The algorithm and program for processing linear spectra
We present the algorithm, which allows to process linear spectra containing overlapped peaks. The program using this algorithm provides a fast processing procedure for any linear spectra at arbitrary radiation background conditions.
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2001
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Gavrikov, V.B. Prokhorets, S.I. 2015-03-17T12:15:53Z 2015-03-17T12:15:53Z 2001 The algorithm and program for processing linear spectra / V.B. Gavrikov, S.I. Prokhorets // Вопросы атомной науки и техники. — 2001. — № 1. — С. 69-70. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 29.85.+c. https://nasplib.isofts.kiev.ua/handle/123456789/78451 We present the algorithm, which allows to process linear spectra containing overlapped peaks. The program using this algorithm provides a fast processing procedure for any linear spectra at arbitrary radiation background conditions. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Experimental methods and computations The algorithm and program for processing linear spectra Алгоритм и программа для обработки линейных спектров Article published earlier |
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The algorithm and program for processing linear spectra |
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The algorithm and program for processing linear spectra Gavrikov, V.B. Prokhorets, S.I. Experimental methods and computations |
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The algorithm and program for processing linear spectra |
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The algorithm and program for processing linear spectra |
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The algorithm and program for processing linear spectra |
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The algorithm and program for processing linear spectra |
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algorithm and program for processing linear spectra |
| author |
Gavrikov, V.B. Prokhorets, S.I. |
| author_facet |
Gavrikov, V.B. Prokhorets, S.I. |
| topic |
Experimental methods and computations |
| topic_facet |
Experimental methods and computations |
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2001 |
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English |
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Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Алгоритм и программа для обработки линейных спектров |
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We present the algorithm, which allows to process linear spectra containing overlapped peaks. The program using this algorithm provides a fast processing procedure for any linear spectra at arbitrary radiation background conditions.
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1562-6016 |
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https://nasplib.isofts.kiev.ua/handle/123456789/78451 |
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The algorithm and program for processing linear spectra / V.B. Gavrikov, S.I. Prokhorets // Вопросы атомной науки и техники. — 2001. — № 1. — С. 69-70. — Бібліогр.: 5 назв. — англ. |
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| first_indexed |
2025-11-24T16:28:05Z |
| last_indexed |
2025-11-24T16:28:05Z |
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1850485043446677504 |
| fulltext |
THE ALGORITHM AND PROGRAM FOR PROCESSING LINEAR
SPECTRA
V.B. Gavrikov, S.I. Prokhorets
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
We present the algorithm, which allows to process linear spectra containing overlapped peaks. The program
using this algorithm provides a fast processing procedure for any linear spectra at arbitrary radiation background
conditions.
PACS: 29.85.+c.
It is in common usage to process linear spectra by
using different fitting functions, as a rule one makes a
use a Gauss function or some linear combination of
such functions[1]. At this it is assumed that dispersions
of single peak does not depend on its positions in a
spectrum [2]. Such approach, in our mind, can result in
loss of information concerning physical nature of
processes that result in occurrence of radiation peaks.
As an illustration of this situation one can see the
spectra of coherent X-ray radiation (CXR) in [3, 4]. In
these spectra the observable radiation lines are
characterized by asymmetry of their form and,
moreover, their linewidths depend essentially on
positions which the weight centers of these lines have
on an energy scale [4].
We elaborated the algorithm and program package
for processing linear spectra, which is free from the
above lacks. This processing algorithm executes the
following steps:
1) Construction of a reduced spectrum S’ by making
a convolution procedure. At this an initial spectrum S is
convoluted with a correlator K which has a width k and
zero area:
( ) ( ) ( )iKiSjS
k3j
k3ji
∑
+
−=
=′ ,
where j is the channel number and ( ) 0iK
k3j
k3ji
≡∑
+
−=
.
2) Definition of non-zero areas in the reduced
spectrum and identification of weight centers of these
areas with weight centers of peaks in the initial
spectrum.
3) Generation for each peak p in S’ a Gauss-like
peak G(σp, hp) having dispersion σp and height hp.
Construction of a reduced Gaussian spectrum by
convolution with K:
( ) ( ) ( )iKi;h,GjG
k3j
k3ji
pp∑
+
−=
=′ σ .
At this stage the initial values for peak dispersions are
assumed to be equal for all peaks in the spectrum and
equal to a value of dispersion in a calibration spectrum
obtained by using standard radioactive sources.
4) Minimization of function (G’-S’)2 for each peak p
with respect to the parameters σp and hp by the Newton's
method (see, for example, [5]). Minimization procedure
is fulfilled for three points, which are at the edges and in
the weight center of the peak non-zero area found on the
step 2.
5) Values σp and hp found on the step 4 are taken as
previous characteristics of the peaks and used for
definition of 3σ-limits in S. If the boundaries of
neighbor peaks are overlapped then peak groups are
formed. Then these peaks are copied to separate buffer
spectra and common boundaries of these buffers are
marked.
6) Subtraction of a background from S. When this
procedure is performed the background under peak and/or
peak groups is approximated by the linear function and
written to the separate buffer spectrum F.
7) Area of overlapping for peak groups is fixed. In
this region the peaks are approximated by a Gauss
function with σp and hp found on the step 4.
Deconvolution of peaks in the overlapping areas is
made as it is described in [2].
8) Definition of sums Ap under peaks, positions Xp of
weight centers and dispersions ∆p in the initial
spectrum.
9) Definition of the statistical importance of found
peaks by a criterion Ap>Fp
1/2, where Fp is the sum of
background counts under peak p which is calculated by
using the background buffer spectrum F defined on the
step 6. If such peak does not satisfy to this criterion then
it is erased from the initial spectrum. In the case when
this peak was marked as a member of a peak group then
the steps 1-7 are repeated for this part of the initial
spectrum.
10) Calculation of statistical errors connected with
definition of Ap, Xp and ∆p.
As we said above, the most acceptable magnitude of
k is equal to a value of dispersion of calibration peaks.
Note that the algorithm will work in that case when
calibration data are absent at all. In this case the initial
value of k can be set arbitrary and on the step 4 that
values of dispersions σp will be found which minimizes
the function (G’-S’)2. If one takes into account that
values of peak dispersions found on the step 4 are used
only as intermediate results, and the true values are
defined on the step 8, it is possible to tell that the
processing of spectra by the algorithm described does
not require special calibration measurements.
The program developed was used for processing
spectral data obtained in investigating the CXR's
properties during the run period at the 40-MeV linear
electron accelerator LUE-40 (NSC KIPT). In these
measurements we used a 5-mm thick Si(Li) solid-state
detector having energy resolution of 350 eV for
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2001, № 1.
Series: Nuclear Physics Investigations (37), p. 69-70.
69
13.7 keV line of a source 241Am. Fig. 1 shows three
radiation spectra, which were obtained during the
experiments with a 54 µm thick germanium crystal [4].
These spectra demonstrate the features of work of the
processing program.
In Fig. 1,a the CXR peak and the Kα peak of 44Ru,
which is an admixture element for the crystal used, are
placed as the isolated ones. Fig. 1,b illustrates that
situation when the peak group is fixed on the step 5. In
Fig. 1,c CXR peak covers the Kα peak completely. In
this case the peak is processed as an isolated one and to
define its A, X, ∆ and statistical errors connected with
these values the data for Kα peak obtained from spectra
like 1b are used. Fig. 2 shows the results of processing
for series of CXR spectra. This figure demonstrates the
dependence of CXR linewidths on position of the
weight centers on the energy scale.
The investigation carried out shows a high reliability
and productivity of the processing algorithm. It should be
noted that execution of step 4 requires not more than 10
iterations even if initial values of σp and hp were chosen
far from the real ones. The program was written using
Visual Basic 5.0, the target system is Windows 9x/NT.
The program has a convenient and understandable
user interface, which allows make changes of the
processing parameters easily. The program prints on the
screen and writes to a file the processing results and it
gives the information about the place and conditions at
which the spectrum was obtained.
There are several data formats, which are supported
by the program. These data can be presented as a
continuous table, which contains only count numbers, or
as the table, which contains channel numbers and count
numbers as well.
The evaluation version of the program is distributed
freely by the request.
200 250 300 350 400
0
100
200
a
αK
CXR peak
N
um
be
r o
f c
ou
nt
s
200 250 300 350 400
0
100
200
CXR peak
αK
b
N
um
be
r o
f c
ou
nt
s
200 250 300 350 400
0
100
200 CXR peakc
Channel number
N
um
be
r o
f c
ou
nt
s
Fig. 1. The series of CXR's spectra demonstrates the
different variants of processing: (a) - two isolated
peaks; (b) – peak group; (c) – complete covering
17 18 19 20 21 22 23 24
300
400
500
600
700
800
900
eV
∆,
Energy , keV
Fig. 2. Dependence of CXR peak dispersion on
energy as it was determined by processing the series of
spectral data
REFERENCES
1. PAW-CERN Program Library Long Writeup Q121.
CERN, Geneva, Switzerland, 1995.
2. H.W. Stockman. Microprocessor-based reduction of
gamma spectra: a fast method for deconvolution of
overlapped peaks // Nucl. Instr. and Meth., 1989, A274,
N1-2, p. 314-318.
3. J. Freudenberger, V.B. Gavrikov, M. Galeman et al.
Parametric X-ray radiation observed in diamond at
low electron energies // Phys. Rev. Lett. 1995, v. 74,
p. 2487-2490.
4. V.B. Gavrikov, V.P. Likhachev, M.N. Martins,
V.A. Romanov. Features of spectral-angular
distribution of coherent X-radiation // Brazilian
Journal of Physics. 1999, v. 29, p. 516-521.
5. J.E. Dennis, R.B. Schnabel. Numerical methods for
unconstrained optimization and nonlinear equations.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey,
1983.
70
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
PACS: 29.85.+c.
References
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