Forward- and back-scattering from certain rough surfaces

Heuristic relations are derived between the specular reflection coefficient, , 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 of shows that , the radar area per unit area of mean plane, is proportional to , where is 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 ; here the argument leads to . In two appendices the law is 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.