Bernd Ruffing’s research while affiliated with Karlsruhe Institute of Technology and other places

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.

The correlation between the intensities of partially or fully developed far-field speckle patterns of two different wavelengths is investigated, assuming Gaussian field amplitudes. The degree of spectral speckle correlation depends mainly on the standard deviation of the surface height distribution, the wavelength difference, the angle of incidence, and the number of independent scattering cells in the illuminated surface spot. It provides a simple way of performing noncontact surface-roughness measurements with a variable measuring range. The theory, which has so far been restricted to fully developed speckle patterns with circular field statistics, is extended to partially developed speckles. Assumptions about the circularity or noncircularity of the speckle patterns are not necessary. An experiment has been carried out to support the theoretical results.