Abstract

The fractional Fourier transform is a mathematical operation that generalizes the well-known Fourier transform. This operation has been shown to have physical and optical fundamental meanings, and it has been experimentally implemented by relatively simple optical setups. Based on the fractional Fourier-transform operation, a new space-frequency chart definition is introduced. By the application of various geometric operations on this new chart, such as radial and angular shearing and rotation, optical systems may be designed or analyzed. The field distribution, as well as full information about the spectrum and the space–bandwidth product, can be easily obtained in all the stages of the optical system.

© 1995 Optical Society of America

Wigner-related phase spaces for signal processing and their optical implementation

David Mendlovic, Zeev Zalevsky, and Haldun M. Ozaktas
J. Opt. Soc. Am. A 17(12) 2339-2354 (2000)

Incoherent fractional Fourier transform and its optical implementation

David Mendlovic, Zeev Zalevsky, Naim Konforti, Rainer G. Dorsch, and Adolf W. Lohmann
Appl. Opt. 34(32) 7615-7620 (1995)

Variable fractional Fourier processor: a simple implementation

Pedro Andrés, Walter D. Furlan, Genaro Saavedra, and Adolf W. Lohmann
J. Opt. Soc. Am. A 14(4) 853-858 (1997)

Extended fractional Fourier transforms

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

Fractional Fourier transformer of variable order based on a modular lens system

Rainer G. Dorsch
Appl. Opt. 34(26) 6016-6020 (1995)