Pulse shape discrimination characteristics of stilbene crystal, pure and 6Li loaded plastic scintillators for a high resolution coded-aperture neutron imager

Pulse shape discrimination performances of single stilbene crystal, pure plastic and 6Li loaded plastic scintillators have been compared. Three pulse shape discrimination algorithms have been tested for each scintillator sample, assessing their quality of neutron/gamma separation. Additionally, the digital implementation feasibility of each algorithm in a real-time embedded system was evaluated. Considering the pixelated architecture of the coded-aperture imaging system, a reliable method of simultaneous multi-channel neutron/gamma discrimination was sought, accounting for the short data analysis window available for each individual channel. In this study, each scintillator sample was irradiated with a 252Cf neutron source and a bespoke digitiser system was used to collect the data allowing detailed offline examination of the sampled pulses. The figure-of-merit was utilised to compare the discrimination quality of the collected events with respect to various discrimination algorithms. Single stilbene crystal presents superior neutron/gamma separation performance when compared to the plastic scintillator samples.


Introduction
Pulse shape discrimination (PSD) is a well-established method of separating fast neutron and gamma-ray interactions within an organic scintillation medium. The method is based on the difference in the decay time of fluorescence emitted within an organic scintillator as a result of an interaction between the ionising particle and the scintillant. The fluorescence decay time observed for heavy ionising particles, such as protons, is longer when compared to electrons [1]. Fast neutrons and gamma-ray photons interact with an organic scintillant predominantly through elastic scattering with a proton and Compton scattering, respectively. Consequently, the fluorescence decay rate exhibited by recoil protons and recoil electrons (Compton scattering) can be compared to infer the origin of the interaction [2].
Fluorescence emission is linked to the kinetic energy of the incoming particle. When it interacts with the organic molecules, the particle excites π-electrons within the structure of the scintillation medium [2]. Thus, the π-electrons are raised to one of the exited electronic states. Depending on -1 -the initial energy of the radiating particle, it can be lifted to a singlet S S or triplet T S state. Prompt fluorescence (also known as fast component of the scintillation process) is emitted when the particle in the S S state returns to the ground electronic state. The lifetime of a S S state is measured in nanoseconds and is short when compared to that of a T S state, which can be up to 1 millisecond. The longer de-excitation time of the T S state is often associated with the π-electron transferring to one of S S states before returning to the ground state. Hence, fluorescence emission is delayed resulting in the occurrence of the slow component of the scintillation process.
The fraction of light in the slow component of the scintillation can be used to infer the origin of the interacting particle. The decay rate of the slow component varies for the incoming particles of different nature but equal kinetic energy. When heavy particles interact with the scintillation medium, they demonstrate greater rate of energy loss. Therefore, the fluorescence decay time of recoil protons (resulting from neutron interactions) is longer when compared to the fluorescence decay time of recoil electrons (resulting from gamma-ray photon interactions) [2]. Thus, the difference in the fluorescence decay rate forms a basis for neutron/gamma PSD techniques in organic scintillators. Fluorescence decay characteristics for a theoretical neutron and a gamma-ray are shown in figure 1. Various PSD techniques have been developed in analogue and digital domains to separate neutron events from gamma-rays effectively and efficiently. When the research into neutron/gamma discrimination was at its origins, the techniques developed were intended for liquid scintillator detectors [1,2,4,5]. As a result, many liquid scintillators have been developed and accurately characterised [6][7][8][9][10]. However, due to flammable properties of some liquid scintillators and their susceptibility to leaks, these were not suitable for many industrial applications. An alternative in a form of solid scintillation detectors was perceived inferior to liquid counterparts with regards to neutron/gamma separation (plastic scintillators) and light output (organic crystals) [2]. Recent progress into techniques of developing solid organic scintillators shows that their PSD performance improved significantly, with stilbene crystal aspiring to outper--2 -
In this paper, a succinct review of selected PSD methods is presented, aiming to identify the most suitable candidate for a real-time scintillation based coded-aperture neutron imaging system. Three chosen techniques are then experimentally tested and the results compared for three different scintillator types. Additionally, performance assessment of the PSD method and scintillator combinations was examined. Online data processing was adopted in this study for the investigation of the three selected methods. Computational complexity of each method was also considered with regards to the real-time operation feasibility. A brief review of the existing organic scintillator characterisation methods, which was performed prior to the characterisation work undertaken in this study, is also presented.

Analogue PSD methods
Discovery of the pulse shape variation between neutron and gamma-ray induced incidents triggered a long search for the most effective separation method. Around the time of its discovery, PSD was dominated by two algorithms implemented in the analogue domain: zero-crossing and charge comparison method (CCM). The former method transforms the photo-detector output pulse into bipolar signal. The time between the trigger and the zero-crossing point is then used as benchmark for neutron and gamma discrimination [17]. Although less often used nowadays, mainly due to the implementation practicality of the digital approaches, the zero-crossing method shows very good PSD performance when implemented in organic scintillator studies [18,19].
The latter method is based on the ratio between the charge integrated over the duration of the entire pulse (long integral) and the charge integrated over the tail of the pulse (short integral). Analogue CCM (also known as charge integration method) was first described by Brooks and utilised various RC circuit combinations to perform the integration of the entire pulse and its tail [1]. A comprehensive investigation of these two analogue methods has been performed by Nakhostin [17].

Digital charge comparison method
The advent of digital electronics enabled complicated analogue circuits to be replaced by a few lines of a computer code. Therefore, both analogue methods were successfully employed in the digital domain, with CCM becoming one of the most powerful PSD algorithms [20]. Recent study, which compared PSD performance of the digital CCM and the analogue zero-crossing method, reports that the estimated figure-of-merit (FOM) for the digital CCM is on average 20% greater than that obtained for the analogue zero crossing method [21]. However, similar investigation conducted over two decades earlier indicates superior performance of the zero-crossing method over the digital CCM which illustrates the progress of the digital approaches [22].
The arrival of fast high resolution analogue-to-digital converters (ADC) enabled integration to be calculated as an area under the digitised pulse. There are three integration algorithms that can be easily employed: running sum, trapezoidal rule and Simpson's rule. The running sum is the simplest algorithm, where the integral is calculated as a sum of the digitised samples. The trapezoidal rule -3 -estimates the area between two digitised samples by taking an average of the two adjacent samples, whereas the Simpson's rule approximates the integral by calculating quadratic polynomials for specific intervals. Since previous research suggests that all three integration algorithms provide identical PSD results when used in the digital CCM implementation, the running sum algorithm was used in this research [17].

Simplified digital charge comparison
Different decay rates of the slow scintillation components for neutron and gamma-ray events define the separation capability of an organic scintillator. The simplified digital charge comparison (SDCC) method focuses on the period between the peak amplitude sample and the final sample of the digitised signal. As the difference in the decay rate between the gamma-ray photon and neutron induced pulses can be observed some time after the peak, an interval was identified when the difference is most prominent [23]. The start sample and the end sample of the interval are defined by a and b parameters in eq. (2.1), respectively. These parameters specify the interval of the short integral.
Generally, a parameter corresponds to three-sixteenths and b to one half of the pulse length where the peak amplitude is considered as the first sample. The discrimination parameter D is then plotted against the magnitude of the peak amplitude to separate the particles. Preceding work advocates a superior discrimination performance of this method in comparison to other digital discrimination algorithms [24].

Pulse gradient analysis
Digital signal processing, implemented using advanced field-programmable gate arrays (FPGA) and high sampling rate ADCs, provided a way of performing PSD faster than it was ever possible in the analogue domain. However, the aforementioned CCM and SDCC algorithms require the whole pulse to be digitised before the discrimination can be performed. Pulse Gradient Analysis (PGA) can be performed with only two samples taken at the early stages of a scintillation pulse [26]. The magnitudes of the peak amplitude and the sample amplitude (known as the discrimination amplitude), recorded a specific time period after the peak amplitude, are plotted against each other to separate neutrons from gamma-rays. Since only the magnitudes of the specific samples are considered the discrimination process can be completed faster in comparison to other methods. Hence, this method was successfully implemented in a multi-channel real-time Mixed Field Analyser (MFA) [27].

Other pulse shape discrimination methods
There exist other digital discrimination methods implemented in the time and frequency domains [28]. Generally, methods not mentioned in the previous sections require more complex and resources-exhausting analysis of the digitised pulses. Some algorithms, such as Neutron Gamma Model Analysis (NGMA), compare digitised signals with neutron and gamma pulses modelled prior to the analysis [24]. Such methods are not desirable for a high resolution real-time neutron imaging system where the discrimination results are to be fed to an image reconstruction algorithm.

Digitiser selection
The digital CCM is one of the most powerful and hence has become one of the most often utilised neutron/photon separation methods in organic scintillator characterisation studies. Due to clear advantages of the digital methods over the analogue counterparts, such as implementation practicality and performance superiority [21], the latter are only rarely used. Thus, an appropriate digitiser must be selected, so that the information contained in the analogue signal is truthfully transferred into the digital domain. Generally, the higher the sampling rate and the resolution of the digitiser's ADC, the more accurate the representation of the analogue signal. However, the ADC's resolution normally decreases as the sampling rate increases.
Previous study performed by Flaska et al. [29] reports that at least 250 MHz sampling frequency is required to obtain good PSD results. Nonetheless, another study, conducted two years after the study by Flaska, successfully carried out crystal scintillator characterisation using 14-bit resolution, 200 MSps digitiser [13]. A digitiser of equal resolution and even lower sampling frequency (150 MSps) was effectively utilised to perform PSD for a neutron survey meter [30].

Performance assessment methods of organic scintillators
With the light output of the scintillator detector adequately represented in the digital domain, further analysis of the pulse shape can be performed. Since liquid PSD scintillation detectors have become a preferred choice in many nuclear facilities, there exist various performance assessment criteria which can be easily adopted for solid organic scintillators. Furthermore, with the continuous development of the new solid organic scintillation materials, they are often contrasted with liquid organic scintillators [16,31].
The most important characteristic of any PSD scintillator is the FOM. It is utilised to compare the separation quality, based on the number of detected particles of different types. The FOM can be obtained by plotting a histogram of the ratio of the maximum and the minimum amplitudes of the digitised pulses [2,28]. Another approach exploits the concept of discrimination line where the histogram is plotted as a function of the orthogonal distance from each particle to the discrimination line [24].
A decent quality PSD with a sufficiently good FOM enables further analysis of the identified particles. Based on the number of neutron events and gamma-ray photons accepted by the digitiser system, it may be feasible to identify the differences between radioactive isotopes detected [32]. One of such methods is R-factor, which computes the ratio of neutron and gamma-ray interactions within the scintillator. The FOM, as well as the R-factor, are described in detail in the following sections. These characteristics are used to perform quality assessment of the chosen samples with regards to PSD.

Experimental method
Three different organic solid scintillator samples were in turn irradiated with 252 Cf (half-life of 2.64 years) source located at Lancaster University, Lancaster, U.K. A pure PSD plastic scintillator sample (25 mm diameter, 25 mm thick) and a 6 Li loaded PSD plastic scintillator sample (40 mm -5 -diameter, 25 mm thick) were both provided by the Lawrence Livermore Laboratory (LLNL), U.S.A. -denoted by the LLNL numbers 5706 and 9023, respectively. A single stilbene crystal (20 mm diameter, 20 mm thick) was obtained from Inrad Optics [33]. The experimental set-up is shown in figure 2 where the radioactive source was in a water tank. The detector front was placed 15 cm away from the source and 10 cm away from Pb shielding. The Pb shielding was utilised to reduce the number of gamma-rays reaching the scintillator detector.
The back of each scintillator sample was covered with EJ-510 reflective coating. Each sample was then coupled to an ET Enterprises 9107B photomultiplier tube (PMT) with EJ-550 silicone grease, used to maximise the light transmission properties between scintillator and the PMT. The PMT was supplied in a B2/RFI housing with a 637BFP tapered distribution voltage divider. The PMT module supplied by ET Enterprises was enclosed in a light-proof tube. Depending on the scintillator type, the positive high voltage supply connected to the cathode of the PMT was varied between 850 V and 900 V. The PMT anode was connected to a bespoke digitiser system which utilises a Analog Devices AD9254 150 MSps, 14-bit amplitude resolution ADC directly linked to a Altera Cyclone IV EP4CE115 FPGA. The system recorded 28 raw samples (taken approximately every 6.67 ns) per each triggered pulse. The registered data were transferred to a laptop running Linux via universal asynchronous receiver/transmitter (UART) configured to transfer data at 8 Mbits/s. The received data were further processed by a bespoke script developed in Python.

Results
Prior to PSD implementation each digitised pulse was run through a bespoke pulse pile-up rejection algorithm. The algorithm simply rejected any pulse where two peaks were detected. Since each scintillator sample was exposed to 252 Cf neutron field for approximately 1 hour, many thousands of pulses were collected, with the number of pulses accepted by the pulse pile-up rejection algorithm varying between approximately 60,000 and 80,000 pulses for the three samples tested.
Reconstructed analogue pulses are often affected by high frequency noise, which may lead to misclassification of a pulse when PSD is performed. Moving average filter was applied to each digitised pulse to smooth out the high frequency component [24]. Given the relatively low number of recorded samples per triggered pulse, a 7-point moving average filter was used with the digitised input samples placed symmetrically around the filtered output point. Thus, each filtered sample is replaced with an average, which leads to the 'raw' digitised samples being lost in the computation. Although the filter removes the 'raw' components from the signal to be discriminated, -6 -

JINST 12 P07023
reduction in the high frequency components in the processed signal results in lower neutron/gamma misclassification probability [25]. Following that, PSD was performed on each pulse using the methods specified earlier. For each method implemented, the neutron and the gamma-ray plumes were separated using a discrimination line (where possible) [34]. In each case, shown in figure 3 to figure 5, plume above the discrimination line is corresponding to neutrons and the plume below the line to gamma-rays.
Based on PSD results obtained for each scintillator sample, FOM was calculated (using (5.1) to compare their performance in particle separation. Peak separation in eq. (5.1) represents the difference between the peak distances from a normal distribution fitting of neutron and gamma-ray plumes; FWHM is the full-width at half-maximum for each particle distribution. Further, eq. (5.2) was utilised to calculate R-factor values. The R-factor is a ratio of the number of gamma-rays over the number of neutrons which is often utilised to quantify the gamma-ray rejection efficiency in neutron detectors. Results are presented in table 1 where Poisson approximation of the distribution was assumed to determine the corresponding uncertainty.

CCM implemented in the digital domain
Scatter plots of the short integral against the long integral for the three samples are shown in figure 3.
There is no discrimination line plotted for 6 Li loaded plastic scintillator sample, as there is no clear separation between fast neutrons and gamma-ray photons when irradiated with 252 Cf radioactive source. Hence, it was not possible to estimate the FOM for this scintillator sample. Estimated FOM values for the plastic scintillator sample and single stilbene crystal were 0.649 and 0.867, respectively. It can be clearly noticed that the stilbene crystal presents superior PSD performance when compared to the two plastic scintillation samples tested. Figure 4 shows scatter plots of PSD performed using SDDC method; in this case discrimination parameter D is plotted versus the peak amplitude. The results obtained show similar characteristics to those obtained with CCM algorithm. The FOM value for single stilbene crystal estimated at 1.033 was far higher than 0.761 obtained for the plastic scintillator sample. Similarly to the results of the PSD using CCM algorithm, SDDC method was also unsuccessful in discriminating between fast neutron events and gamma-ray photons in 6 Li loaded plastic scintillator.

PGA implemented in the digital domain
Results of PSD implemented using PGA method are shown in a form of scatter plots in figure 5 and they are comparable to those obtained using the other two methods. In this instance discrimination amplitude was plotted against peak amplitude, with the estimated FOM values of 0.631 for the plastic scintillator sample and 0.823 for single stilbene crystal. In the same way as for the CCM and SDDC algorithms, it was not possible to draw a discrimination line between fast neutrons and gamma-rays for 6 Li loaded plastic scintillator.

Separation quality assessment
Distribution of each point from the discrimination line plots are shown in figure 6 for all scintillator/PSD method combinations. The distribution plots are corresponding to the cases with the highest FOM value estimated for each of the scintillator samples. Based on the distributions presented, a good agreement can be observed across the three methods tested with regards to PSD performance of the two scintillation samples compared. Statistical analysis of the distributions shows that 95% confidence level in the results can be assumed for stilbene crystal using CCM and SDCC. The data generated for these two methods was further validated by chi-square test against the normal distribution hypothesis. It follows that 95% of the detected particles will be correctly discriminated in this specific experimental scenario. For the remaining scintillator/PSD method combinations, a clear separation can only be observed within one standard deviation of the mean. Hence, the resulting confidence interval is considerably smaller than for the aforementioned cases. Although the stilbene PGA combination still claims reasonably good separation (approximately 90% confidence level), the plastic scintillator Peak amplitude (a.u.) Peak amplitude (a.u.) separation performance is significantly inferior as evidenced by the results on the left in figure 6. Although chi-square normality test validated the normal hypothesis for all the distribution fits considered within their respective confidence intervals, it must be noted that the test was performed against single Gaussian distributions (separately for each neutron and gamma-ray distributions). This was necessary to ensure that FWHM correctly represents the fluctuations of Gaussian distribution. Neutron and gamma-ray distribution fit lines were only plotted to the zero point (discrimination line), in order to clearly show the difference in misclassification quality between stilbene and plastic scintillator samples. A general consistency across the three separation methods can be found, as presented in table 1, with the single stilbene crystal providing results of supreme quality when compared to the pure plastic scintillator sample. Since there is a clearer separation between the neutron and gamma-ray normal distribution fits in figure 6(b), (d) and (f) than in figure 6(a), (c) and (e), there is a lower chance of particle misclassification for the single stilbene crystal than for the pure plastic scintillator.
Optimisation of the estimated FOM values was performed, as shown in figure 7. The length of the short integral was varied for CCM method by adjusting the starting sample number. Samples investigated range between sample number 4 and sample number 12, with the peak amplitude being considered as sample number 1. The optimal sample numbers for the pure plastic and the stilbene crystal scintillators were 10 and 8, as presented in figure 7(a) and figure 7(b), respectively. These sample numbers correspond to 66.70 and 53.36 ns after the sample of the peak amplitude. With the peak amplitude usually occurring within first 20 ns of the pulse, the shortest window inspected was approximately 86.71 ns. This specific interval was considered because outside this range no clear separation between neutron and gamma-ray plumes was observed. The length of the short integral was also varied for SDCC method where the value of parameter a was adjusted. In this case the optimal values were found approximately 53.36 and 46.69 ns (sample numbers 8 and 7) after the peak amplitude for the pure plastic and stilbene crystal scintillators, respectively. Similarly to CCM algorithm, sample numbers outside the range presented in figure 7(c) and figure 7(d) were excluded because of the two particle plumes not being distinguishable.
The discrimination amplitude sample number was inspected for PGA algorithm. Since PGA method only considers magnitudes of two samples, there is no need to specify a window to be considered with reference to the peak amplitude. Both scintillators exhibit the optimal PSD -10 -

Discussion
Three solid organic scintillation samples were exposed to 252 Cf fission source, and the collected data discriminated between neutrons and gamma-rays using three different PSD techniques. Results obtained are in general agreement across the three algorithms implemented, with single stilbene crystal showing superior neutron/gamma separation performance. All three algorithms failed to separate fast neutrons from gamma-rays within 6 Li loaded plastic scintillator, whereas the FOM values estimated for the pure plastic scintillator suggest relatively good discrimination performance. This difference in discrimination quality is associated with the doping of the former, which enables neutrons thermalized within the organic detector to be captured by the high neutron capture crosssection 6 Li.
Since the neutron energy spectrum of 252 Cf averages at approximately 2.1 MeV, a large number of neutrons emitted would fall below the 1 MeV threshold. Previous studies support the claim that PSD performance of organic plastic scintillators increases when exposed to higher energy neutron fields (> 1 MeV). When exposed to 241 AmBe neutron field 6 Li loaded plastic sample tested in this study performed considerably better in terms of fast neutrons and gamma separation [28]. Moreover, 252 Cf source at Lancaster University, U.K. is in a water tank, where neutrons are thermalized as a result of their interaction with H atoms. It can therefore be concluded that 6 Li loaded plastic can be beneficial for certain applications but neutron capture events are difficult to separate from gamma-ray photons in relatively lower energy fields, such as from a moderated 252 Cf source, as presented in this and previous studies [28].
R-factor measurements show reasonable consistency across the algorithms tested for the two scintillator samples, where neutron events and gamma-ray photons were successfully separated. However, the average R-factor value of approximately 1.098 is lower than the expected 2.118 (based on the average number of neutrons and gamma-rays per fission event of 3.767 and 7.980, respectively [35,36]). It is thought that the difference is associated with a Pb block, which was -12 -2017 JINST 12 P07023 -13 -used to reduce the number of gamma-rays reaching the detector, placed adjacent to the water tank, as shown in figure 2.
One of the aims of this study was to find a suitable scintillation material for a scintillator based coded-aperture neutron imager to potentially extend the neutron detection range. A preceding study identified single stilbene crystal as a suitable solution for the imaging system [37]. The results obtained not only do support the claim of the preceding study, but also show that neutrons and gamma-ray photons can be clearly separated within the stilbene crystal. As such, stilbene crystal can be perceived as an ideal candidate from the performance point of view for applications where neutron/gamma separation is required to extend to below the 1 MeV neutron energy threshold.
The FOM values obtained for CCM and PGA algorithms are comparable, whereas the FOM values estimated for SDDC method are significantly higher. These results are resembled most clearly in the scatter graph presented in figure 4(c), where the results of PSD performed using SDDC for the stilbene crystal are plotted. An evident separation between neutron and gamma-ray plumes enables a reduction in misclassification of particles which may sometimes occur in lower energy areas.
The neutron/photon misclassification problem in lower energy regions (< 1 MeV) for CCM has been thoroughly investigated. The method proposed by Polack et al. [38] enables misclassification reduction when there is a clear overlap of the neutron and gamma-ray plumes in the lower energy ranges. However, in this study there is a clear distinction between the two plumes for PSD using CCM for the stilbene crystal as shown in scatter plot in figure 3(c). Therefore, no further method of plume separation was sought. While SDCC method transpired to be the most effective, it is also the most computationally exhaustive which may be of concern for real-time applications. However, continuous advancement in the FPGA technology makes this matter a less prevailing factor.
It is worth noting that a relatively low speed digitiser (i.e. 150 MSps) was used throughout this research which could contribute to the misclassification of the digitised pulses. Prior study, which investigated the influence of the sampling properties on the PSD performance, claims that 250 MHz digitiser would be a sensible choice when good PSD performance is required [29]. Nonetheless, successfully implemented PSD is consistent with the claim of the preceding work where the same digitiser was tested with simulated neutron and gamma-ray pulses [39]. The digitiser was also utilised in a novel neutron survey meter, which further advocates the statement that good PSD results can be obtained with 150 MSps system [30].

Conclusion
As evidenced by the results of the three PSD methods, single stilbene crystal outperforms the plastic scintillators when neutron/gamma separation capabilities are considered. In spite of that, relatively large machining costs and fragility of stilbene (in comparison with plastics) hinder widespread adaptation of the single stilbene crystal scintillator in nuclear decommissioning applications. Plastic scintillators on the other hand, such as EJ-299-34 from Eljen Technology, are easily machined to build scintillator arrays as required for the coded-aperture imaging system described [40].
Although SDCC method exhibits the best FOM out of the three methods tested, its computational overhead, tested using online processing, may be too high for a real-time application. PGA method offers the fastest response out of the three algorithms tested. However, its estimated FOM -14 -is the lowest. Moreover, since it only considers values of the digitised pulse at two separate points, part of the information contained may be missed. This information may be crucial when the system is required to operate in multi-channel configuration, due to the levels of high frequency noise expected. Despite the highest error associated with its FOM results of neutron/gamma separation, using CCM presents a good compromise between the digital implementation difficulty and PSD performance for the application described in the paper.
Three digital methods were employed to compare neutron/gamma discrimination performance of the chosen solid organic scintillators. Observed consistency in PSD quality for the three methods tested can be discerned as a cross validation of the test dataset collected in this study. Furthermore, the results obtained in this work are consistent with the previous studies conducted with similar organic solid scintillators [11,31]. Hence, it can be surmised with a sufficient level of confidence that the results obtained represent a valid PSD performance of the tested samples.