The Local Spectral Expansion Method for Scattering From Perfectly Conducting Surfaces Rough in One Dimension

Abstract

We present a new analytical approach for scattering from perfectly conducting surfaces that are rough in one dimension. The method is based on expanding the Helmholtz equation using a set of local basis functions. The transformed equations contain the field and its normal derivatives at the surface as source functions. The first order approximate solution, sought for slightly rough surfaces, is obtained using the local tangent plane approximation at the surface. It is shown analytically that the new method reduces to the first order perturbation method in the proper limit. A systematic series solution is proposed using perturbation theory in conjunction with the present formulation. The second order result is given and analyzed. The results of the present theory are not reciprocal and a reciprocity rule is formulated to overcome this disadvantage. We compare numerically the bistatic scattering cross section for Gaussian-randomly rough surfaces predicted by the first order solution with numerical results and other first order theories. It is shown that the present formulation is overall more accurate than other existing theories.