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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. 10, Iss. 12 — Dec. 1, 1993
  • pp: 2522–2531

Fractional Fourier transforms and their optical implementation. II

Haldun M. Ozaktas and David Mendlovic  »View Author Affiliations


JOSA A, Vol. 10, Issue 12, pp. 2522-2531 (1993)
http://dx.doi.org/10.1364/JOSAA.10.002522


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Abstract

The linear transform kernel for fractional Fourier transforms is derived. The spatial resolution and the space–bandwidth product for propagation in graded-index media are discussed in direct relation to fractional Fourier transforms, and numerical examples are presented. It is shown how fractional Fourier transforms can be made the basis of generalized spatial filtering systems: Several filters are interleaved between several fractional transform stages, thereby increasing the number of degrees of freedom available in filter synthesis.

© 1993 Optical Society of America

History
Original Manuscript: March 1, 1993
Revised Manuscript: June 3, 1993
Manuscript Accepted: June 10, 1993
Published: December 1, 1993

Citation
Haldun M. Ozaktas and David Mendlovic, "Fractional Fourier transforms and their optical implementation. II," J. Opt. Soc. Am. A 10, 2522-2531 (1993)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-10-12-2522


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References

  1. D. Mendlovic, H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation. I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993). [CrossRef]
  2. H. M. Ozaktas, D. Mendlovic, “Fourier transforms of fractional order and their optical interpretation,” Opt. Commun. 101, 163–169 (1993). [CrossRef]
  3. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993). [CrossRef]
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  12. D. Mendlovic, H. M. Ozaktas, A. W. Lohmann, “The effect of propagation in graded index media on the Wigner distribution function and the equivalence of two definitions of the fractional Fourier transform,” submitted to Appl. Opt.
  13. G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, New York, 1985), pp. 712–760.

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