Application of coherence theory to propagation of a quasi-monochromatic field in a random medium

Starting from the partial differential equation for scalar wave propagation in a random medium, an integral equation is derived for the propagation of the second-order correlation function. In order to obtain the exact integral equation without resorting to perturbation theory, it is necessary to assume statistical independence of the wave function and the refractive index fluctuations. The physical basis for this assumption is reviewed, and a criterion for its applicability is proposed. The integral equation for the second-order correlation is then transformed into a wavenumber-spectral representation, resulting in appreciable simplification and permitting some direct interpretation.