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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 30, Iss. 5 — May. 1, 2013
  • pp: 969–978

K speckle: space–time correlation function of doubly scattered light in an imaging system

Dayan Li, Damien P. Kelly, and John T. Sheridan  »View Author Affiliations


JOSA A, Vol. 30, Issue 5, pp. 969-978 (2013)
http://dx.doi.org/10.1364/JOSAA.30.000969


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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.

© 2013 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(030.6140) Coherence and statistical optics : Speckle
(030.6600) Coherence and statistical optics : Statistical optics
(110.6150) Imaging systems : Speckle imaging

ToC Category:
Imaging Systems

History
Original Manuscript: January 30, 2013
Revised Manuscript: March 28, 2013
Manuscript Accepted: March 30, 2013
Published: April 23, 2013

Citation
Dayan Li, Damien P. Kelly, and John T. Sheridan, "K speckle: space–time correlation function of doubly scattered light in an imaging system," J. Opt. Soc. Am. A 30, 969-978 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-5-969

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