Abstract
We present in this paper, approximate analytical expressions for the intensity of light scattered by a rough surface, whose elevation in the -direction is a zero mean stationary Gaussian random variable. With and being two points on the surface, we have with a correlation, , where is the distance between these two points. We consider with , showing that and for . The intensity expression is sought to be expressed as , where and are the wave vectors of scattering, as defined by the Beckmann notation. In the paper, we present expressions for and , in terms of , , and . The closed form expressions are verified to be true, for the cases and , for which exact expressions are known. For other cases, i.e., , 2 we present approximate expressions for the scattered intensity, in the range, and show that the relation for , given above, expresses the scattered intensity quite accurately, thus providing a simple computational methods in situations of practical importance.
© 2013 Optical Society of America
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