Multiple scattering by a collection of randomly located obstacles - numerical implementation of the coherent fields

A numerical implementation of a method to analyze scattering by randomly located obstacles in a slab geometry is presented. In general, the obstacles can be of arbitrary shape, but, in this first implementation, the obstacles are dielectric spheres. The coherent part of the reflected and transmitted intensity at normal incidence is treated. Excellent agreement with numerical results found in the literature of the effective wave number is obtained. Moreover, comparisons with the results of the Bouguer-Beer (B-B) law are made. The present theory also gives a small reflected coherent field, which is not predicted by the Bouguer-Beer law, and these results are discussed in some detail.