Gaussian rough surfaces and Kirchhoff approximation

Electromagnetic scattering is often solved by applying the Kirchhoff approximation to the Stratton-Chu scattering integral. In the case of rough surfaces, it is usually assumed that this is possible if the incident electromagnetic wavelength is small compared to the mean radius of curvature of the surface. Accordingly, evaluation of the latter is an important issue. This paper generalizes the groundwork of Papa and Lemon (see ibid., vol.36, p.647-50, May 1988) by computing the mean radius of curvature for Gaussian rough surfaces with no restriction on its correlation function. This is an interesting extension relevant to a variety of natural surfaces. Relations between the surface parameters and the mean radius of curvature are determined and particular attention is paid to the relevant small slope regime