title: K speckle: space-time correlation function of doubly scattered light in an imaging system.
abstract: The scattering of coherent monochromatic light at an optically rough surface, such as a diffuser, produces a speckle field, which is usually described by reference to its statistical properties. For example, the real and imaginary parts of a fully developed speckle field can be modeled as a random circular Gaussian process. When such a speckle field is used to illuminate a second diffuser, the statistics of the resulting doubly scattered field are in general no longer Gaussian, but rather follow a K distribution. In this paper we determine the space-time correlation function of such a doubly scattered speckle field that has been imaged by a single lens system. A space-time correlation function is derived that contains four separate terms; similar to the Gaussian case it contains an average DC term and a fluctuating AC term. However, in addition there are two terms that are related to contributions from each of the diffusers independently. We examine how our space-time correlation function varies as the diffusers are rotated at different speeds and as the point spread function of the imaging system is changed. A series of numerical simulations are used to confirm different aspects of the theoretical analysis. We then finish with a discussion of our results and some potential applications, including controlling spatial coherence and speckle reduction.
authors.affiliation: School of Electrical, Electronic and Communications Engineering, College of Engineering and Architecture, University College Dublin, Belfield, Dublin 4, Ireland.
authors.forename: Dayan
authors.initials: D
authors.lastname: Li
authors.forename: Damien P
authors.initials: DP
authors.lastname: Kelly
authors.forename: John T
authors.initials: JT
authors.lastname: Sheridan