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

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.