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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 28, Iss. 2 — Feb. 1, 2011
  • pp: 82–95

Eigenfunctions and self-imaging phenomena of the two-dimensional nonseparable linear canonical transform

J.-J. Ding and S.-C. Pei  »View Author Affiliations

JOSA A, Vol. 28, Issue 2, pp. 82-95 (2011)

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The two-dimensional (2D) nonseparable linear canonical transform (NSLCT) is a generalization of the fractional Fourier transform (FRFT) and the LCT. It is useful in signal analysis and optics. The eigenfunctions of both the FRFT and the LCT have been derived. In this paper, we extend the previous work and derive the eigenfunctions of the 2D NSLCT. Although the 2D NSLCT is very complicated and has 16 parameters, with the proposed methods, we can successfully find the eigenfunctions of the 2D NSLCT in all cases. Since many optical systems can be represented by the 2D NSLCT, our results are useful for analyzing the self-imaging phenomena of optical systems.

© 2011 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.2590) Fourier optics and signal processing : ABCD transforms
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms
(080.2575) Geometric optics : Fractional Fourier transforms

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: September 14, 2010
Revised Manuscript: November 10, 2010
Manuscript Accepted: November 10, 2010
Published: January 5, 2011

J.-J. Ding and S.-C. Pei, "Eigenfunctions and self-imaging phenomena of the two-dimensional nonseparable linear canonical transform," J. Opt. Soc. Am. A 28, 82-95 (2011)

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