 197 X CURVE FITTING RESULTS 199 XI SIGNIFICANT PEAKS IN AN IRRADIATED LIVER SiVMPLE 205 XII EXPERIMENTAL CONDITIONS FOR THE LIVER ANALYSIS 207 XIII RESULTS OF THE LIVER ANALYSIS 209 XIV RESULTS OF THE LIVER ANALYSIS 210 XV EXPERIMENTAL AND NATIONP.L BUREAU OF STANDARDS RESULTS OF THE ANALYSIS OF STANDARD REFERENCE MATERIAL 1577 (BOVINE LIVER) 225 vii

PAGE 8

LIST OF FIGURES Figure Page 1. Two possible peak shapes in a digital, gaimnaray spectrum 11 2. Quantitative peak areas from three different methods 17 3. Physical interpretations of the eight parameters in a photopeak fitting function 22 k. Block diagram of the experimental system ^1 5. Interface between an analog to digital converter and a PDP-8/L computer 55 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+ ^ preset on the thumbwheel switch 57 7. Flowchart of the data acquisition software k2 8. Timing relations between the computer and analog to digital converter ^5 9. Flowchart of the data printout software kB 10. Sample page from the computer printout of a stored spectrum 50 11. Flowchart of the display software 52 12. Flowchart of the data smoothing software 5k 15. Flowchart of the peak detection (method one) software 57 Ik. Flowchart of the software which tests for peak validity and permanently stores valid peak locations and boundaries 59 viii

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Figure Page 15. Flowchart of the peak detection (method two) software • 63 16. Flowchart of the software which determines the first differences and prints the firicil results of the peak searches • 65 17. Flowchart of the software which .calculates the average height of the noise over -lO channels ... 68 18. Flowchart of the software which calculates and prints the peak areas by the total peak area and Wasson methods . 71 19. Flowchart of the software which converts the integer data to floating point and stores the results in core locations accessable by the FOCAL subroutine FNEW 73 20. Plot of spectrun 6, attenuated by a factor of (x 8) . The full energy range of the spectrum is 0-1.378 MeV (0.62liKeV/channel) • 78 21. Plot of spectrum 6, unattenua ted. The full energy range of the spectrum is 0-1.378 MeV (0.621+ KeV/channel) 80 22. Plot of spectrum 6, attenuated by a factor of (x 1/2) . The full energy range of the spectrum is 0-1.378 MeV (0.62^+ KeV/channel) .... 82 23Plot of channel number vs. photopeak energy for the full energy range used in the research (data obtained from spectrum 6) 84 2k. Plot of channel number vs. photopeak energy for the low energy region (data obtained from spectrum 10) • ^7 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) "0 26. Effects of the statistical scatter on the total peak area, resulting in too large (peak A) or toe small (peak B) a quantitative area ^2 ix

PAGE 10

Figure ^age 27. Plot of spectrum 9, unattenuated. The full energy range of the spectrum is 0-965 KeV (0.U71 KeV/channel) ^^ 28. Plot of spectrum 7, unattenuated. The full energy range of the rpectrura is 0--5J57 KeV (0.163 KeV/channel) '"^^ 29. Plot of spectrum 11, attenuated by a factor of (x 1/2) . The full energy range of the spectrum is U77-955 KeV (0.255 KeV/channel ^^^ 50. Plot of spectrum k, unattenuated. The full energy range of the spectrum is 0.1.578 MeV iO.eZk KeV/channel) 51. Plot of the percent change in the residual sum of squares vs. the number of iterations performed in the curve fitting process II5 52. Raw data and fitted curve (offset) for the 1115.51 KeV Zn 65 peak taken from spec trum 2 55. Raw data and fitted curve (offset) for the 88lv.5 KeV Ag llOm peak taken frorn ^^^ spectrum 1 5!+. Raw data and fitted curve (offset) for the 88k. b KeV Ag 110m peak taken from spectrum 9 55. Raw data and fitted curve (offset) for the 957.5 KeV Ag 110m peak taken from spectrum 1 36. Raw data and fitted curve (offset) for the 957.5 KeV Ag 110m peak taken from spectrum 9 57. Raw data and fitted curve (offset) for the 88ii.5 KeV Ag-llOm peak taken from spectrum 11 58. Raw data and fitted curve (offset) for the 520. 08 KeV Cr 51 peak taken from spectrum 7 59. Raw data and fitted curve (offset) for the 1099.27 KeV Fe 59 peak taken from spectrum 5 X

PAGE 11

Figure p^^^ kO. Raw data and fitted curve (offset) for the 937.3 KeV Ag llOm peak taken from spectrum h -^^g kl. Raw data and fitted curve (offset) for the 88i|.5 KeV Ag llOm peak taken from spectrum k i|,-i k2. Raw data and fitted curve (offset) for the 121.13 KeV Se 75 peak taken from spectrum 7 j^j^t k^. Raw data and fitted curve (offset) for the 511 KeV annihilation peak taken from spectrum 8 ]^]|5 kk. Raw data and fitted curve (offset) for the 817.9 KeV Ag llOm peak taken from spectrum 1 jl^y k5. Raw data and fitted curve (offset) for the 817.9 KeV Ag llQm peak taken from spectrum 9 ii^g hS. Raw data and fitted curve (offset) for the Ui|6.2 KeV Ag 110m peak taken from spectrum 1 j^5]^ k7. Raw data and fitted curve (offset) for the i+00.6i^ KeV Se 75 peak taken from spectrum 10 2^5:5 iv8. Raw data and fitted curve (offset) for the 817.9 KeV Ag llQm peak taken from spectrum k ]^53 k9. Raw data and fitted curve (offset) for the Ui;6.2 KeV Ag llOm peak taken from spectrum 10 i57 50. Raw data and fitted curve (offset) for the 620.1 KeV Ag llOm peak taken from spectrum 9 i^q 51. Raw data and fitted curve (offset) for the 96,75 KeV Se 75 peak taken from spectrum 7 ]^g2 52. Raw data and fitted curve (offset) for the 96.73 KeV Se 75 peak taken from spectrum 10 j^gh xi

PAGE 12

Figure Page 55. Raw data and fitted curve (offset) for the 817.9 KeV Ag llOra peak taken from spectrum 11 167 54. Raw data and fitted curve (offset) for the 620.1 KeV Ag llOm peak taken from spectrum 11 159 55. Raw data and fitted curve (offset) for the 303.89 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 1175.2 KeV Co 60 peak taken from spectrum 6 175 58. Raw data and fitted curve (offset) for the 1175.2 KeV Co 60 peak taken from spectrum 5 177 59. Raw data and fitted curve (offset) for the 7A4.2 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 1°^ 61. Raw data and fitted curve (offset) for the 1175.2 KeV Co 60 peak taken from spectrum 5 '' 62. Raw data and fitted curve (offset) for the 1175.2 KeV Co 60 peak taken from spectrum 5. The data was smoothed before the fit was obtained 185 63. 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 llOm peak taken from spectrum 6. The data was smoothed before the fit was obtained. 190 Xll

PAGE 13

Figure Page 65. Ravj data and fitted curve (offset) for the 677.5 and 686.8 KeV Ag 110m peaks taken from spectrum 1 I93 65. Plot of an irradiated liver spectrum, unattenuated. The full energy range of the spectrum is 2.583 MeV (1.164 KeV/channel) .... 202 67. Plot of an irradiated liver spectrum, attenuated by a factor of (x 0.208). The full energy range of the spectrum is 2.333 MeV (1.164 KeV/channel) 20^^ 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 1.645 MeV CI 38 peak . . 212 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 CI 58 peak . . 21l^ 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 . . 216 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 218 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 220 75. Plot of the total peak area (open circles) and VJasson 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 I.568 MeV Na 24 peak 222 xiii

PAGE 14

Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfill^ient of the Requirements for the Degree of Doctor of Philosophy DATA ACQUISITION AND REDUCTION OF HIGH RESOLUTION GAbZ'ii.-SJiY 3PECTM By David Baldwin Cottrell March, 1975 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 determine the locations and boundaries of photopeaks in a gamma-ray spectra. A technique was devised to perform curve fitting by the method of nonlinear least squares on a mini-computer. A new function, which defines 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

PAGE 15

INTRODUCTION The principles of activation analysis, which have been reviewed by Lynn (1), were first introduced by Hevesy and Levi (2,5) in 1936 and Seaborg and Livingood (4) in 1938. 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 resolution, lithium-drifted germanium detectors has made possible the instrumental 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

PAGE 16

2 data under the control of a dedicated mini-computer was developed to maintain the high resolution of the detector and the integrity of the pulseheight. 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 activation analysis by gamma-ray spectrometry. Connally and Leboeuf (5) were among the first to demonstrate the value of this new analytical technique. Morrison and Cosgrove (6,7) demonstrated the usefulness of gammaray spectrometry in the determination of trace impurities in a bulk component, and several researchers proved the practicality of totally instrumental 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

PAGE 17

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 computational power and speed of the digital computer. Guinn and Lasch (15) noted that comparison of photopeak areas with those in standard spectra was still the easiest and most practical quantitative approach. Computer routines were written to obtain this information by fitting a mathematical function to the experimental data (li|, 15), or by simply analyzing the raw digital data (16-13). Often, however, the limited resolution of the Nal(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 subtraction. The theory of spectrum stripping was quickly expanded and computerized (13,21-25) • Standard spectra of pure elements were collected 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 experimental spectrum was obtained. Another approach, based on the same

PAGE 18

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 (53,54), but the above were by far the most comnionly used methods for the analysis of complex scintillation 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) detector (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 (56,57) quickly demonstrated 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 analytical information lying underneath (58-40). 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 (43) studied the

PAGE 19

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 contained 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 determination. Dooley and co-workers (47) looked for significant count increases 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 baseline from which to begin and end peak integration. An automated peak detection method particularly suitable for efficient 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) reported 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.

PAGE 20

6 Once tha 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 Che 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 (33i 38,31,57) . 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 (^3) . 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 baseline 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 principles 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

PAGE 21

7 channels immediately surrounding the peak, center. The author then examined the precision obtainable by the methods described above. Baedecksr's experiments showed that the more complex methods did not provide a significantly greater precision than the simple ones. Ue therefore recommended the Wasson technique, except for cases where there u-ere large deadtine differences between samples or where changes in resolution created a problem. For these latter cases he recommended the T?A method. More complex approaches to photopeak quantitation, such as curve fitting, ^^;ere also reported. The least squares technique for fitting a function to a set of data points, discussed by Roberts, Wilkinson, and Walker (65), was the usual method of choice, although Ciampi and coworkers i^h) used a maximum probability technique. Early authors (55,6U,65) used a pure Gaussian fitting function to approximate the photopeak shape in Ge(Li) spectra. However it soon became 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 conditions of high counting rates. Many functional forms were suggested to account for the tailing of the main Gaussian shape. Sanders and Holm (56) 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 exponential contribution for tailing. Kern (69) and Pratt and Luther (70)

PAGE 22

8 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 scientific world. Much of this work involved the chemical separation and isolation of the desired element (79,80) or the removal of large interferences, such as sodium (81). Recently, however, instrumental analysis, using Ge(Li) detectors, was used for the multielement analysis of biological materials (82). Linekin and co-workers (85). however, indicated that the majority of this research used data reduction techniques developed 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.

PAGE 23

THEORETICAL Modern activation analysis experiments usually involve the acquisition 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 information. 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

PAGE 24

10 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 = ( E C.Y )/N (1) -' i=-m -* where Y. = smoothed data value, in counts i = running index for the data block m = (number of points in the block l)/2 C, = convoluting integer for the ith point in the block Y. .= raw data for the ith point in the block, in counts j = index for the channel number . N = normalization factor, a scaler Yule (42,44) has shown that a single smoothing does not det;rade the analytical information if the number of points in the smoothing interval 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 boundary minimum to the peak maximum, and a negative first derivative from the maximum to the right boundary minimum. The second peak, however.

PAGE 25

11 CO a) o. 03 a a 0) m n O a o i-i o 00

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12 has several rainiir.a 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. Hie first derivative will change signs several times within the true peak boundaries. In order to lirait the size and complexity of the peak detection software, and still locate both types of valid peak shapes, two detection routines are used. Together they occupy less than 127o of the available 4K of core and require only two to eight minutes to search a 2043 channel spectrum and print all qualitative and quantitative information. 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 satisfactory 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

PAGE 27

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 boundaries 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 peakto-noise ratio. The tv;o 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 boundary channels. A complete search of the spectrum by both routines is therefore necessary to insure a complete and accurate analysis.

PAGE 28

Ik Peak Quantitr. tion Once the peak boundaries arc determined, 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 uf this, devised by Wasson and cited by Baedecker (62) , are used in this research. The total peak area n>ethod yields the largest value for the peak area within the selected boundaries. The area is calculated from i=R ^TPA = ^ ^i ^^L ^ ^R^^^ L + l)/2 (2) i=L where A „ = total peak area, in counts TPA *^ C = number cf counts in channel i, LSi^ 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 A. = E C. (N + l/2)(C^^j, + C^.^) (5) i = M-N

PAGE 29

15 where A^ = 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 tvo methods. The usable Wasson area is calculated from i=M+N '^"ifM-N'l""'^2'
PAGE 30

en •o o u § «) A) U-l 0) o M-l a CO CO eg « o > a 3 cu 0) 9 DO

PAGE 31

17 o en < -J -J LJ O O

PAGE 32

18 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, vhich 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 j = 1,2, ...,m 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, ,P^, . . . ,P ,X.) = the theoretical function X id mi evaluated at point X. 1 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.

PAGE 33

19 The residual sun of squares ' = ,f/i(^-V^ (5) 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 APj^, ZiP^, . . . ,AP^. For the kth iteration the function F. is given by F*^ and new estimates of the parameters are calculated from P^-"^ = P^ + AP^ . j = 1.2,....m (7) The process converges when Urn P^ P j = l,2,...,m (8) k-«o -" 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 detector. The tail on the leading edge of the Gaussian is caused by the incomplete 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 emperical function successfully used by Chesler and Cram (84) to

PAGE 34

v£) 20 •^\ CM ^ I/O b I b I b I b a. ^ /o 3 b b /O /O

PAGE 35

21 fit chromatographic peaks. It is composed of a leading exponential edge, a hyperbolic tangent joining function, and a central Gaussian. The functional forn is -(X -p,)2 F^ = ?^{exp[ — ] + 0.5 {l-Tanh[P2(X.-P^)]} x (9) 2,1/2 where ^ rP6exp(.p^[{(P3-X.)^]^^'=^ + (Pq-X.J])]} Pj^ = the height of the Gaussian, in counts Pg = the rate of change of the joining function P^ = the center of change of the joining function, in Sigma units P^ = the center of the Gaussian, in sigma units 2 Pc = cr of the Gaussian ^6 " ^^^ initial height of the exponential, in counts P^ = the rate of decrease of the exponential Pg = 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 illustrated 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

PAGE 36

22 c o u e 3 00 CO 0) o. o u o o. a u u V u CO o. JJ X oo 93 c o 10 u u 0) 03 u « M 3 00

PAGE 37

23 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. Therefore the signs of P^, P^, P^, P^, and P^ should always be positive, k k while those of P and P should remain negative. Only the sign of P*^ JO 4 should be allowed to vary. The signs of the parameter estimates are checked following the solutions 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 )^ A. = exp[-^^ ] (10) B. = 0.5 (l-TanhfP^CX.-P^)]) (H) C^ = P^exp(-P^[ ((Pg-X.)2]l/2 ^ (p^-xjl) (12) and therefore ^ = \^\ ^ \^i^ (13) The partial derivatives may then be calculated from a?. W: = ^i^ ^i^i (U)

PAGE 38

where 2k ^F SB. (15) 3 3 (16) (17) ^F, = Pi (^) ^p^ " 1 ^ap (18) ^ ^1 Sp^ ^i^i ^W^ 6 (19) ap ac a?: ^ ^«i (a?:> (20) ap. ac. 8 8 (21) ^1 -<^-^i)^ ap, (X.-P,)A. P. (22) aA, I ap. (X.-P,)'^A. 1 U' 1 2P (25)

PAGE 39

SB -2(X -P ) i. i 1. 2 (exptP^CX.-P^)] + exp[-P2(X.-P^)]}' ^ __ ^ ^^3 (exptP^CX^-P^)] + evp[-P^(X.-P^)])2 ^, C. i 1 25 (21^) (25) ^^6 ' ^6 (26) Sc ^=-C,{[(P3-X.)2]^/2^ (Pg-Vi (27) 8 KPg-xp^l^^'' The baseline on either side of the peak is approximated by the polynomial ^ = ^ -^ ^O^i ^ 'lA ' h2^l (29) where X. is expressed in channel units. The same nonlinear least squares process is used to fit this four parameter function. The partial derivatives are calculated from a?J = 1 (30)

PAGE 40

26 ^i 2 W^^ = ^i (32) a^, = ^i (53) The total fitting function which approximates the combined peak and baseline shape is therefore X^ = F. + D^ , i = 1,2,...,N (3lv) The solution of this total function, however, requires the filling of a twelve by twelve matrix, and the solving of twelve equations in twelve unknovms. 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 determined from the value of the baseline at the left peak boundary. The initial values of P,„> P-, •> . ai^d P are set to zero. The values of the eight peak parameters may be estimated from the corrected digital data, follovjing the baseline subtraction. The estimate of P is obtained directly from the corrected data. The values of P^, P,, P., P^, and Pq are usually estimated by 3-0, -1.5> 0, 1.0, and -1.5 respectively. o 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.

PAGE 41

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 A^ = k(W. + S^) (55) where and where i i A = peak area for sample i, in counts k = a constant W = the amount of element in sample i, in grams S = the amount of element added to sample i, in micrograms ^p = *^%) (56) A = peak area of a pure sample, in counts W = the amount of element in a pure sample, in grams

PAGE 42

28 Before they can be compared, however, all results must be normalized to a standard sample weight. The normalization factor is given by pp _ desired standard weight 1 .00 grams 1 sample weight in grams ~ sample weight in grams ^^^ After normalization, equations (55) and (36) become A.CF. = k(W.CF^ + S.CF.) (38) and A CF = k(W CF ) (^Q\ P P P P ^^^^ Since ^i^^ = v^ ^^^ then subtraction of equation (59) from equation (58) yields A.CF. = k(S CFJ + A CF (1|1) L 1 i i' P P The X-intercept of a plot of A.CF. as a function of S^CF. is therefore L 1 i 1 -A CF X-intercept = — ? — ^ = -W CF (1^) 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

PAGE 43

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)

PAGE 44

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-amplif ier, a linear pulse-height amplifier, and an ADC. The experimental system developed for this research utilized a 50 cc lithiumdrifted germanium detectcr made by Nuclear Diodes. The detector was a wrap-around coaxial design which was rated at 8% efficiency, relative to a 5x3 Nal(Tl) detector. The resolution of the Ge(Li) detector was rated at 2.3 KeV, measured at the 1.33 ^^V cobalt peak, and the peakto-compton ratio was rated at 23:1* The detector was biased at 2500 volts by an Ortec Model 456 highvoltage power supply. A Nuclear Diodes Model 103 pre-amplif ier was connected to an Ortec Model 451 spectroscopy amplifier. An Ortec Model 444 biased amplifier was available as an option. The 0-lOV output of the linear amplifier was digitized by a Northern Scientific Model NS-629 analog to digital converter. The Wilkinson type ADC was capable of 8192 channels of resolution and used a 50 MHz 50

PAGE 45

51 UJ o o CO =^ 6 « m >. m ^».g? ^^_>»t-i — -Q. < j^ g ••-I u V (X M « J= o 8 CO M M « o u 3 00 PC4

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32 clock rate for the digitization process. The dead time of the ADC was rated at J + 0.02N p,sec per event, where N is the channel address of the converted signal. The ntiximum dead time of the system was therefore 167 jisec. All signals necessary for the transfer of the digital data and the control of the ADC operation were 0-5V positive logic, and were accessible 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 20^8 channels of available 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 acquisition, printout, display, and data reduction. The computer was a PDP-8/L from Digital Equipment Corporation. With 8K of available core, kK was used for memory storage and UK was allotted for core resident software. The PDP-8/L used 12-bit words, had a cycle time of 1.6 |isec, contained one common bus, and had one level of program interrupt. All major input and output was achieved through a Model ASR 35 Teletype, which typed ten characters a second. The spectra were displayed on an ITT Model 1955D fifteen-inch display oscilloscope, and were plotted on a Model 7127A strip chart recorder from HewlettPackard. A Tri-Data Model U096 magnetic tape unit, capable of trans-

PAGE 47

33 fering 1+62 12-bit words a second, was used for all bulk storage. Hardware The computer based pulse-height analyzer system, described above, required the design and construction of two critical hardware components. An interface was built to allow computer control of the data acquisition by the ADC, and to provide a means for transfering the digital address data to the computer. A high precision digital clock was built to accurately control all count times. These two components are discussed in detail 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 parallel transfer of digital data from Che 13-bit ADC output register to the 12-bit accumulator register of the computer. Since only 20U8 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 (lOT) , software command (6XXY_) , caused a 8 logical "1" to be generated for lj..25 ^sec on the six memory buffer lines indicated by the two octal digits XX (56 for the ADC interface). Therefore, by connecting a siic-input nand gate to the appropriate MBR lines, a specific device, such as the interface, was individually controlled.

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. 35 Ql O a: ijj CCuj O Oq: _ u 2 a. => cr UJ «z a: < UJ O — WfOTTintDh-ODCDO — _| OOOOOOOOOO O en "q. o CM n j:jj:|QQQQQQj:)j:jQQ|j^y

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56 The same 6XXY comnand caused the computer to generate any com8 bination of three input-output pulses (lOP's), each 600 nsec in duration. The octal digit Y designated which combination of lOP's were generated. If more than one lOP was designated by the software command, the order of generation was lOPl, I0P2, and lOPU, 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 lOP's passed through the logic of the device selector. This prevented the lOP's intended for other peripherals from activating the ADC interface. Each of the three lOP's performed a specific function in the ADC interface. The lOPl 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 lOPl 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 I0P2 was used to open a 12bit 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 I0P4 was used to send a pulse to the clear input of the ADC. This pulse caused the ADC to clear the output register, reset the ready flag to a logical "O", 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

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37 s^'S ai -c: £ 3." ft.— sso =T1 2 l a a T^ T-. X LM I r X QtQ—] >N=>rp:>-i n V rr l_7Y e o • E a» o x: )^ >^ u •U T3 3 u-i 0) 01 O 4J 0) CO 1-t )-< a> C X. T^ B U) M 3 -w -w ^ 3 JJ O" (1) u n
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58 to allow the highly precise and accurate control of experimental count times required by this research. A 1 >K2 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 divideby-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 decades 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 T, to time T„ . This enabled the contents of a four decade A B 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 T_ , which allowed the passage of the 1/6 Hz clock B pulses. The leading edge of the first pulse through the input gate (at time T„ ) caused the Q output of the control flip-flop to go from B+ 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 interrupt 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 remaining for data acquisition was constantly shown on the lighted display. When the counter reached zero, at time T , the gated output of the

PAGE 53

59 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 T , 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 counting 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 \;as chosen all clock pulses were passed to the counter. Software The complex mathematical calculations required by the curve fitting and linear least squares processes were performed using the conversational computer language FOCAL, developed by Digital Equipment Corporation. The FOCAL programs written to perform these mathematical 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 UK. of core allotted for that purpose, and included all routines necessary for the operation of the

PAGE 54

experimental system and all data reduction routines except those involving curve fitting. Also present in core was Digital Equipment Corporation's floating point package, DEC-08-YQ2B-PB, designed to perform basic mathematical operations and to provide a means for obtaining formatted digital input and output through a Teletype. A complete program listing, excluding the floating point package, is found in Appendix I. The follov;ing 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 acquisition and have an adequate memory. To satisfy these requirements with a PDP-8/L computer, the data were stored as 2ii-bit, double precision words in one UK 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 20*^8 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 interface 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 kK 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) ware entered

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Figure 7. Flowchart of the data acquisition software

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42 NO SET POINTER TO HALT JSSET LINK TURN INTERRUPT ON TURN INTERRUPT OFF FOLLOW ABOVE POINTER (A OR HALT) YES YES INPUT PRINTOUT PARA.METEP3 THROUGH TTYP SET POINTER TO (A) SET LINK FLAG ^^ "V,^ SET? ^0^ YES 1'

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45 CLEAR ADC 'A CHECK __L FLA6 FROM DEVICE SELECTOR i_ ADC DEADTIMEo U SET ADC FLAG INPUTOUTPUI TRANSFER STORE DATA CLEAR ADC 10 IS 20 TIME, >J89C. 25 30 35 40 Figure 8. Timing relations between the computer and analog to digital converter

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44 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 tv;o software loops. The outer loop vas a service routine for the interrupt facility of the PDP-8/L. When the interrupt was on, the computer continually 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 (lOT) command, 6561_, called the ADC o interface and generated an lOPl 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, hovjever, the next lOPl 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, 6566o, which again called the ADC interface, and generated an 10P2 and an lOPlj.. As Figure 8 illustrates, the I0P2 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 lOPli, 100 nsec later, cleared the ADC output register and ready flag, which allowed the ADC

PAGE 59

45 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 ^isec, and the overflow, which occurred only once every i+096 counts In any given channel, required an additional 8 ^asec . 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 "O", 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 lasec computer dead time between the clearing of the ADC and the generation of the first lOPl to check the ready flag. The conversion time for the ADC was rated at 5 + 0.02N |j.sec, 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 1^-10 channels. For these lower energy pulses the flag was set before the first lOPl was generated. For all channels above UlO, however, the computer had to wait in a 5.85 |isec loop until the ADC conversion was completed.

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46 In Figure 8 the latter case is illustrated. A sequence of lOT's, each 1|.25 ^isec in length, generated the lOPl's to check the ADC ready flag. Tliese pulses were separated by a 1.6 ^isec repeat command until the flag was set, at which time a second lOT immediately followed the first. This lOT generated both the I0P2 and the IOPl+, which initiated the storage process and cleared the ADC respectivaly. The only variable time in the sequence was the length of the ADC dead time, which depended 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 printout parameters (first and last desired channels), obtained by direct input through the Teletype, the computer initialized all necessary counters 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 20i+-7, 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 remaining 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 included 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

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Figure 9. Flowchart of the data printout software

PAGE 62

48 YES f INITIALIZE COUNTERS Ai;D VARIABLES PRINT NEW PAGE HEADER RE-INITIALIZE COUNTERS FOR NEW LINE PRINT LINE < PRINT DATA YES YES / INPUT PRirrrouT PAPAMETERS THP£)UGH TTYP 1 HALT

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

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50 bPFX-n-.^M = TAPE = DATF. 6/ ii/ 12 1530

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51 visual display of the data contained in cemory, 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 ? 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 U095 (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 1;095^ (to yield a full scale display). The initialization routine was then entered at point C. VHien all data were ready for display, the first and last desired channels were entered 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

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52 INITIALIZE COUNTER / INPUT riSPLAY / / THROUGH TTVP / tOTATE rNTISX CORE ONCE TO RIGHT .lAJtE APPROPRIATE CHA-'iOES 1 CHECK SVITCH REGISTER 1 INITI.SJ-IZE COUNT £P-S OUTPUT OATA TDPOUGH OAC EXECUTE DPLAV IXiCP (IF PLOT) CH-ECJ SVITCH PiGISTER MAJTE APPROPRIATE CHANGES Figure 11. Flowchart of the display software

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55 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 v.-ere made in the subroutine. A delay loop of approximately 6U 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 dipplfiy 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 (Ul) 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 repeated until the entire spectrum had been replaced by smoothed data. Peak Detection The two peak detection routines were discussed earlier in the

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54 INPUT SMOOTHING PARAMETERS THROUGH TTYP -± INITIALIZE POINTERS, COUNTERS, AND VARIABLES INITIALIZE STRING OF RAW DATA POINTS Jl MOVE STRING UP ONE POINT PUT NEXT RAW DATA POINT AT ENT) OF STRING I MULTIPLY EACH RAW DATA POINT BY CORRECT WEIGHTING CONSTANT A:1D ADD TO SUBTOTAL J' CALCULATE SMOOTHED DATA POINT AS (SUBTOTAL/DIVISOR) TRANSFER SMOOTHED DATA TO SPECTRUM Figure 12. Flowchart of the data smoothing software

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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 raethod of detection, described in Figures I3 and Ik, was specifically developed to locate the second peak shape in Figure 1. This peak shape, v/hich has several statistical minima superimposed on the peak, was commonly found in spectra which had not been previously smooched, and with peaks which had a small peak-to-noise ratio. Peaks of this typs 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 1+0 channels immediately preceding the possible left boundary. The height from the boundary minim.um to the maximum was then compared to a multiple (designated by the variable MIITHT, 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

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

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57 SET PEAX PRINTOUT POINTER TO 2ND SEARCH INITIAiIZE POINTERS, COUNTERS, AND VARIABLES SAVE POSSIBLE LETT BOL-NCARY SAVE POSSIBLE PEAK MAJtIMUM CALCLXATE AVERAGE PEAX-TO-PEAK NOISE (N) COMPARE PEAK HEIGHT (PiLATIVE TO LEFT BOUNDARY) TO MINHT'NOISE f

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u B C to (0

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59

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60 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, vas 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 compared, 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 lU, 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 determined 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

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61 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 consecutive 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 Ij-O 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-tonoise ratio exceeded the value designated by the variable N, the subroutine beginning at point I was called to permanently store the peak

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

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63 SET PEAK PRINTOUT POINTER TO HALT I INITIALIZE POINTERS, COUNTERS, Af.T) VARIABLES SAVE POSSIBLE RIGHT BOUNDARY CALCULATE AVERAGE PEAK-TO-PE.AK NOISE (N) SAVE POSSIBLE LEFT BO0NT3ARY CLEAR 1ST IN i SERIES FLAG I (5

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64 parameters. The routine 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 20^+7 was reached, however, the peak search was terminated, and the peak printout routine, described in Figure 16, was entered at point M. 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 subroutine entered at point N and described in Figure 17 was called by the peak search routines. First the channel counter v;as moved back kO 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 subroutine 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 extremity, the minimum to maximum height was calculated and added to a subtotal, and a counter was incremented for a divisor. VThen the kO channels were evaluated, the average noise was calculated by dividing

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Figure 16. Flowchart of the software which determines the first differences and prints the final results of the peak searches

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66 INCREMENT CHANNEL COUNTER o YES PRINT rrjMBER OF PEAKS SUBTRACT DATA IN CURRENT CHANNEL FROM DATA IN CURRENT CHA.NNEL+1 I TYPE HEADER FOR PEAJC PRINTOUT i PRINT LEFT BOUNDARY, PE;i.K .'•lAxiMUM, a:;d FIGHT BOUNDARY I CALCULATE hlTQ PRINT PEAK AREAS (Q) NO YES jl FOLLOW PEAK PRINTOUT POINTER: 2ND SEARCH (J) OR HALT

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Figure 17. Flowchart of the software which calculates the average height of the noise over kO channels

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68 i SET CHA.V>fEL COUNTER EACK 40 CH-VK>'El.S INITIALIZE COUNTERS AND VARIABI^S SXVZ LOCATION OF MINIMUM SAVE LOCATION or fUJCIMUM 1 USE LAST NOISE VAL'JE CALCULATE AVERAGE PEAX-TO-PEAX NOISE: (SUBTOTAL/DIVISOR) tefRESTORE CHAjraZL COUNTER >.'t CALCULATE MINI.ML'M TO kajii>c.:m height ADD HEIGHT TO SUBTOTAL INCR^MEJJT DIVISOR

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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 parameters to calculate a total, trapezoid, and quantitative area according to equation (2). The areas were then printed as total peak area values. Tlie peak parameters were then altered according to the Wasson peak area method. The number of channels to the left and right of the peak maximum included in the Wasson calculation were designated by the variable N\s'ASON. If either of the original peak boundaries were inside the Wasson boundaries, the subroutine was exited without further printout. 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 locations 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 entered directly through the Teletype. After initializing the required counters and variables, the data block was relocated in integer form

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Figure 18. Flowchart of the software which calculates and prints the peak areas by the total peak area and Wasson methods

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71 1 SET: XI « LEFT BOUNDARY MAX = PEAK MAXIMUM X4 « RIGHT BOUNDARY CALCULATE TRAPEZOID AREA BOUNDED BY XI AND X4 CALCULATE TOTAL AREA BY SUMMATION CALCULATE QUANTITATIVE AREA AS (TOTAL TRAP. ) PRINT TOTAL, TRAPEZOID, AND QUANTITATIVE AREAS «"• ^ YES SET: X3 = MAX + NWASON RETURN YES X2 SET: MAX NWASON CALCULATE SLOPE: (Y4-Y1)/(X4-X1) I CALCULATE: Y2=SL0PE* (X2-X1)+Y1 y3=SL0PE* (X3-X1)+Y1 SET: Y1«=Y2 X1-X2 Y4=Y3 X4=X3

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Figure 19. Flowchart of the software which converts the integer data to floating point and stores the results in core locations accessable by the FOCAL subroutine FNEW

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73 START y^ INPUT FIRST AND L.ZIST CKAr;:CEL OF DATA BLOCK THROUGii TTYP vv INITIALIZE COUNTERS AND VARIABLES \/ RELOCATE DATA BLOCK TO BEGIN IN CHANNEL ZERO J CON'X'EHT INTEGER DATA TO FLOATING POINT JL RELOCATE CONVERTED DATA TO EVEN FNEW LOCATION SL CLEAR ODD FNEW LOCATION

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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 Iciter use as storage locations for the fitted data.

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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 magnetic tape. Pure isotopes of p/Cr , p^Fe , ir(-,2^" > i^/,^^ » ^j^^ ' and ,-,Ag , obtained from New England Nuclear, were used to prepare Che radioactive samples, thus insuring that spectra of known composition were experimentally generated. Table I lists the experimental conditions 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 recorder was generated by a lO-bit digital to analog converter. The display 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 23 illustrates the linearity between 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 1.4S channel/KeV, the zero energy intercept of 0-37, and the standard deviation of 0.72 channel. The peak locations were determined by the 75

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85 peak detection software and were given by the integral channel location of the peak maxima. The possible error in these values was therefore on the order of + 1 channel. For this reason the standard deviation 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 2k 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 intercept, and standard deviation were k.J)Q channel/KeV, -5.J+7, 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, hov?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 experimental conditions. The sLx spectra had a m.ean slope of l.i^.8 channel/ KeV and a standard deviation of 0.001 channel/KeV, only + C.07 of the mean. The resolution of the Ge(Li) detector was shown to be a linear

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88 function of gamma-ray energy over the region of interest. The resolution values were calculated from the digital data. The peak height was measured relative to the left peak boundary and the value of the full width at half maximum was obtained by interpolating between two data points on either side of the peak. The width, in channels, was then converted to an energy value by using the channel/KeV value cf the spectrum. Data from all eleven spectra were used to evaluate the linear function, with the results shown in Figure 25. The linear least squares analysis yielded a slope of 2.0 x 10 , a standard deviation of 0.05 KeV, and a zero energy intercept of 1.9 KeV. Data Smoothing To evaluate the effect of smoothing on the digital data, the eleven spectra were smoothed by the method of Savitsky and Golay (41), using the weighting constants for a quadratic-cubic polynomial fit. As Yule (44) suggested, the number of points in the smooth was determined by the number of data points in the full width at half maximum of the photopeaks. Since this number, as shown by Figure 25, was essentially constant throughout any of the sample spectra, the smoothing interval was held constant over the entire spectra. Spectra 1-6 required a five point smooth; spectrum 10, nine points; spectrum 11, eleven points; and spectra 7 and 8, thirteen points. From the eleven sample spectra listed in Table I, ninety-seven photopeaks, ranging in peak area (corrected for background) from 115 to 142,202 counts, were selected to evaluate the effect of the smoothing. Using the photopeak boundaries determined by the peak search routines, the total spectrum areas beneath the smoothed photopeaks (including the background contribution) were compared to the total areas in the raw

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91 data. These ninety-seven values had a mean of 100.087, and a standard deviation of only 0.39%. This clearly indicated that the total areas beneath the photopeaks were not degraded by the smoothing process, when the above smoothing criteria were used. In the regions between photopeaks, however, the effectiveness of the smoothing was clearly evident. Using spectrum 6 as an example, several of these baseline regions were compared before and after smoothing. As expected the average minimum to maximum height of the statistical fluctuations was reduced 25-50%. The total areas beneath the baseline regions were relatively unchanged by the smooth, with results similar to the total areas above. The difference in the total spectrum area and the peak area was due to the trapezoidal area representing the Compton and background contributions. The trapezoid area was determined exclusively by the location and contents of the boundary channels, as shown by Figure 2. Therefore the choice of the boundary channels was critical for accurate calculations, Peak detection method two, previously described in the theory section, was designed to locate the integral channel locations of the minima on either side of the peak maximum. As the two peaks in Figure 26 illustrate, selection of the boundary channels was often influenced more by statistical scatter than by the true spectral minima created by the photopeak. Since this scatter was more pronounced in the wings of a peak, the boundary locations in unsmoothed data were strongly influenced by the statistical nature of a gamma-ray spectrum. The sharp minima created by the "noise" spikes were generally at a lower activity than the true value of the spectral curve at that channel.

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92 Figure 26. Effects of the statistical scatter on the total peak area, resulting in too large (peak A) or too small (peak B) a quantitative area

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95 Peak A in Figure 25 illustrates the problem encountered vhen the boundary location, as determined by a digital minimum, corresponded closely to the channel location of the true photopeak minimum. Since the activity in this left boundary channel was lower than the true spectr^^l curve, the trapezoid area was too small, resulting in too Icirge a peak area. Peak B in Figure 26 illustrates a more frequently occuring problem. A false minimum, due to counting statistics, was detected between the true photopeak minimum and the peak maximum. The activity in this channel was therefore too high, resulting in too large a background correction and too small a peak area. In either of the above cases smoothing contributed to more accurate peak areas. The suppression of noise spikes helped eliminate undesired minima in the digital data. This led to the selection of boundary channels which were closer to the true photopeak minima and helped to bring the activity in these channels closer to the true spectral curve. In order to examine the two problems illustrated in Figure 26, 67 of the original 97 peaks were again analyzed. These peaks were located by the second peak detection m.ethod in both the smoothed and unsmoothed sample spectra, and were wide enough to allow quantitation by a nine-point Wasson method. The 67 peak areas were first determined from the original, unsmoothed spectra by both the total peak area (TPA) method and the Wasson method. A second set of areas was determined from the smoothed spectra. Each smoothed peak area was then compared to the corresponding raw peak area. The 67 comparative values from the TPA method ranged from 87% to 128%, with a mean of 105.26% and a standard deviation of 19.71%. The 67 Wasson values had a range of 90% to 112%, a mean of I02.il2%.,

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94 and a standard deviation of 9.8J%. The TPA method yielded a wider range, a higher mean, and a larger standard deviation. This was expected since the Wasson method did not include an area contribution from the wings of the peak, where the statistical scatter was greatest. High mean values from both method:-; indicated that the scatter in the unsmoothed spectra contributed to high baselines, as illustrated by peak B in Figure 26, and therefore to lost quantitative information. Based on the above results it was concluded that smoothing of the digital data before searching the spectra and analyzing the photopeaks was highly advantageous. The total spectrum area was unaffected, but the accuracy of the final peak area was improved by as much as 28%. These conclusions were based on the assumption that the correct smooth was performed. Peak Detection The peak detection software developed for this research was designed to locate all valid peaks, even when the peak-to-noise ratio was small. The detection routines were also written to operate on a small, laboratory computer, with limited core space and a relatively long cycle time. For these reasons the peak recognition criteria were kept to a minimum. As Mills (54) suggested, the operator could easily reject undesired information when the routines located an invalid pseudo-peak. Method two, the major detection routine, was based on the first derivative technique described by Yule (51), and was discussed in the theory section. This method assumed that the first derivative was continuous throughout the peak and successfully located most peaks in a smoothed spectrum. However the routine failed to locate peaks which

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95 contained false minima, caused by statistical scatter, in the central peak region. To aid in locating these peak shapes, illustrated by the second peak in Figure 1, method one was developed. This peak detection method required that the first minimum to maximum height in a peak exceed the average height of the noise in the l+O channels preceding the peak. Except for this requirement all other peak detection criteria, such as a minimum peak-to-noise ratio, were similar to method two. Table II lists the results of the computer searches performed on the eleven sample spectra. All possible photopeak energies emitted by the six pure isotopes mentioned earlier were obtained from the literature (85-87) . Each search routine was performed on both smoothed and raw spectra, and the validity of each peak was verified by a visual check of the data and spectral printouts. The dash signifies the absense of the isotope from the sample. Those photopeaks which were known to exist, but were too weak to form a valid peak in the digital data (as confirmed by the visual check), and therefore were not sensed by the peak detection routines, are designated by the letter A. Valid peaks which were detected by at least one of the search routines are labeled by a letter C, while those which were overlooked by the software, but were actually present in the spectra, are designated by the letter E. The D label indicates that the peak was missed by method two, but was found by method one. The B label refers to peaks which were located by the software searches but were too small to be found by the visual check. Only three of the 120 possible peaks were not detected by the computer search routines. Two of these, the 305-89 KeV Se peak

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96 TABLE II COMBINED RESULTS OF THE AUTOmTED PEAK SEARCHES PERCENT SP-CTRL'M NUMBER ENERGY RELATIVE br^LiK^in au.Ji^K (KeV) ISOTOPE INTENSITY 12^ h. 1 §. 1 89lOn, 66.05 Se-75 1.1+ C^C-CC96.75 Se-75 k.8 C C C C 121.15 Se 75 29.2 .---C C -C C 156.00 Se 75 96.0 C C -C C li^2.i+5 Fe 59 l.U C C C E^ 192.25 Fe 59 k.k C C C D 193.60 Se-75 2.5 C C C C 26i|.65 Se 75 100.0 ----C C -C C 279.52 Se-75 i+1.5 C C C C 505.89 Se-75 2.1 ED-DC520.08 Or 51 100.0 ^a*^ '" 55U.8I Fe-59 0.4 --C-CA'^A---1+00. 6U Se 75 19.2 C CC C l+i+6.20 Ag 110m 5.5 C--C-A AC C 511.00 -CBCCC-C--620.10 Ag 110m 2.9 C--C-A-AC-C 657.60 Ag 110m 100.0 C-C-C CC C 677.50 Ag 110m 12.2 C-C-B -E C 686.80 Ag 110m 7.4 C-C-A -C C 706.60 Ag 110m 17.2 C-C-C -C C 71<-U.20 Ag 110m k.k C--C-A--C-D 765.80 Ag 110m 2U.O C-C-A -C C 817.90 Ag 110m 7.8 C--C-A--C-C 88i+.50 Ag 110m 79.6 C-C-C -C C 957.50 Ag 110m 56.5 C-C-A -C C 1078.00 Rb 86 100. C 1099.27 Fe 59 100. --C -CC 1115.51 Zn 65 100.0 -CCCC -1175.20 Co 60 100.0 --C -CC 1291.58 Fe 59 77.0 --C -CC 1552.50 Co 60 100.0 --C -CC The element was present, but the signal was too weak to form a valid peak ^ peak was ] by a manual check. A peak was located by the software, but was too small to be detected A valid peak was detected by the software. A valid peak was detected by method one, but was missed by method two. ^A valid peak was missed by both software routines. Annihilation peak.

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97 at channel 452 of spectrum 6 (Figure 22) and the 677.5 KeV Ag^^^"* peak at channel 11+57 of spectrum 9 (Figure 27), were relatively large, but they exhibited extensive scatter throughout. The nuaber of statistical minima superimposed on these peaks was so large that the basic height criterion of method one was never met. The lli.2.U5 KeV 59 Fe peak at channel 860 of spectrum 7 (Figure 28) was included inside the boundaries of the large I36.OO KeV Se''^ peak at channel 820 by me thod one . Figure 28 also shows two examples of peaks located by method one but missed by method two. The 192.23 KeV Fe^^ peak at channel 1165 and the 303-89 KeV Se peak at channel 18!f6 exhibited statistical minima throughout, even when properly smoothed. Figure 22 shows the apparent absence of a peak at channel 1006, although method one detected the presence of the 677.5 KeV Ag^^^™ at that location. This indicated that, in some cases, the detection software was more sensitive to the presence of photopeaks than a visual search. Although only six pure isotopes were used to prepare the samples, gamma-rays from seven radioisotopes were detected. The two Co^° photopeaks were found in all spectra which contained the Fe photopeaks. This was probably due to the initial 3" decay of the Fe^° during ir59 radiation. The resulting stable Co was then partially irradiated to Co Table III gives the number of peaks detected by each of the search methods. No one method was mutually exclusive of the others. Best results were obtained by performing all four searches. Valid peaks were verified by a visual check of the spectra and a knowledge of the exact sample composition. Table III shows the greatly increased

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102 TABLE III NUMBERS OF PEAKS FOUND BY THE AUTOMATED PEAK SEARCHES

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103 efficiency of method two with the smoothed data. This was especially notable in spectra 7 (Figure 28), 8, 10, and 11 (Figure 29), where the increased ADC resolution and decreased energy range resulted in broader peaks and significantly greater scatter throughout the peak region. Table III also shows the effect of changing the major peak detection criterion, the minimum allowable peak-to-noise ratio (P/N) . As this value was increased from two to four, the number of pseudopeaks located by the search routines was greatly reduced. This was accomplished, however, by reducing the ability of the computer routine to detect small, valid peaks. The peak search routines also selected the peak boundary channels. As noted before, these channels played a very important role in the determination of the photopeak area. Method two was designed to select the first minima on either side of the peak maximum. It has been previously shown that, with proper smoothing, these minima were usually relatively close to the true spectral minima, both in location and content. Method one, however, used different detection criteria which often resulted in the selection of different peak boundary channels which were further from the peak maximum. Ninety-three common peaks were detected in the eleven smoothed spectra by both methods. The two peak detection methods selected different boundaries for 39 (U2/<.) of these 93 peaks. Of the 39 peaks with different boundaries, 37 (957.) had a different left boundary while only 19 (lj-9%) had a different right boundary. As previously discussed the selection of the left boundary by method one was critical to the final choice of the right boundary. This was verified by the fact

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106 that only tvjo peaks, selected by method one, had the same left boundary but a different right boundary. Thus the selection of the left boundary by method one was critical to the entire peak detection process. Unfortunately this selection process was strongly influenced both by the slope of the Compton upon which the peaks were located and by overlapping peaks which created large background bases. These problems not only led to the selection of erroneous peak boundaries, but also resulted in the inclusion of more than one peak maximum within a set of peak boundaries. A few examples of the overlap problem were found in the sample spectra. Method one detected the I36.OO KeV Se peak at channel 202 of spectrum 6 (Figure 21), but the left boundary at channel 108 included both the 96.73 ^nd 121.13 KeV Se peaks. In the same spectrum the left boundary of the 1115.51 KeV Zn peak at channel 1658 included the 1099.27 KeV Fe^^ peak. The large positive slopes associated with Compton edges also created problems for method one. The 88U.5 KeV Ag peak at channel 1315 of spectrum 6 (Figure 22)was assigned a left boundary at channel 1055, near the base of the Compton edge. The slope of the spectral curve was so large that the initial height criterion of method one was satisfied by the Compton edge. Once this occurred, however, a right boundary minimum, whose absolute height was comparable to the left boundary, was not detected until the Compton edge was passed. A similar situation occurred in spectrum h (Figure 30) . Method one again detected the 881+. 5 KeV Ag peak at channel 1315, with a left boundary at channel 1198. In this case, however, the left boundary included the 817.9 KeV Ag ™ peak at channel 1215. In each of the above cases,

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E 3 U 4J U 0) o. en 0) o 0) 00 c >% 00 >-l c V 4)

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108 o o o O O CO hi z z < X u .01 X *13NNVH0 y3d SINHOO

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109 method two detected all the peaks vjith reasonable boundaries. C urve Fi tting The technique of mather.c tically fitting a function to digital data has been used for many years to determine both the peak maximum and the photopeak area in gaaima-ray spectra. The accuracy of this method is greatly influenced by the choice of the functional form. It is common knowledge that the major component of the photopeak shape in a Ge(Li) spectrum is Gaussian, but Routti and Prussin (56) explained that this does not completely describe the total peak shape. Although many researchers have proposed fitting functions, no two have agreed on an exact form. The majority of the functions, however, have skewed a central Gaussian with an exponential contribution to approximate the low energy tail common to most photopeaks in a Ge(Li) spectrum. Sanders and Holra (66) observed that the only true test of the functional form was how well it approximated the digital data. Tominaga and co-v7orkers (43) stated that smoothing was often unnecessary for curve fitting, but Mills (sU) observed that the smoothed spectra gave better estimates of the initial parameters of the fitting function. The function chosen for this research was an emperical form of a Gaussian skewed by a leading exponential tail. These two major components were smoothly combined by an arctangent joining function. The eight parameters of this three function convolute have been discussed in a previous section. The final functional form was similar to that used by Chesler and Cram (84) in their studies with gas chromatographic peaks. The conversational computer language FOCAL was used to program the fitting function. The mathematical basis for this least squares technique was explained in the theory section, and the FOCAL programs

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110 are listed in Appendix II. Once a peak was chosen for fitting, an appropriate block of integer data was converted to floating point and stored in memory locations accessible by the FOCAL compiler. Whenever possible at least twenty to forty baseline points were included on either side of the photopeak. The number of data points in the peak ranged from 10 to 57 points. The solving of the square matrix (equation 6) constituted the major portion of the computational time. Each additional parameter substantially increased this time, with the eight parameter function requiring six to eight minutes per iteration. For this reason a four parameter polynomial was fitted separately to the baseline data points. The boundaries selected by the peak detection routines were used as guidelines, and all points within these boundaries were excluded from the baseline calculation. Using the basic fitting program, the polynomial approximation of the baseline was determined. Only the constant parameter was initially approximated, with all others being initially set to zero. No more than three iterations were ever necessary to obtain the best possible fit, and each iteration required approximately one minute. The calculated baseline was then extended through the peak and subtracted from the original digital data. The result was an estimate of the pure photopeak shape, resting on a flat, zero baseline. The data was positive throughout the peak area and oscillated about zero in the regions of pure baseline. The first negative value on either side of the central peak was therefore used to determine the boundaries for the peak fit. All data within, but not including, these boundaries

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Ill were used to evaluate the eight parameters of the fitting function. The original estimate of P was obtained directly from the data. The initial values of P , P , P. , P , and P were normally set to 3.0, £1 ^ 4 J -1.5, 0, 1.0, and -1.5 respectively. The estimates of P and P de7 pended upon the actual shape of the peak, but were between zero and one. The abscissa values were expressed in sigma units, the standard deviation of the central Gaussian. To determine the X values in the fitting function, the right side of the peak was assumed to be pure Gaussi,-;n in shape. The number of abscissa points from the peak maximum to the right boundary was therefore assumed to be equal to three sigma units. With this estimate the values of the increment (IN) and the initial abscissa value in the fitting interval (XO) were determined. A measure of the improvement in the fit following each iteration was dcLerrained by the percent change in the calculated residual sum of squares. Figure 5I shows a plot of this percent change versus the number of itcrctions performed for two of the peaks fit. These curves illustrate that a sharp decrease in the early iterations was followed by a gradual change in the latter calculations. The shoulder on curve B in Figure 3I indicated that the fitting process passed through a local minimum in the residual sum of squares. A point was quickly reached, however, where the improvement gained by the iteration was not worth the time involved for the computation. For the fitting program used in this research this crossover point was judged to be either ten iterations or a percent change of less than 5% in the residual sum of squares. The absolute values of the residuals were not used in this consideration because they were

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Figure J)l. Plot of the percent change in the residual sum of squares vs. the number of iterations performed in the curve fitting process

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115 Q CO UJ a: UJ < 5 10 NO. OF ITERATIONS 15

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114 found to be dspendent upon the peak size, the amount cf scatter present, the number of points in the fitting interval, and the values of the initial parameter estimates. In Figure Jl, curve A had initial and final residual values of 530O and 1552, respectively, while curve B fell from 1^, 1*^15, 190 to 126,069. Table IV lists the percent change in the residual sum of squares for the first, tenth, and final iteration for ench peak fit. Table IV shows the large reduction in the first iteration and the fact that the majority of the peaks showed a change of less than 5% v.'ithin ten iterations. To demonstrate the validity of the fitting procedure, 55 peaks of all sizes and shapes were chosen from the eleven sample spectra. The digital data were fit as described above, and the curve was evaluated at each point by adding the contribution from the peak to that of the background polynomial. The spectral data displayed in the following figures are the raw curves and the fitted functions with the latter offset for the purpose of illustration. Table V lists the location, size, and background shape for each of the peaks. The peak heights were taken from the final P values of the fitted functions while the average noise heights were calculated from the baseline region of the fitting interval immediately preceding the peak. The peak-to-noise ratios (P/N) were calculated from these two values and represent a dynamic range of 500. The descriptions of the baselines pertained to the relative shape and slope of the baseline immediately surrounding the peaks. Table VI lists the complete fitting information for each of the peaks. The calculation of the increcent, in sigma units, was discussed

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.115 TABLE IV PERCENT CHANGE IN W.E RESIDUAL OF THE CURVE FITTING FUNCTION

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116

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117 TABLE VI INITIAL AND FINAL VALUES FROM TriE CURVE FITTING CALCULATIONS OF PEAK i::c?j::'Ent points ite.^a.tiom 1 5 k 10 11 12 13 Ik 15 16 17 0.375 0.U3 0.30 0.1+3 0.333 0.167 0.17 0.33 0.1+3 0.50 0.20 0.12 0.50 0.333 0.75 0.20 0.30 1)6 3U 30 25 29 57 52 3'f 21 21 1+8 1+6 16 26 10 31+ 19 10 59 23 10 10 10 10 10 10 10 10 5 15 6 60 6 10 10225 5.00 9329 0.1+9 61+li0 3.00 6120 0.67 3600 3-00 3583 1.20 2778 3.00 2335 1.16 1560 3-00 1533 1.22 181(1+ 5-00 1731+ 0.70 1682 3.00 161+1 0.88 9830 3.00 9863 1.19 11+63 3.00 11+69 1.99 3lai 3-00 51+91 1.28 2963 3. CO 28S2 0.11 500 3.00 289 1.35 750 3.09 715 1.23 385 3.00 366 0.99 Pt P| p.: P^ p., Po _2 -it _5 _6 _7 _8 -1.50 1.00 0.50 0.50 -1.50 -1.67 0.033 0.67 0.65 0.'+8 -1.51 -1.50 1.00 0.50 0.50 -1.50 -1.82 0.059 0.71 0.71 0.52 -1.39 -1.50 1.00 0.20 0.50 -1.50 -1.30 0.169 0.76 0.1+2 0.1j6 -I.30 -1.50 0.30 0.30 0.50 -1.50 -1.55 0.151 0.79 0.1+2 0.1+2 -I.5I -1.50 1.00 0.25 0.25 -1.50 -1.21 -0.11,3 0.33 0.31+ 0.32 -1.88 -1.50 1.00 0.25 0.50 -1.50 -1.31 -0.019 0.93 0.36 0.31+ -l.Sl -1.50 1.00 0.01 0.10 -1.50 -0.00'+ 0.020 105 0.03 1.08 -3.1i9 -1.50 0.75 0.30 0.50 -1.50 -1.1+9 0.053 0.56 0.'i4 0.55 -1.30 -1.50 1.00 0.10 0.25 -1.50 -1.12 0.01(2 0.86 0.20 O.5I+ -1.92 -1.50 1.00 0.25 0.25 -1.50 -1.35 -0.069 1.00 0.23 0.30 -1.83 -1.50 -3.02 -1.50 -0.1+0 -1.50 -1.57 -1.50 1.10 0.10 0.50 -1.50 -O.OIS 1.15 0.07 0.16 -0.1+1+ 1.10 0.10 0.10 -1.50 0.001+ 1.21; 0.03 3.01 -2.37 1.00 0.10 0.10 -1.50 0.01+6 0.9S 0.22 0.27 -2.12 1.00 0.10 0.10 -1.50 910 895 3.00 6.25 650 3.00 61|5 11.21 370 3.00 355 8.57 -0.73 -0.152 0.85 0.15 0.27 -2.63 -1.50 1.00 0.25 0.50 -1.50 -1.5S -0.031+ 1.26 0.29 0.70 -2.05 -1.50 1.00 0.10 0.25 -1.50 -1.91 O.Ol+O 1.00 0.13 0.39 -1.87 -1.50 0.75 0.01 0.10 -1.50 -1.36 -0.107 0.1+5 0.09 0.13 -1+.214-

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Table VI continued 118

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118 earlier. The number of points in the fitting interval ranged from ten to fifty-seven. The original and final parameter estimates are listed, along with the number of iterations actually computed. Peak 28 illustrates that once the fitting process converged to a minimum residual sum of squares, further iterations did not significantly change any of the parameter estimates. Table VII lists some of the information obtained from the eight parameter estimates shown in Table VI. The initial and final residual values were calculated from the initial and final parameter estimates. The raw sum was obtained by suioming the digital data, following the polynomial baseline subtraction, over the total peak fitting interval. The fitted sums were obtained by evaluating and summing the fitted functions, using both the initial and final parameter estimates, at each channel location in the peak fitting interval. The percentage ratio of the final fitted sum to the raw sum was calculated for each of the 5^ peaks, using the values shown in Table VII. These ratios had a range of 97.70% to 100.86%, a mean of 99.80%, and a standard deviation of only 0.74%. This demonstrated that the fitted curves were truly representative of the actual areas encompassed by the raw data. Since the raw data, in this case, had no background contribution, the fitted curves were representative of the quantitative areas enclosed by the photopeaks. The seven peaks shown in Figures 32-53 were examples of large peaks which rested on relatively flat baselines. The large peak-tonoise ratios (greater than 75) indicated that there was little scatter associated with the data in the central region of the peak. The peaks in Figures 37 and 58 were taken from spectra with increased ADC

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120 TABLE VII INITIAL AND FINAL VALUES FROM THE CURVE FITTING CALCULATIONS

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Figure 52. Raw data and fitted curve (offset) for the 1115.51 KeV Zn 65 peak taken from spectrum 2

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Figure 35. Raw data and fitted curve (offset) for the 8814^.5 KeV Ag llOra peak taken from spectrum 1

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Figure ^k. Raw data and fitted curve (offset) for the 88i4-.5 KeV Ag 110m peak taken from spectrum 9

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Figure 35. Raw data and fitted curve (offset) for the 957.5 KeV Ag llOm peak taken from spectrum 1

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Figure 56. Raw data and fitted curve (offset) for the 957,3 KeV Ag 110m peak taken from spectrum 9

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Figure 37. Raw data and fitted curve (offset) for the 88^.5 KeV Ag llOm peak taken from spectrum 11

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Figure 38. Raw data and fitted curve (offset) for the 320.08 KeV Cr 51 peak taken from spectrum 7

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153 resolution and therefore had a greater number of data points in the peak fitting interval. For all of these peaks the initial parameter estimates were easy to make, and the fits, as shov;n by the comparison curves, were excellent. The peaks shown in Figures 39-J|2 were again large, but v^ere located on sloping baselines. The slopes v;ere the result of Ccrapton edges froni higher energy peaks, and the degree of the slope depended upon the intensity of the higher energy peak. The cubic polynomial easily approximated the sloping backgrounds so that, following the polynomial subtraction, all skew associated with background was removed. Again the comparison curves clearly illustrate the excellent simulation achieved by the fitted function. Figure k^ shows a smaller peak (less than 1000 counts at the peak maximum) which was located on a flat background. The apparent negative slope of the baseline to the right of the peak vjas the result of too few points used to estimate this region. However the simulation agreed with the apparent slope of the raw data for this narrow region. The peaks shown in Figures UU-50 also had less th?ui 100 counts at the peak maxima. Again, the baselines were sloped due to a Corapton edge present in the spectrum. The fitted peaks shown in Figures 47k9, however, displayed some form of complex behavior on the left side of the peaks. Figures k7 and k9 show a small shoulder which was real and vjas caused by the irregularity of the raw data. The best fit obtainable in these cases did not have a smooth joining of the Gaussian and exponential parts of the fitting function. It is significant to note, however, that the fitting function characterized the shoulders

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Figure 39. Raw data and fitted curve (offset) for the 1099.27 KeV Fe 59 peak taken from spectrum 5

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Figure ifO. Raw data and fitted curve (offset) for the 957.5 KeV Ag 110m peak taken from spectrum k

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Figure ^4l . Raw data and fitted curve (offset) for the 88^;. 5 KeV Ag llOm peak taken from spectrum k

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Figure 1+2. Raw data and fitted curve (offset) for the 121.15 KeV Se 75 peak taken from spectrum 7 (•

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Figure hj). Raw data and fitted curve (offset) for the 511 KeV annihilation peak taken from spectrum 8

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Figure kh. Raw data and fitted curve (offset) for the 817.9 KeV Ag 110m peak taken from spectrum 1

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Figure k5. Raw data and fitted curve (offset) for the 817,9 KeV Ag llOm peak taken from spectrum 9

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Figure k6. Raw data and fitted curve (offset) for the Jl-i|6.2 KeV Ag llOni peak taken from spectrum 1

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Figure k7 . Raw data and fitted curve (offset) for the i+00.6n KeV Se 75 peak taken from spectrum 10

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Figure ii^S. Rnw data and fitted curve (offset) for the 817.9 KeV Ag 110m peak taken from spectrum k

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Figure 1+9. Raw data and fitted curve (offset) for the UH6.2 KeV Ag 110m peak taken from spectrum 10

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Figure 50. Raw data and fitted curve (offset) for the 620.1 KeV Ag 110m peak taken from spectrum 9

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160 very effectively and was sensitive to their pres&nce. As seen from the comparative curves, the fits ';-jere accur-;te representations of the raw data. Figure k8 shows a high baseline near the left edge of the fitted peak. This high baseline was due to both the extreme scatter in the raw data and the method of choosing the fitting interval. If more data points (including negative points) fron the left side had been included in the fit, the rate of decrease of the exponential tail would have been greater. Figures 51 and 52 show two different examples of the 96.73 KeV Se peak, taken from spectra 7 (Figure 23) and 10. The peak, shown at channel 580 of Figure 28, was located directly on top of a Corapton edge from a higher energy Se peak. Since the Corapton edge was caused by a photopeak from the same Se isotope, the peaks from both spectra were very similar in shape but, as indicated in Table V, differed in height and peak-to-noise ratio by a factor of two. Due to the Compton edge, the slope of the baseline was positive to the left of each peak and negative to the right. As the curves in Figures 51 and 52 show, however, the cubic polynomial correctly simulated the baseline over the entire fitting interval. Although the fitting function simulated a slight shoulder on the low energy side of the peak in Figure 51, this was, as in the examples above, the result of the best fit of the chosen function to the available data. Since the purpose of the fitting function was just that, the final shape of the fitted curve was an accurate representation of the experimental data . The above examples clearly demonstrate that the chosen function and fitting technique were applicable to the major photopeaks in a

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Figure 51. Raw data and fitted curve (offset) for the 96.73 KeV Sc 75 peak taken from spectrum 7

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Figure 52. Raw data and fitted curve (offset) for the 96.75 KeV Se 75 peak taken from spectrum 10

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165 Ge(Li) spectrum. The remaining peaks will demonstrate the applicability of the technique to small peaks (less than 200 counts at the peak maximum) which, because of their small peak-to-noise ratios, had excessive scatter superimposed on the peak shapes. The peaks shown in Figures 55-56 were located on essentially flat baselines. Although the raw data showed considerable scatter throughout the region of the peak, the fitted curves were representative of the basic peak shapes. Even the apparent sloping baseline in Figure 5k was truly representative of the raw data over the narrow region immediately surrounding the peak. The peaks in Figures 57-60 were typical of small peaks which occurred at energies which coincided with large Compton edges from higher energy peaks. Although the baselines were high and sharply sloping, the polynomial approximation and subtraction easily removed this strong interaction, leaving only the basic peak shapes. As the figures show, these composite curves clearly approximated the original raw da ta . In all of the above examples the original, unsmoothed data were utilized. In a few cases, however, the scatter altered the basic photopeak to such an extent that the fitting function was no longer able to simulate the resultant shape. In these cases the data were smoothed once and then fitted. This was not always successful, but a few examples of successful applications are discussed below. Figures 61 and 52 show the results of two fits to the same peak. Figure 61 shows the result of the fit to the raw, unsmoothed data, while Figure 62 shows the outcome when the data were smoothed first. In both figures the unsmoothed peak is compared to the final, fitted

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Figure 55. Raw data and fitted curve (offset) for the 817.9 KeV Ag llOra peak taken from spectrum 11

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Figure 5k. Raw data and fitted curve (offset) for the 620.1 KeV Ag llOm peak taken from spectrum 11

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Figure 55. Raw data and fitted curve (offset) for the 303.89 KeV Se 75 peak taken from spectrum 7

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Figure 56. Raw data and fitted curve (offset) for the 503-89 KeV Se 75 peak taken from spectrum 10

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Figure 57. Raw data and fitted curve (offset) for the 1173.2 KeV Co 60 peak taken from spectrum 6

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Figure 58. Raw data and fitted curve (offset) for the 1173.2 KeV Co 60 peak taken from spectrum 5

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Figure 59. Raw data and fitted curve (offset) for the 71^*4-. 2 KeV Ag llOm peak, taken from spectrum 11

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/ Figure 60. Raw data and fitted curve (offset) for the 657.6 KeV Ag 110m peak taken from spectrum 6

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Figure 61. Raw data and fitted curve (offset) for the 1173.2 KeV Co 60 peak taken from spectrum 3

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Figure 62. Raw data and fitted curve (offset) for the 1175.2 KeV Co 60 peak taken from spectrum ^. The data was smoothed before the fit was obtained.

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186 curve. The basic difference occurred at the top of the peaks in the two fitted functions. The sharp minimum in the raw data was best approximated by a separation of the Gaussian and exponential parts of the fitting function, as shown in Figure 61. The smoothing reduced this minimum to such an extent that the fitted function failed to show it, although there is still a slight shoulder on the final curve near the top of the peak in Figure 62. Since the two fitting intervals were not exact, the suras in Table VII were not comparable, although the ratios between the fitted and raw sums in each case were nearly exact. Figures 63 and 6h show examples of peaks whose shapes were distorted to such an extent that pre-smoothing was necessary to obtain any valid fit. In both cases the best fit showed a distinct shoulder on the leading edge of the peak. Because the peak in Figure 6^1 was located near the top of a large Compton edge, the number of data points included in the polynomial baseline fit was limited on the right side of the peak. Enough points were included on the left, however, to accurately establish a correct baseline approximation. The eight parameters utilized in the fitting function were, for practical purposes, the upper limit for the PDP-8/L computer. Since each new parameter expanded the square matrix which was the heart of the least squares procedure, the computational time greatly increased with the number of parameters. For this reason the simultaneous fitting of two overlapping peaks was impractical. Overlapping peaks presented few problems, however, due to the tremendous resolution of the system. A simple expansion of the energy scale solved most of the problems.

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Figure 63. Raw data and fitted curve (offset) for the 657.6 KeV Ag llOm peak taken from spectrum 8. The data was smoothed before the fit was obtained.

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Figure 6^4-. Raw data and fitted curve (offset) for the 8SU.5 KeV Ag 110m peak taken from spectrum 6. The data was smoothed before the fit was obtained.

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191 In a few cases, however, there was a small amount of overlap between two major peaks which did not prevent the detection routines froni locating the peak boundaries, but affected the final quantitative results. Such a case resulted when the low energy tail of one peak extended below the base of another. The tail was usually treated as a positively sloped baseline and approximated by the polynomial. This approach, however, did not solve the area problem of the higher energy peak. A more accurate solution involved the individual fitting of each peak. The peaks in Figure 65 illustrate such a case. The basic fitting function assumed that the photopeaks were pure Gaussian on the high energy side. It was therefore assumed that the data to the right of the separating minimum did not include any overlap contribution. Since enough of the higher energy peak shape was represented to allow a valid fit, the functional form for this peak was calculated. This function was then subtracted from the lower energy peak, leaving a new set of data from which a second function was calculated. Each set of parameters was then used to calculate the individual peak areas. The total curve was obtained by adding the contribution from each peak to the background. The results of the above procedure were used to verify the original Gaussian assumption. The total peak area was determined for each of the fitting intervals by adding the contribution from each of the individual peaks. VThen the total areas were compared to the individual contributions, it v;as found that the second peak in Figure 65 contributed over 4'7o of the total peak area to the left of the separating minimum while the first peak was responsible for less than 0.1% of the

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Figure 65. Raw data and fitted curve (offset) for the 677.5 and 686.8 KeV Ag llOra peaks taken from spectrum 1

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195 5000 Ksrsan vO in d X UJ LU CL O O 4000 3000 2000 1000 950 1025 1100 CHANNEL NO.

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191; areas to the right. This verified the assumption that the right side of the first peak was Gaussian and did not contribute significantly to the shape of the second peak. Peak Areas The curve fitting results were used to obtain the true peak areas of Llie >5 fitted peaks. The areas were obtained by numerically integrating the fitted functions by the trapezoid method, using an interval of 0.1 channel. The fitted sums were calculated by adding the functional values at each channel. The boundaries cr the orginal data blocks were used to fix the limits for these calculations. The fitted sums were calculated as a percentage of the total integrated areas to determine the necessity for the lengthy integration procedure. The 5^ values had a narrow range of 99.7% to 100.87. and averaged 100.0 + 0.5 %. These results indicated that the simplified summation technique was as accurate as the more complicated numerical integration process. However, in order to maintain as high a degree of accuracy as possible the integrated areas were utilized in the remainder of this research. Because of the nature of the least squares method, the curve fitting approach offered the most accurate technique for determining the peak areas. The complications and time involved, however, often offset the increased accuracy achieved. Therefore the peak detection routines, together with the more simplified methods for approximating the peak areas directly from the digital data, were used for routine analysis . There were two major sources of error associated with the simplified peak area methods. The first involved the correct location of

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195 the peak boundaries, and the second involved the method of choice for calculating the peak area. To test the boundary selections obtained from the peak detection routines the fitted functions were reevaluated. With the limits for the integration of the fitted functions fixed by the boundary channels selected by the search routines from smoothed data, the partial integrated areas were calculated. The boundaries selected by method two were given precedence whenever conflict arose. The partial integrated areas were then compared to the total integrated areas previously calculated. Table VIII lists both of these areas and the comparison values. The low results from peaks 17,25,52, and 55 were understandable in view of the earlier curve fitting discussion regarding these peaks. The high exponential tail of peak 17 and the unusual separation of the exponential tail from the Gaussian in the three other cases were all indications of severe scatter in the region of the peak, which led to an increased chance of a poor boundary selection. The comparison values for all 55 peaks averaged 95.5 + 7.0%. VJhen the above four peaks were excluded from consideration the remaining 51 values averaged 97.i+ + '^.h'L. These results clearly indicated that the majority of the peak area was included within the peak boundaries selected by the peak detection routines. In a similar study the peak areas determined by the total peak area (TPA) method on smoothed data were compared to the total integrated areas. Table DC lists these results. The comparison values for all 55 peaks had an average of 93-8 + 16.57., while removal of the same four values raised this average to 97.7 + 11.57o. These results indicated that the TPA method also produced the majority of the total available

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196 TABLE VIII CURVE FITTING RESULTS

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197

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198 area, but with a greater margin for error and with less precision. This, however, was to be expected since the original data included an uncertainty in not only the boundary channel locations, but the contents of these channels as well. The accuracy of the TPA method was verified by comparing the TPA peak areas to the partial integrated areas, which were calculated from the same boundaries. The 55 values, listed in Table X, had an average of 100.0 + 15.9%. Removal of the four problem values led to an average of 100.3 + ll-^°/». These results indicated that the TPA peak areas determined from the smoothed digital data were representative of the true area enclosed by the chosen boundaries, within the limits of the uncertainty created by the scatter present in the digital data. All of the above results indicated that the peak search routines utilized in this research, together with the TPA method of quantitation, offered a fast, accurate method for the data reduction of Ge(Li) spectra. The curve fitting technique provided an excellent means for obtaining more accuracy when desired and time permitted. For routine analysis, however, the direct reduction of the digital data yielded rapid, accurate results. Liver Analysis The application of the proposed system to the analysis of biological materials was demonstrated by the quantitative determination of four elements of bovine liver. The sample was Standard Reference Material 1577, obtained from the National Bureau of Standards in the form of a dry powder. The method of standard addition was chosen to insure a constant matrix effect in all of the samples.

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199

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200 Two samples of pure liver were initially irradiated for five minutes and one hour, respectively, at a neutron flux of approximately 12 2 10 neutrons/cm /sec. Since the longer irradiation time did not produce any new peaks upon immediate analysis, the shorter time was chosen for the experiment to reduce the total activity and allow immediate handling of the samples. Figures 66 and 67 show two views of an irradiated liver sample, and Table XI lists the significant peaks. Both spectra had a full scale energy range of 2.385 MeV. Figure 66 is a plot of the untreated data and has a full scale ordinate value of 4095 counts. Figure 67 shows the same spectrum after the contents of each channel had been multiplied by a factor of 4.8. This was done to highlight the regions of low activity and still keep the largest peak on scale. All samples were counted directly in the irradiation vials, which were made of Nalgene and supplied by the Nalge Company. Blank spectra 41 contained only the 1.294 MeV Ar peak, produced from the air trapped inside the vials during irradiation. Since, as Figure 67 shows, this 41 Ar photopeak was completely resolved, no blank correction was performed on any of the sample spectra. _ .1.x J_ j_ Standard aqueous solutions of CI , Mn , K , and Na were prepared from high purity LiCl, metallic Mn, K Co and Na CO,, obtained from the Alpha Products division of the Ventron Corporation. Because of the limited size of the reactor port only two irradiation vials could be placed side by side in the reactor. Therefore in order to maintain the assumption of a constant neutron flux, only six samples could be Irradiated simultaneously. From a knowledge of the total activity of the previously irradiated samples the experimental sample size was

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PAGE 216

202 O z UJ z z < z .01 X 'laNNVHD a3d SINHOO

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«

PAGE 218

204 o z u z z < X o o

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205 TABLE XI SIGNIFICANT PEAKS IN AN IRRADIATED LIVER SAMPLE

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206 chosen to be 0.1-0.2 grains. This ensured that the total activity of the irradiated samples did not prevent immediate handling of the samples. Four samples were used in each of the chlorine and managanese experiments, five for potassium, and six for sodium. Because of the dilute nature of the manganese standard a pure sample was included as a check against error. Two pure samples were included in each of the potassium and sodium runs to demonstrate the precision of the overall technique . The dry liver was weighed directly into the irradiation vials. The samples were ordered according to their weight, and the larger samples received the least amount of standard in an attempt to equalize the final peak areas. When two pure samples were included the largest and smallest were chosen to further demonstrate the reproducibility of the technique. All vials were then heat sealed to prevent spillage. The exact experimental conditions are listed in Tjble XII. The samples were counted directly in the irradiation vials to eliminate transfer errors. Chlorine samples were counted for three minutes live time and all others for five minutes live time. All samples were counted at a distance of at least six inches from the face of the detector to eliminate any errors due to surface effects. This distance was varied for each run to insure a maximum dead time of 57,, for any sample . Peak detection method two was used on smoothed data to obtain the peak boundaries. Both a total peak area and a nine-point Wasscn area were calculated. The quantitative areas and the values of standard

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207 TABLE XII EXPERIMENTAL CONDITIONS FOR THE LIVER AN..\LYSIS ELEMENT

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208 added were corrected for decay and varying sample size according to the equations introduced in the theory section. The final experimental results are listed in Tables XIII and XIV and are displayed in Figures 68-73. The actual concentrations of manganese, potassium, and sodium were certified by the National Bureau of Standards (N3S) , based on the results of six to tvjelve determinations by two independent methods. In the case of potassium and sodium the results included a homogeneity test performed on 28 samples. Both sodium and potassium were analyzed by flame emission spectrometry (homogeneity test) and neutron activation analysis (NAA) , while manganese was analyzed by atomic absorption spectrometry and IL\A. A value for chlorine, based on NAA results alone, was reported but not certified. Reduction of activation analysis data at the National Bureau of Standards was performed on a Univac 1108 computer, using the computer program ALSPIS written by Yule (83). The reduction algorithm located peak boundaries by using the first derivative values determined by the Savitsky and Golay (f;l) convolution technique. The constants for both a quadratic and cubic polynomial were used, and several checks were performed on the peaks to insure that complete resolution had been achieved. After locating the peak boundaries the total peak area method was used to determine the peak area. The final NBS certified concentrations were obtained by giving approximately equal weight to the experimental results of the two independent methods of analysis. Table XV lists the JvBS results from each of the reported methods, the final certified concentrations, and the experimental results obtained in this research for each of the

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TABLE XIII RESULTS OF THE LIVER ANALYSIS 209 ADJUSTED ELEMENT

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TABLE XIV RESULTS OF THE LIVER ANALYSIS 210 ESTIMATED ELEMENT

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Figure 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 I.6U5 MeV CI 58 peak

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212 -3 3 6 AMOUNT OF STANDARD ADDED, MG/GR

PAGE 227

Figure 69. Plot of the total peak area (open circles) and V7asson 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 2.16S MeV CI 58 peak

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214 -3036 AMOUNT OF STANDARD ADDED, MG/GR

PAGE 229

Figure 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 0.3^+7 MeV Mn 56 peak

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216 -10 10 20 30 AMOUNT OF STANDARD ADDED, UG/GR

PAGE 231

Figure 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

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218 12 X 10 -10 jO 20 30 AMOUNT OF STANDARD ADDED, UG/GR

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s Figure 72. Plot of the total peak area (open circles) and Wssson 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 h2 peak

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220 3 X 10 CO 8 2X10^ < UJ < < LU IX 10 -10 10 . 20 AMOUNT OF STANDARD ADDED, MG/GR

PAGE 235

Figure 75. 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 I.568 MeV Na 2\ peak

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222 3 X 10 -2 2 4 6 AMOUNT OF STANDARD ADDED, MG/GR

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225 TABLE XV EXPERIMENTAL A^fD NATIONAL BUREAU OF STANDARDS RESULTS OF THE ANALYSIS OF STANDARD REFERENCE MATERIAL 1577 (BOVINE LIVER ) NATIONAL BUREAU OF STANDARDS RESULTS (ua/gni') ELEMENT CI Mn Na METHOD 1 NAA CERTIFIED 2610+ 90 11.2+0. I*9.96rt0.85 10.5+1.0 9820+500 9600+600 9700+600 2ltOO+100 21+60+ 70 21+50+150 EXPERIMENTAL RESLT.TS (uK/om)

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22 i^ four elements examined. Since the reduction algorithm used by NBS was similar to that used in this research, the lower NAA results reported by NBS for both manganese and potassium could have resulted from the problem illustrated by peak B in Figure 26, which was earlier discussed in detail. The experimental values from this research were means of all results obtained by both the TPA and Wasson method. The means were calculated from four values for chlorine and manganese and from two values for potassium and sodium. The approximate error limits on the mean results were calculated by assuming that the variance of each individual result could be obtained from the mean square deviation calculated by the linear least squares method. Both the 16^6.7 and 2167.6 KeV chlorine peaks were analyzed, and the peak areas were found to be approximately equal. For both peaks the TPA method yielded results smaller than the reported NBS concentration while the Wasson method yielded results that were larger. However each of the four experimental results fell within the reported uncertainty of the NBS value, and the experimental mean, as shown in Table XV, agreed with the NBS value to the three significant figures reported. In the manganese determination both the 3^6.7 and 1811.2 KeV peaks v?ere analyzed, but the higher energy peak, as seen from Figure 67 (channel 1556), was much smaller and was nearly buried in the baseline scatter. All four experimental results were smaller than the certified NBS value, but all fell within the reported uncertainty of this concentration. The results obtained from the smaller peak were larger in value, and the estimated error ranges were considerably larger due to the small peak-to-noise ratio of this peak. The exper-

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225 imental mean was well within the uncertainty limits of the NBS certified concentration and was 5.8% smaller in absolute value. When compared to the NBS value obtained from NAA results, however, the experimental mean v;as only 2. 6% smaller in absolute value. The two potassium results straddled the NBS certified value. The TPA value was large but fell v;ithin the reported uncertainty limits. The Wasson value was small, had a greater uncertainty, and fell outside the error range of the certified concentration. From the plot in Figure 72 it is apparent that the major deviation from the linear least squares fit occurred in the three points which were obtained from spiked samples. The two experimental points from pure samples were close in absolute value and showed little deviation from the fitted line. This suggested that some of the apparent error in the results may have been introduced by the experimental technique used to add the standard solution to the samples. While the experimental mean was 1,67c, smaller than the certified NBS concentration it was only O.67o smaller than the NBS value obtained from N-i^A results. In the sodium determination the certified value again fell between the two experimental results. In this case, however, the Wasson value was large but within the reported uncertainty limits. The TPA result was small and fell outside of the uncertainty limits of the NBS certified concentration. Figure 75 and Table XII show that the two pure samples had little difference in their adjusted peak areas and showed little deviation from the fitted curves. The deviation from the fitted curves by the spiked samples, however, supported the possibility that the spiking technique may have introduced much of the error found in the final ex-

PAGE 240

226 perimental results. As before, the mean value fell within the reported uncertainty of the NB3 concentration and was only 5-57« smaller than this certified value.

PAGE 241

APPENDICES

PAGE 242

APPENDIX I CORE RESIDENT SOFTWARE The following is a computer printout of the software used in this research. The programs are written in assembly language and the printout includes a listing of the location and octal value of each instruction. 228

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PAGE 0301 229 /ADC y.OSinOh DAVID P. COTTHELL FIVAL VERSION /COMPLETE PROGhA_M LISTINGS FOh HIGH PhECIblJM /DATA ACQUISITIQNJ A.MD DATA KEDUCTIJnJ FOR /MEUTRONJ ACTIVATIO^J AMALYSIS DOES MOT /TMCLUDE DEC'S FLOATING PO I \J T PACKAGE

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250 PAGE 0002 0034 0000 0035 0000 0036 0000 0037 0000 CKSUM, C>JT, COU\JT, L0C3A, FIMAL, LSECSW, >J PEAKS, L0C35, I.MDEX, MDAIPT, PEAKST, L0C36, IMDX, LINJE» ^5PTSP1, MPilGHT, OBLCT» L0C37» *65 0065 0000 0066 0000 0067 0000 0070 0000 007 1 0000 LEFT, .VLI.MES, PKLEFT, MPTS, STKTMl, L0C65, LI.NJDEX, MAX, PIMDEX, PKMX, PTEMP, TEMPI, L0C66, PKHT, RIGHT, L0C67, OUTTAP, L0C78, LDPTMS, TAPE>J, L0C71 , /LOCATIJ^Jb 7 3 S 7 1 ARE /KESEHVED EXCLUSIUELY /FOR THE LIP. GEM.

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PAGE 0033 231 /CONJSTAMTS S POIVTEHS CPAGE 0) 0072 360Q AhEA, 0073 037^ 0075 0076 0077 0100 0101 0102 0103 010^ 0105 0106 0107 01 10 01 1 1 01 12 01 13 01 1^ 01 15 01 16 01 17 0120 0121 0122 0123 0124 0125 0126 0187 0153 0131 0132 0133 0134 0301 0013 0387 0003 0304 0307 4400 2251 2400 6600 2471 2333 3357 2313 4466 4200 7663 7777 7773 2132 1600 0236 1000 3200 2231 2553 0214 2370 2270 0253 2105 1 120 0600 1127 CI , C13, C27, C3, C4, C7, CHKPKS, DIFF, D>JOISE, DNJOHM, FIX. FLOAT. FPSTOh, GET, G:^JOISE, MAGTPE, MSPECF. Ml , X5, PKTEbT, SCDSY, SEK. SICO>J, SYOOTH, SPPKNJT, STAhT. STKTCH, STORPK, SUBTHC, TEH. TEST, TYCi-., TYPST. TY5P. PKAREA 1 13 27 3 4 7 PKSHCH DI F S\'OISE 6630 FFIX FFLOAT FSTOHE GGET MWMOIS SETUP -120 -1 -5 PKTST SSCDSY SR 1000 SMOTH SPPhT CFP + 3 214 SAVEPK SUETR Tn COMPAh TTYCP. 630 TTYSP • /PEAK AhEA CALCuLATI3>J /2NJD PEAK SEAhCH ROUTIME /MOVIMG POI^JT DIFFEhE^J riAL /NJOISE DETEHMINJATIJXI /F. P. MOKMALIZATI JvJ /FLOATIMG TO FIXED /FIXED TO FLOAT I ''JG /STOKE F(AC) INJ COKE /DATA FETCH & FLOAT /SETUP. MOISE DETEKMI^JATIO^J /SETUP, MAG. TAPE OUTPUT /hAMGE FOh DM0 1 SE /TEST FOP. VALID PEAK /DISPLAY /STORAGE ROUTIME /S. P. DECIMAL IMPUT /LEAST SQUARES SMOOTH /S.P. OUTPUT THROUGH F. P. /LOC FOR PK. SER. STPIMG /I ST CHA.MvJEL I ^J PK. SEARCH /STORE PEAK BOU\]DARIES /D.P. SUBTRACT I OM /TERM I MAT IMG ROUTIME /PK. HT. COMPARISON TEST /TYPE C.R. /L. F. /MESSAGE STRIMG PRIMT /TYPE A SPACE /IMTERRUPT COMTROL ROUTIME 0135 0136 0137 0140 6201 7420 5530 6001 INJTRUP, 0141 6534 0142 5520 I TER CDF S-M L jyip lOM 6534 JMP I SER /IS LIMK ZERO? /YES, GO TO TEr.M. ROUTIME /MO, TURM INJTERRUPT OM /CLEAR ADC /GO TO STORAGE ROUTIME

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232 PAGE 0004 /CLEAi. CJ..E, DECIDE OM /R BEGIM DATA STORAGE PhlMTDUr* 0200 0201 0202 0203 0204 0205 0206 0207 0210 021 I 0212 0213 0214 0215 0216 0217 0220 0221 0222 0223 0224 0225 0226 0227 0230 0231 0232 0233 0234 0235 7340 3310 6676 30 34 621 1 3410 2334 5235 6201 1367 4533 6031 5213 6036 6046 6041 5217 0373 7650 5233 1363 3130 4773 1370 4533 6001 7320 1362 3130 5227 ADC, COLECT, MOPRT, *200 CLL CLA CMA DC A IR10 6676 DCA CMT CDF+10 DCA I IK10 IS?, C^JT JXP. -2 CDF TAD JMS KSF JMP. KHB TLS TSF J>1P. ^Xi D SMA jr-ip TAD DCA jys TAD JMS lOM CLA TAD DCA JMP MAGI I TYFST -1 -1 CI CLA \JOPKT CTR TER I STPRT MAG2 I TYPST STL CHLT TER COLECT /REXOVE C3NJFLICTIMG /INTERRUPT REQUEST /A.NJD CLEAR CORE /"PRIM TOUT?' /IMPUT /ECHO Y Or. M /SET INTERRUPT EXIT /ADDRESS FOR MO PRIMTOUT /IMIT. PRIMTOUT PARAMETERS /••START TIMER TO^' /" STORE DATA" /UAIT FOR TIMER /SET LINJK FOR INTERRUPT /SET IMTERRUPT EXIT /ADDRESS FOR PRINTOUT /STORAGE ROUTIME 0236 7 133 SR, CLL 0237

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^33 PAGE

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254 PAGE 0006 /DATA PHIMTOUT THROUGH FLOAT IMG POIMT OUTPUT 0312 103-^1 PhDATA, TAD CMT /PKIMT DATA IM 0313 7 10^ CLL P.AL /CUKhEMT CHAM MEL 0314 3066 DCA PTEYP 0315 681 1 CDF+10 0316 l'^66 TAD I PTEMP 0317 3046 DCA 46 0320 2366 I SZ PTE.MP 0321 1466 TAD I PTEMP 0322 3945 DCA 45 0323 6201 CDF 0324 1075 TAD C27 0325 3044 DCA 44 0326 4407 JX5 I FP 0327 7000 FMOK 0330 0000 FEXT 0331 1100 TAD C7 /7 DIGIT OUTPUT FOhXAT 0332 3062 DCA 62 0333 4406 JMS I OUTPUT /PhlsJT DATA 0334 2034 ISZ CMT /IMCREMEMT TO M EXT CHAMMEL 0335 1034 TAD CMT /PASSED CHAMMEL 2047(10)? 0336 7510 :.PA 0337 5351 JMP LASTPG /YES 0340 1035 TAD FIMAL /M0» PASSED FIMAL CHAMMEL? 034 1 7740 SMA SZA CLA 0342 5351 JMP LASTPG /YES 0343 2036 ISZ IMDEX /M0» FIMISHED LIME? 0344 5312 UMP PhDATA /MO 0345 4532 J>5S I TYCR /YES 0346 2065 ISZ MLIMES /FIMISHED PAGE? 0347 5276 JMP PPhlMT /MO 0350 527 1 UMP PAGER /YES /OUTPUT FOR LAST PAGE 0351 7300 LASTPG. CLL CLA /SKIP SOCIO) LIMES 0352 1372 TAD M62 0353 3066 DCA LIMDEX 0354 4532 JMS I TYCR /TYPE CR. /L.F. 0355 2066 ISZ LIMDEX 0356 5354 JMP. -2 0357 7402 CEMD, HLT /TEKMIMATE PROGRAM /DATA PRINTOUT WITHOUT STORAGE 0360 4773 PTOMLY, JMS I STPRT /IMITIALIZE PARAMETERS S 0361 5253 JMP TR /EEGIM DATA PRIMTOUT

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PAGE 3037 /VAhlAPLES 235 0362 0363 0364 0365 0366 0367 0373 0371 337 2 0373 0357 0253 3005 043-^ 0557 34 74 05C5 7774 7716 0403 CHLT, CTK. C5» HEADEK, MAGDSH, XAG 1 , .YAG2, M4, M62, STPHT, CEMD Th 5 HEDEK ADC5 i.uC 1 ADC2 -4 -62 STPT /ADDhESS OF HLT CJMMANJD /IMITIALIZE DATA PMnJTGUT AMD HEADEh PAhAYETEhS 0400 0401 0432 0403 0404 0405 0406 0437 0410 04 1 1 0412 0413 0414 0415 0416 0417 0423 0421 0422 0423 0424 0425 042 6 0427 0430 0431 0432 0433 0300 7300 1255 4533 4521 3334 1256 4533 4521 7041 3035 4223 141 1 4533 4521 3412 2066 5214 5603 3003 7300 1 1 15 3366 1257 3011 1266 3012 5623 STPT, HDHGLI I>JITAL, *430 0333 CLL CLA TAD JVS jyis OCA TAD JXb JMS CIA DCA JMb TAD JMS JMS DCA ISZ jy.p JMP 0030 CLL CLA MAG 3 I TYPST I bIC0>3 CNJT MAG4 I TYPST I SICO^J FINJAL I>JITAL I I r. 1 1 I TYPST I SIC3\] I I h 1 2 PIMDEX HDRGET I STPT TAD DCA TAD DCA TAD DCA JMP M5 PIMDEX START 1 Ihll STAhT2 Ihl2 I i:\irr AL /"I^JITIAL CHAMMEL = /"FINJAL CHA^JMEL = /PRIMT HEADEK MESSAGE /READ IM APPhOPKIATE # /STORE *'S IM SThl.NJG /FINISHED? /MO /YES» EXIT /INITIALIZE CMTR'S /FOR HEADER /EXIT

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236 PAGE 000 6

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2j57 PAGE 0009

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238 PAGE

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239 PAGE 031 1 /DIGIiAL 8/CHAkACTEh P.Q-U (XODIFIh.D) ST-KIMG TYPE-OUT /MODIFIED FOr. USE k I TH DBC ' S ADC XO^'ITOk /CALL i'JITH STi^JNJG /ALL CODES MAY BE /JiETUh>J FOLLO'/.'IMG ADDhESS Tv] DEVELOPED THE JMS ACJ 0603 0000 06G1 3262 0602 3264 TYPSTG, *638 0000 DC A TEMQ DCA FLAG /PKOCEoS THE SThlMG /STOKE /CLEAr. I ^J I T I AL FLAG ADDhESS 0603 1662 TSCCl, TAD I TEXQ 604 06Q5 060 6 0637 0610 061 1 0612 0613 0614 0615 0616 0617 0620 0621 0622 0623 0624 0625 0626 0627 0630 7012 7312 7 3 12 4214 1662 4214 2262 5203 HTh KTP RTH J^S TAD JMS ISZ, JXP TSCC2 I TEMQ TSCC2 TEMO TSCCl /PICK UP DATA /hOTATE 6 BITS KI GHT /TYPE FIPST CHAHACTEH , /PICK UP DATA /TYPE SEC3MD CHAhACTER /IvJCi.EXEvJT STORAGE ADDhESS /GO BACK FOk .MOKE /CHECK FOh OUTPUT CODES 5 OUTPUT A CHAKACTEH 0000 TSCC2, 0000 0265 3263 12 64 7640 5231 1263 7 4 50 52 2 7 42 50 5614 2264 5614 A>JD K77 /MASK OFF 6 BITS TYPAT DCA TAD SZA JMP TAD SJA JMP JMS JMP ISZ JMP TEMK i-LAG CLA TYPSP TEMh . +3 TYPE I TSCC2 FLAG I TSCC2 /SAVE /TEST CHAKACTEh "SPECIAL" FLAG /SET: TYPE SPECIAL /SiO: hEGULAh CHA.^ACTER /IS IT ZF.hDl /YES: SET FLAG /.\]0: r-KIMT I r /hETUh>J /SET "SPECIAL" FLAG /HETUhM

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240 PAGE 001c?

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241 PAGE 0013 /DIGITAL 8-{i8-U-ASCI I OjODIFIED) /SKvcLE PhEClJlOM DECIMAL ISiPVT FhOM KEYEOAr.D /MODIFIED FOR USE WITH DBC ' S ADC MOMITOK /CALL IMG SEGUENJCE: J>'S SICOMV /ACC IGMOHED, RETUhM '.vITK EIMARY WORD IM ACC

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PAGE 0014 242 /UPDATE THE CURREMT ASSEMBLED ^UY.BER 1046 1347 1050 1051 1352 1053 10 54 10 55 1056 1 3 1 P 7 10 6 1312 7 034 3312 131 1 0302 1312 3312 SIM.ViBH. TAD CLL TAD PAL DCA TAD A >J D TAD DCA SIHOLD hTL SIHOLD SIHJLD SI SAVE SI>jASK SIHOLD SIHOLD /MULTIPLY CUhhENJT /ASSEMBLED # BY 1 /PICK UP C UHK E>J T D I C1 1 /MASK OFF THE H.O. BI'l /ADD TO ASSEMBLED # /STOhE BACK l^i SIHOLD /I^JPUT S ECHO hOUTIME 1057

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PAGE 0015 243 /DIGITAL 8-I5/-U OiODIFIED) /TELETYPE OUTPUT PACKAGE CPOhTIONJS) /MODIFIED FOR USE V/I'iK DBC'S ADC .XO\)ITOf-: /TYPE C. H. /L. F. *11£3 1 120 1 121 1 182 1 123 1 124 I 125 BO00 7300 13^13 A33A 1342 4334 TTYCh 1 125 5720 'J CLL

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244 PAGE 0316 /ivDTATK UPPEi: COKE O^JCF TO LEFT (MULTIPLY PY ;?). /ROUTI>JE F.\1DS AT A HLT. PhESS CO^JTIViUE TO LEVEL /ANJD PLOT hOTATED DATA. LOAD ADDhESS A'JD /HESTAKT TO r.OTATE AGAI\'. *1800 1200 7 301 hOTUP, CLL CLA I AC 12G1 3031 DCA L0C31 1202 3032 DCA L0C3& 1203 6211 CDF+10 1204 1432 }.EPET» TAD I L0C32 /ROTATE S; hESTOhE 1205 7 134 CLL KAL /L. 0. VOP.:D 1236 3432 DCA I L0C32 1207 1431 TAD I L0C31 /hOTATF S i.FSTOf.F. 1210 7 004 KAL /H.O. V.Oi-.D 1211 3431 DCA I L0C31 1^12 2031 ISZ L0C31 1213 2331 ISZ L0C31 1214 2032 IbZ L0C32 12 15 2032 157. L0C32 /FIXUSHED ALL DATA? 1216 5234 j::p KEPET /^J0 12 17 6201 CDF /YES 1220 7402 HLT /V;AIT FOK PP.OGh.AMMEr: /LEVEL DOUPLE PKECISIO\i DATA IM UPPER CORE BY /PUTTIMG A 7777C6) INi THE L.O. WORD OF EACH /DATA POIMT THAT EXCEEDS SINJGLE Pi-.ECISIOM. 1221

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245 PAGE 0017 /hOTATE UPPE^. COhE O^JCE TO hlGHT (DIV/IDE bY fc; ) . /hOUn.NjE EMDS AT A HLT. PhEbS CJMTI^UE TJ LEVEL /AMD PLOT KDTATED DATA. LOAD ADDhESb ANID /iiEbiA:.! TO r.OTATE AGAInJ. 1243 46A6 KOTDW.M. JM5 I hOTDM /ROTATE UPPEK COKE DOV.nI 19AA 7432 HLT /VAIT FOh PhOGHAMMEh 1245 58^1 JMP LEVEL 1246 1443 HOTD.M, hOTAT /HOUTi:\iE TO ADJUST PLOTTEIi OUTpiJT FJr. LOV.EST /AMD HIGHEST DESIhED SETTINGS. BY PPiESSI^JG /COMTI>JUE THE COSITE.NJTS OF "PE^JLv." ^ "PKAiHGH" /'.-ILL ALTEhNJATELY BE DISPLAYED 0\J THE PLOTTER. 1S47 7 303 PE^JLO'v. , CLL CLA 1250 1260 TAD PEMLW /ZERO PLOTTER PE.NJ 1251 6562 6562 12 52 7402 HLT /WAIT FOR PROGRAMMER 1253 7330 PENJHI, CLL CLA 1254 1261 TAD PEMHGH /FULL SCALE PLOTTEP. PE>J 1255 6562 6562 1256 7402 HLT /WAIT FOR PHOGRAMyiER 12 57 524 7 JMP PflMLOW /REPEAT 12 60 0000 PE-NJLk. , 1261 7777 PEMHGH, 7777

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PAGE 001b 246 /EOUTIME TO ROTATE UPPEK COKE FhJ>5 /DOUBLE TO bIMGLE PKECIbIO:^J TO /ALLOV: DISPLAY OM A SCOPE 0?. PLOTTEH /CHECK HIGH-OHDEh PAi-.TS OF DATA LOCAlIO\iS /IN] UPPEh COLE A.^JD hOTATE E^JTIHF COLE /INTIL ALL DATA IS SI^JGLF PLECISIOnJ

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247 PAGE 0019 /SUB/-.OUTINJE TO ROTATE tvJTIKE UPPEK COKE OF /DOUbLE PKECISIO.\J PACKED DATA O.MCE TO RIGHT 14^)3

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PAGE 0020 2A8 /MESSAGE STRINJGS FOR SCLSY 1^7 1 0015 KOTl, 0015 1A72 0012 0012 1473 0012 0012 1474 04 11 04 11 1475 2320 2320 1476 1431 1401 1477 3140 3140 1503 0622 0622 1501 17 15 17 15 1502 4040 4040 1503 0001 0001 1504 4040 K0T2. 4040 150 5 24 17 24 17 1506 4040 4040 1507 0001 0001 1510 0315 hOT3» 00 15 1511 0012 0012 1512 0312 0012 1513 3533 0530 1514 0305 0305 1515 0534 0534 1516 2340 2340 1517 0317 0317 1520 2235 2205 152 1 40 14 4014 1522 1115 1115 15S3 1124 1124 1524 2354 2354 1525 4324 4024 1526 2231 2231 1527 4301 4031 1530 0701 0701 1531 1116 1116 1532 0001 0001 /C. H. /L.V. TWICE /"DISPLAY Fi-.0>3 /E\JD MESSAGE /" T3 " /ENJD MESSAGE /C»K. /L. F. TWICE /"EXCEEDS COhF LIMITS, /"TRY AGAI>J" /EMD MESSAGE

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249 PAGE 0021 /DISPLAY r.OUTIvJE FOR PIITHEh SCOPE OR PLOTTEH. /THIS IS A SPECIFIC UEhSlOsl. WHICH I G:\JOJvS THE /I.^GhEME>JT SPECIFIED lJG COMXAMD /AMD EXECUTES A FIXED I^ChE>iEgT OF TVO. /SET PIT 11 OF THE SVITCH hEGISTEh TO FOH A /SCOPE ADAPTABLE DISPLAY AMD TO 1 FOP A PLOTTER. /THIS KOUTIME SHOULD BE E>]TEf.ED WITH THE FIRST /LOCATIOM, LAST LOCATION], AMD IMCREMEsJT IM THE /FIRST, SECOMD, AMD THIRD POSITIOnJS AFTEi-. THE /CALLIMG COXMAMD. THE IMCRFMFINJT WILL BE IGMORED. /BUT THIS FORMAT WILL MAKE THE CALLIMG COMMAMD /COMPATIBLE WITH THE GEMERALI'/.ED SCDSY ROUTIME. /TO EXIT FROM THE ROUTINJE, SET BIT 3 0^ THE /SWITCH REGISTER TO I (APPLICABLE OMLY TO SCOPE). /THE DELAY TIME FOR THE PLOTTER DISPLAY (TO /GIVE THE PEM TIME TO RESPOMD) IS COnJTROLLED /BY TWO DELAY LOOPS. THE IMMER LOOP DELAYS /ABOUT 20 MILLISECOMDS EETWEEM POIMTS. THE /OUTER LOOP CO^JTl-.OLS THE MUMBER OF TIMES /THE IMMEk LOOP IS EXECUTED. THE VARIABLE /"COUMTl", FOUvID IM LOCATIOnI 161 OF THE /APPROPRIATE PAGE, IS THE MEGATIVE OF THE /MUMBER OF TIMES THE IM^ER LOOP IS EXECUTED. /DECISIOsi SECTIO\i FOR SCOPE OR PLOTTER *i6y0 1633 0000 SSCDSY, 0003 1601 7303 CLA CLL 1602 7404 OSR /CHECK BIT 11 1603 0262 AMD C0301 1604 7650 SMA CLA /SCOPE(S) OR PLOTTER(P)? 160 5 5215 JIvJP. + lS 1606 1267 TAD VJMP /PLOTTER, MAKE THE 1637 5244 DCA CHANJGl /APPi-.OPRI ATE CKAMGES 1613 1251 TAD CHAM62+2 161 1 3247 DCA CHA_MG2 1612 127 3 TAD VMOP 1613 3256 DCA CHAMG3 1614 5223 JMP.+7 /BEGIM REGULAR PROGRAM 1615 1201 TAD SSCDSY+1 /SCOPE, MAKE THE 1616 3244 DCA CHA.MGl /APPROPRIATE CHAMGES 1617 1232 TAD SSCDSY+2 1620 3247 DCA CHAMG2 1621 1263 TAD C6561 1622 3256 DCA CHAMG3

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PAGE 002?

PAGE 265

PAGE 0023 251 /VAr.IAELES 1662 1663 166<^ 1665 1666 1667 1670 0001 6561 0030 000i3 0003 5271 7000 00001 , C6561 , CMTti, FLOC, MPMTS, ^MOP, 1 c o6 1 3 JMP DELAY MOP /DELAY SECTION FJh PLOTTER OUTPUT 1671 167 2 167 3 157-^ 1675 167 6 1677 17 03 1701 1702 1703 7300 1303 3301 2 302 527^ 2301 5274 52-^5 0000 0300 7774 DELAY, COUX'Tl , C0U;vJT2, OUTEh, CLL TAD DCA ISZ. JMP. 152: JMP. JMP 3 -4 CLA OUT Eh COUvJTl C0UvJT2 -1 co^^n 1 -3 DbPLj' + 4 /KUM THROUGH IMMEK LOOP / F I \il S H ED OUT EH LOO P ? /NJO /YES, RETUP.V TO bCDSY

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252 PAGE 002-^ /IbT PEAK bEAhCH hOUTI^E /PROGf.AM TO SEAr.CH FOh PEAKS I ^J A /SPECTnUM AMD DETE:.MI.^E THE *» /MAXIMUM, ANJD B3U'>]DhIE5 U5IMG A /MO\/I>JG pJI.^iT DIFFEr.EMTIAL. THIS /SEARCH USES A MI>3IMUM HEIGHT /ChlTEnIA DM THE FlhST MAX. /IMITIALIZATIQvJ OF UAr.IAELES

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253 PAGE 0025

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254 PAGE 0026 /SUBROUTI-NJE TO COMPAr.E HEIGHT JF EITHEK PEAK /MAXIMUM Oh hIGHT BOQMDAhY (RELATIVE TO LEFT /BOUNIDAI-.Y) ';.ITH APPF.OPKIATE .^JOISE VALUE. 2105

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PAGE 302 7 255 /bUEr.OUI I\JE iJ DEiEnXigf-. IF t-^jEUDJ-PEAK XEETi /HEIGHT r.EuUInEXEM ib OF: / 1. (XAX-hIGHI)> J+^OIbE / 2. CXAX-LEr f )>\;*>1 JIbE 2132

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256 PAGE 01326

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257 PAGE 002 :i /bUBKOUTIME TO OUTPUT PEAK PAKPYETEnS 2243 003G PrsT\JU>5, 0030 824A 1413 IAD I Ihl0 /GET LOCATIOxT OF PAr.AMETE.h 2245 7 110 CLL hAi. /DECODE LOCATIOvJ TO CHAsJ>JEL 2246 4231 JXS SPPRT /OUTPUT PAhA>!FTEh 2247 4534 J>;S I TlfSP 2250 5543 JMP I PKTvJU^I /EXIT />JO^;iNJG POINJT DIFFEhEMTIATIOvJ SUB r.OUT I \J E 2251 0300 DIF, 0000 2252

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258 PAGE 0333 /SPECIAL SUBhJUTIME TO FETCH DJUPLE /PKECI-.IJ,' DATA FhOM UPPEK COhE, /COMVEhT IT TO FLOAT IMG PJIVJT. AMD /STOhE IT I>J THE DESIGNATED LOCATIOvJS. /THE hOUTINJE IS CALLED BY A J^S. /FOLLOWED EY THE Flr.Sf LOCATIJnJ OF /THE DESIRED STOhAGE SPACE. THE /CONJTEMTS OF THE AC SHOULD COMTAIM /THE LOCATIO^J OF L.J. UOKD OF DATA 2310 0000 GGET. 0000 231 1 111^ TAD y.l 2312 3011 DCA n.LOC 2313 17 10 TAD I GGET 23 1-^ 3352 DCA STOhE 2315 1075 TAD 0^7 /SET FCAC) EXP TO 27Co) 2316 30^*^ DCA 44 2317 6211 CDF+10 2320 1411 TAD I InLOC /STOnE LO'*-OhDEh WOhD 232 1 3346 DCA 46 /IM FCAC) L.O. >1A.>JTISSA 2322 14 11 TAD I IhLOC /STOKE HIGH-OKDEh v^OhD 2323 3345 DCA 45 /IM FCAC) }".. J. XAMTISSA 2324 623 1 CDF 2325 4437 jy.S I FP 2326 7000 FNJOh />J0K>3ALI 2;E FCAC) 2327 6752 FPUT I STOhE /STOhE NJOhMALI/^ED DATA 2330 0300 FEXT 2331 2310 ISZ GGET 2332 57 10 JMP I GGET /EXIT /FIXED TO FLOATIMG POI^JT COMUEKSI 0^] . /CALL WITH 12 BIT, UMSIC-NJED IMTEGEh /IM THE AC. FOLLO^k THE JYS WITH THE /DESIhED STOhAGE LOCATIOM F Oh THE /MOKVALIZED F. p. DATA. /PUT iNJTEGEh I^J L.O. MAxJTISSA /CLEAh H.O. .YAOriSSA /PUT £7Cb) l:\] EXP 2333

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PAGE 003! 259 /VARIABLES 2350

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260 PAGE 0038 /DETEKMIxJATIJ^ OF RAvJDJM bTATISTICAL ^JOISE-/SUBh.OUTI\'F DF.TEhMI>JEb THE AvEhAGE t^FAK TD /PEAK ^JOIbE PETv. EEnJ IVO SPECIFIC CHANJMELb. THE /STAz-.TlNJG CHANjvJEL IS DETE^.XI^JED hi THE PEAK /DETECT I OnJ r.OUTIvJE, AMD THE DETEhMI nJ ATI OM IS /OVEh A FIXED hAV'GE OF CHAvJMELS.

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261 PAGE 0033 2^31

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262 PAGE 033^1 /FLOATIMG TO FlAFD CD. F. ) C 0\I UEr.SI OvJ . /CALL V. ITH jys FOLLOWED Br LOCATIJvJ /OF f-.F. WORD. EXIT UIIH D. P. INTEGER /IM LOCATIONJS -^6 CL. 0. ) % ^5 CH.O. ). /SET IMlEGEh 10 IF THE h". P. WOi-D IS gEG. 2^7 1 0000 FFIX. £033 2-^72 7333 CLL CLA 2^73 1671 TAU I FFIX /SAVE DATA LOCAIIOvJ 2^1^ 3336 DCA STOh 2475 -Q^O? JMS I FP 2A76 5736 FGET I bTOH 2477 7030 F>JOii. /.MOHMALIZE F.p. ^..OhD 2500 0330 FEXT 250 1 y27 1 IbZ FFIX 2502 1044 TAD 44 /IS THE *JOUGH? 2527 5315 JXP hEP2 /:^0 2530 567 1 J>;P I FFIX /YES. EXIT /VARIABLES 2531

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263 PAGE 0335 /SUBKOUTlvJE TO hlJvJ A SAVITZKY i GOLAY /LEAST SOUAhES b.vlOJTH 0^ A 20/id(13) /CHAM >J EL SFECTKUM WHICH IS ST3hED /I^J DOUBLE PhECIblOxJ I \i UPPEh COhE

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PAGE 0036 264 /I>JITIALIZE VAnlAELFS S POlNJTEhS 32^0

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265 PAGE 0037 /CALCULATE SMOOTHED DATA i TRA>JSFER IT /TO IT'S Pr.OPEh PLACE I J THE SPECThUM 3315 4337 JMS AUEhAG /CALC WEIGHTED AVERAGE 3316 ^^dl J^S I FP 3317 5023 FGET FPA /GET WEIGHTED AVEKAGE 3320 -4765 FDIV I CSTAhT /DIVIDE BY DIVISOR 3321 6J23 FPUT FPA /SAVE SMOOTHED DATA PO I \] T 3322 0000 FEXT 3323 4505 JMS I FIX / 1 NJ lEGERI ZE SMOOTHED DATA 3324 3380 FPA 3325 6211 CDF+10 3326 1046 TAD 46 /TRAnJSFER SMOOTHED DATA TO 3327 3414 DCA I IRSTOR /COiihECT PLACE I xJ SPECTnUM 3330 1045 TAD 45 3331 34 14 DCA I IRSTOR 3332 6201 CDF 3333 2331 I SZ CvJTEH 3334 ^334 IS'd CMT /FIMISHED ALL DATA? 333 5 52 7 3 JMP RELOC /MO 3336 5600 JMP I SMOTH /YES, EXIT /CALCULATE THE TOTAL WEIGHTED AVERAGE 3337

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PAGE 003d 266 /\/Ar.IAELES 3365

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267 PAGE dQ39

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268 PAGE 00A0 /bUBKDUTIME TO DETEh>5I.ME THE GUAXJT I TA F I UE /AhEA IV A GAMXA-hA^ PHJTOPEAK /CALCULATI3:>J UbES TOTAL PEAK AhEA /TOTAL Ar.EA IS CALCUALAIED BY bUXXAFIOM /OF DATA OUEr. ALL CHAM^ELb l^ PEAK, THE>J /THE TP.APEZOIDAL Ar.EA DETEhXIxJED BY THE /TWO bJUJDAx.y Ch!A.\)\JELS I :> SUBTr.ACTED TO /YIELD THE QUANTITATIVE AhEA DESIhED. 3600 3630 0300 PKAhEA, 0000 3601 73'^6 CLL CLA CXA hTL /(-3) 3602 10 10 TAD Ihl3 /hESET hEGIbTEh FOh 3603 3010 DC A Ihl0 /PROPER PEAK 3604 7343 CXA /SET DECISION' POJNJTEh 3605 3374 DCA OnJETWO 3606 1410 GETPK. TAD I IhI0 /GET LEFT EOUvJDAhY 3637 7 110 CLL nAh 3610 3065 DCA PKLEFT 3611 14 10 TAD I Inl3 /GET PEAK XAX 3612 7 1 10 CLL nAh 3613 3066 DCA PKXX 3614 14 10 TAD I Inl0 /GET hIGHT FOUODAhr 3615 7 110 CLL hAh 3616 3067 DCA PKhT 3617 1365 TAD PKLEFT /FLOAT S STOhE 3620 7 104 CLL hAL /LEFT BOU^jDAhI' 3621 4510 JXS I GET 3622 0002 FPD 3623 1067 TAD PKRT /FLOAT £ STOh.E 3684 7 104 CLL HAL /RIGHT BOUMDARY 3625 4510 JVJS I GET 3626 0031 FPTEXP 3627 1065 CALC, TAD PKLEFT /FLOAT a STOhE # 3630 7041 CIA /CHANJNELS In] PEAK 3631 1367 TAD PKhT 3632 7301 lAC 3633 4506 JXS I FLOAT 3634 0326 FPC /# CHAMM ELb= C hi GHT-LEFT ) + 1 3635 4437 JXS I FP 3636 5031 FGEI FPTEMP /CAL. ThAPEZOID AhEA AS 3637 1302 FADD FPD /<^J * C LEFT + hl GHT ) /2> 3640 3026 FMPrFPC 3641 4370 FDIV FP2 3642 6023 FPUT FP5 /STOr.E ThAPEZOID AhEA 3643 0303 FEXT 3644 1367 TOTAL* TAD PKhT /CALC TOTAL Ar.EA 3645 7041 CIA /BY SUXXATUN 3646 337 5 DCA XPKRT 3647 3020 DCA EPA 3650 3021 DCA FPA+ 1 3651 3022 DCA FPA+2 3652 1365 TAD PKLEFT 3653 3034 DCA CMT

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269 PAGE

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270 PAGE 0G42 3730 1373 TAD ^JWASDM /IS (M AX-Xl ) > 0^.= \%. AS J^J ? 3731 1365 3732 7041 3733 1066 3734 7510 3735 5633 JMP I PKAKEA /MO, EXIT 3736 1065 TAD PKLEFT /YES, FIMD '.vASS3\J'S PKLEFT 3737 337 5 DCA PKTEMP /PUT I^ TEMP. STOhAGE 3740 1065 TAD PKLEFT /CALC CX2-X1) 3741 7341 3742 1375 3743 4506 3744 0323 3745 1375 TAD PKTEMP /CHAVJGE PKLEFT T3 X2 3746 3065 3747 4407 3753 5031 3751 2002 3752 4326 37 53 6326 FPUT FPC /SLOPE= ( Y4r 1 ) / C X4-X 1 ) 3754 5026 3755 3023 3756 1002 3757 6031 FPUT FPTEMP /Y3=SL0PE* ( X3-X 1 ) + Y 1 3763 5026 37 61 3020 3762 1002 3763 6032 FPUT FPD /Y2=SL3PE* ( X2-X I) + Y 1 3764 0300 3765 5227 JXP CALC /CALCULATE THE AKEAS /VAhlABLES 3766 2553 CCFP, CFP 3767 5015 FPSThT, 50 15 /CFGET FPA-3) 3770 0332 FP2, 3332 /2. 3 3771 2000 2000 3772 0000 0300 3773 0004 NJWASOM, 4 3774 0000 OMETWO, MPKRT, 3775 0300 PKTEMP, 3776 2543 PM T , PPM T TAD

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271 PAGE 0043 /SUBROUTIME TO FHIMT AKEAS

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PAGE 0a^ii 272 /MESSAGE STKIM6 FOK HEADING /FOK PEAK PhlMTOUT CCOMT. ) 4721

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PAGE !45 ?75 /LIBr.AP.Y GE«JEhATOR hOUriME SUBhOUTIvE V. ! LL /HEAD THhOUGH FhE^IOUbLf hECJhDED HhOthAXb /A>1D THEM bTOHE A PKOGhA.M WHICH lb CjJTAIxJED /IN] UPPEh COhE I^ A FJhy'AT COMPATIPLE *ITH /TKI-DATA'b LIPr.Ar.Y GENJEhAFOh hO'jfI\'F. V.HE'J /THE PhOGrA.V; * lb 0* TAPE i-. ILL MOT r.E«IMD 6 /PhOGPAM WILL BE bTOhED IXMEDIATELf J^JTJ TAt-E. /I^JPUT TAt^E A.MD Pr.JGnAM « ' b

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PAGE 02)A6 274 /bKIP OVEh PREUlOUSLir.ECOhDED PHJGhAViS -^036 A 037 4040 404 1 4042 4043 404*^ 4045 4045 4047 4050 4051 4052 4053 4354 4055 4056 4057 4060 4061 4062 4063 4064 4065 4066 4067 4070 437 1 4072 4073 4074 4075 4076 4077 4100 4101 4102 4103 4104 4105 4106 4107 41 10 411 1 4112 4113 41 14 41 15 41 16 41 17 1071 6314 7326 1371 7041 337 1 1365 6314 6332 5245 6335 3066 6335 03 65 7650 5245 1066 0076 7650 2371 5244 1065 3016 303 5 621 1 6324 1 1 15 3066 3034 1336 7550 5303 1370 7540 5304 2035 5305 1370 3036 1362 3037 1037 1364 4772 1037 7041 3037 1016 703 1 4772 PkOG» KEAD. DWRITE, hEP6, REP7» Dl , D2, D3. PhOG^]0 IMTAPE TAD LDPTMS AC^^D CLA bTL hlL TAD PhOGNJO CIA DCA TAD ACXD ShWC JMP HEAD RTB DCA TEXPl LTSA AMD I^JTAPE CLA READ TEXPl C3 CLA PROG.\]Q PROG bTr.TM 1 InDATA LSECbW b\JA iWP TAD A>JD SMA ISZ MP TAD DCA DCA Cur + 10 LTB TAD DCA DCA TAD SPA JMP TAD SMA JMP ISZ vJMP TAD DCA TAD DCA TAD TAD JM5 TAD CIA DCA TAD I AC M5 TEMPI CKSUM \'DATPT S>JA Dl M7 7 7 SZA D2 LSECSW D3 M7 77 vJDATPT C777 OBLCT OELCT DATAFD I bWRITE OBLCT OBLCT IRDATA r SV.RITE /GO 10 LOAD PT. /C + 2) TO ALLOi^ FOR LOADPRb /I^JITIALIZE PROG. COu^TK.r. /bTART READINJG A PROGRAM /IMITIATE READ ACTIO>J /IS READ WORD FLAG SEX.' />J0 /YES, READ A WORD /STORE LAST '.-.ORD READ /IS READ ^.EADY FLAG SET? /nJO. i-.FAD A^OrHER WORD /YES, ENJD OiPROGRAM? /YES. LAST PROGRAM? />iO, READ A\] OTHER PROGRAM /(STAi.TlAJG ADD.'-.ESSn /CLEAR LAST SFCTIO^J SWITCH /RESET Wr.ITE /SET COU.>JTER /BLOCKS IM A /CLEAr. CHECK /C# DATA PTS /4030(8) DATA /YES /M0» ARE THERE FLAG JO LIMIT * SECTION TO 5 SUM LEFT ig PROG. ) PTS LEFT? 7 7 7(B)? /YES /nIO» SET LAbT SECTIO'vJ Si-, ITCH /(# DATA PTS INJ FLOCK) /RECALC. * DATA PTS LEFT /SET UP OUTPUT BLOCK COCMT /WRI IE BLOCK COUMT S /FIELD I\I THE FIr.ST WORD /OF THE SECTION) /InJitialize output COUnJTER /WRITE DATA OUTPUT /ADDRESS IvJ THE 2^JD /WORD OF THE SECTIOM

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275 PAGE 412D 4121 4122 4123 4124 4125 4126 4127 4130 4131 4 132 4133 4134 4135 4136 4137 4140 4141 4142 4143 4144 4145 4146 4147 4150 4151 4152 4153 4 154 4155 4156 4157 4160 0047 1416 4772 2037 5320 2066 7410 5332 1035 7653 5273 6201 1034 1361 7041 3066 1066 0076 4772 1361 47 72 1066 0363 3066 1035 7650 7001 1066 4772 4773 1035 7650 5266 5600 WhTDATt E?JDSEC. TAD J^S ISZ ISZ SKP J>5P TAD S^JA J>!P CDF TAD TAD CIA DCA TAD A>JD jy.s TAD JXb TAD AMD DCA TAD S>JA I AC TAD JMS JMS TAD SMA JMP JMP I IhDATA I Sv.hlTE OPLCT WKTDAT TF.ypi ENJDSEC LSECSW CLA hEP7 CKbU-< C200 TEXPl T E.yi P 1 C3 I bl'.hlTE C200 I SV.hITE TE^Pl C7 7 74 TEMPI LSECbw CLA TEMPI I SV.nlTE I SUhSTP LSFCbW CLA hEP6 I LIPGEM /Wh.ITE A DATA ItJhD /FINISHED PL3CK? /MO /YES, FT N] I SHED A SFCTIJ-.'.' /YES /^O. LAST SFCTIOM FIJI S-"D? /MO. KEPEAr /YES, E.MD A SECTION] /LAST 3 f*OhDS OF SFCTIOM /ARE COMFUSIMG. IST OJE /COMTAIMS COMTKOL ThAMSFEh /FIELD # S LAST 2 BITS /OF CHECK SUM. i^MD OM E /HAS COMThOL ThAMSFEh /ADDhESS. 3hD OM E HAS /IST 10 BUS OF CHECK /SUM S LAST 2 BITS AhE /LAST SECTION SV. ITCH /(00 IF LAST SECTIO>J). /LAST SECTIOM? /NJO. INDICATE MOhE TO COME /YES /PUT A UhlTE STOP OM TAPE /LAST SECIIOM? /MO. REPEAT /YES. EXIT /VARIABLES 4161

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276 PAGE 0348 /ROUTIME TO SET UP STAhTlNJG DATA LJCATIJNJ /AMD # DATA WOhDS I.NJ THE Piv3GhAJ>] FOh /THE LIBhARY GF^NJEhATOh SUBRJUTIME /"STARTIMG CHANJM^L =

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277 PAGE 004J /bUBhOUTIME 10 Wi-.ITE A DATA WOhD OnJ XAG TAPE 42^0 3000 WHITE* 0000 42A1

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278 PAGE 0050

PAGE 293

PAGE

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PAGE 005^ 280 /PR0GRA>1 TO SEARCH F3h PEAKS I>J A /SPECThUM A\'D DETEf.XIME THE #, /.YAXIXUX* A^JD EOU^DhlES USI^JG A /VOUIMG POINJT DIFFFhE^TIAL. THIS /SEAKCH USES A >!I\iI>:U-<1 SE.hlES OF /POS. !^ >JE6. DEh. 'b AS Cr.ITEhlA.

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281 PAGE 0053 /PEAK DETECT I OM ROUT I ME 4430 4502 PKDET, JMS I DIFF /YES, GET DI FFFi-;F:^ TI AL 4431 7700 SMA CLA /IS IT ^JEGATIVE? 4432 5230 J>!P. -2 /NJQ 4433 1034 TAD CDU^JT /YES, STOKE PEAK MAX 4434 3066 DCA MAX /DETECT I OM OF VALID hIGHT BOU\JDAhY /RESET SEf.IES INJDEX FJiv MEG /IMChFME^JT FOR LAST DATA /GET DIFFERENJTIAL /POSITIVE YET? /YES, RLN CHECKS />J0 FOR VALID PEAKS /VIM I MUM MEG SERIES /COMPLETED? /^O, REJECT /YES, SAVE RIGHT DOU^JDARr /SET GMOISE TO FIMD 1*J0ISE /CALC. STATISTICAL MOISE /VALID PEAK? /YES, STOr.E BOUNDARIES /^O, SAVE POSSIBLE /LEFT EOUMDARY /IMCREMEMT FOR LAST DATA /BEGIM SEARCH FOR M EU PEAK 4435

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282 PAGE 0354 /SUPKOUTIVE TO DErEhvUviF BOLNDAhlES FOR /CALCULAi IO>J OF hA.VJDOM STAilSTICAL vJOlSE 4466 0303 MaMOIS* 0000 44 67

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PAGE 0055 283 /HOUTTJE TO FLOAT S ST3.-.E SPE.CThAL /DATA INJ F\JF* LJCATIOMS FOh PEAK /FITTI.NJG USIvJG FDCAL PhOGHAyMlNJG 4600 4601 4602 4603 4604 4635 4606 4607 4610 461 1 4612 4613 4614 4615 4616 7343 1264 3015 1265 4533 4521 7 104 3033 1266 4533 4521 7105 7041 1033 303 1 KELCTE» 4600 CLL CLA TAD DCA TAD JM5 JMS CLL DCA TAD jyis JMS CLL CIA TAD DCA FME Ihl XAG I T I b hAL LFT MAG I T I S I AC LFT CnJT CM A 5 17 YP5T ICO\J BDtT Id ypbT ICONJ hAL PDY /"bTAhTlNJG CHAM.MF.L = /•FI'JAL CHAM.NJEL =" Eh /RELOCATE BLOCK OF DATA TO EEGi:^ AT LOCATION 4617

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284 PAGE 3356 4635 A636 4637 4640 4641 4 64 2 4643 4644 4645 4646 4647 4650 4651 4652 4653 4654 4655 4656 4657 4663 4661 4662 4663 1412 3346 1412 3345 620 1 1375 3044 4504 6211 1344 3415 1045 34 15 1046 34 15 34 15 3415 3415 2031 2031 5235 6201 5512 /FLOAT DATA S STOhE IM THE EVEN! FMEW /LOCATION!* EEGINJ>3I.MG WITH F^EWC158) VUF>JEW» TAD DCA TAD DCA CDF TAD DCA JWS CDF+ TAD DCA TAD DCA TAD DCA DCA DCA DCA ISZ ISZ JMP CDF JXP I I h 1 2 46 I Inl2 45 C27 44 I DvJOhM 10 44 I I r. 1 5 45 I I h 1 5 46 I Ihl5 I I h 1 5 I IK15 I I K 1 5 CNJ T Et. C>J T Eh >5UF^EW I XAGTPE /PUT DATA I^ FCAC) /SET EXP. TO 23C10) /MOKMALIZE l-CAC) /STOhE F. P. DATA I >J FnJ EV, /SET ODD FME'/ ' S TO /FINISHED ALL DATA? /\]0 /YES /STOhE OM XiAG. TAPE /VARIABLES 4664

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285 ADC 0ii00 ADC4 05A4 CCFP 37 65 CHALl -^511 CHANJG^ cil57 CHLT 036i^ CLAST ^£27 CM In 1664 COUNJTl 1701 C0001 1662 CI 0073 C8'!l0 0670 C5 036A C7774 4163 DIFF 0102 DNJOISE 0103 DTPKPK 2450 Dl 4103 F.NJDbTG 3314 FETCH 1403 FlhST 1431 FLOC 166b FPB 0023 FPbThi 37 67 GET 0110 6M0ISE 0111 HEDEhl 1150 HFDEr.5 07 70 INJDEX 0036 IMPUr 0005 IhGET 00 10 IhSTOK 00 14 IR15 0015 LPGEM 42 30 LEVEL 1221 LIMDEX 0066 L0C33 0033 L0C37 0037 LOC70 0070 LSECb'.^' 0035 XAGFPE 0112 MAG12 4167 VAGI 6 4237 yAQ2 37 yAG4 04 56 MAG^ 2 3 50 yGTP2 4334 MGTP6 4356 MM UM 4 5 14 ypTSPl 0037 y. 1 114 ADCl 0474 ADC5 3557 AvH,i.AG 3337 CEMD 0357 CHAMGl 1644 CHA\'G5 4512 CHOICE 2230 CMbTPT 0052 CJLECT 0227 C0LW1'2 1702 C0212 1142 CI 00 667 C27 007 5 C6561 lb63 DATAhD 4164 DIrl 2264 D\I0.-.y 0104 DTPKl 24 61 D2 4 104 Er.KOr. 14 37 FFIX 24 7 1 FIX 0105 FMEv. 4 664 r I' J 2 6 FPTEyp 00 31 GETDAI 0033 HUi.GET 04 14 HEDE.-.2 1164 HIGH 14 64 I\'DX 0037 IMTAPE 4165 n.L0C 00 11 I/-. 10 00 10 K77 0665 LDPiyG 4260 LFIBDr 0033 LIME 0037 L0C34 0034 L0C65 0065 LOG 7 1 007 1 yAGDbH 0366 yAGl 0367 yAG13 4264 VAGI 7 4 665 1VAG20 3367 yAG6 1466 yAA 0066 yGTP3 4313 yiMLET 2414 MODIFY 0673 MhlGHT 00 3 7 M27 2532 ADC2 0505 ADPMTh 0017 BOU\:Db 14 11 CrP 2550 CHAMG2 1647 CHECK 4513 CJyP 2 156 C^JT 0034 COypAi. 2 105 CSIAhl 3365 C02 15 1143 C13 0074 C3 0076 C7 0100 DELAf 167 1 DIF2 2265 DJvJE 444 6 DTPK2 24 62 D3 4105 EX I r lo60 FhLOAr 2333 FLAG 0664 FP 0007 FPD 0002 FP2 3770 GhfPK 3606 HEADE.ii 365 HEDfc>.3 07 60 IDbPLir 1652 IMIIAL 0423 IvIfhUP 135 IhPK 0012 Ii:ll 0011 LAST 14 32 LDPTMb 007 1 LFTDET 20 13 LOG 3 1 00 3 1 LJC35 0035 L0C66 0066 LOOP 36 54 vAGEr.r. 42 53 yA610 235 1 XAG14 4231 XAGld 4666 yAG2 1 337 yAG7 14 67 yAXDET 2422 yGTP4 ^^3^5 y I ^1 i'.\! D 2 10 7 yOVF:-) 46 17 XbP^CF 0113 M4 337 1 AijC3 0530 AhEA 0072 CALG 3627 CFPX 5264 CHAMG3 1656 CHXPKb 0101 CKbUX 00 34 CMTEh 0031 COUMT 0034 CTh 0363 C0240 1144 C200 4161 C4 007 7 C7 7 7 4 162 DIF 22 51 DIUISh 2531 DbpLY 164 1 Dt,iaTE 4063 EMDbEC 4 132 FDIFF 244 3 FIMAL 003 5 FLOAT 106 FPA 0020 FPSTOh 0107 FbTJhE 3357 GGEr 23 10 HEDEh 0434 HEDEh4 7 66 IMCyslT 1433 IMPTCb 3226 n.DATA 00 16 IhPUr 0013 Inl2 0012 LAbTi-'G 0351 LFF: 0065 LIBGEn! 4000 L0C32 0052 L0C36 0036 L0C67 0067 L0V, 14 65 XAGTAP 4022 yAGll 4 166 KAG15 4c:!32 yAGl:^ 5366 yAG3 0455 yAG8 1470 yGTPl 4 2 74 MGTPS 4343 MIMHT 2 160 yPKhT 3775 yifFMKU 4635 y40 0656

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286 M5

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APPENDIX II FOCAL PROGRAMS All computer programs listed in this appendix were run on an 8K Digital Equipment Corporation PDP-8/L computer with a Model ASR 53 Teletype input and output. All programs were written in FOCAL (FOrmula CALculator) conversational language. The following new functions were user defined: common storage functions FNEW(1, ...... .) and FNEW(2, ), and integer scaling function FNEW(5, .,.,...) , and an oscilloscope display function FNEW(lt, .,.,...) . 287

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283 Program 1 Photopeak Fitting Routine This program performs the nonlinear least squares iterative fit of an eight parameter function, described in the theory section, to the digital data stored in the even FN'EW locations, beginning with FNEW(150) . The original parameter estimates, the value of the increment, the number of points in the fit, and the initial abscissa value are input through the Teletype. New values of the parameter estimates, the residual sura of squares, and the raw and fitted sums are printed following each iteration. PS = number of parameters C(V) = parameter estimate IN = abscissa increment, in sigma units NP = number of points in the fitting interval XO = initial abscissa value, in sigma units

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289 C-8K FOCAL §l3i6;> 01.01 01.02 01.03 01.0-a 01.05 01.07 01. 10 01. 15 01 01 01 01 01 01 01 01 01 01 01 01.75 01. 80 01. 85 01.93 01.S<5 23 2 5 30 35 40 A5 50 55 60 65 70 E T F A F T S c s s b s s s s s s s b b b %8.0 v=l , ?Pb? V=l. !;a 1 = 0; bl=C b3 = C S5=F Q1 = F Q2=. Q3=C D( I ) Y=C( b8 = C U=U + D(3) D(2) D(A) D(5) D(6) DC7) D(8) 5o;b ! ! s; A INJ?, X= X 2)*( &)-X XPCb aPC*( 16)*F G l + Q )*D( 1 )*Q ; s 7. 2*SS D(3) 2*C( b2*D b^/C -bv^^ D(7) Z: = FMEWC1 ,\/,0) ?C( ?MP o;s x-c ;b 1 ); (b5 FXP 2*Q 1 ) 3;s = F>J *C( * ( ( 1 ) + CA) C6) *C( ^)?. ! ? , ?X0? , ! U=75;S bM=0 C3));i b2= (X-CC4) )/y*C( 5) b4=FbQT(S3T 2) b b6=FEXP(-bl);b S7=S5+S6 (X-CC^) ) ) -b6)/:^7) (-C(7)*(b4+b3) ) 3 S3» = b8*Q2 EWC 1 ,2*U1 »y ) 2)/b7t 2 C(3)-X)/CC2) ) b2*01 + 53) 7)/b4 02.40 02.45 02. 50 02. 55 02. 65 02.90 03. 03. 03. 03. 03. 03. 03. 03. 03. 03. 03. 03. 03. 03. 03. 03. 03. 05 10 15 23 25 30 35 40 45 50 55 63 65 73 74 78 83 hb = FNJEW(2.2*U.W)-F^EWC2,2 + U1 .U);b bM = SM + KST2 J=l»Pb;b ?; = F>JE'*(2, J+PSt2,U )+DC J)*r.b; 5 7:i=FNlEt^( I , J+PbT 2.Z) j= 1 ,Pbi F K= 1 . j;d 4 x=x+i\j;b 1 = 1 + i; I (I -MP) 1.15; !; T ?b>i? . ! ;g 6. 1 "GG";b Z = F^JEW(4, 150.653) 1 1 :'<=0.\];d 5 Z=F:^EW(2,P + L*K+l » W)/M; b 2 1 = FMEU( 1 ,P + L*X + IT=IT+ 1 L=Pb; b ^j = Li; b 1 = K='df'^i^ hCK) = K+l M=lE-6 j=Q,Nj; F hCP)=3 k=3.l; b 1,7.) J= 3 » NJ ; D 6 1 = 1 + 1 ; I (I-\J)3.2.3.5.3.2 J=0,>];P r.^^,:liu 7 !!!"# OF ITEhAriONJi",%2, IT !;F K=3,^J;T ! %2"X(".K+1,") " , ?;8. 05 , XCK ) !!;f v/=i,pb;b C(U)=C(^) + xc V1 ); T C(U),! \;=i ,2;d 3. 9 V=5»7; D 3. J y = 3» 5, 8; D 3. 95 1.03

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290 03.

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291 Program 2 Baseline Fitting Routine This program performs the nonlinear least squares iterative fit of a cubic polynomial to up to five separate segments of the digital data stored in the even FNEW locations, beginning with FNEW(150) • The original parameter estimates, the value of the increment, the number of points in the fit, the initial abscissa value, the number of baseline segments, and the first and last channel location of each segment are input through the Teletype. New values of the parameter estimates, the residual sum of squares, and the raw and fitted sums are printed following each iteration. PS = number of parameters C(V) = parameter estimate IN = abscissa increment, in channels NF = number of points in the fitting interval XO = initial abscissa value, in channels SS = number of baseline segments in the fit N(J) = first or last channel location of a baseline segment ^

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292 C-8K FOCAL '11969 01.01 E 01.03 F V=1,150;S Z=FMEi'-Cl ,U.0) 01.0^ A ?Pb? . ! ! 01.05 F V=1.PS;A ?C(U)?,! 01.07 T !;A ? IM? , ?NJP? , ?X0? , ! ! 01.08 T "# SECri J\'b"J A bSJ T " ";F J= 1 , 2* C 5b1 ) ; A ? ^J ( J )? 01.10 S I=0JS X=X9;b u=75;s SX=3 01.15 s B=i;b i'=cci);b Dcn^^i 01.23 F II=2,Pb;D3 5.9 01.60 b U=U+i;b Z=FMEW( 1 .2*U-1 .y ) 01. 65 I C I-\i ( 1) )2. '^; 01.73 I (I->J (2)+l)2. 55; 01.75 I CI->J(3))c;.^iJ 01.80 I ( I-:\J (^)+l )2. 55; 01.85 I (I-M(5))y.^; 01.90 I CI-M (6)+l )2. 55; 01.95 I CI-^J (7) )2.'!i; 02.05 I CI-NJ(8)+1 )2. 55; 02. 10 I CI-\J C9) )2. iAj 02. 15 I (I-M( 13) + 1 )2. 55; 02.40 b Rb=F\JP:WC2,2*U.\;. )-F\IE'a (2, 2*U1 . U);5 bM=b>! + t.ST 2 02.'!i5 F J=l,Pb;S Z=F.\IEWC2, J+PSf 2.W) + Df J)*hb;S Z1 = F\JEW(1, J+PSf 2,Z) 02.53 F J=l,Pb;F K=l,Pb;D H 02.55 5 x=A+i:vi;b i = i + i;i c i-.\ip) i. 15; 02. 85 T !;T ?bX? , ! ;G 8. 1 02.90 T "GG'Sb Z=F\JEW(A, 153* 650) 03.05 b IT=IT+1 03.10 b L=Pb;b >J=L-i;b I = -l 03.15 F K=3..Nj;b KCK) = K+1 03.20 b X=lE-6 03.2 5 F j=0,n];f k=j,.j;d 5 03. 30 b hCP)=0 03.35 F K=0.L;5 Z = F>JEWC2.F + L*K+ 1 , W)/m; S Z1 = F^E'vv( 1 ,P+L*K + 1 ,Z) 03.40 F j=0.m;d 6 03.45 b I = I+i;l (I-M )3. 2.3. 5.3. 2 03.50 F j=0,nj;f k=0,nj;d 7 03.55 T !!!"* OF I TEhAT lOM b" . %2 , I T 03.60 T !;F K=0,M;r • ?2"XC",K+ l .") ", %d. 35.xc:-<) 03.65 T !!;F v;=I,Pb;b C(U) = C( V)+X( Vl ) ; T CCV/),! 03.70 I C-Cfl))3.&;b C( 1 )= (C( 1 )-X(3) )/2; r "CC 1 )".C( 1 ) . ! 03.80 D 1. 33 03.85 G 1. 1 04. 10 b V = J+K*PS-Pb 04.15 5 Z = FMEv, (2,U,W) + D( J)*D(K) 04.20 b Zl = F>JEwC 1 ,U,Z)

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295 05. 10 I (h(J-> )0,5. 3,5. 15 05.15 I fFABbCRvJEWCy, J+;-<*L+l,V;))-FABSCy) )5.3; 05.iia S M=F\}EWfg, J+K + L+l.W) 05.25 S P=j;b Q=K 05.30 h 05.93 S B=B*x;b Y = Y + Cf I I )*B; b DCII) = B 06.10 I fJ-P)6. 15.6. 25.6. 15 06.15 b D=F\JE;v (h, J + L*J+1 .'a ) 06.20 F K=0.LJS U=J+K*L+i;b Vl=U-J+PjD 6.3 06.25 K 06.30 b Z=FMEV. (2, V.W)-FNJFW(2. l/l ,k )*D;b ?: 1 = F>J Fw CI , V , Z ) 07.10 I ClE-6-FAB5(FME'.'.(2, J+X + L+1 ,;0) )7. 2;R 07.20 S XCK) = FNJEwf2, J+L + L+l.W) 08. 10 S R=0; S S=0 0b. 15 F 1 = 76. (MP-1 ) + 76JD 9 08.20 T !"hAW bUM",h;T " SMOOTH SUM".b.! 08. 25 G 2. 9 09.02 b J=I-76 09.05 I < J-NJCl ))^. 6.: 09. 10 I CJ-s; (2)+ 1 )^. 7; 09. 15 I ( J-NJC3))^. 6; 09.20 I f J-NJ CA)+1 ):^. ?; 09.25 I C J-MC5) )9. 6; 09.30 I ( J-M(6)+l)^. 7; 09.35 I C J-N3C7 ) )9. 6; 09.^4 I (J-NJ(6)+1)^.7; 09.45 I CJ-V(y))9.6; 09.50 I C J-MC10)+1 ):<. 7; 09.60 b R=n + FNJE'.v (2,2*1 .1.; ) 09.65 S b= b+FNJEWC 2,2*11 ,vv) 9.70 h *

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294 Program 5 Calculation of the Total Fitted Curve This program uses the final parameter estimates from Programs 1 and 2 to calculate the total fitted curve. The total curve is obtained by adding the polynomial baseline contribution to the fitted peak function. The calculated values are stored in the odd FNEW locations, beginning with FNEW(151) . The program assumes that the original raw data are stored in the even FNEW locations, beginning with FNEW(150) . The residual sum of squares and the raw and fitted suns are calculated, and the raw and fitted spectra are simultaneously displayed on an oscilloscope. PS = number of parameters C(V) = final calculated parameter estimates IN = abscissa increment, in sigma units NP = number of points in the fitting interval XO = initial abscissa value, in sigma units

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295 C-8K FOCAL 9 1^6:^ 01 01 01 01 01 01 01. 01 01 01. 01 01 01 01 01. 01 01 01 02 0-!) 3 5 07 10 15 20 8 5 33 35 45 53 52 55 63 18 ?P V = ! ; 1 = SI 53 S5 Ql 02 Q3 DC Y = JJ II 0'= .05 b?. • 1 .PS A ?! 0; s = CC2 = CCB = FEX = FEX = . 5* = CC6 1 ) = Q CC 1 ) = 1+ 1 -13. u+i; ; A ? C (I' ) ? . ! ^J ? , ?-^JP? . ?A0? . ! x=x3;s u=75;s sm=0 ) * C XC ( 3 ) ) ; S b 2= ( XC f -^ ) ) / 2 > C C 5 ) )-X;S S'^=FSQrCS3t2) PfSl);S S6=FF.XP(-Sl ); S S7 = S5+S6 PC-S2*(X-C('4) ) ) ( 1-(S5-S6)/S7 ) )*FEXF(-CC7 )+ CS4 + S3) ) 1+G2+Q3 + D( 1 ) ;s p=i;s Y=r + C(:^) Hs;s B=B*jj;b r-i' + ccin + B S Z=FMEvv ( 1 f-^.*U1 ,Y) 02.-^0 02. 55 02. 63 02. 65 02.70 02.75 02. ^a 02. 95 hS=FNJEWC2.2*U. V ) x=x+i:vj;s 1 = 1 + i; I F.\JEW(g,2 + 'J(I-NJh-) 1. 15J i.k);s sy.=SM + };ST2 !"r.ESIDUHL h=a;s s=0 I=76,MF+75;D 3 !"nAW SUM". ft; T U>: jF SG'JAhES".syi, ! SXJOl'H SU"^".i. ! 'GG";S ?:=FnJF'a (A, 1 53.^^53) 03. 03. 03. 10 S 20 S 30 h h=h+FMFw'(2,2*I .V) S=S+F^JFWf 2,2*1I . V )

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296 Program 14^ Numerical Integration by the Trapezoid Method This program performs the numerical integration of the eight parameter fitting function, using the trapezoid method and an increment of 0.1 channel. The final parameter estimates from Program 1, the abscissa increment used with the fitting function, and the channel locations of the peak boundaries are input through the Teletype. The integrated area is printed and the process is repeated. C(V) = final calculated parameter estimates IF = abscissa increment, in sigma units, used with the fitting function

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C-8K FOCAL '3 1969 297 01.01 E 01. Oa T %8.06. ! ! ! ! ! 01.05 T "PEAK"; A PK. ! 1 01. 37 F V= 1 , b; A ?C( V)? . ! 01.08 A !"hIlTI>JG iNiChEMDJ T", I F 01.10 A !!"LEFT BOUM DAnY" » Lbi A " T BOUMDPu.r'"..'/^ 01.15 S HH=3. l;b XO=CLB-MX)*If ;b 01.i?d S NJ=CCkB-LB)*IF/K) + l; I !!"* 01.25 S S=3;5 X=X0 01. 30 F 1 = 1 ,NJ + . -^JD 2 01.35 5 A=S*HH/2;T !!"AhEA",A 01.^0 A ! ! !"CO>JTI^JUE?",CC; I C20-CC)1.5; 1.^5 T !!!!•; Q 01. 53 T !;G 1.1 PEAK v,ax",>ix;a .' YX+3 ( J2 ) * C XC J 1 ) t ( J21) ) 08.15 5 D=YCJl)-YX;b SD=SD+D*D 8. 17 t. 08.20 T %2,J1," ",S6. 36. Y( Jl ) ," "»Ya," " , D . ! J H 1^.05 S NJ=K+i; S DD=A(M + I I*L) /ACI I + I I+L) M.13 F J=II»LJ 5 AC.M + J+L) = AC-J + J*L)-ACI 1 + J*L)+DD 14.15 s YX(>J)=YX(:^J )-YX{i r )*dd; n 15.05 b MM=L-1 15.10 F 11=1, yM;F K=ii»yMi d 14.3 15.15 S B(L)=YXCL)/A(L+L*L) 15.20 F y=£?,L;S >J = L+1-MJS KK=NJ + l;b B(M ) = YX(NJ )/ACnJ+\]*L) ;d 15.25 15.21 G 15.33 15.25 F K = KK,L; b ECM )=BCM )-ACM + K + L)*E(K)/AC^J+'J*L) 15.33 h

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BIOGtL^PHICAL sr^TCH David Baldwin Cottrell was born on September 17, 1946, at Covington, Virginia. He was educated in the public school systems of Fishersville and Newport News, Virginia. He graduated from Ferguson High School, Newport News, Virginia, in June, 1964, where he was elected to the National Honor Society. In September, 1954, he began his undergraduate studies at the University of Virginia, Charlottesville, Virginia. In June, 1968, he received the degree of Bachelor of Science, With Distinction, in Chemistry and was named the outstanding graduate in analytical chemistry. He entered graduate school in Septenber, 1968, at the University of Florida, Gainesville, Florida, majoring in analytical chemistry. He held teaching and research assistantships until September, 1971, when he was awarded a Traineeship from the National Science Foundation, He married the former Elizabeth Neil Blackwell of Newport News, Virginia, on May 27, 1967. He has been a member of the American Chemical Society and the Society of Sigma Xi. 305

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I certify that I have read thle 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. Stuart P. Cram, Chairman, Assistant Professor of Chemistry 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. Roger GJ Bates, Professor of Chemistry 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, Jamss D, Winefordner/ vProfessor of Chemistry

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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. William H. Ellis, Associate Professor of Nuclear Engineering I certify that I have read this study and that in my opinion it confonns to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Frank G. Martin, Associate Professor of Statistics This dissertation was submitted to the Department of Chemistry in the College of Arts and Sciences and to the Graduate Council, and vas accepted as partia?. fulfillment of the requirements for the degree of Doctor of Philosophy. March, 1973 Dean, Graduate School