New approximations in the theory of rough surface scattering

Abstract

Since the exact evaluation of the scattered by a random rough dace electromagnetic field is impossible, one has to fall back on some approximate methods. The recently suggested such approximations are result of the efforts to deal with the scattering process from natural (earth or sea) or man-made surfaces whose characteristic roughness dimension is of order of the wavelength of the sounding field. Such a necessity comes fiom the limited range of validity of the classical approximate methods - the Kirchhoff approximation (KA) and the perturbation theory (PT) which are accurate in two limiting cases only: when the incident field wavelength X is much smaller than the lateral correlation length or much greater than the nns surface height, respectively. Often, however, the roughness spectrum of the aurfaces of interest is very wide in which case neither KA nor PT done applies. In this report we review four of the mod promising approaches to the problem of interest, namely, the phase perturbation theory (PPT) [1,2] the Lynch variational method (LVM) 131, the local parabolic approximation (LPA) [4], and the small slope approximation (SA) 151 and compare their respective ranges of validity. The approximations are examined in the case of one-dimensional normally distributed random rough surfaces on which either Mchlet (PPT and LVM) or Neumann (SSA) or both Dirichlet and Neumaan (LPA) boundary conditions hold. Some of the most important findings and results (based on our own studies) whicb will be discussed, include: 1) The PPT is not limited to cmes of either mall roughness or gentle undulations and smoothly interpolates between the two classical approximations 16-81. 2) The asymptotic expansions of the phase perturbation scattering CTOSS section using the ratio of the rms height and slope as large parameter facilitate the practical application of the method 3) By comparing the PPT and the LVM it will be shown that a considerable part of the shadowing is incorporated in the local diffraction phenomena [SI. 4) The results from the numerical studies of the modified variational approximation proposed in 19) will be shown. The comparison with the exact Monte Carlo results shows that the approximation accurately account for the local diffraction phenomena 191. 5) The local parabolic approximation of the surface irregularities accounts for the local Waction effects. It is demonstrated that the method improves the Kirchhoff approximation for large and intermediate values of the lateral correlation length especially in the backscattering region 6) Based on the mall slope approximation a model that includes the shadowing corrections is proposed. It is demonstrated that the model is accurate for non-grazing angles of incidence for wide range of correlation length values, provided that the rms slope of the surface is moderate 17).