Multiple scattering by a collection of randomly located obstacles Part I: Theory - coherent fields

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 finite or semi-infinite slab containing discrete, randomly distributed scatterers. Typical applications of the results are found at a wide range of frequencies (radar up to optics), such as attenuation of electromagnetic propagation in rain, fog, and clouds, etc. 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 an integral equation in the unknown expansion coefficients. Of special interest is the slab geometry, which implies an integral equation in the depth variable. Explicit solutions for tenuous media and low frequency approximations can be obtained for spherical obstacles