Abstract

A stochastic representation of the Green function, i.e., the radiation field from a point source above a homogeneous Gaussian random surface, is obtained as a stochastic nonlinear functional of the random surface, which is constructed by integrating the random wave field for a plane-wave incidence given in previous papers [ Radio Sci. 15, 1049 ( 1980); Radio Sci. 17, 558 ( 1982)]. Any mode of radiation can therefore be treated using the stochastic Green function. The stochastic analog of the optical theorem is established. The asymptotic expression of the Green function is evaluated by the saddle-point method, and statistical properties and radiation patterns of the coherent and the incoherent field are calculated.

© 1985 Optical Society of America

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