Abstract

A new set of optical implementations of the fractional Fourier transform (FRT) is developed by use of Wigner matrix algebra. The reinterpretation of some elementary operations that synthesize a rotation in the phase-space domain allows us to propose a lensless setup for obtaining the FRT. This compact configuration is also very flexible, because the fractional degree of the transformation can be varied continuously by shifting the input and the output planes along the optical axis by proper amounts. The above results permit one to build an optical FRT processor formed by two FRT systems in cascade, with a spatial filter between them. We present the design of such a variable FRT processor, which contains only one lens.

© 1997 Optical Society of America

Variable fractional Fourier processor: a simple implementation: erratum

Pedro Andrés, Walter D. Furlan, Genaro Saavedra, and Adolf W. Lohmann
J. Opt. Soc. Am. A 14(12) 3432-3432 (1997)

Extended fractional Fourier transforms

Jianwen Hua, Liren Liu, and Guoqiang Li
J. Opt. Soc. Am. A 14(12) 3316-3322 (1997)

Scaled fractional Fourier transform and its optical implementation

Jianwen Hua, Liren Liu, and Guoqiang Li
Appl. Opt. 36(32) 8490-8492 (1997)

Fractional Fourier transform description with use of differential operators

B. Ruiz and H. Rabal
J. Opt. Soc. Am. A 14(11) 2905-2913 (1997)

Optical correlation based on the fractional Fourier transform

Sergio Granieri, Ricardo Arizaga, and Enrique E. Sicre
Appl. Opt. 36(26) 6636-6645 (1997)