Exact forward photocounting distributions for a source of optical radiation with arbitrary statistics are obtained in the presence of photodetector dead time. In particular, we examine the counting and pulse-interval distributions that arise from amplitude-stabilized radiation, from chaotic radiation, and from a Van der Pol laser with arbitrary excitation. The exact dead-time-corrected Poisson distribution is graphically compared with a previous approximate result and with the uncorrected Poisson. Plots of the Bose-Einstein distribution clearly indicate the dramatic anti-bunching effects of the dead time in overcoming the inherent bunching of this distribution. A simplified approximate solution is also found for the Van der Pol laser above threshold; this result is similar to light from an amplitude-stabilized source incident on a photodetector with a gaussian-distributed dead time. Information about photodetector dead-time variation can therefore be obtained either by using an amplitude-stabilized source or by properly choosing system parameters such that irradiance fluctuations are averaged out.
B. I. Cantor and M. C. Teich, "Dead-time-corrected photocounting distributions for laser radiation," J. Opt. Soc. Am. 65, 786-791 (1975)