Scattering from Moderately Rough Surfaces

Abstract

Electromagnetic scattering from a moderately rough surface model will be studied here. By a moderately rough surface we mean one whose height and slope variations are moderate as described by

• kz(x,y) < 1

• $\tfrac{{\partial z}}{{\partial x}},\tfrac{{\partial z}}{{\partial y}} < 1,$

• l _x ,l _y << L

where z is the surface height at (x, y), l _x , l _y , and L denote respectively the x-and y-component of the roughness correlation length l and the dimension of the illuminated area. The surface is also restricted to be highly conducting so that the assumption of perfect conductivity is approximately valid. For this type of the surface model, we will describe a method of estimating the stochastic radar cross section in bistatic scattering by carrying out in detail the mathematical procedures, based on the S-matrix formulation developed in the preceding chapter. It is generally believed that the random variations of the surface height and the surface slope of this type of rough surface obey the Guassian statistics. Our discussion is based on this belief (cf. for example, W. Hoffman [5.4], P. Beckmann and A. Spizzichino [5.1], J. Kong, et al. [5.5], A. Fung, et al. [5.3]). The material of this chapter is an outgrowth of joint work with C. M. Chu of the Radiation Laboratory of the University of Michigan.