Complex amplitude correlations of dynamic laser speckle in complex ABCD optical systems

Abstract

Within the framework of complex ABCD-matrix theory, exact theoretical expressions are derived for the spacetime-lagged cross-covariance functions of the fields valid for arbitrary (complex) ABCD-optical systems, i.e., systems that include Gaussian-shaped apertures and partially developed speckle. Specifically, we show and discuss the results for the three generic systems, i.e., free-space propagation, Fourier transform configuration, and imaging. To cope with various surface structures of varying rms surface heights, we apply two models in addition to employing the usual model for surfaces giving rise to fully developed speckle. The theoretical results found for free-space propagation are supported by interferometrically obtained data. © 2006 Optical Society of America.