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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. 16, Iss. 4 — Apr. 1, 1999
  • pp: 821–830

Metaxial correction of fractional Fourier transformers

Kurt Bernardo Wolf and Guillermo Krötzsch  »View Author Affiliations


JOSA A, Vol. 16, Issue 4, pp. 821-830 (1999)
http://dx.doi.org/10.1364/JOSAA.16.000821


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Abstract

We study fractional Fourier transformation in the metaxial regime of geometric optics. Two commonly used optical arrangements that perform fractional Fourier transformation are a symmetric thick lens and a length of graded-index waveguide. By means of Lie methods in phase space, we can correct some of their aberrations: for the first, through deforming the lens surfaces to a polynomial shape, and for the second, by warping the output screen at the end of the waveguide. We correct the planar cases to third, fifth, and seventh aberration orders; checks are provided on the convergence of aberration series in phase space. We add some comments on the usefulness of these corrected devices for fractional transformers in scalar wave optics.

© 1999 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(080.1010) Geometric optics : Aberrations (global)
(080.2720) Geometric optics : Mathematical methods (general)

History
Original Manuscript: June 29, 1998
Revised Manuscript: October 8, 1998
Manuscript Accepted: November 13, 1998
Published: April 1, 1999

Citation
Kurt Bernardo Wolf and Guillermo Krötzsch, "Metaxial correction of fractional Fourier transformers," J. Opt. Soc. Am. A 16, 821-830 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-4-821


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References

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