Within the framework of ABCD matrix theory an exact analytical expression is derived for the space–time-lagged photocurrent covariance that is valid for arbitrary (complex) ABCD optical systems, i.e., systems that include Gaussian-shaped apertures and partially developed speckle. General expressions are derived for the mean spot size and both the mean speckle size and the temporal coherence length. Additionally, a general description of both speckle boiling and speckle translation in an arbitrary observation plane is given. Included in the analysis is the effect of a finite wave-front-curvature radius for the Gaussian-shaped laser beam illumination of the target. The effects of diffraction and wave-front-curvature radius are discussed for both imaging systems and a Fourier transform system. It is shown that, whereas diffraction affects the speckle dynamics in both cases, a finite wave-front curvature affects only the speckle dynamics in the Fourier transform system. Further, the effects of finite detector apertures are considered, in which the effects of speckle averaging are included and discussed. In contrast to previous work, the obtained analytical results are expressed in a relatively compact form yet fully contain all diffraction effects and apply to an arbitrary ABCD optical system.
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