ABCD-Tool, a software suite for the analysisof a/b spectra from liquid scintillation counting
Romolo Remetti • Daniele Franci
Received: 21 November 2011 / Published online: 8 February 2012
� Akademiai Kiado, Budapest, Hungary 2012
Abstract This paper presents the alpha/beta complete
deconvolution tool (ABCD-Tool), a C?? application for
the analysis of spectra from liquid scintillation counting
(LSC) measurements. In addition to the basic algorithms
for standard gross alpha/beta analysis and the determina-
tion of the counting efficiency, the software implements a
recent unfolding technique based on Fourier transforms,
which gives precise and reliable results even in the case of
complex, strongly overlapping spectra. The application is
designed to be used with alpha/beta spectra generated from
Perkin Elmer Wallac Quantulus 1220. However, future
upgrades are scheduled in order to extend the compatibility
to spectra from other LSC instruments in commerce.
Keywords Liquid scintillation counting � Beta spectra �Deconvolution � Alpha/beta separation � Fourier transforms
Introduction
During the last decades, liquid scintillation counting (LSC)
has played a leading role in the field of radiometric
measurements for the characterization of nuclear wastes
produced by industrial facilities. In particular, it represents
the most reliable technique for quantitative determination of
hard to measure radionuclides (HTMR). These radionuclides
have the distinctive feature of being only a/b and low energy
X-rays emitters. For this reason, the traditional radiometric
approach based on c spectrometry is generally useless for
HTMR, while LSC technique provides reliable results [1].
The LSC technique is based on the counting of the light
pulses generated by a mix of the radioactive sample with a
scintillation cocktail, composed of an aromatic organic sol-
vent plus a fluorescent substance, commonly referred to as
scintillator. The scintillator converts the energy released by
charged particles into photons, which are detected with a
system of photomultipliers and then counted by a multi-
channel analyzer. The sample spectrum is finally recorded,
allowing for a rapid and precise determination of the sample
activity [2–4].
The LSC analysis of mixtures of different radionuclides
may result rather hard to perform, due to the presence of
wide, continuous b spectra, which extend from zero up to a
maximum energy characteristic of each radionuclide. In the
case of mix of several a/b emitters, the resulting spectrum
may be affected by significant overlap between the dif-
ferent shapes. In order to avoid expensive radiochemical
separation procedures, different techniques for analytical
deconvolution of LSC spectra have been proposed [5–13].
Recently, a very promising approach based on the use of
Fourier transforms has been presented by Remetti and
Sessa [14], leading to encouraging results.
This paper presents the ‘‘alpha/beta complete deconvo-
lution tool’’ (ABCD-Tool), a software suite oriented to the
analysis of a/b spectra. ABCD-Tool implements the
deconvolution technique discussed in [14], with some
additional features such as the algorithm for the self-choice
of the number of harmonics. In addition to this, ABCD-
Tool allows to perform standard gross a or b analysis and
the determination of the counting efficiency by means of
standard quench parameter [SQP(E)] method [15].
Alpha/beta complete deconvolution tool is a stand-alone
C?? application, running on Microsoft Windows operating
R. Remetti (&) � D. Franci
Department BASE—Basic and Applied Sciences
for Engineering, ‘‘Sapienza’’ University of Rome,
Via Antonio Scarpa 14, 00161 Rome, Italy
e-mail: [email protected]
123
J Radioanal Nucl Chem (2012) 292:1115–1122
DOI 10.1007/s10967-012-1664-7
systems. The software is designed for an optimal visualiza-
tion with a 1,200 9 800 screen resolution. It is founded on
ROOT libraries, the object-oriented framework for particle
physics data analysis developed at European Organization
for Nuclear Research (CERN) [16]. Currently, ABCD-Tool
is able to manage a/b spectra generated from Perkin Elmer
Wallac Quantulus 1220 only. Future upgrades are scheduled
in order to allow ABCD-Tool to analyze spectra from other
LSC instruments.
Software description
The main window of ABCD-Tool (Fig. 1) offers a rapid
access to all the software analysis routines:
• Gross a/b analysis, to determine the total activity in the
case of very simple spectra.
• Alpha/beta separation routine, based on pulse shape
analysis—PSA [17], a method to distinguish between aand b spectra based on the differences between the
pulse shapes. Spectral separation is performed by
Quantulus and the resulting spectra can be analyzed
with ABCD-Tool.
• Determination of counting efficiency, based on
SQP(E) method [15].
• Analytical deconvolution of complex spectra, using
Fourier transform method described in [14].
In the following a detailed description of the deconvo-
lution method is provided. Subsequently, a rapid overview
of the other ABCD-Tool features is presented.
Deconvolution method
Spectral deconvolution is carried out by loading a spectrum
from Quantulus file and specifying the correct multichan-
nel index (e.g., ‘‘11’’, ‘‘12’’, ‘‘21’’ or ‘‘22’’). A count-
per-minute versus channel histogram is shown in the upper-
left canvas (Fig. 2).
A Fourier series fitting is then performed by means of a
dedicated mask where the order of the series, e.g., the
number of harmonics (NH), and the start and stop channels
used for fitting can be defined. Instead of a manual search
with ‘‘Perform fit’’ button, an automatic search algorithm
for the optimal NH value can be invoked. This ‘‘Optimized
NH search’’ is particularly helpful in the case of complex
spectra with shapes strongly affected by quenching effects.
The automatic search algorithm is composed by the fol-
lowing steps:
1. Starting from an user-defined NH value, a 20 steps loop
is performed. For each step, NH is increased by one and
Fourier fit is computed. The procedure is iterated until
the summed squared fit deviation at the (n ? 1)th step
varies less than 5% with respect to the value at the nth
step, for the entire 20 steps loop. The summed squared
deviation is defined as:
S2 ¼X1;024
i¼1
FNHið Þ � c ið Þ½ �2 ð1Þ
where i runs over all the channels of the spectrum and
FNHið Þ and c(i) represent respectively the value of
Fourier fit and the histogram content corresponding to
the ith channel.
2. The algorithm comes back to the starting NH value and
performs a 5 steps loop. For each step, NH is decreased
by one and Fourier fit is computed. The procedure is
iterated until NH is equal to five, or until the value of
the penalty function at the (n - 1)th step is larger than
the value at the nth step, for the entire 5-steps loop.
The penalty function is defined as:
PF ¼ S2 �ffiffiffiffiffiffiffiNH
pð2Þ
3. For each NH, the value of penalty function is stored
(Fig. 3). The NH value that minimizes the penalty
function is chosen as optimal.
The lowermost part of the window is devoted to the
unfolding procedure. Users must enter nuclide name, the
composite channel range in which nuclide is defined
(e.g., [2,20] [ [753,952]) and the start/stop channel for
integral calculation. The resulting nuclide, obtained from an
interpolation through the cubic spline method, can beFig. 1 The main window of ABCD-Tool
1116 R. Remetti, D. Franci
123
checked using ‘‘Try it!’’ button: the lower-left canvas shows
the original spectrum with the deconvoluted nuclide super-
imposed, while the lower-right canvas shows the subtracted
residual spectrum. Moreover, the total cpm of deconvoluted
nuclide is shown in a dedicated text box. When users are
satisfied with the deconvolution results, the current nuclide
can be added to the list of identified nuclides using ‘‘Add to
the nuclide list’’ button.
At the end of the unfolding procedure, a complete result
summary can be printed using ‘‘Show summary’’ button
(Fig. 4). A pop-up canvas will show the experimental
spectrum together with Fourier fitting and all the decon-
voluted nuclides. In addition, a report file is created with
the most important information.
Another interesting feature of ABCD-Tool is the possi-
bility to export Fourier fit or deconvoluted nuclides into a
.001 file, which is the output format for Quantulus files and
the input format for ABCD-Tool.
Experimental tests
To test the capabilities of ABCD-Tool, three different
spectra have been resolved:
1. A mixture of about 12.5 kBq of 90Sr in secular
equilibrium with 90Y.
2. A mixture of about 12.5 kBq of 90Sr in secular
equilibrium with 90Y plus 1 kBq of 241Am.
3. A simulated spectrum, where three alpha peaks have
been added to the 12.5 kBq 90Sr plus 90Y mixture.
Sample 1 and 2 are the same already used in [14].
Fig. 2 Deconvolution window showing both the input spectrum and the results of unfolding procedure
Fig. 3 Penalty function as a function of the number of harmonics NH.
NH value corresponding to the minimum is chosen as optimal
ABCD-Tool, a software suite for the analysis of a/b spectra from liquid scintillation counting 1117
123
The first sample is fitted with 20 harmonics, in the range
[10,952]. 90Y is then identified in the range [2,21] [[753,952] and the residual spectrum is assigned to 90Sr. A
summary of unfolding procedure is presented in Fig. 5. The
integrals of the unfolded nuclides are:
– 743.432 cpm for 90Y
– 743.658 cpm for 90Sr
confirming the hypothesis of secular equilibrium.
The second sample is fitted with 52 harmonics, in the range
[35,952]. The mixture of 90Sr plus 90Y is identified and
unfolded in the range [30,665] [ [744,952] The residual
spectrum is assigned to 241Am (Fig. 6). In order to estimate the
individual contribution of 90Sr and 90Y, the alpha spectrum is
subtracted to the original one and the unfolding procedure is
repeated on beta mixture spectrum only. 90Y is identified in the
range [2,43] [ [749,941] and the residual spectrum is
assigned to 90Sr. The integrals of unfolded nuclides are:
– 755.238 cpm for 90Y
– 746.401 cpm for 90Sr
– 78.846 cpm for 241Am
The third sample is fitted with 58 harmonics, in the
range [10,952]. Following a similar approach as before,
beta mixture is unfolded in the range [50,370] [[445,665] [ [735,820] [ [885,960]. The residual spectrum
comprises all the alpha peaks (Fig. 7). Alpha peaks are
then separated, as shown in Fig. 8. 90Y is then identified, in
the range [2,49] [ [750,952] and the residual spectrum is
assigned to 90Sr. The integrals of unfolded nuclides are:
– 738.513 cpm for 90Y
– 739.063 cpm for 90Sr
– 51.347 cpm for alpha1
– 73.205 cpm for alpha2
Fig. 4 Summary from deconvolution procedure. Input spectrum with unfolded nuclides superimposed is shown. A report file with the most
important information is also printed
Fig. 5 Unfolding of the 90Sr ? 90Y mixture
1118 R. Remetti, D. Franci
123
– 46.903 cpm for alpha3
Secular equilibrium is still respected and the integral of
alpha peaks is in agreement with the simulated values
(alpha1 = 51.7, alpha2 = 63.5, alpha3 = 45.5). The larg-
est deviation from the simulated value is observed for
alpha2. A possible explanation is the strong influence of
both 90Y and 90Sr in the region of alpha3.
Standard gross alpha/beta analysis
In the case of simple spectra composed by only one nuclide
or many well separated nuclides, the traditional approach
of gross spectrum integral gives excellent results. For this
reason, ABCD-Tool implements a window devoted to
standard gross a/b analysis (Fig. 9). This routine is com-
posed by the following steps:
– Loading of the signal spectrum.
– Loading of the background spectrum.
– Definition of the region of interest (ROI) boundaries;
– Definition of counting efficiency.
– Drawing the spectra.
– Calculation of activity, uncertainty and MDA (if any
background had been loaded).
Alpha/beta separation based on PSA method
A distinctive feature of Wallac Quantulus is the possibility
to distinguish between a and b particle thanks to a dedi-
cated analysis of the pulse shapes. This technique is
referred to as PSA [17], it allows to separate a from bevents into their respective spectra within a mixed sample.
ABCD-Tool implements a window that fully exploits
Quantulus capabilities, providing a simple tool for ana-
lyzing mixed samples processed with PSA technique
(Fig. 10). This routine is composed by the following steps:
– Loading of the signal spectrum.
– Loading of the background spectrum.
– Definition of the appropriate multichannel for both aand b.
– Definition of the ROI boundaries.
– Definition of a and b spillover, i.e., the beta (alpha)
fraction wrongly identified as alpha (beta).
– Definition of a and b counting efficiency.
– Drawing the spectra.
– Calculation of activity, uncertainty and MDA (if any
background had been loaded) for both a and b spectra.
Fig. 6 Unfolding of the 90Sr ? 90Y ? 241Am mixture
Fig. 7 Alpha peaks from deconvolution of the 90Sr ? 90Y ? 3 a-
peaks mixture
Fig. 8 Unfolding of the 90Sr ? 90Y ? 3 a-peaks mixture
ABCD-Tool, a software suite for the analysis of a/b spectra from liquid scintillation counting 1119
123
Fig. 9 Window for standard gross a/b analysis
Fig. 10 Window for PSA-based a/b separation analysis
1120 R. Remetti, D. Franci
123
Determination of counting efficiency using
SQP(E) method
Quantulus is equipped with an external high-energy, low
activity external source of 152Eu used to determine the
SQP(E) of the analyzed sample. This approach [15] is one
of the most popular for the determination of counting
efficiency. For this purpose, set of primary standards with
different quenching level are commonly used to extrapo-
late an efficiency versus SQP(E) curve. In this way, the
calculation of SQP(E) index with the 152Eu source permits
to establish the correct value of counting efficiency to be
applied to the unknown sample. ABCD-Tool implements a
window for the determination of the calibration curve
(Fig. 11). Users can add the primary standard spectra,
declaring the reference activity and start/stop channel for
integral calculation. When the SQP(E) index of the ana-
lyzed sample is known, it can be inputted through a text
box. Otherwise, the 152Eu spectrum collected by Quant-
ulus can be loaded as input for the automatic calculation
of quenching index. Experimental points are then fitted
using a third-order polynomial and the counting efficiency
for the unknown sample is shown, together with the fit
parameters.
Conclusions
Alpha/beta complete deconvolution tool is a general pur-
pose software for analysis of LSC spectra from Perkin
Elmer Wallac Quantulus 1220. It is written in C?? using
ROOT libraries and runs on Microsoft Windows operating
systems. At the moment, it is highly recommended a screen
resolution of 1,200 9 800 for an optimal visualization.
Alpha/beta complete deconvolution tool implements the
deconvolution algorithm described in [14], which is based
on Fourier fitting of the experimental spectrum and an
unfolding technique of the single nuclide based on cubic
spline method. ABCD-Tool has been tested with complex
a/b mixed spectra, providing remarkable results.
In addition to this, ABCD-Tool is able to accomplish
other common tasks in LSC analysis such as gross count-
ing, a/b separation with PSA method and efficiency
determination with SQP(E) technique.
Further improvements are scheduled, in order to make
ABCD-Tool able to manage spectra also from the other
LSC instruments in commerce, and to make the visuali-
zation independent from the screen resolution. In addition,
conversion for the other operating systems is planned for
the near future.
Fig. 11 Window for the determination of counting efficiency with SQP(E) method
ABCD-Tool, a software suite for the analysis of a/b spectra from liquid scintillation counting 1121
123
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