Quick algorithms for realtime discrimination of neutrons and gamma rays
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Abstract
Several new methods for the digital discrimination of neutrons and gammarays in a mixed radiation field are presented. The methods introduced discriminate neutrons and gamma rays successfully in the digital domain. They are mathematically simple and exploit samples during the life time of the pulse, hence appropriate for field measurements. All these methods are applied to a set of mixed neutron and photon signals from a stilbene scintillator and their discrimination qualities are compared.
Keywords
Gamma detection Neutron detection Particle identification methodsIntroduction
The range of applications of neutron detectors grows fast. Nowadays, neutron detectors are used for neutron imaging techniques, nuclear research, nuclear medicine applications, and safety issues, and their usage spans on various branches of science including nuclear physics, biology, geology, and medicine. The main problem in neutron detection is the discrimination of neutrons from the background gamma rays. Fast neutrons produce recoil protons whose detection is the most common method to detect neutrons. Organic scintillators are widely used to detect these recoil protons. Fast neutrons in organic scintillators produce recoil protons through (n, p) elastic scattering and energy of a recoil proton at the highest level is equal to the energy of the neutron [1].
Among organic scintillators, stilbene and NE213 come with some advantages 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 NE213 scintillators produce very good results using pulse shape discrimination (PSD) methods.
 1.
Risetime inspection;
 2.
Zerocrossing method;
 3.
Charge comparison.
In this paper, we introduce several discrimination methods and compare their separation qualities. These proposed methods are categorized into four groups: distancebased methods, areabased methods, anglebased methods, and some other simple mathbased methods. To obtain the sampled data of mixed neutron and gammaray pulses, we use two differentlyfeatured digitizers (explained in Sect. 2) which differ mainly in their sampling rate and output quantization level resolution. Doing so, we could find the effect of resolution and sampling frequency of the digitizers on the quality of the discrimination result for each method discussed in this article. 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 gamma rays and some neutrons.
Experimental setup
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 \(k\varOmega \) was used. A preamplifier matched it to the coaxial cable whose characteristic impedance was 50 \(\varOmega \). 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 \(\varOmega \), 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 8bit resolution and set at 1 and 2 GS/s, and Acqiris DC440 with 12bit resolution and set at 250 and 420 MS/s. While realtime 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.
Distancebased methods
In this section, we propose several quick algorithms which are based on the distances between points on the curves of the signals and/or points on the axes of the coordination system. Such methods do not have complexity and run during the life time of the signals. One popular distancebased method is risetime technique. In the following subsection, we review and study this method and point out the problems with it. Then, in the rest of this section, we introduce our novel methods for a higher quality discrimination.
Classic risetime technique
The risetime technique, [5], [6], integrates the light pulse (e.g., of the PMT anode), and then measures the time at which this integral reaches a certain fraction of its maximum amplitude. The light output of a heavily ionizing particle, which in \(n/\gamma \)ray discrimination is proton (neutron scatter interaction), has long tail; hence, the time at which this fraction is reached is longer than that of an electron (gamma ray interaction) [2]. Therefore, if the measured rise time is higher than a specific threshold, the signal is attributed to a neutron, otherwise it is attributed to a photon.
Since the pulses from the stilbene scintillator have fast rise and decay times, it is better to set the threshold level percentage as minimal as the maximum noise amplitude of the pulse baseline signal. This gives more room for the pulses to rise and decay, and increases the difference in measured times for neutron and photon signals. Hence, the pulses are better spread at the final plot resulting in a better discrimination.
DP210 digitizer (8bit resolution, 1 GS/s)
The data obtained at 1 GHz sampling rate and recorded at 8bit resolution contains some level of noise which should be filtered out. Our experiments show that using a 5point moving averager removes the noise without any significant data loss. It is worth noting that data filtering is always needed, even with the lowest rate of data sampling. The higher the sampling rate is, the more level of noise reduction is required. With DP210 digitizer, while the sampling rate is high, the resolution is evidently too low to be able to discriminate the two radiation types efficiently.
The FoMs of “RiseTime” method for various low threshold levels, when DP210 digitizer (with 8bit resolution) is used at 1 GS/s
Threshold level  0.01  0.02  0.03  0.04  0.05  0.06  0.07 

FoM  N/A  0.78  N/A  N/A  0.98  0.98  N/A 
One solution for the problems mentioned above is to set the threshold level to higher values, typically over 10 %. However, in general, for the threshold levels higher than 10 %, the figure of merit starts decreasing, specially when the sampling frequency is low. Therefore, the quality of discrimination will not be satisfactory at higher levels. In Sect. 3.2, we propose a simple novel method to resolve this problem.
DP210 digitizer (8bit resolution, 2 GS/s)
The FoMs of “RiseTime” method for various low threshold levels, when DP210 digitizer is used at 2 GS/s
Threshold level  0.01  0.02  0.03  0.04  0.05  0.06  0.07 

FoM  N/A  N/A  N/A  N/A  1.04  0.85  N/A 
DC440 digitizer (12bit resolution, 250 MS/s)
The FoMs of “RiseTime” method for various low threshold levels, when DC440 digitizer (with 12bit resolution) is used at 250 MS/s
Threshold level  0.01  0.02  0.03  0.04  0.05  0.06  0.07 

FoM  N/A  N/A  N/A  N/A  1.18  0.76  N/A 
DC440 digitizer (12bit resolution, 420 MS/s)
The FoMs of “RiseTime” method for various low threshold levels, when DC440 digitizer (with 12bit resolution) is used at 420 MS/s
Threshold level  0.01  0.02  0.03  0.04  0.05  0.06  0.07 

FoM  N/A  N/A  N/A  N/A  1.42  0.85  N/A 
Generalized risedecay method
In the preceding method, the best threshold level for discrimination varies from one set of data to another and could be found by trial and error. In general, this threshold depends on the maximum magnitude of the baseline noise and also the amplitude over which the longest difference between the two pulse types exists. The best level is dependent on several factors including the physical material used, environment, and the settings of the detectors.
The FoMs obtained when using “Generalized RiseDecay” method on the data captured by digitizers with different resolutions and sampling rates
Digitizer  8bit, 1 GS  8bit, 2 GS  12bit, 250 MS  12bit, 420 MS 

FoM  1.26  1.20  1.16  1.24 
Basic amplitude difference
The FoMs of “Basic Amplitude Difference” method for digitizers with different resolutions and sampling rates
Digitizer  8bit, 1 GS  8bit, 2 GS  12bit, 250 MS  12bit, 420 MS 

FoM  0.83  0.85  0.95  0.99 
Unlike the risetime method in which moving the threshold level even in small steps could result in ambiguous or nonqualified discrimination, here in this method, the time range within which the curve values can be compared and still give acceptable results is wider. However, the FoMs obtained are less than the ones in risetime method, as Table 6 shows. In the following section, we try to improve this simple method.
Generalized amplitude difference method
The FoMs of “Generalized Amplitude Difference” method for digitizers with different resolutions and sampling rates
Digitizer  8bit, 1 GS  8bit, 2 GS  12bit, 250 MS  12bit, 420 MS 

FoM  0.99  0.93  0.94  1.09 
Two dimensional method
The FoMs of “Two Dimensional” method for digitizers with different resolutions and sampling rates
Digitizer  8bit, 1 GS  8bit, 2 GS  12bit, 250 MS  12bit, 420 MS 

FoM  1.01  1.03  0.94  1.10 
Distance on trailing edge
Exploiting the curve of a pulse in both coordinates of time and amplitude provides an efficient result. In preceding section, we used such a method for discrimination. An ideal approach which captures a large difference between the two radiation types is to cross a straight line, with a positive slope, to the trailing edge of the pulse curve, such that the two intersections occur within its low energy segment. The distance between the two crossing points would be an efficient discrimination factor. However, finding this line with positive slope should be done with trial and error, and once a fixed line is found, there is always the possibility of facing a pulse which does not cross the line at any point. Therefore, this is not considered a solid method.
The FoMs of “Distance on Trailing Edge” method for digitizers with different resolutions and sampling rates
Digitizer  8bit, 1 GS  8bit, 2 GS  12bit, 250 MS  12bit, 420 MS 

FoM  1.18  1.73  N/A  N/A 
The FoMs of revised “Distance on Trailing Edge” method for digitizers with different resolutions and sampling rates
Digitizer  8bit, 1 GS  8bit, 2 GS  12bit, 250 MS  12bit, 420 MS 

FoM  1.18  1.07  N/A  1.13 
Areabased methods
Numerical integration within trailing edge
FoMs of “Integration” method for the pulses obtained from the digitizer DP210 (8bit, 1 GS/s), when the area is bounded by 2 % level A (in Fig. 11) and by various level B percentages as shown in the Table
Peak  90 %  80 %  70 %  60 %  50 %  40 %  30 %  20 %  10 %  

FoM  0.94  1.00  1.05  1.08  1.13  1.11  1.20  1.21  1.23  1.15 
FoMs of “Integration” method for the pulses obtained from various digitizers, when the area is bounded by 2 % level A (in Fig. 11) and by 20 % level B
Digitizer  8bit, 2 GS  12bit, 250 MS  12bit, 420 MS 

FoM  1.21  1.10  1.22 
Anglebased methods
Another efficient approach to discriminating neutron and photon pulses is use of angles in the measurements. Anglebased methods prove to be more sensitive to the differences between pulse types. The vertex of an angle can easily be placed at the best point on the curve coordinate system to provide us with high quality discrimination. Discrimination quality of anglebased methods are easily affected by the curve smoothing approach, hence, filtering of the signals should be done properly.
Based on time difference (horizontal difference)
FoMs of “AngleBased” method (horizontal difference) for the pulses obtained from various digitizers
Digitizer  8bit, 1 GS  8bit, 2 GS  12bit, 250 MS  12bit, 420 MS 

FoM  1.16  1.11  1.25  1.39 
Based on energy difference (vertical difference)
FoMs of “AngleBased” method (vertical difference) for the pulses obtained from various digitizers
Digitizer  8bit, 1 GS  8bit, 2 GS  12bit, 250 MS  12bit, 420 MS 

FoM  0.88  0.92  1.06  1.34 
Other simple methods
“Mean vs. standard deviation” method
Analyzing the features of neutron and photon signals reveals that the plot of mean vs. standard deviation (std.), or mean vs. variance (var.), of the mixed pulses could be used to provide an excellent discrimination factor. While both of these methods provide decent discrimination results, the pulses of the two radiation types on the mean vs. var. plot are lined up in a curved fashion, while on mean vs. std. plot, they are grouped in two straight lines, as shown in Fig. 14. Therefore, our focus in this section is on the latter one.
 1.
Normalization of the pulses is not required;
 2.
No noise filtering is necessary, since mean and std. both contain average filtering properties;
 3.
Mean and std. can be processed quickly using running statistics while receiving every new sample from the digitizer, without requiring all the samples to be involved in each new calculation. This feature makes mean vs. std. method ideal for realtime processing.
FoMs of “Mean vs. Std.” method for the pulses obtained from various digitizers
Digitizer  8bit, 1 GS  8bit, 2 GS  12bit, 250 MS  12bit, 420 MS 

FoM  1.13  1.10  1.15  1.11 
Application of FFT method
 1.
Hamming window is applied to the said segment of the normalized pulse;
 2.
Mean of the windowed curve is subtracted from every point;
 3.
The signal is padded with enough number of zeros to make the total number of points a power of two;
 4.
FFT is taken.
In Step 1, the Hamming window is used because it is raised on a pedestal. This property of Hamming window helps retain the sloped shape of the cuts of the two radiation types (red segment in Fig. 15) as much as possible. As we will explain, this sloped shape helps exploit the differences between the radiation types.
 1.
It is simple. Even with low number of points in FFT, this method works;
 2.
The amplitude of only two bins is enough for the discrimination. Therefore, there is no need for fullspectrum FFT calculation. Employing methods like Goertzel algorithm is enough to do the required measurements while keeping the process simple.
In Table 16, the FoMs for 12bit resolution data are obtained using the method explained above, i.e., the slope of the line connecting the bins \(N/21\) and \(N/2\). A 64point FFT is used for the data obtained using the DC440 digitizer with 12bit resolution and at 420 MS/s, and a 32bit FFT is used for the data obtained using the same digitizer but at 250 MS/s. As explained before, while this mirror image of the spectra in the higher frequency region is an easy approach to distinguishing neutrons and photons, this property cannot be used for the data obtained using digitizers featuring lowerresolution, e.g., 8 bits. For lowresolution data, the mirror image does not occur consistently with neutrons and photons. In highresolution data, even the differences in lowfrequency region can be easily used to discriminate the pulses, as Fig. 18 illustrates, but in lowresolution data, this difference is not enough for proper discrimination.
FoMs of the pulses obtained from various digitizers, applying FFT method
Digitizer  8bit, 1 GS  8bit, 2 GS  12bit, 250 MS  12bit, 420 MS 

FoM  N/A  N/A  0.89  1.00 
Discrimination using variable window
According to Eq. 5, those parts of the neutron and photon signals that differ most will have greater weights and the similar parts will have negligible weights. The similar segments could have weights with large absolute values when they are very close to zero; but according to Eq. 6, the final effect is minimal. Since the leading edges and the endtail segments of neutrons and gammarays have almost the same shape, there will be insignificant weights or effects for corresponding points when these segments are included. However this minimal improvement of the discrimination caused by these segments will help us better identify the particles in low energy region. Inclusion of these parts is directly related to the capabilities of the hardware at hand. Omitting these segments will have the benefit of fewer number of multiplications (based on Eq. 6), but a slight decrease in the quality of the results. For this work, the area of interest starts from the point where the leading edge hits the 1 % threshold level and the end point is a constant number of samples after this starting point for all signals, such that this interval covers a signal as much as possible.
FoM and counts of the pulses obtained from DC440 digitizer
Data format  FoM  Neutron counts  Photon counts 

12bit, 420 MS/s  1.20  9149  90851 
FoMs and counts of the pulses obtained from DC440 and DP210 digitizers under different sampling rates
Data format  FoM  Neutron counts  Photon counts 

12bit, 250 MS/s  1.13  8807  91193 
8bit, 1 GS/s  1.12  9725  90275 
8bit, 2 GS/s  1.04  9204  90796 
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 [10]. Therefore, the minimum necessary sampling frequency for neutron and photon signals is about 200 MS/s. The exact impact of the sampling rate on a specific separation method will depend on how the method functions. The separation method could mainly rely on the time difference, energylevel difference, or both time and energylevel differences of neutron and photon pulses, resulting in respectively high, low, and average impact of sampling rate on the separation quality. The estimation of exact effect of sampling rate on the FoM of a discrimination technique can be involved.
The techniques presented in this article are all computationally simple; they exploit samples as early as possible in the life of the signals. This characteristic has several advantages. First, it helps alleviate pulse pileup situation. This situation arises due to the random nature of the radiation, where a second event commonly occurs before the pulse from a previous event is completely in the output. This may cause false record of the second pulse’s energy levels. Since almost all the methods discussed in this article are fast, i.e., they try to detect the characteristics of either pulse type early in the lifetime of a pulse, there is less pulse pileup problem when applying these methods. Second, typical embedded system technologies could be easily used for realization due to the simplicity of these methods. Third, in many industrial applications, neutron/gamma discrimination is required to be done in realtime fashion. Discrimination of the pulses through simple methods which exploit timedomain data (or quick algorithms in frequency domain) brings about quickness needed for realtime operations.
FoMs of “PGA” method for the pulses obtained from various digitizers
Digitizer  8bit, 1 GS  8bit, 2 GS  12bit, 250 MS  12bit, 420 MS 

FoM  0.88  0.91  0.94  1.00 
Conclusion
In this article, we introduced several novel quick algorithms to discriminate the neutron and photon pulses captured in a mixed environment. These methods are appropriate for online measurements. Two digitizers, each featuring a different resolution and each set at two different sampling rates, were used to observe the reaction of each method to the data sampling conditions.
We categorized our discrimination techniques according to the type of measurement used to differentiate the neutron pulses from the photon ones. In general, in order to do the discrimination, the methods in each category could exploit the difference between neutrons and photons in their timing, or in amplitude, or both. In “DistanceBased Methods,” all these three cases were practiced separately. In “AreaBased Methods,” we only considered the experiment exploiting both differences in time and amplitude.
In “AngleBased Methods,” we either exploited the difference in time, or energy, but not both. However, it is possible to make a combination of these methods, e.g., by addition of the angles generated by each method and use it as the discrimination factor, hence obtaining a better separation of the pulses. However, the FoMs of each method, either based on the horizontal difference or vertical, were efficient enough to stop short of more processing. The timebased method works for both low and high resolution data, and the energybased method works for high resolution data.
Three other successful methods were also introduced. “Mean vs. Standard Deviation” method provides a high quality discrimination, almost irrespective of the resolution and sampling rate used to sample data. The “FFT” method, however, is promising only for the data recorded with high resolution. Finally, counting/discriminating using “Variable Window” always performs efficiently.

Digitizer with high resolution (but not necessarily with high sampling rate): “Anglebased methods” (Sect. 5);

Digitizer with high sampling rate (but not necessarily with high resolution): “Distance on trailing edge method” (Sect. 3.6);

Digitizer with neither high resolution nor high sampling rate: “Generalized risedecay method” (Sect. 3.2), “Areabased method” (Sect. 4), and “Mean vs. std. method” (Sect. 6.1).
Notes
Acknowledgments
This work is supported by Technology Agency of the Czech Republic under contract No. TA01011383/2011
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