A simplified approach to counting statistics with an imperfect pileup rejector

A simplified theoretical model is developed to predict counting statistics for a stationary Poisson processes passing through a spectrometer with pulse-pileup rejection. The model is applicable to digital counters used for spectrometry as well as set-ups utilising analogue electronics for pulse shaping and pileup rejection. In comparison with an existing model for a perfect pileup rejector, the new model addresses the common imperfection of having a finite time resolution of the fast channel, allowing quasi-coincident signals to pass through the pile-up rejector. From the Laplace transform of a simplified interval-density distribution, approximate expressions are derived for the throughput factor and the variance of the number of counted events. The results are compared with computer simulations of a cascade of extending dead time and subsequent pileup rejection. In addition, a rigorous throughput factor is derived from probabilistic reasoning, as well as an effective throughput factor for singular and coincident events.

POMME Stefaan;  PELCZAR Krzysztof; 

2024-11-22

ELSEVIER

JRC139359

1872-9576 (online),    0168-9002 (print),   

https://www.sciencedirect.com/science/article/pii/S0168900224009938?via%3Dihub,    https://publications.jrc.ec.europa.eu/repository/handle/JRC139359,   

10.1016/j.nima.2024.170067 (online),