Kirchhoff-Tangent Plane Approximation

Abstract

Along with the perturbation theory the geometrical optics (quasiclassical) approximation represents another general approach in analyzing the scattering processes. The method may be employed when characteristic spatial scales of irregularities somewhat exceed the radiation wavelength. The approach is based on the assumption that the wave field locally has the structure of a plane wave whose amplitude and wave vector vary slowly from point to point. For scattering from a rough boundary this ansatz is formulated as follows: at each boundary point the incident wave is reflected in such a way as if the boundary is a plane. One can say that the boundary is approximated at each point by the tangent plane. Based on this representation, the scattered field and its normal derivative at the boundary can be easily expressed through the incident field. When these values are known it is possible to reconstruct the scattered field in the total space and, in particular, calculate SA, for instance, by formula of the kind (3.2.6). The above method was first proposed by Brekhouskikh [5.1, 2] and referred to as the tangent plane approximation or the Kirchhoff approximation (for the statistical case this approximation was developed by Isakovich [5.3]).