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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. 27, Iss. 2 — Feb. 1, 2010
  • pp: 358–365

Fractional Fourier transform of flat-topped multi-Gaussian beams

Yan-Qi Gao, Bao-Qiang Zhu, Dai-Zhong Liu, and Zun-Qi Lin  »View Author Affiliations


JOSA A, Vol. 27, Issue 2, pp. 358-365 (2010)
http://dx.doi.org/10.1364/JOSAA.27.000358


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Abstract

The fractional Fourier transform (FRFT) of the flat-topped multi-Gaussian beam (FMGB) is investigated based on the three kinds of FRFT optical systems: Lohmann I, Lohmann II, and quadratic graded-index systems. The analytical expressions for the FRFT of the FMGB are derived based on the propagation of the FMGB through the three systems. By introducing a hard-edge aperture function, the analytical expressions for the FRFT of the FMGB carried out by the apertured FRFT optical systems are presented. The FRFT characteristics of the FMGB for the three kinds of FRFT optical systems with and without apertures are discussed in detail. Results show that the three types of FRFT optical systems have the same function when the apertures are ignored but that significantly different characteristics are exhibited when the apertures appear.

© 2010 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(260.1960) Physical optics : Diffraction theory
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms
(080.2575) Geometric optics : Fractional Fourier transforms

ToC Category:
Physical Optics

History
Original Manuscript: November 3, 2009
Revised Manuscript: December 9, 2009
Manuscript Accepted: December 10, 2009
Published: January 29, 2010

Citation
Yan-Qi Gao, Bao-Qiang Zhu, Dai-Zhong Liu, and Zun-Qi Lin, "Fractional Fourier transform of flat-topped multi-Gaussian beams," J. Opt. Soc. Am. A 27, 358-365 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-2-358


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