A fast digital filter algorithm for gamma-ray spectroscopy with double-exponential decaying scintillators

Scintillators like CsI(Na), having double-exponential decay times, typically cannot be used in high-count rate applications due to the complicated pulse shapes created by the convolution of their light output decay curves with the decay constant of charge integrating preamplifiers. We present here a novel digital filtering algorithm that is capable of using CsI(Na) at input count rates exceeding 250 kcps, while still achieving good energy resolution. We used a 2.54 cm diameter and 2.54 cm long CsI(Na) crystal, whose scintillation light can be best described by a short component with a 550 ns decay time and a long component with a 4 μs decay time. The crystal was coupled to a 2.86 cm diameter photomultiplier tube. The digital filtering algorithm was implemented in XIA´s all-digital Polaris spectrometer, in which five running sums were captured from each digitized scintillation pulse and the Polaris´s on-board DSP read these sums and used a set of precomputed coefficients to reconstruct the pulse´s total light output as a measure of the deposited energy. The algorithm was tested at different input count rates, ranging from 19 kcps to 270 kcps using a 1 mCi ¹³⁷Cs source. The energy resolution (full-width at half-maximum) at 662 keV was 10.7% at 19 kcps and 11.7% at 270 kcps with a filter rise time of 1.0 μs, and improved to 7.0% and 8.4%, respectively, with a filter rise time of 3.2 μs. The energy peak shifted by less than 0.3% for input count rates below the maximum throughput point. Output count rates of 65.3 and 17.8 kcps were obtained with filter rise time of 1.0 and 3.2 μs, respectively, at an input count rate of 270 kcps. This algorithm can be easily adapted to other double-exponential decaying scintillators by changing the decay times used in the energy reconstruction formula.