## Fractional Fourier transforms in two dimensions

JOSA A, Vol. 17, Issue 12, pp. 2368-2381 (2000)

http://dx.doi.org/10.1364/JOSAA.17.002368

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### Abstract

We analyze the fractionalization of the Fourier transform (FT), starting from the minimal premise that repeated application of the fractional Fourier transform (FrFT) a sufficient number of times should give back the FT. There is a qualitative increase in the richness of the solution manifold, from U(1) (the circle *N*-dimensional case. The parameterization of this manifold (a fiber bundle) is accomplished through two powers running over the torus

© 2000 Optical Society of America

**OCIS Codes**

(070.2590) Fourier optics and signal processing : ABCD transforms

(080.2730) Geometric optics : Matrix methods in paraxial optics

**History**

Original Manuscript: March 30, 2000

Revised Manuscript: July 13, 2000

Manuscript Accepted: July 13, 2000

Published: December 1, 2000

**Citation**

R. Simon and Kurt Bernardo Wolf, "Fractional Fourier transforms in two dimensions," J. Opt. Soc. Am. A **17**, 2368-2381 (2000)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-12-2368

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