Green's function method of light scattering from random surfaces compares with Kirchhoff's approximation

Abstract

Starting from the Helmholtz Equation, we obtain the integral equations of the light field at the medium interfaces by use of Green's theorem. Then the integral equations are discretized into a linear equation set, from which the values of the light field and its derivatives at the interface can be numerically solved. We also obtain the expression for the transmissive light waves from the Green's-function integral in the case of Kirchhoff's approximation. By an analogy to the derivation process of the autocorrelation functions of speckles in Frauhofer plane, we propose the method for the generation of random self-affine fractal surfaces and Fourier transformation method for the numerical derivative of random surfaces. Then we study the accuracy of Kirchhoff's approximation in the scattering of light field from the random self-affine fractal surface. We find that the accuracy of Kirchhoff's approximation is relatively high when the root-mean-square roughness w is small. for random surfaces with the same value of w but smaller values of roughness exponent α, the Kirchhoff's approximation gives higher accuracy in the calculation of scattered light fields. We believe that the results of this paper would be of significance in understanding the validity range of the Kirchhoff's approximation when it is applied to light scattering from self-affine random surfaces.