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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. 28, Iss. 9 — Sep. 1, 2011
  • pp: 1896–1903

Three-dimensional static speckle fields. Part I. Theory and numerical investigation

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


JOSA A, Vol. 28, Issue 9, pp. 1896-1903 (2011)
http://dx.doi.org/10.1364/JOSAA.28.001896


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Abstract

When monochromatic light is scattered from an optically rough surface a complicated three-dimensional (3D) field is generated. These fields are often described by reference to the 3D volume (extent) of their speckles, leading to the definition of lateral ( x , y ) and longitudinal speckle sizes (z). For reasons of mathematical simplicity the longitudinal speckle size is often derived by examining the decorrelation of the speckle field for a single point lying on axis, i.e., x = y = 0 , and this size is generally assumed to be representative for other speckles that lie further off-axis. Some recent theoretical results, however, indicate that in fact longitudinal speckle size gets smaller as the observation position moves to off-axis spatial locations. In this paper (Part I), we review the physical argument leading to this conclusion and support this analysis with a series of robust numerical simulations. We discuss, in some detail, computational issues that arise when simulating the propagation of speckle fields numerically, showing that the spectral method is not a suitable propagation algorithm when the autocorrelation of the scattering surface is assumed to be delta correlated. In Part II [ J. Opt. Soc. Am. A 28, 1904 (2011)] of this paper, experimental results are provided that exhibit the predicted variation of longitudinal speckle size as a function of position in x and y. The results are not only of theoretical interest but have practical implications, and in Part II a method for locating the optical system axis is proposed and experimentally demonstrated.

© 2011 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
(200.2610) Optics in computing : Free-space digital optics
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: June 15, 2011
Manuscript Accepted: July 12, 2011
Published: August 25, 2011

Citation
Dayan Li, Damien P. Kelly, and John T. Sheridan, "Three-dimensional static speckle fields. Part I. Theory and numerical investigation," J. Opt. Soc. Am. A 28, 1896-1903 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-9-1896

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