GENERALIZATION OF THE GEOMETRICAL-OPTICS SCATTERING LIMIT FOR A ROUGHCONDUCTING SURFACE

We consider the backscattering coefficient of a perfectly conducting, one-dimensional random rough surface in the physical-optics approximat ion. The high-frequency limit of physical optics yields the geometrica l-optics scattering coefficient with Gaussian dependence on incidence angle. We demonstrate that for finite frequencies and surfaces with in finite slope variance the Gaussian form of the geometrical-optics limi t generalizes to an cu-stable distribution function. The proof of this result employs an asymptotic method that can be interpreted as a refi nement of the central-limit theorem of probability theory for infinite -variance random variables. The theory leads to an effective cutoff of the surface-height power spectral density. The backscatter is not sen sitive to surface components with wave number above this spectral cuto ff, thus eliminating the nonphysical dependence of geometrical optics on surface features much smaller than the wavelength of the incident f ield. The composite or two-scale surface model is also derived as a te rm in a series expansion of the stable distribution. Comparison with n umerical results shows that the approximation, although asymptotic, re mains accurate for relatively low values of the surface roughness para meter. (C) 1998 Optical Society of America.