Probability density function of the intensity of light reflected from a moderately rough surface in the far field

A general expression for the probability density function P(I) of the intensity of light reflected from a moderately rough surface in the far field is derived by the cumulant expansion of the random variable. It is shown that P(I) satisfies the modified Rician statistics for some general surface models in the limit of large L/T, where L is the dimension of the illuminating area, and T is the correlation length.