Wavelength decorrelation of speckle in propagation through a thick diffuser

Abstract

We present a careful theoretical analysis for the wavelength decorrelation of speckle intensity that occurs when plane-polarized laser illumination is propagated through an optical system consisting of a thick diffuser in cascade with the space-invariant 4F imaging system and a CCD monitoring configuration. Based on Maxwell's equations for propagation into the right half-space, our formulation for a scalar component of the electric field is accurate well inside of the Fresnel zone and in the nonparaxial regime as well. The diffuser is described as an artificial dielectric consisting of tiny dielectric spheres embedded in a host medium and randomly spaced. We model the thick diffusers using a thin multilayer decomposition, and we write computer software describing the output speckle pattern amplitude which results from the propagation of an input plane wave. This model provides a good description for opal milk glass (OMG), and we illustrate the usefulness of this software by two applications. First, for a series of OMG diffusers of varying thickness, we present curves for the wavelength decorrelation of speckle that are found to be in good agreement with earlier experiments by George et al.[Appl. Phys. 7, 157 (1975)]. Also, these results are used to compute internal parameters of these diffusers. Second, using these values, we present some first-order statistics of the intensity for this diffuser series and show that they are in accord with the published literature.