Neutron/Gamma-Ray Discrimination through
Measures of Fit
Moslem Amiri, V´aclav Pˇrenosil, and Frantiˇsek Cvachovec
Abstract—Statistical tests and their underlying measures of fit
can be utilized to separate neutron/gamma-ray pulses in a mixed
radiation field. In this article, first the application of a sample statistical
test is explained. Fit measurement-based methods require
true pulse shapes to be used as reference for discrimination. This
requirement makes practical implementation of these methods
difficult; typically another discrimination approach should be
employed to capture samples of neutrons and gamma-rays before
running the fit-based technique. In this article, we also propose
a technique to eliminate this requirement. These approaches are
applied to several sets of mixed neutron and gamma-ray pulses
obtained through different digitizers using stilbene scintillator in
order to analyze them and measure their discrimination quality.
Index Terms—Counter/discriminator, statistical test, measures
of fit, neutron spectroscopy, organic scintillator.
I. INTRODUCTION
ORGANIC scintillation detectors are widely used for neutron
detection and spectroscopy. The primary reaction
producing neutron field and scattering reactions of neutrons
with materials in the environment lead to the production of γray
as a background radiation. The main problem in neutron
detection is the discrimination of neutrons from the γ-rays. A
composite curve often comprises a fast and a slow component
of scintillation. The long-lived slow component often reveals
the nature of the particle striking the detector. This fact
is usually used to separate different kinds of particles; this
process is called pulse shape discrimination (PSD) [1]. PSD
techniques are mainly used to discriminate neutrons from the
γ-rays.
Among organic scintillators, stilbene and NE-213 are favored
for neutron spectroscopy purposes; they have rather
low light output per unit energy, but this light output induced
by charged protons can be easily distinguished from
electrons/photons. Hence, stilbene and NE-213 scintillators
produce very good results using PSD methods.
Time-domain PSD methods are not computationally intensive,
and hence are suitable for real-time applications.
Classically, following analog PSD techniques were most often
used for n/γ-ray discrimination [2]:
1) rise-time inspection;
Manuscript received April 6, 2015. This work was supported by Technology
Agency of the Czech Republic under contract No. TA01011383/2011.
M. Amiri is with the Faculty of Informatics, Masaryk University, Botanicka
68a, 602 00 Brno, Czech Republic (e-mail: amiri@mail.muni.cz).
V. Prenosil is with the Faculty of Informatics, Masaryk University, Botanicka
68a, 602 00 Brno, Czech Republic (e-mail: prenosil@fi.muni.cz).
F. Cvachovec is with the Faculty of Military Technology, University of
Defence, Kounicova 156/65, 662 10 Brno, Czech Republic (e-mail: fran-
tisek.cvachovec@unob.cz).
2) zero-crossing method;
3) charge comparison.
Although analog techniques make acceptable n/γ-ray discrimination,
availability of precise and fast digitizers and
various PSD algorithms have made it possible to do a better
discrimination of these radiations digitally. Among digital PSD
methods, pulse rise-time algorithm and charge comparison are
probably the most favorable ones.
Measures of fit of statistical tests can be easily used to
discriminate neutrons and γ-rays. The underlying operations
in these tests are generally the same. In this article, the
application of a statistical test, namely Pearson’s chi-squared
test, is utilized to separate n/γ-ray pulses in a mixed radiation
field. Since fit measurement-based methods require
two reference pulse shapes to be preliminarily available for
discrimination, an update to the original implementation is
introduced later in this article to eliminate this requirement.
To obtain the sampled data of mixed neutron and γ-ray pulses,
two differently-featured digitizers (explained in Section II) are
used which differ mainly in their sampling rate and output
quantization level resolution. Doing so, the effect of resolution
and sampling frequency of the digitizers on the quality of the
discrimination result for the methods discussed in this article
could be found. Every experiment is carried out under the
same experimental conditions, using 100,000 pulses of mixed
neutron and photon signals. For this work, the field consists
of mostly γ-rays and some neutrons.
A comparison among various techniques, applied to data
obtained from the different digitizer types and settings, is
done by using the Figure of Merit (FoM) for the n/γ-ray
discrimination, defined as:
FoM =
S
FWHMn + FWHMγ
(1)
where S is the separation between the peaks of the two events,
FWHMγ is the full-width half-maximum (FWHM) of the
spread of events classified as γ-rays and FWHMn is the
FWHM of the spread in the neutron peak [3]. FWHMs are
calculated using the Gaussian fits to the neutron and γ-ray
events on experimental distribution plot.
II. EXPERIMENTAL SETUP
For this work, stilbene scintillation detector was used with
45x45 crystal, and the neutron-gamma radiation source used
was 252Cf(sf). A typical scintillation detector consists of a
scintillator and a photomultiplier. The latter is employed to
change weak light signals impinging to photocathode (generated
by the scintillator) into electric impulses. We used the
photomultiplier RCA7265 [4] throughout these experiments.
DETECTOR
Preamplifier
A/D
digitizer
Fig. 1. Block diagram of a digital two-parameter analyzer.
0 20 40 60 80 100
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
Time (ns)
Normalizedamplitude
Neutron
Photon
Fig. 2. Comparison of a sample smoothed neutron with a sample smoothed
photon. These signals are obtained from the stilbene scintillator.
The block diagram of our digital apparatus is shown in Fig.
1.
A preamplifier is selected so as to match the detector output
impedance. Two variants of the anode load resistance were
tested in conjunction with the organic scintillation detectors.
In the first variant, a load resistance of 40 kΩ was used. A
preamplifier matched it to the coaxial cable whose characteristic
impedance was 50 Ω. In this case, the different waveforms
of the neutron and photon pulses can be detected in the voltage
pulse leading edge. If the magnitude of the load resistance is
selected to be close to the characteristic impedance of the
coaxial cable, which is 50 Ω, the different shapes of the
neutron/photon pulses will appear to take effect during the
decay time. In this case, no preamplifier is necessary. The
latter option was employed here.
Two commercially available Agilent digitizers were used to
digitize the output pulses: Acqiris DP210 with 8-bit resolution
and set at 1 and 2 GS/s, and Acqiris DC440 with 12-bit
resolution and set at 250 and 420 MS/s. While real-time
digitizers are also employed in industry today, we used these
specific commercial digitizers to study the effects of their
various data resolution and sampling frequency features on
digital processing.
III. NEUTRON AND PHOTON SIGNALS
A sample smoothed neutron is compared with a sample
smoothed photon pulse in Fig. 2. These signals are obtained
from the stilbene scintillator. As seen in this Figure, these signals
are composed of a leading and a trailing edge. The leading
edges could not be exploited for discrimination purposes. On
the other hand, the trailing edge of the neutron signal has
higher rise time than that of the photon signal. This property
could be used to separate these two radiations.
An innovative discrimination approach is to remove the similar
segments of the two signal types and apply the technique
only to the differing segments.
0 10 20 30 40 50
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
Discrete−time index
Normalizedamplitude
Neutron
Photon
Fig. 3. Segments of neutron and γ-ray true pulse shapes, obtained by
averaging multiple normalized neutron and γ-ray pulses. The original pulses
are obtained from DC440 digitizer (12-bit resolution, 420 MS/s). The same
segment of every unknown pulse from the data set will be used for the
measurements.
IV. MEASURES OF FIT
Measures of fit of statistical tests can be employed to
discriminate neutrons and γ-rays. The underlying operations
in these tests are generally the same. In [5], [6], a similar
approach, called ”model pulse algorithm”, is adopted. In the
following, we propose a simpler and more practical approach
to separating radiations.
First, we construct two normalized reference pulse shapes,
called true pulse shapes, one for neutrons and the other for γrays.
The γ-ray true pulse shape can be obtained by averaging
some normalized signals captured from different pure γray
sources, and the neutron true pulse shape is obtained
by averaging some normalized neutron pulses captured by
discrimination through some method, e.g. integration method
(the latter approach can be used to build the γ-ray true
pulse shape too). For this work, the starting point of the two
normalized true pulse shapes is where the amplitude of the
leading edge is 10% fraction of peak-amplitude, and the end
point is some specific time after the starting point such that this
interval includes the differing tail segment between neutrons
and γ-rays. The same approach used to cut a segment from
the true pulse shapes will also be used to cut a segment from
each normalized unknown pulse from a mixed n/γ-ray field.
Although the starting point could be set to be the peak of
a pulse since the leading edges of neutron and γ-ray pulses
almost map on each other, the inclusion of the leading edge
(from 10% level to the peak) will make the calculations more
precise. This segment is shown in Fig. 3, and used throughout
our experiments.
Second, a statistical test is applied to separate n/γ-ray pulses
in a mixed radiation field. In this article, Pearson’s chi-squared
test is utilized as an example statistical test. By applying
the test, two values are obtained by measuring the fit of the
captured pulse and the two true pulse shapes (χ2
n, χ2
γ). The
measurements are done only within a specific segment of the
pulses and the true pulse shapes, as explained above. The lower
resulting value assigns the particle type. This approach can be
extended to the other statistical tests available. The distribution
of the (χ2
n, χ2
γ) values provides an excellent discrimination of
neutrons and γ-rays.
The equation to implement Pearson’s chi-squared test for
−100 0 100 200 300 400
0
500
1000
1500
2000
2500
3000
Discrimination value
Counts
Fig. 4. Discrimination of γ-ray and neutron signals, applying the statistical
test approach. The pulses are obtained using DP210 digitizer (8-bit resolution,
1 GS/s).
TABLE I
FOMS AND COUNTS OF THE PULSES OBTAINED FROM DC440 AND DP210
DIGITIZERS UNDER DIFFERENT SAMPLING RATES. STATISTICAL TEST
APPROACH IS APPLIED TO THE DATA.
Data format FoM
Neutron
counts
Photon
counts
12-bit, 250 MS/s 1.10 9876 90124
12-bit, 420 MS/s 1.02 9795 90205
8-bit, 1 GS/s 1.02 10076 89924
8-bit, 2 GS/s 1.09 9920 90080
n/γ-ray discrimination is:
χ2
=
n
i=1
(Oi − Ei)2
Ei
(2)
where Oi is the observed value and Ei is the expected value.
For discrimination application, Oi and Ei are the corresponding
points in the sequences of captured pulse and the true
pulse shapes respectively. Two χ2
values are calculated; one
between the input pulse and the neutron true pulse (χ2
n), and
the other between the input pulse and the γ-ray true pulse
(χ2
γ). The smaller value between these two will determine the
input pulse type. Hence this method could be used to count the
number of pulses from each category. The subtraction of the
two resulting χ2
values for each input pulse could be used to
calculate the FoM for that set of pulse data. This subtraction
will scatter neutrons and γ-rays on two different sides of the
zero base line of the plot. Figure 4 illustrates the discrimination
plot for the case of DP210 digitizer (8-bit resolution) with
1 GS/s sampling rate. As seen in this Figure, neutrons have
positive and γ-rays have negative discrimination values in this
experiment.
FoMs and n/γ-ray counts for various data sets with different
resolutions and frequency rates are shown in Tab. I. The results
are solid; this method discriminates well irrespective of the
digitizer features.
V. IMPROVED ALGORITHM
In the preceding technique, multiple detected neutrons and
γ-rays are needed to build the fixed true pulse shapes to be
used throughout the experiment. This requires the application
of another discrimination technique prior to the statistical test
in order to build the true pulse shapes. It is possible to build the
true pulse shapes without the preliminary separation technique
application, as will be explained in this section.
−100 0 100 200 300 400
0
500
1000
1500
2000
2500
3000
3500
Discrimination value
Counts
Fig. 5. Discrimination of γ-ray and neutron signals, applying the improved
statistical test approach. The pulses are obtained using DP210 digitizer (8-bit
resolution, 1 GS/s).
A simple method to build the two reference pulses is to pick
two random pulses (e.g. the first two pulses at the beginning
of the experiment) regarding each as representing a true pulse
shape. The identity of these pulses are unknown and they
may be even of the same type. The statistical test technique
is applied to the rest of the pulses, using the two selected
reference pulses. Every input pulse is categorized under one of
the reference pulses which produces the lower resulting value,
and the reference pulse is updated with that input pulse. Using
this strategy, one reference sequence will be gradually moved
toward the neutron and the other toward a γ-ray pulse shape.
Instead of the initial random selection of the two reference
pulses, a better method is to average multiple random pulses
and build up two new sequences by roughly shaping the
resulting averaged sequence, once as neutron and once as γray
(it is not necessary to be precise). Then the statistical
test approach is applied to every pulse, using the two rough
references. The references are updated as the experiment goes
on.
Using either of the methods explained above in this section,
the pulses will be divided and grouped with either of the
two reference sequences. If not detected, at the end of the
experiment, when the reference pulses are completely refined
and shaped, a simple test will reveal the identity of the two
reference sequences, hence the identity of the pulses grouped
with each reference pulse. For example, since the reference
and input pulses are normalized throughout the experiment, if
the samples of each reference pulse are summed up, the one
with the lower sum will be γ-ray and the other one will be
neutron. Fig. 5 illustrates the experimental distribution plot of
neutrons and γ-rays for the data obtained from DP210 digitizer
with 8-bit resolution and set at 1 GS/s frequency rate, when
this method is applied.
FoMs and n/γ-ray counts for various data sets with different
resolutions and frequency rates are shown in Tab. II. The same
data sets used for the experiments of Section IV are used
here for comparison purposes. Although this method does not
require the true pulse shapes prior to the experiment, it does
not produce acceptable FoMs or accurate pulse counts. The
lowest discrimination quality and the most inaccurate pulse
count is when the sampling rate of the digitizer is low.
TABLE II
FOMS AND COUNTS OF THE PULSES OBTAINED FROM DC440 AND DP210
DIGITIZERS UNDER DIFFERENT SAMPLING RATES. IMPROVED
STATISTICAL TEST APPROACH IS APPLIED TO THE DATA.
Data format FoM
Neutron
counts
Photon
counts
12-bit, 250 MS/s 0.78 22780 77220
12-bit, 420 MS/s 1.03 9496 90504
8-bit, 1 GS/s 0.98 9817 90183
8-bit, 2 GS/s 0.84 10289 89711
VI. DISCUSSION
Two important factors affecting the FoM of a discrimination
method are resolution and sampling rate of the digitizer.
According to Nyquist criterion, the sampling rate must be
greater than twice the bandwidth of continuous digitizer input
signal. The FFT of the recorded neutron and photon signals
indicates frequency components up to 100 MHz [7]. Therefore,
the minimum necessary sampling frequency for neutron and
photon signals is about 200 MS/s. The exact impact of the
sampling rate on the separation quality of a specific method
depends on how the method functions, and estimation of
this effect can be involved. For the approaches introduced in
this article, as Tabs. I and II show, increasing from the low
sampling rate of 250 MHz (which is close to the minimum
200 MHz required) to 420 MHz or increasing from the high
sampling rate of 1 GHz to 2 GHz does not necessarily improve
the FoM.
The factor with a greater impact on discrimination quality is
digitizer resolution. The process of converting a discrete-time
continuous-amplitude signal into a digital signal by expressing
each sample value as a finite number of digits is called
quantization. The resolution (or quantization step size) is the
distance between two successive quantization levels. The error
introduced in representing the continuous-valued signal by a
finite set of discrete value levels is called quantization error
or quantization noise. The quality of the digitizer output could
be measured by signal-to-quantization noise ratio (SQNR).
Since quantization errors of neutron and photon signals are
almost uniformly distributed over the quantization interval,
the following well-known equation [8] reliably estimates the
quality of a b-bit digitizer output:
SQNR(dB) = 1.76 + 6.02b (3)
Eq. 3 implies that SQNR increases approximately 6 dB for
every bit added to the digitizer word length. This relationship
gives the number of bits required by an application to assure
a given signal-to-noise ratio.
In order to verify the performance of the methods introduced
in this article, we apply PGA method to the same pulse data
sets as used for the methods in this paper. PGA method,
introduced in [3], is recognized as an efficient n/γ-ray discrimination
method with a high FoM. The slower decay of the light
function of a scintillator for a neutron interaction than that for
a γ-ray interaction is exploited in this method. The gradient
between the peak amplitude and the amplitude a specified time
after the peak amplitude (called the discrimination amplitude)
on the trailing edge of the pulses are compared and used
0 20 40 60 80 100
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
Time (ns)
Normalizedamplitude
Neutron
Photon
constant time
later
(t
p
, y
p
)
(td
, yd
)
Fig. 6. The points on smoothed neutron and photon signals used in PGA
discrimination method.
TABLE III
FOMS OF PGA METHOD FOR THE PULSES OBTAINED FROM VARIOUS
DIGITIZERS.
Digitizer 8-bit, 1 GS 8-bit, 2 GS 12-bit, 250 MS 12-bit, 420 MS
FoM 0.88 0.91 0.94 1.00
500 550 600 650 700
0
1000
2000
3000
4000
5000
6000
7000
8000
Discrimination valueCounts
Fig. 7. Discrimination of photon and neutron signals, applying PGA method.
The pulses are obtained using DC440 digitizer (12-bit resolution, 420 MS/s).
as the discrimination factor. Fig. 6 illustrates the peak and
discrimination amplitudes on neutron and photon signals. The
gradient is calculated using
m =
∆y
∆t
=
(yp − yd)
(tp − td)
(4)
where m, yp, yd, tp, and td are the gradient, the peak amplitude
(which is a constant for normalized pulses), the discrimination
amplitude, the time of peak amplitude occurrence, and the
time of discrimination amplitude occurrence, respectively. For
this work, we used some training pulses to locate the best
discrimination amplitude, which occurred about 36 ns after
the peak of the pulse. In general, the optimal timing for the
discrimination amplitude which makes the highest difference
between the two radiation types is dependent on the scintillator
properties and also on the PMT. The FoMs obtained are
listed in Tab. III. A comparison shows that the novel methods
introduced here are either better or at least have the same
discrimination quality as the PGA method does. Fig. 7 shows
the best discrimination plot obtained by PGA method.
VII. CONCLUSION
In this article, we first introduced n/γ-ray discrimination
through measures of fit, particularly using Pearson’s chisquared
test. This approach counts and discriminates the pulses
in a mixed environment very efficiently, however, it requires
sample neutron and γ-ray pulses in advance of the experiment
run to build the true pulse shapes. This requirement leads to
the employment of another technique prior to the statistical
test method to provide proper reference sequences. Since
this may not be practically acceptable, an improvement to
the original statistical test method is made in this article
to build the true pulse shapes during run time. The true
pulse shapes are gradually updated and used as the reference
throughout the experiment. Two digitizers, each featuring a
different resolution and each set at two different sampling
rates, were used to observe the reaction of the methods to
the data sampling conditions. The original approach (requiring
true pulse shapes prior to the experiment) provides promising
results while the improved approach is inefficient specially
when applied to the data sampled at low rates.
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