Measurements of electromagnetic back-scattering from known, rough surfaces

We have measured the cross section for backscattering of laser beams from rough aluminum surfaces and a magnesium oxide slab. These surfaces were specially prepared and their statistical properties were measured. The laser wavelengths were λ &equal; 0.63, 1.15, and 3.39μ, and both parallel and perpendicular polarizations were used. The angle of incidence was varied from 0° to 89°. In these experiments the ratio of the surface rms height h (from the mean surface) to the wavelength λ is larger than 1/4; for such surfaces the cross section for backscatter at normal incidence is inversely proportional to the square of the rms surface slope, h/l, and is independent of wavelength. At large angles of incidence the cross section increases with increasing slope and also with increasing h/λ, approaching an upper limit which appears to be predicted by a Lambert scattering law. The angular dependence of the cross section differs for the two polarizations; at grazing incidence the cross section is larger for the parallel polarization. The published characteristics of the angular dependence of the cross section of microwave backscattering from the sea and the moon are in remarkable agreement with the backscattering cross section obtained from the various randomly-rough laboratory prepared surfaces at all angles of incidence. Comparison of the laboratory results with published moon data yields for the moon surface an rms height of 40 ± 10 cm, a mean correlation distance or mean scale size of 2.8 ± 0.7 meters,