The scattering and depolarization of electromagnetic waves from perfectly conductive slightly rough random surfaces is studied using the small perturbation method through the Ewald–Oseen extinction theorem. This permits predictions in those cases in which the physical optics, or the Kirchhoff approximation, fails, namely, at grazing incidence and when the wavelength of the incident radiation is comparable with the correlation length of the random heights. In this way it is seen, for example, that, as with the Rayleigh–Fano method, the depolarization of the fields is obtained from the second order of the expansion and exists even in the backscattering and specular directions. Also, unlike the predictions of the Kirchhoff approximation, this depolarization depends on the surface shape. However, this approach yields in the specular direction the same result as the Kirchhoff approximation for those cases in which the latter is known to be valid, i.e., for large correlation lengths and non-grazing-incidence directions and establishes precise conditions under which the Kirchhoff approximation is retrieved in the backscattering direction.
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