Detector Deadtime Distortion in Counting Statistics and Deadtime Correction

Detector deadtime impact on counting statistics was investigated using our in-house simulation tool Pulse-WIZ. A thorough investigation on the quality of MATLAB's pseudo-random number was performed. The repeat frequency of MATLAB pseudo-random number generator EXPRND function is extremely high, 2¹⁹⁹³⁷ - 1. Testing of the function very faithfully predicted the theoretical values giving us confidence in the random number. For ideal non-paralyzable deadtime, there seems to be a saturation observable count rate for a given detector deadtime. For a deadtime of 140 µs the saturation point seems to be at 10,000 counts per second. Due to limited range of simulation true count rate the peaking point was not identified for higher deadtime values. For the simulated deadtime of 225 µs, both the skewness and kurtosis show a very good exponential fit against the true count rate. Fano factor on the other hand first increases to reach a maximum value before showing a rapid drop. The histogram inter-event gap also shows a profound effect of deadtime where all the events with gaps smaller than the deadtime are removed from the observed events. Moreover, the ideal exponential behavior is also degraded.