Multiple Scattering Volume-Surface Interactions

The combined problem of scattering from random media with rough boundaries is fairly complicated. Hence, it is important to understand the scattering processes involved so that one may develop approximate methods appropriate for the application at hand. To facilitate this we have presented three different approaches: two using statistical wave theories and the third using the transport theory. Each approach gives a different perspective of the scattering processes involved. Although the transport theory is popularly used for this problem we find that certain multiple scattering volume-surface interactions are ignored in this approach. In contrast, our ‘unified approach’ properly takes into account all multiple scattering processes. One reason for this is that it treats volumetric scattering and surface scattering on an equal footing. We observe that because of multiple scattering, the contributions from volumetric scattering and surface scattering get inextricably coupled, and hence cannot be treated separately as it is done in the transport theoretic approach. However, if one component is much weaker than the other the combined problem may be split into two parts: (1) volumetric scattering, and (2) surface scattering. Thus, the computation of the difficult combined problem may be reduced to the computations of two simple problems. This splitting is not the same as that obtained when employing the single scattering approximation. Our detailed analysis of the problem has enhanced our understanding of the multiple scattering processes involved.