Intensity profile of light scattered from a rough surface

Chatterjee, S and Vani, VC and Banyal, Ravinder K (2013) Intensity profile of light scattered from a rough surface. In: Applied Optics, 52 (24). pp. 6000-6010.

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Abstract

We present in this paper, approximate analytical expressions for the intensity of light scattered by a rough surface, whose elevation. xi(x,y) in the z-direction is a zero mean stationary Gaussian random variable. With (x,y) and (x',y') being two points on the surface, we have h. <xi(x,y)> = 0 with a correlation, <xi(x,y)xi(x',y')> = sigma(2)g(r), where r = (x - x')(2) + ( y - y')(2)](1/2) is the distance between these two points. We consider g(r) = exp-r/l)(beta)] with 1 <= beta <= 2, showing that g(0) = 1 and g(r) -> 0 for r >> l. The intensity expression is sought to be expressed as f(v(xy)) = {1 + (c/2y)v(x)(2) + v(y)(2)]}(-y), where v(x) and v(y) are the wave vectors of scattering, as defined by the Beckmann notation. In the paper, we present expressions for c and y, in terms of sigma, l, and beta. The closed form expressions are verified to be true, for the cases beta = 1 and beta = 2, for which exact expressions are known. For other cases, i.e., beta not equal 1, 2 we present approximate expressions for the scattered intensity, in the range, v(xy) = (v(x)(2) + v(y)(2))(1/2) <= 6.0 and show that the relation for f(v(xy)), given above, expresses the scattered intensity quite accurately, thus providing a simple computational methods in situations of practical importance.

Item Type:	Journal Article
Publication:	Applied Optics
Publisher:	Optical Society of America
Additional Information:	Copyright of this article belongs to Optical Society of America.
Department/Centre:	Division of Physical & Mathematical Sciences > Instrumentation Appiled Physics
Date Deposited:	10 Oct 2013 05:24
Last Modified:	10 Oct 2013 05:24
URI:	http://eprints.iisc.ac.in/id/eprint/47488

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