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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 17, Iss. 12 — Dec. 1, 2000
  • pp: 2319–2323

Wigner distribution and fractional Fourier transform for two-dimensional symmetric optical beams

Tatiana Alieva and Martin J. Bastiaans  »View Author Affiliations

JOSA A, Vol. 17, Issue 12, pp. 2319-2323 (2000)

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A useful relationship between the fractional Fourier transform power spectra of a two-dimensional symmetric optical beam, on the one hand, and its Wigner distribution, on the other, is established. This relationship allows a significant simplification of the standard procedure for the reconstruction of the Wigner distribution from the field intensity distributions in the fractional Fourier domains. The Wigner distribution of a symmetric optical beam is analyzed, both in the coherent and in the partially coherent case.

© 2000 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.2590) Fourier optics and signal processing : ABCD transforms

Original Manuscript: February 24, 2000
Revised Manuscript: June 23, 2000
Manuscript Accepted: June 27, 2000
Published: December 1, 2000

Tatiana Alieva and Martin J. Bastiaans, "Wigner distribution and fractional Fourier transform for two-dimensional symmetric optical beams," J. Opt. Soc. Am. A 17, 2319-2323 (2000)

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  1. E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932). [CrossRef]
  2. M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978). [CrossRef]
  3. W. Mecklenbräuker, F. Hlawatsch, eds., The Wigner Distribution: Theory and Applications in Signal Processing (Elsevier, Amsterdam, 1997).
  4. M. G. Raymer, M. Beck, D. F. McAlister, “Complexwave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994). [CrossRef] [PubMed]
  5. D. F. McAlister, M. Beck, L. Clarke, A. Mayer, M. G. Raymer, “Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms,” Opt. Lett. 20, 1181–1183 (1995). [CrossRef] [PubMed]
  6. Y. B. Karasik, “Expression of the kernel of a fractional Fourier transform in elementary functions,” Opt. Lett. 19, 769–770 (1994). [CrossRef] [PubMed]
  7. A. Sahin, H. M. Ozaktas, D. Mendlovic, “Optical implementations of two-dimensional fractional Fourier transforms and linear canonical transforms with arbitrary parameters,” Appl. Opt. 37, 2130–2141 (1998). [CrossRef]
  8. A. Sahin, M. A. Kutay, H. M. Ozaktas, “Nonseparable two-dimensional fractional Fourier transform,” Appl. Opt. 37, 5444–5453 (1998). [CrossRef]
  9. A. W. Lohmann, “Image rotation, Wigner rotation and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993). [CrossRef]
  10. M. J. Bastiaans, P. G. J. van de Mortel, “Wigner distribution function of a circular aperture,” J. Opt. Soc. Am. A 13, 1698–1703 (1996). [CrossRef]
  11. L. Yu, Y. Lu, X. Zeng, M. Huang, M. Chen, W. Huang, Z. Zhu, “Deriving the integral representation of a fractional Hankel transform from a fractional Fourier transform,” Opt. Lett. 23, 1158–1160 (1998). [CrossRef]
  12. E. Wolf, “New theory of partial coherence in the space-frequency domain. I. Spectra and cross spectra of steady-state sources,” J. Opt. Soc. Am. 72, 343–351 (1982). [CrossRef]
  13. F. Gori, M. Santarsiero, G. Guattari, “Coherence and the spatial distribution of intensity,” J. Opt. Soc. Am. A 10, 673–679 (1993). [CrossRef]

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