Scattering from fractal surfaces: Its physical reading in terms of alpha-stable distributions

Electromagnetic models for surface scattering represent a handy analytical tool useful in many remote sensing applications which exploit the prediction of the scattered field. Of course, the better is the surface model employed to compute the electromagnetic scattering, the more accurate are the forecasts on the scattered field, provided that closed form solutions for the statistics of the field are attainable. Accordingly, it is widely recognized that statistical scale-invariance properties exhibited by natural surfaces within a wide observation scale range are very efficiently described by means of fractal geometry. In this paper we focus on the Kirchhoff solution for the scattering from both classical and fractal surfaces, so allowing us to provide a novel physical interpretation of the Kirchhoff scattering integral in terms of the probability density function of the slopes of an equivalent rough surface.