Finite frequency generalization of the geometrical optics rough surface scattering coefficient

This paper presents an asymptotic method for computing the backscatter from a rough conducting surface in the physical optics approximation. For intermediate and high frequencies, the backscattering coefficient is determined by an /spl alpha/-stable distribution function which generalizes the Gaussian form of the geometrical optics limit. The parameters of this distribution are determined by a truncation of the surface height power spectrum, which corrects the nonphysical dependence of the geometrical optics limit on high wavenumber surface components with small feature size. The backscatter in the physical optics approximation is not sensitive to components of the surface spectrum above an effective spectral cutoff wavenumber. We also show that the composite surface model results from a binomial expansion of the multiple convolution of the surface spectrum. This expansion provides higher order correction terms to the composite model. This derivation demonstrates that the composite model is valid for surfaces which do not naturally separate into two scales, and for such surfaces the theory fixes the optimal scale separation parameter. In addition, the expansion naturally specifies the transition between near-normal and mid-range incidence angle scattering.