Speckle from a cascade of two thin diffusers

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Abstract
Propagation through a generalized thick diffuser and a spaced cascade of two thin diffusers is analyzed using methods of statistical optics. Second- and fourth-order moments are derived for the scalar component of the farzone field. In the formulation two states a and b are used, permitting one to consider variations of speckle with angle of illumination and wavelength of an input plane wave and with observation direction as well as with in-plane and longitudinal motion between the two thin diffusers. This two-state correlation function of intensity, i.e., fourth-order moment, is evaluated without the assumption of circularity, and explicit calculations of decorrelation with respect to the state variables are presented for a cascade of two paraboloidal diffusers. Decorrelation occurs with slight transverse motion of one of the diffusers that is essentially independent of the separation H. Decorrelation of the on-axis speckle occurs for a change in spacing ΔH that is also independent of H. For single thin diffusers or a closely spaced diffuser pair, decorrelation with changes of angle of illumination is quite slow. However, rapid angular decorrelation is obtained for large spacings. Wavelength decorrelation of the diffuser pair arises from two unrelated effects, i.e., the dependence of the individual diffusers and of the propagation between diffuser planes on wavelength. Plots are given to illustrate the different speckle dependencies. This analysis of speckle decorrelation can be used in various remote-sensing applications.

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