Wave scattering from two-dimensional self-affine Dirichlet and Neumann surfaces and its application to the retrieval of self-affine parameters

摘要

Wave scattering from two-dimensional self-affine Dirichlet and Neumannsurfaces is studied for the purpose of using the intensity scattered from themto obtain the Hurst exponent and topothesy that characterize the self-affineroughness. By the use of the Kirchhoff approximation a closed form mathematicalexpression for the angular dependence of the mean differential reflectioncoefficient is derived under the assumption that the surface is illuminated bya plane incident wave. It is shown that this quantity can be expressed in termsof the isotropic, bivariate ($\alpha$-stable) L\'evy distribution of astability parameter that is two times the Hurst exponent of the underlyingsurface. Features of the expression for the mean differential reflectioncoefficient are discussed, and its predictions compare favorably over largeregions of parameter space to results obtained from rigorous computersimulations based on equations of scattering theory. It is demonstrated how theHurst exponent and the topothesy of the self-affine surface can be inferredfrom scattering data it produces. Finally several possible scatteringconfigurations are discussed that allow for an efficient extraction of theseself-affine parameters.