Rytov Series Approximation for Rough Surface Scattering

A Rytov series approximation for rough surface scattering is presented for an analytical description of the close relation of topographic statistics and topographic scattering. The Rytov series approximation is not subject to the stringent restrictions that apply to the Born series approximation. Numerical calculations of the Rytov series approximation are conducted for several benchmark models. Comparisons with the full-waveform numerical solution and the Born series approximation are made for all examples to investigate the ranges of validity of the Rytov series approximation. The first-order Rytov approximation ignores multiple scatterings between any two surface points. In general, it has been considered valid for the large-scale roughness components. The high-order Rytov approximation accounts for multiple scattering between surface points and, therefore, becomes a realistic method for multiscale surfaces. Tests with the Gaussian/semicircular convex topographies and two randomly rough topographies show that the Rytov series approximation improves the Born series approximation in both amplitude and phase. For the two sharp edges in the semicircular convexity model, the fourth-order Rytov approximation is required to account for strong wave fluctuations. For general rough surfaces without infinite gradients and extremely large surface heights, the second-order Rytov approximation might be sufficient to guarantee the accuracy of rough surface scattering.