11 November 1991 Improved formalism for rough-surface scattering of acoustic and electromagnetic waves
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The integral operator connecting the normal gradient of the scattered field to its boundary values can be represented by an expansion in roughness amplitude that is more rapidly convergent than conventional solution. Each term in the operator series consists of alternating applications of Fourier transforms and multiplications by functions of surface position and wavenumber. The procedure is consequently efficient enough to provide accurate scattering solutions for two-dimensional surfaces (zetz) (x,y) of high roughness amplitude and substantial detail. The appropriate expansion parameter for the scalar problem is the Fresnel roughness, which for a composite random surface scales like the rms slopes times the rms Rayleigh height. For the vector electromagnetic problem an additional, partially independent, parameter arises in the form of squared slope for those roughness scales shorter than the radiation wavelength.
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D. Michael Milder, D. Michael Milder, } "Improved formalism for rough-surface scattering of acoustic and electromagnetic waves", Proc. SPIE 1558, Wave Propagation and Scattering in Varied Media II, (11 November 1991); doi: 10.1117/12.49628; https://doi.org/10.1117/12.49628

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