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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 29, Iss. 8 — Aug. 1, 2012
  • pp: 1615–1624

Improved implementation algorithms of the two-dimensional nonseparable linear canonical transform

Jian-Jiun Ding, Soo-Chang Pei, and Chun-Lin Liu  »View Author Affiliations


JOSA A, Vol. 29, Issue 8, pp. 1615-1624 (2012)
http://dx.doi.org/10.1364/JOSAA.29.001615


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Abstract

The two-dimensional nonseparable linear canonical transform (2D NSLCT), which is a generalization of the fractional Fourier transform and the linear canonical transform, is useful for analyzing optical systems. However, since the 2D NSLCT has 16 parameters and is very complicated, it is a great challenge to implement it in an efficient way. In this paper, we improved the previous work and propose an efficient way to implement the 2D NSLCT. The proposed algorithm can minimize the numerical error arising from interpolation operations and requires fewer chirp multiplications. The simulation results show that, compared with the existing algorithm, the proposed algorithms can implement the 2D NSLCT more accurately and the required computation time is also less.

© 2012 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

History
Original Manuscript: April 2, 2012
Revised Manuscript: June 13, 2012
Manuscript Accepted: June 18, 2012
Published: July 20, 2012

Citation
Jian-Jiun Ding, Soo-Chang Pei, and Chun-Lin Liu, "Improved implementation algorithms of the two-dimensional nonseparable linear canonical transform," J. Opt. Soc. Am. A 29, 1615-1624 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-8-1615


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