SCATTERING OF LASER BEAM BY RANDOMLY DIFFUSING SURFACES——A SIMPLIFIED STATISTICAL MODEL

Abstract

The scattering of laser beam by a rough plane surface with one-dimensionally random fluctuations is treated by a simplified statistical method. The real surface is replaced by a series of taps of width λ along the direction of scores. The height hn, of the n-th tap is the average of the heights of real surface over the interval corresponding to the n-th tap. All the random variables hn are assumed to be independent and every one of them varies in the same inteval [-h,h] with the same probability distribution, h being the scale of roughness of surface. The problem thus becomes one of seeking the expected value of the light intensity produced by the interference of a series of element sources with certain random phases. This probabilistic problem can be solved strictly only with difficulty. With an approximate simplification it reduces to the problem of seeking the position of center of gravity of an arc and a simple "random walk" problem.The expression of the expected value of light intensity distribution I(θ) in the recording plane is deduced. The expression of the ratio R of the total energy in the central region to that in the two side wings in the recieving plane is very simple.The numerical results are given. Several methods of measurement are discussed. It is pointed out that the generalization of this model to the cases of surface with two-dimensionally random fluctuations and surfaces of other shape (non planar) is not difficult.