Scattering cross section modulation for arbitrarily oriented composite rough surfaces: Full wave approach

Abstract

As a synthetic aperture radar scans different portions of a rough surface, the direction of the unit vector normal to the mean surface of the effective illuminated area (resolution cell) fluctuates. In this paper the modulation of the like and cross polarized scattering cross sections of the resolution cell are determined as the normal to it tilts in planes that are in and perpendicular to the fixed reference plane of incidence. By using the full wave approach, the scattering cross sections are expressed as a weighted sum of two cross sections. The first cross section is associated with scales of roughness within the effective illuminated area that are large compared to the radar wavelength, and the second cross section is associated with small‐scale spectral components within the resolution cell. Thus both specular point scattering and Bragg scattering are accounted for in a self‐consistent manner. The results are compared with earlier solutions based on first‐order Bragg scattering theory.

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

“…In equation (10), the first and second superscripts P5V, H and Q5V, H correspond to the polarizations of the scattered and incident waves, respectively. The first term in equation (10) is the contribution to the scatter cross section associated with the tilt modulated smaller-scale surface, h s , by the slope of the larger-scale surface (Bahar et al 1983b):…”

Light Scattering by Composite Rough Surfaces

“…The composite rough surface can now be constructed by superposing a smallscale structure on the slowly varying undulations of the large-scale irregularities . Contrary to Brown's [35,36] approach, but in analogy with Leader's [32][33][34] and Bahar's [37][38][39], the small-scale height deviations are defined with respect to the large-scale rough surface (not relative to the x-y plane) . Corresponding to the two contributions of the small-scale cross-section, the composite surface also leads to incoherent and coherent scattering components .…”

“…Corresponding to the two contributions of the small-scale cross-section, the composite surface also leads to incoherent and coherent scattering components . As is well known [29,33,34,[37][38][39], the incoherent component results from a sort of convolution integral of the large-scale and small-scale cross-sections, equations (4) and (18) . The calculations are complicated owing to the fact that the reference coordinate system of the linear polarization states in equation (18) changes with varying large-scale slope .…”

“…cos a = cos O i cos /3 -sin 'V i sin /3 sin 6, [43,44], confine themselves to small large-scale slopes [27][28][29], or consider only small-scale correlation lengths 1 much larger than the wavelength [32][33][34][37][38][39] so that the approximate coherent reflection coefficients (25) can be used .…”

“…In addition, more elaborate models as for example that by Bahar [37][38][39] have to be reduced to the two-scale model for the actual numerical computation of differential cross-sections .…”