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Applied Optics

Applied Optics


  • Vol. 34, Iss. 26 — Sep. 10, 1995
  • pp: 6016–6020

Fractional Fourier transformer of variable order based on a modular lens system

Rainer G. Dorsch  »View Author Affiliations

Applied Optics, Vol. 34, Issue 26, pp. 6016-6020 (1995)

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The fractional Fourier transform is a new topic in optics. To make use of the fractional Fourier transform as an experimental tool, I design a fractional Fourier transformer of variable order: I introduce a lens system that is able to perform equidistant fractional Fourier transforms that cover the whole range of orders and that consist of a minimum number of modules. By module, I mean an elementary fractional Fourier transform of certain order that consists of a lens between two free-space lengths. Because of the commutative additivity of the transform, various fractional orders can be achieved by means of different constellations of the modules. It is possible to perform a large variety of fractional Fourier transforms with a small number of modules.

© 1995 Optical Society of America

Original Manuscript: September 14, 1994
Revised Manuscript: April 24, 1995
Published: September 10, 1995

Rainer G. Dorsch, "Fractional Fourier transformer of variable order based on a modular lens system," Appl. Opt. 34, 6016-6020 (1995)

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  1. E. U. Condon, “Immersion of the Fourier transform in a continuous group of functional transformations,” Proc. Natl. Acad. Sci. USA 23, 158–164 (1937). [CrossRef] [PubMed]
  2. V. Bargmann, “On a Hilbert space of analytic functions and an associated integral transform, Part I,” Commun. Pure Appl. Math. 14, 187–214 (1961). [CrossRef]
  3. V. Namias, “The fractional Fourier transform and its application in quantum mechanics,” J. Inst. Math. Appl. 25, 241–265 (1980). [CrossRef]
  4. A. C. McBride, F. H. Kerr, “On Namias's fractional Fourier transform,” IMA J. Appl. Math. 39, 159–175 (1987). [CrossRef]
  5. H. M. Ozaktas, D. Mendlovic, “Fourier transform of fractional order and their optical interpretation,” Opt. Commun. 110, 163–169 (1993). [CrossRef]
  6. A. W. Lohmann, “Image rotation, Wigner rotation and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993). [CrossRef]
  7. Y. Bitran, D. Mendlovic, R. G. Dorsch, A. W. Lohmann, H. M. Ozaktas, “Fractional Fourier transforms: simulations and experimental results,” Appl. Opt. 34, 1329–1332 (1995). [CrossRef] [PubMed]
  8. R. 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]
  9. D. Mendlovic, Y. Bitran, R. G. Dorsch, A. W. Lohmann, “Optical fractional correlation: experimental results,” J. Opt. Soc. Am. A (to be published).
  10. R. G. Dorsch, A. W. Lohmann, “Fractional Fourier transform, used for a lens design problem,” Appl. Opt. (to be published).
  11. D. Mendlovic, H. M. Ozaktas, A. W. Lohmann, “Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform,” Appl. Opt. 33, 6188–6193 (1994). [CrossRef] [PubMed]

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