Abstract

The properties of a speckle pattern are determined by the light source, the rough surface, and the optical system. The degree of correlation of the intensities of two slightly different speckle patterns can be applied to measure surface roughness since it depends on the variance of the surface height distribution. The two speckle patterns are produced by illuminating a rough surface with coherent light of either two different wavelengths or two different angles of incidence. A unified description of the theory for the spectral and angular speckle-correlation methods is presented, and explicit solutions are derived for both far-field and image-plane geometries. The theoretical results essentially yield a factorization of the degree of speckle correlation into a roughness-dependent and a space-dependent part. By maximizing the space-dependent part, one obtains the requirements for experimental arrangements with optimal measuring conditions. Examples of possible setups for each method are presented, and cross references to earlier work published in this field are given.

© 1986 Optical Society of America

Spectral correlation of partially or fully developed speckle patterns generated by rough surfaces

Bernd Ruffing and Jürgen Fleischer
J. Opt. Soc. Am. A 2(10) 1637-1643 (1985)

Measurement of random processes at rough surfaces with digital speckle correlation

Thomas Fricke-Begemann and Klaus D. Hinsch
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Higher-order statistical properties of speckle fields and their application to rough-surface interferometry

U. Vry and A. F. Fercher
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Surface-roughness dependence of the intensity correlation function under speckle-pattern illumination

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Real-time measurement of surface roughness by correlation of speckle patterns

D. Léger and J. C. Perrin
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