Coherent scattering by a collection of randomly located obstacles --- an alternative integral equation formulation

Scattering of electromagnetic waves by discrete, randomly distributed objects is addressed. In general, the non-intersecting scattering objects can be of arbitrary form, material and shape. The main aim of this paper is to calculate the coherent reflection and transmission characteristics of a slab containing discrete, randomly distributed scatterers. The integral representation of the solution of the deterministic problem constitutes the underlying framework of the stochastic problem. Conditional averaging and the employment of the Quasi Crystalline Approximation lead to a system of integral equations in the unknown expansion coefficients. Of special interest is the slab geometry, which implies a system of integral equations in the depth variable. Explicit solutions for tenuous media and low frequency approximations can be obtained for spherical obstacles.