BRDF evaluation from a two-dimensional fractal rough surface

The physical mechanism of scattering of electromagnetic beams from a surface can be quantified by either a differential scattering coefficient or a bidirectional reflectance distribution function (BRDF). In this paper, the rough surface are modeled by a band-limited Weierstrass fractal function. According to the Kirchhoff stationary phase approximation for rough surface scattering, an expression of the BRDF for the fractal rough surface is derived. The angular distributions of the BRDF of the fractal surface for different fractal dimensions and different height standard deviation are studied by theoretic analysis and numerical calculations.