Determination of the Statistical Properties of Light by Photodetectors with a Finite Dead Time

The problem of obtaining the probability density of the fluctuating light intensity from the knowledge of photocounting statistics, when the detectors have a finite dead time, is considered. The integral relation for the probability of registering $n$ photocounts in the time interval $T$ in the presence of a dead time $\tau$ is inverted, and an expression is obtained for the probability density of the fluctuating intensity of the incident light radiation. The method is illustrated with a few specific examples.