## Eigenfunctions of the offset Fourier, fractional Fourier, and linear canonical transforms

JOSA A, Vol. 20, Issue 3, pp. 522-532 (2003)

http://dx.doi.org/10.1364/JOSAA.20.000522

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### Abstract

The offset Fourier transform (offset FT), offset fractional Fourier transform (offset FRFT), and offset linear canonical transform (offset LCT) are the space-shifted and frequency-modulated versions of the original transforms. They are more general and flexible than the original ones. We derive the eigenfunctions and the eigenvalues of the offset FT, FRFT, and LCT. We can use their eigenfunctions to analyze the self-imaging phenomena of the optical system with free spaces and the media with the transfer function

© 2003 Optical Society of America

**OCIS Codes**

(070.2580) Fourier optics and signal processing : Paraxial wave optics

(070.2590) Fourier optics and signal processing : ABCD transforms

(070.6020) Fourier optics and signal processing : Continuous optical signal processing

**History**

Original Manuscript: October 11, 2002

Manuscript Accepted: October 15, 2002

Published: March 1, 2003

**Citation**

Soo-Chang Pei and Jian-Jiun Ding, "Eigenfunctions of the offset Fourier, fractional Fourier, and linear canonical transforms," J. Opt. Soc. Am. A **20**, 522-532 (2003)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-3-522

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