Surface Scattering Near Grazing Angles: The Distorted Wave Born Approximation forRough Surfaces

摘要

The scattering of radiation by mildly rough surfaces of non-absorbing materialsis analyzed in the distorted wave Born approximation wherein the roughness is treated as a perturbation. The basic formulae for the scattering cross-section are derived and cooresponding expressions for the reflectivity and transmissivity are given. It is shown that off-specular scattering is proportional to the Fourier transform of an autocorrelation function involving phase factors produced when the actual surface deviates from a flat reference surface. In the specular direction the Fourier transform reduces to a simple surface average. The theory is then applied to periodic surfaces where the Fourier transform is reduced to a weighted sum of delta-functions. Numerical reflectivities are given for a piecewise rectangular and a sinusoidal grating. For such surfaces it is shown that plausible results are obtained even when the deviations are large. Random roughness is considered and explicit results are given for a surface with a Gaussian distribution of the height variation. It is demonstrated that the surface roughness for this type of surface must be small for our perturbative technique to be valid. (Copyright (c) Council for the Central Laboratory fo the Research Councils 1995.)