Backscatter cross sections of composite random rough surfaces based on the selection of variational parameters to determine the surface height spectral densities of the larger‐ and smaller‐scale surfaces

Abstract

No single scattering theory can be used to evaluate the scatter cross sections of surfaces with multiple scales of roughness. In this paper a two‐scale unified full‐wave approach is used to evaluate the backscatter cross sections for vertically and horizontally polarized waves. The total cross sections are expressed analytically as weighted sums of a tilt‐modulated smaller‐scale surface height backscatter cross section and a larger‐scale surface physical optics backscatter cross section, reduced by the square of the smaller‐scale surface characteristic function. Consistent with the large radii of curvature criteria, only the slopes of the larger‐scale surface contribute to tilt modulation. Unlike the conventional hybrid perturbation/physical optics solutions, the unified full‐wave approach used here is not restricted to small Rayleigh roughness parameters. The total surface is decomposed continuously and smoothly into smaller‐ and larger‐scale surfaces. It is shown that the total backscatter cross sections are stationary over a very broad range of the variational parameters, proportional to the ratio of the mean square slopes or heights of the larger‐scale surface and the total surface. At grazing angles of incidence, the vertically and horizontally polarized cross sections are shown to be of the same order of magnitude, consistent with recent experimental data. This is because at grazing angles, tilt modulation impacts significantly on the horizontally polarized cross sections and marginally upon the vertically polarized cross sections. This is consistent with the observation that the original full‐wave solutions (that do not account for tilt modulation) underestimate the values for the horizontally polarized cross sections. These investigations also impact on the feasibility of relating the backscatter cross sections to the remote sensing of soil moisture content.