Generalized K distribution: a statistical model for weak scattering

The generalized K distribution, introduced recently by Barakat [ J. Opt. Soc. Am. A3, 401 ( 1986)] as a model for the intensity of radiation scattered with a nonuniform distribution of phase by a fluctuating population of objects, is derived on the bases of simpler and more general arguments. In particular, Barakat’s analysis is based on a random walk in two dimensions and a specific model for the phase distribution; our analysis is presented in terms of an n-dimensional walk with a directional bias that, apart from its scaling property as a function of the mean number of scatters, is arbitrary. The relationship of the generalized K model with possible underlying scattering mechanisms is also discussed.