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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 36, Iss. 32 — Nov. 10, 1997
  • pp: 8490–8492

Scaled fractional Fourier transform and its optical implementation

Jianwen Hua, Liren Liu, and Guoqiang Li  »View Author Affiliations


Applied Optics, Vol. 36, Issue 32, pp. 8490-8492 (1997)
http://dx.doi.org/10.1364/AO.36.008490


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Abstract

The scaled fractional Fourier transform is suggested and is implemented optically by one lens for different values of ϕ and output scale. In addition, physically it relates the FRT with the general lens transform—the optical diffraction between two asymmetrically positioned planes before and after a lens.

© 1997 Optical Society of America

History
Original Manuscript: January 2, 1997
Revised Manuscript: May 7, 1997
Published: November 10, 1997

Citation
Jianwen Hua, Liren Liu, and Guoqiang Li, "Scaled fractional Fourier transform and its optical implementation," Appl. Opt. 36, 8490-8492 (1997)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-36-32-8490


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References

  1. V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Its Appl. 25, 241–265 (1980). [CrossRef]
  2. A. C. McBride, F. H. Kerr, “On Namias’ fractional Fourier transforms,” IMA J. Appl. Math. 39, 159–175 (1987). [CrossRef]
  3. L. M. Bernardo, O. D. Soares, “Fractional Fourier transforms and imaging,” J. Opt. Soc. Am. A 11, 2622–2626 (1994). [CrossRef]
  4. H. M. Ozaktas, B. Barshan, D. Mendlovic, “Fractional Fourier transforms as a tool for analyzing beam propagation and spherical mirror resonators,” Opt. Lett. 19, 1678–1680 (1994). [CrossRef] [PubMed]
  5. G. Dorsch, A. W. Lohmann, “Fractional Fourier transform used for a lens-design problem,” Appl. Opt. 34, 4111–4112 (1995). [CrossRef] [PubMed]
  6. G. Dorsch, A. W. Lohmann, Y. Bitran, D. Mendlovic, H. M. Ozaktas, “Chirp filtering in the fractional Fourier domain,” Appl. Opt. 33, 7599–7602 (1994). [CrossRef] [PubMed]
  7. H. M. Ozaktas, B. Barshan, D. Mendlovic, H. Urey, “Space-variant filtering in fractional Fourier domains,” Inst. Phys. Conf. Ser. 139, 285–288 (1994).
  8. S. Granieri, O. Trabocchi, E. E. Sicre, “Fractional Fourier transform applied to spatial filtering in the Frenel domain,” Opt. Commun. 119, 275–278 (1995). [CrossRef]
  9. Z. Zalevsky, D. Mendlovic, R. G. Dorsch, “Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 22, 842–844 (1996). [CrossRef]
  10. T. Alieva, “Fractional Fourier transform as a tool for investigation of fractal objects,” J. Opt. Soc. Am. A 13, 1189–1192 (1996). [CrossRef]
  11. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993). [CrossRef]
  12. D. Mendlovic, H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993). [CrossRef]
  13. H. M. Ozaktas, D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II,” J. Opt. Soc. Am. A 10, 2522–2531 (1993). [CrossRef]
  14. A. W. Lohmann, D. Mendlovic, “Fractional Fourier transform: photonic implementation,” Appl. Opt. 33, 7661–7664 (1994). [CrossRef] [PubMed]
  15. P. Pellat-Finet, “Fresnel diffraction and the fractional-order Fourier transform,” Opt. Lett. 19, 1388–1390 (1994). [CrossRef] [PubMed]
  16. L. Bernardo, O. D. D. Soares, “Fractional Fourier transform and optical system,” Opt. Commun. 110, 517–522 (1994). [CrossRef]
  17. C.-C. Shih, “Optical interpretation of a complex-order Fourier transform,” Opt. Lett. 20, 1178–1180 (1995). [CrossRef] [PubMed]
  18. L. Bernardo, O. D. D. Soares, “Optical fractional Fourier transforms with complex orders,” Appl. Opt. 35, 3163–3166 (1996). [CrossRef] [PubMed]
  19. J. Hua, L. Liu, G. Li, “Observing the fractional Fourier transform by free-space Fresnel diffraction,” Appl. Opt. 36, 512–513 (1997). [CrossRef] [PubMed]
  20. S. Liu, J. Xu, Y. Zhang, L. Chen, C. Li, “General optical implementation of fractional Fourier transforms,” Opt. Lett. 20, 1053–1055 (1995). [CrossRef]
  21. G. Dorsch, “Fractional Fourier transforms of variable order based on a modular lens system,” Appl. Opt. 34, 6016–6020 (1995). [CrossRef] [PubMed]

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