Dead-time-modified photocount mean and variance for chaotic radiation

General expressions are obtained for the mean and variance of the number of events in a fixed but arbitrary sampling time for a nonparalyzable dead-time counter. The input is assumed to be a Poisson point process whose rate is a stochastic process, and the dead time is assumed to be small in comparison with the fluctuation time of the driving process. The mean is shown to depend only on the first-order statistics of the rate, whereas the variance is formally shown to depend on both the firstand the second-order statistics of the rate. For the particular process arising in the detection of chaotic light, an explicit expression is obtained for the dependence of the dead-timemodified variance on the power spectrum of the radiation. It is demonstrated that the variance takes on a particularly simple form for chaotic light with Lorentzian and Gaussian spectra. In the regime in which our study is valid, it turns out that the dead-time dependence of the variance is contained in a multiplicative function that is essentially independent of the spectral properties of the light.