Effects of dead time and after-pulses in photon detector on measured statistics of stochastic radiation

摘要

Many physical experiments require analysis of the statistics of fluctuatingradiation. In the case of an ideal single-photon detector, the contribution ofphoton noise to the statistics of the registered signal has been thoroughlyexamined. However, practical photon counters have a dead time, leading tomiscounting of certain true events, and sometimes the counters generate falseafter-pulses. This study investigate the impact of these two effects, and it presents thetheoretical relations between the statistical moments of the radiation and theregistered counts while also accounting for dead time and the probability ofafter-pulses. Expressions for statistical moments of any order are obtained onthe basis of the generalized Poisson distribution (GPD). For counters withparalyzable dead time, alternative relations for the mean and variance arederived using generally accepted formulas. As an example, the measurements of stellar scintillation and the result ofsimple experiment are considered. The results of the experimental verificationof the theoretical expression confirm the need to account for the non-idealnature of detectors in almost all similar measurements.