The validity of the Kirchhoff approximation for fractal surface scattering

In this paper a novel theoretical framework for calculating the mean radius of curvature of fractal surfaces is depicted. In particular, the case of surfaces represented by means of functions belonging to the set of the Weierstrass-Mandelbrot functions is hereafter detailed. The applicability of the Kirchhoff approximation in scattering from fractal surfaces is discussed and a set of numerical results is presented.