Three-dimensional intensity correlation and power spectra of fully developed speckle fields

Abstract

In recent years coherent optical techniques have become of growing interest, which require a full three-dimensional analysis of the encountered light distributions, which often show random fluctuations known as speckle. The geometrical properties of such speckle fields are usually determined by the intensity autocorrelation function (ACF) or equivalently by its corresponding counterpart in Fourier-space, the spatial power spectral density (PSD)' . It is well-known that spatial stationarity of the underlying quantities is only given for monochromatic fully developed gaussian fields in planes transversal to the main propagation direction. In the more general 3D case, or for non-monochromatic or time-dependent speckle fields (as one is concerned with for example in vibration analysis, rough surface interferometry and other multi-wavelength techniques) a straightforward analysis is only possible if at least local stationarity may be assumed. This requires, that the diffusing object is modelled (at least picewise) as a quasi-homogeneous planar source, for which the object mutual intensity separates into a product of the macroscopic source intensity distribution and the autocorrelation of its microroughness.