Abstract

It is well known that the photocount possesses approximately a gamma probability density function when the detected optical intensity follows a negative-exponential distribution. In some problems of laser propagation through turbulent media, however, it has been shown that the detected laser intensity possesses a K distribution. Here the notation K represents a modified Bessel function with an imaginary argument. The probability density function for the photocount associated with such a K distribution for laser intensity is evaluated. The theory presented can be applied to two situations: (1) probability distribution for photon number in a certain time interval collected by a small detecting aperture; (2) probability distribution for photon number per unit time interval collected by a large detecting aperture. To this end, the probability distribution for the detected energy or detected power, depending on different situations, is computed first. For this purpose, a standard procedure in probability theory can be followed through using the characteristic function. Then a Poisson distribution is introduced to compute the probability distribution of the photocount. Different orders of K distribution are to be considered.

© 1987 Optical Society of America