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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 4 — Feb. 1, 2012
  • pp: A1–A10

Speckle orientation in paraxial optical systems

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

Applied Optics, Vol. 51, Issue 4, pp. A1-A10 (2012)

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The statistical properties of speckles in paraxial optical systems depend on the system parameters. In particular, the speckle orientation and the lateral dependence ( x and y ) of the longitudinal speckle size can vary significantly. For example, the off-axis longitudinal correlation length remains equal to the on-axis size for speckles in a Fourier transform system, while it decreases dramatically as the observation position moves off axis in a Fresnel system. In this paper, we review the speckle correlation function in general linear canonical transform (LCT) systems, clearly demonstrating that speckle properties can be controlled by introducing different optical components, i.e., lenses and sections of free space. Using a series of numerical simulations, we examine how the correlation function changes for some typical LCT systems. The integrating effect of the camera pixel and the impact this has on the measured first- and second-order statistics of the speckle intensities is also examined theoretically. A series of experimental results are then presented to confirm several of these predictions. First, the effect the pixel size has on the measured first-order speckle statistics is demonstrated, and second, the orientation of speckles in a Fourier transform system is measured, showing that the speckles lie parallel to the optical axis.

© 2012 Optical Society of America

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(030.6600) Coherence and statistical optics : Statistical optics
(050.1940) Diffraction and gratings : Diffraction
(110.6150) Imaging systems : Speckle imaging
(070.7345) Fourier optics and signal processing : Wave propagation

Original Manuscript: October 3, 2011
Revised Manuscript: November 29, 2011
Manuscript Accepted: November 30, 2011
Published: January 25, 2012

Dayan Li, Damien P. Kelly, Raoul Kirner, and John T. Sheridan, "Speckle orientation in paraxial optical systems," Appl. Opt. 51, A1-A10 (2012)

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