Temporal and spatial variance in pixelated counting detectors with dead time and retrigger capability

Abstract

In single particle counting detectors, the existence of dead time modifies the statistical distribution of the recorded counts in the time domain. In particular, for increasing incoming event rates it has a regularizing effect as by its nature it prevents events to be recorded within a certain time window after the last one occurred, with non-trivial consequences on the statistical moments of the counting process outcome. Moreover, spatial correlation between neighboring channels – e.g. in pixelated detectors – leads to additional effects on the ensemble properties. In this study we present the derivation of the exact expression of the temporal and spatial mean and variance for multi-channel particle counting systems equipped with retrigger capability, a feature that allows the system to work in non-paralyzable mode, and in presence of spatial cross-correlation among the channels. The analytical derivations are cross-validated with the help of Monte Carlo simulations. The case of non-ideal signals and the possibility to achieve sub-Poisson signal-to-noise ratios for increasing incoming rates are also discussed.