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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

  • Vol. 20, Iss. 8 — Aug. 1, 2003
  • pp: 1528–1536

Transformation and spectrum properties of partially coherent beams in the fractional Fourier transform plane

Yangjian Cai and Qiang Lin  »View Author Affiliations


JOSA A, Vol. 20, Issue 8, pp. 1528-1536 (2003)
http://dx.doi.org/10.1364/JOSAA.20.001528


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Abstract

An analytical and concise formula is derived for the fractional Fourier transform (FRT) of partially coherent beams that is based on the tensorial propagation formula of the cross-spectral density of partially coherent twisted anisotropic Gaussian–Schell-model (GSM) beams. The corresponding tensor ABCD law performing the FRT is obtained. The connections between the FRT formula and the generalized diffraction integral formulas for partially coherent beams passing through aligned optical systems and misaligned optical systems are discussed. With use of the derived formula, the transformation and spectrum properties of partially coherent GSM beams in the FRT plane are studied in detail. The results show that the fractional order of the FRT has strong effects on the transformation properties and the spectrum properties of partially coherent GSM beams. Our method provides a simple and convenient way to study the FRT of twisted anisotropic GSM beams.

© 2003 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.2590) Fourier optics and signal processing : ABCD transforms

History
Original Manuscript: October 22, 2002
Revised Manuscript: March 4, 2003
Manuscript Accepted: March 4, 2003
Published: August 1, 2003

Citation
Yangjian Cai and Qiang Lin, "Transformation and spectrum properties of partially coherent beams in the fractional Fourier transform plane," J. Opt. Soc. Am. A 20, 1528-1536 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-8-1528

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