Gaussian rough surfaces and Kirchhoff approximation

Electromagnetic scattering is often solved by applying Kirchhoff approximat ion to the Stratton-Chu scattering integral. In the case of rough surfaces, it is usually assumed that this is possible if the incident electromagneti c wavelength is small compared to the mean radius of curvature of the surfa ce. Accordingly, evaluation of the latter is an important issue. This paper generalizes the groundwork of Papa and Lennon [1] by computing the mean ra dius of curvature for Gaussian rough surfaces with no restriction on its co rrelation 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.