Rough surface Green's function based on the first-order modified perturbation and smoothed diagram methods

This paper presents an analytical theory of rough surface Green's functions based on the extension of the diagram method of Bass, Fuks, and Ito with the smoothing approximation used by Watson and Keller. The method is a modification of the perturbation method and is applicable to rough surfaces with small RMS height. But the range of validity is considerably greater than for the conventional perturbation solutions. We consider one-dimensional rough surfaces with a Dirichlet boundary condition. The coherent Green's function is obtained from the smoothed Dyson's equation using a spatial Fourier transform. The mutual coherence function for the Green's function is obtained by first-order iteration of the smoothing approximation applied to the Bethe-Salpeter equation in terms of a quadruple Fourier transform. These integrals are evaluated by the saddle-point technique. The equivalent bistatic cross section per unit length of the surface is compared with that for the conventional perturbation method and the Watson-Keller result. With respect to the Watson-Keller result, it should be noted that our result is reciprocal while the Watson-Keller result is non-reciprocal. Included in this paper is a discussion of the specific intensity at a given observation point. The theory developed will be useful for RCS signature related problems and low grazing angle scattering when both the transmitter and the object are close to the surface.