Second-order Statistics of Light Diffracted from Gaussian, Rough Surfaces with Applications to the Roughness Dependence of Speckles

Abstract

The second-order statistics of light diffracted from gaussian rough surfaces is shown to be given by a locally stationary degree of coherence of scattered amplitudes in the reciprocal object space. The corresponding degree of speckle correlation is derived by analogy with intensity interferometry. This unified approach is applied to describe the roughness dependence of spectral and angular speckle correlations, as well as the first- and second-order statistics of polychromatic speckle patterns. For general scattering geometries a simple formula for the polychromatic speckle contrast is derived. For normal incidence and paraxial scattering a formula is derived that describes the roughness dependent fibrous structure of a polychromatic pattern.