The Local Perturbation Method for Solving the Problem of Diffraction from a Surface with Small Slope Irregularities

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Abstract
An approximate solution for the problem of wave diffraction from irregular surfaces with small height and small slope irregularities can be obtained using the small perturbation method (SPM). If the irregularities have large heights but their radii of curvature are much larger than the radiation wavelength, the tangent plane method (TPM) is usually used. In this paper we propose a new method for solving the problem of diffraction from a surface with small slope irregularities of arbitrary height: the local perturbation method (LPM). It allows us to obtain the result in the form of an iteration series which is an asymptotic expansion in two small parameters. The characteristic slope is one of them, and the other one characterizes radii of curvature of the irregularities on the scale of the electromagnetic field changing near the surface. In the appropriate limits the result coincides with those obtained by the SPM or TPM. With the help of the LPM we have shown that some integral characteristics of scattering can be computed by the formulae of the SPM for irregularities with arbitrary height.

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