Abstract
A photon counting process is a stochastic one, which is called a Homogeneous or a Non-homogeneous Poisson process, and the time intervals of transitions of quanta fluctuate with a certain statistical nature.
Consequently, if the time intervals of successive transitions of quanta are small enough, a photon counting system can not respond to these transitions because of its Dead Time.
The dead time causes the distribution of quanta counted in a certain time interval to deviate from that of incident photons. So statistical values evaluated from the counted distribution differ from the true ones.
In this paper, a fundamental analysis of the distribution of the waiting times is made in case that a photon counting system has a dead time which follows an arbitrary probability law. As a result of this analysis, statistical methods have been developed for deriving the distribution of the waiting times of counted quanta and the probability density function of the number of quanta counted in a certain time interval, in terms of the probability distribution of the dead times and that of the inter-arrival times of incident photons.
