2.1. Charge comparison method

The CCM is based on comparing the long and short integrals over different scales of one pulse. The long integral is a summation of the entire pulse samples, while the short integral is a summation of several samples near the maximum sample. In this paper, the optimum short integral is the summation of 16 samples: 5 samples before and 10 samples after the maximum sample. The regions for the long and short integrals are illustrated in Fig. 1. The short integral corresponds to the region of the fast component, whilst the long integral represents the sum of the fast and slow components. The γ-induced events, with larger fast/slow component ratios than the α-induced events, should have larger short integrals for long integrals in the same length as those of the α-induced events.

2.2. Pulse peak analysis

The PPA is based on comparing the long integral and amplitude of the maximum sample, i.e. peak of the pulse. As shown in Fig.1, for the same peak amplitudes, γ-induced pulses have smaller long integrals than α-induced pulses, due to larger fast/slow component ratios in BaF₂ scintillation.

2.3. Pulse gradient analysis

The PGA is based on comparing the long integral and the amplitude difference between the peak and the sample occurring at a defined time interval after the peak. The amplitude difference is often referred as the discrimination gradient, and the specific sample’s amplitude is known as the discrimination amplitude. The time interval was 5 ns in this work, considering different decay times of the fast and slow components, and timing property of the photomultiplier tube (PMT). The decay time of the digitized fast component was 3–4 ns, therefore the discrimination amplitude mainly depends on the amplitude of the slow component, while the peak mainly depends on amplitude of the fast component. Due to the larger fast/slow component ratios, the γ-induced events have bigger discrimination gradients for long integrals in same length as those of α-induced events.

2.4. Finite impulse response filter comparison method (FCM)

Through frequency spectrum analysis, the fast components in BaF2 pulses correspond to higher frequencies, at about 100 MHz, whereas the slow components are mostly lower than 2 MHz in the frequency domain. The pulses from BaF2 crystal are processed by a FIR low-pass filter. A proper low-pass filter reduces the amplitude of fast component much more than that of the slow component. In this study, the passband frequency of 3 MHz was chosen for the filter after tests from 2 MHz to 100 MHz. The filter-output-amplitude/filter-input-amplitude ratio of a γ-induced event, owing to its greater fast/slow component ratio, should be smaller than that of an α-induced event. This ratio is called the FIR-Peak-Ratio.

2.5. Pulse information extraction

When sampling BaF2 scintillation signal, the data rate is extremely high in consideration of the high sampling rate and high event rate (~50–200 Hz, depending on the source activity). Instead of sending the raw pulse shapes (a 2080 bytes package for each pulse) and analyzing the pulses in a computer as in most prior works, bad pulse elimination and pulse information extraction are executed in field programmable gate array (FPGA), and the pulse information (a 32 bytes package for each pulse) are sent to a computer. This reduces the data transfer by 64 times. At the USB transfer rate of 20 MBps, the transmission time decrease to 1.6 µs from 100 µs, which tremendously reduces the dead time correspondingly.

After digitization of the pulse, a simple baseline restorer algorithm is applied. The baseline value is calculated as mean value of the first 16 samples, as shown in Fig.1, and subtracted from the whole pulse form. Then all the information needed for the four PSD methods are extracted from each pulse form, namely long integral, short integral, peak amplitude, discrimination gradient and filter-output-amplitude. Fig. 2 shows the flow of digital processing. Finally, together with packet flags, information of each pulse is sent to the computer through USB port as a 32 bytes package.

Fig. 2.Full-screen View

Digital signal processing flow chart.

3.1. Experimental set-up

In this work, a cylindrical BaF₂ crystal ofΦ5 cm × 3 cm was instrumented with a XP2020Q PMT, and a collimated ²²Na source was placed 5 cm apart from it. The PMT was biased at −1.8 kV, which was considerably lower than the maximum rating value (−2.6 kV). To verify the PSD algorithms, a NaI detector was placed opposite to BaF₂ detector for coincidence.

The PMT anodes were connected to inputs of a 2 Gsps fast sampling board based on a DRS4 chip^[12], the fourth version of Domino Ring Sampler (DRS) from Paul Scherrer Institute (PSI), Switzerland. The sampling board was capable of sampling 4 independent input channels of 1024-cell sampling depth, and with 300 MHz sine wave input, the signal-to-noise and distortion ratio (SINAD) of this sampling board reached 39.7dB, which corresponded to an effective number of bits (ENOB) of about 7 bits^[13]. Using this sampling board, we achieved 7.5% energy resolution of the full-energy peak of ²²Na at 1.275 MeV. A low-end FPGA from Xilinx Spartan-3 family (XC3S5000)^[14] was employed for digital signal processing on the sampling board. The experimental arrangement is shown schematically in Fig. 3.

Fig. 3.Full-screen View

Schematic diagram of the experimental set-up.

3.2. Results: Natural background

As previously mentioned, a characteristic of BaF2 crystals is the background caused by radium impurities constituted by α-particles, γ-rays and electrons. Thus, we used the internal natural radioactivity to calibrate digital pulse sampling and α/γ discrimination algorithms, and to determine the discrimination threshold. Only the BaF2 detector was used in this part.

After extracting the pulse information, the results are presented in a 2-D scatter plot of the variables corresponded to each PSD algorithm, as shown in Fig. 4. Fig.4 (a) shows the scatter plot of the CCM algorithm. The short integrals for 170000 events plotted against the long integrals: γ-rays are identified as points above the discrimination threshold (the black solid line), while α-particles are identified as points lay below it. Figs.4(b) and 4(c) are scatter plots of PPA and PGA. Particularly, in Fig.4 (d), for the FCM algorithm, with the FIR-peak-ratio being in the ordinate, and the ratio of short integral/long integral in the abscissa, γ-rays are identified as points below the discrimination threshold, while α-particles are identified as points above it. Furthermore, to evaluate the separation of γ-ray and α-particle regions, in Fig.5 the identification spectra are obtained by calculating the distance to the discrimination threshold line in the scatter plots for each event. The spectra are fitted with Gauss function shown as the red curves, and the full width at half maximum (FWHM) of the γ-peak as well as the α-peak in the spectra are compared in Table 1. More intuitively, figure-of-merit (FOM) values for the four methods can be calculated by Eq. (1), as shown in Table 1:

Fig. 4.Full-screen View

Scatter plots of the PSD algorithms. The black solid line indicates the discriminate threshold between γ-rays and α-particles.

Fig. 5.Full-screen View

Identifying the spectra by distance from the discrimination threshold using the PSD algorithms. The red curves are Gauss fitting results.

3.3. Results: ²²Na γ-source

Due to the two-photon radiation of 22Na, the coincidence events of BaF2 detector and NaI detector can be identified as γ-ray events except for α-induced random coincidence events. Fig.6 shows distribution histograms of the distances to the discrimination threshold line of 20000 coincidence events from BaF2 detector, correspond to each of the four PSD algorithms. Most of the coincidence events are identified as γ-rays for all algorithms. False Alarm Rate (FAR) is defined as the proportion of coincidence events identified as α-particles, including α-induced random coincidences and wrong results of corresponding algorithms. The FARs of each algorithm are shown in Table 1.

Fig. 6.Full-screen View

Distribution histograms of the distances to discrimination threshold of coincidence events, using the PSD algorithms.

3.4. Method comparison

Performance of the four PSD algorithms is compared in Table 1. Little variations are seen in the FOMs and FARs of the algorithms. FOM indicates the performance of separation, and the PPA and PGA algorithm are slightly better than the other two. According to the consistency of FARs for different algorithms, most of the misidentified events are likely belong to α-induced random coincidence events, being a fixed proportion among the whole events.

FPGA resource occupancy is also a considerable issue. With the Xilinx Spartan-3 family (XC3S5000) FPGA, for CCM, PPA and PGA algorithms, 10% LUTs (6831 of 66560), and 13% Slices (4389 of 33280) were used. And for FCM algorithm, due to the use of the FIR filter, 59% LUTs (39545 of 66560), and 85% Slices (28618 of 33280) were used. Except for FCM algorithm, other algorithms show small FPGA resource utilization, considering that Spartan-3 family FPGA is low-cost and has small chip size.

In summary, FCM achieves similar performance but costs much more FPGA logical resources than the other algorithms. Comprehensively consider the performance and FPGA usage, PGA turns out the best of all the four algorithms.