Method of moments applied to the analysis of rough surfaces modelled by fractals

The Scattering and Emissivity of rough surfaces involve solutions to non-linear differential equations. Different approaches have been used in the literature to obtain approximate solutions under some hypothesis. For example Kirchhoff solution is used when the roughness is gentle on the scale of the wavelength. In this paper the Method of Moments is used to analyze the scattering of arbitrary surfaces. No approximation about the scale roughness is necessary. Both Gaussian and Fractal surfaces have been modeled and compared. The introduction of fractal geometry provides a new tool to describe natural rough surfaces. A first inside to the properties and parameters that describe fractal geometry has been done in order to characterize them statistically. It has been demonstrated that geometrical and scattering characteristics are controlled by Fractal descriptors, including fractal dimension. As a first step, our simulations refer to a (topological) one-dimensional (1-D) profile embedded in a two-dimensional (2-D) space. Physically, this corresponds to assume that both the electromagnetic field and the surface height are constant along a fixed direction. Extension to the case of a 2-D surface embedded in a three-dimensional (3-D) space is not conceptually difficult, but any simulation run requires a much longer computational time. Furthermore, scattering results obtained for 1-D profiles give also a good indication of scattering dependence on 2-D surface parameters.