The validity of shadowing corrections in rough surface scattering

A rigorous examination of the validity of the shadow corrected Kirchhoff approximation is initiated for the purpose of validating this result for use as an asymptotic check on complicated multiple scattering theories. The magnetic field integral equation is iteratively solved in the quasi-optical limit to determine if it leads to incident and scatter shadowing functions. The incident shadowing function can be rigorously derived in the absence of multiple scattering and, although it represents something more than single scattering, its true purpose is the conversion of mathematical rays to real rays which obey Snell's law. The scattering shadowing function is fundamentally flawed because it forces the current on the surface to be a function of the point of observation for the scattered field. The possibility of focusing from a point of specular reflection on the surface to a shadowing point causes further difficulties with the scatter shadow function. In general, shadowing functions are shown to be either inadequate or insufficiently rigorous as to provide a valid asymptotic check on complex multiple scattering theories when multiple scattering exists on the surface.