A Multiplexing Method for SiPM Readout with Pulse Shape Restoration Capability

Introduction: Various multiplexing methods for SiPM readout based on charge division circuits have been proposed. However, most multiplexing methods resulted in the loss of important information, such as the position of inter-crystal scattering and the variance of light distribution, because only a single interaction position is derived from the data set obtained with a single trigger. The variance of the light distribution can be estimated using the row/column sum method. However, this method still requires 2N readout channels for the N ´ N SiPM array. In this study, we propose a multiplexing method for SiPM readout using an artificial neural network and high pass filters, which can restore individual signals of SiPM channels from a single multiplexed signal. We expect that this method can be used to measure the 2D position of interaction, the identification of inter-crystal scattering, and the variance of light distribution with highly reduced readout channels.

Methods: In this pilot study, we designed and simulated a multiplexing circuit for four SiPM inputs. The signals from each SiPM channel were filtered by high pass filters with different time constants. High pass filtering with different time constants allows each channel output to have the unique shape required to restore each signal from multiplexed signals. Two summed signals, each of which is a signal summed before the buffers and a signal summed after the buffers, were recorded at a 1GHz sampling rate (1024 sampling points per signal) (Figure 1(a)). To find the optimal set of high pass filters, signals from an individual channel of a SiPM array were shaped with 207 high pass filters (Figure 1(b)). For accurate restoration, the filtered SiPM signals should have distinguishable shapes with small covariance between filtered signals. Therefore, we measured the CRLB value with the combination of all four out of the 207 filtered signals as a criterion to select the candidate for the experiment (Figure 2(a)). We selected 8 high pass filter sets, 4 with the lowest CRLB, 2 with the most concentrated CRLB, and randomly selected 2 with large CRLB (Figure 2(b)). We compared two different estimation methods: pseudo-inverse matrix (Figure 3(a)) and artificial neural network (Figure 3(b)). We measured and compared the energy histogram and the energy resolution with the true amplitude and the estimated amplitude of four filtered signals, respectively.

Results: The method using pseudo-inverse matrix resulted in poor estimation: In some cases, the amplitudes of the estimated signals were negative (Figure 4). The artificial neural network trained using a fidelity loss function with positive constraints on the output signal amplitude provided more accurate estimates. One of the filter sets with the lowest CRLB provided the best results, yielding the average R² value of 0.991 with the summed signals before the buffers and 0.992 after the buffers (Figure 5). Each time constant of high pass filters was sufficiently spread, so the filtered signals in each channel had distinguishable shapes (Figure 6(a)). The slope and y-intercept of the regression lines between the estimated amplitudes and the ground truth of all four channels were 1.00 ± 0.01 and 0.00 ± 0.01, respectively (Figure 6(b)). The energy resolution of the estimated amplitude ranged from 10 to 12% (Figure 6(c)). The energy histograms generated using the amplitude of the best-estimated signals were in good agreement with ground truth (Figure 6(d)).

Conclusions: In this study, we propose a new multiplexing method for SiPM readout which can restore individual signals using high pass filters and an artificial neural network. Several applications of this method are in progress, such as reducing readouts in the row/column sum method, inter-crystal scatter event identification, and light distribution variance estimation.

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