Shadowing function with single reflection from anisotropic Gaussian rough surface. Application to Gaussian, Lorentzian and sea correlations

In this paper, the monostatic (transmitter and receiver are located at the same place) and bistatic (transmitter and receiver are distinct) statistical shadowing functions from an anisotropic two-dimensional randomly rough surface are presented. This parameter is especially important in the case of grazing angles for computing the bistatic scattering coefficient in optical and microwave frequencies. The objective of this paper is to extend the previous work (Bourlier C, Berginc G and Saillard J 2002 Waves Random Media 12 145-74), valid for a one-dimensional surface, to a two-dimensional anistropic surface by considering a joint Gaussian process of surface slopes and heights separating two points of the surface. The monostatic average (statistical shadowing function average over the statistical variables) shadowing function is then performed in polar coordinates with respect to the incidence angle, the azimuthal direction and the surface height two-dimensional autocorrelation function. In addition, for a bistatic configuration, it depends on the incidence angle and azimuthal direction of the receiver. For Gaussian and Lorentzian correlation profiles and practically important power-type spectra such as the Pierson-Moskowitz sea roughness spectrum, the numerical solution, obtained from generating the surface Gaussian elevations (Monte Carlo method), is compared with the uncorrelated and correlated models. The results show that the correlation underestimates the shadow slightly, whereas the uncorrelated results weakly overpredict the shadow and are close to the numerical solution.