Forward- and back-scattering from certain rough surfaces

Abstract

Heuristic relations are derived between the specular reflection coefficient,R, and the radar echoing power of rough surfaces in which induced current elements are constrained to radiate equal powers in the reflected ray's direction and back toward the radar. To the extent that currents in the surface and fields scattered by it are calculable through a self-consistent formulation, a simple Fresnel-zone computation ofRshows that\sigma_{o}, the radar area per unit area of mean plane, is proportional to| R^{2} |\sin^{2} \theta, where\thetais the angle incident rays make with the mean plane. It is plausibly assumed that large scatterers on the surface cast shadows with "beamwidth" proportional to radar wavelength\lambda; here the argument leads to\sigma_{o} \propto ( |R^{2}| \sin^{2} \theta)/\lambda. In two appendices the law\sigma_{o} = 4 \sin^{2} \thetais derived for a lossless surface obeying Lambert's law, and a known self-consistent "solution" of a rough surface problem is examined by three generally applicable criteria.