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

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