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  • Vol. 28, Iss. 24 — Dec. 15, 2003
  • pp: 2443–2445

Moments of the Wigner distribution of rotationally symmetric partially coherent light

Martin J. Bastiaans and Tatiana Alieva  »View Author Affiliations


Optics Letters, Vol. 28, Issue 24, pp. 2443-2445 (2003)
http://dx.doi.org/10.1364/OL.28.002443


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Abstract

The Wigner distribution of rotationally symmetric partially coherent light is considered, and the constraints for its moments are derived. Although all odd-order moments vanish, these constraints lead to a drastic reduction in the number of parameters that we need to describe all even-order moments: whereas in general we have (<i>N</i> + 1)(<i>N</i> + 2)(<i>N</i> + 3)/6 different moments of order <i>N</i>, this number reduces to (1 + <i>N</i>/2)<sup>2</sup> in the case of rotational symmetry. A way to measure the moments as intensity moments in the output planes of (generally anamorphic) fractional Fourier-transform systems is presented.

© 2003 Optical Society of America

OCIS Codes
(030.5630) Coherence and statistical optics : Radiometry
(070.2580) Fourier optics and signal processing : Paraxial wave optics

Citation
Martin J. Bastiaans and Tatiana Alieva, "Moments of the Wigner distribution of rotationally symmetric partially coherent light," Opt. Lett. 28, 2443-2445 (2003)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-24-2443


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References

  1. E. Wigner, Phys. Rev. 40, 749 (1932).
  2. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).
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  7. M. J. Bastiaans and T. Alieva, J. Opt. Soc. Am. A 19, 1763 (2002).

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