Abstract

An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and flexible configuration is tested with a chirplike input signal, and the good experimental results obtained support the theory.

© 2000 Optical Society of America

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)

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)

Anamorphic fractional Fourier transform: optical implementation and applications

David Mendlovic, Yigal Bitran, Rainer G. Dorsch, Carlos Ferreira, Javier Garcia, and Haldun M. Ozaktaz
Appl. Opt. 34(32) 7451-7456 (1995)

Scaled fractional Fourier transform and its optical implementation

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

Achromatic Fourier transforming properties of a separated diffractive lens doublet: theory and experiment

Enrique Tajahuerce, Vicent Climent, Jesús Lancis, Mercedes Fernández-Alonso, and Pedro Andrés
Appl. Opt. 37(26) 6164-6173 (1998)