## Metaxial correction of fractional Fourier transformers

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)

**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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