Illuminated height PDF of a random rough surface and its impact on the forward propagation above oceans at grazing angles

When solving electromagnetic rough-scattering problems, the effect of shadowing by the surface roughness often needs to be considered, especially as the illumination angle thetas approaches grazing incidence. Indeed, due to the surface roughness, only a part of the surface is illuminated. This phenomenon is characterized by the statistical illumination function which gives the probability that a point on a rough surface is illuminated. In this paper, we propose to calculate the bistatic statistical illumination function for any one-dimensional random rough surface and to analyse its impact on the forward propagation above rough sea surfaces by considering Gaussian statistics and for grazing angles Phi of the order of one degree.