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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN 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)
http://dx.doi.org/10.1364/AO.34.006016


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Abstract

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

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

Citation
Rainer G. Dorsch, "Fractional Fourier transformer of variable order based on a modular lens system," Appl. Opt. 34, 6016-6020 (1995)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-34-26-6016


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References

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  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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