A NEW THEORY FOR SCATTERING FROM A SURFACE

A new formal approach to the problem of scattering from a rough surface is derived. The first ingredient of this approach is a formal statement of the composite model. This consists of an approximate expression for the change in the scattering amplitude corresponding to a perturbation of a reference surface. It is good to first order in the perturbation, and exact with respect to the reference surface. The derivation of this result makes use of the general asymptotic form of the scattering solution. The expression is simplified using the boundary conditions. When the formal composite model is applied to an unfinitesimal translation, a new representation of the scattering amplitude is obtained. Unlike the traditional representation, this expression depends on two full solutions to the wave equation, and it manifestly exhibits reciprocity. This article is the first in a series. Application of the results will be considered in future papers.