Scattering of light by rough surfaces: high and low roughness approximations

Abstract

Scattering of light by rough surface is considered in the Kirchoff approximation. Analytical expressions are presented for the scattered intensity by considering the elevations in the z-direction. «(x, y) at any point (x,y) all the surface to be a zero mean, correlated Gaussian, stationary random variable, such that < ((x, y)>=0 and < (x1,y1)(x2,y2)>= σ/sup2g(r), where r = [(x1- x2)/Sup2 + (yl - y2)/Sup 1/2 with g(0) = 1 and g(r)→ 0 for r » l. In the forgoing assumptions σ gives the measure of the height of the 'grooves' on the random surface g(r) is the correlation function and 'l' is the correlation length of the randomness. The correlation function is considered to be of the form of g(r) = exp [-(r/l)/Sup β] where 1≤β≤2. We present analytical expressions, for the values of the β in the above given range. In the above expression β is related to the fractal dimension of the surface. Special distinctions are made for α « 1 and α » 1, where α – σ/λ is a dimensionless quantity which measures the depth of the grooves w.r.t. the wavelength λ of the light. Several representative cases are considered, with reference to potentials applications.