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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 11 — Nov. 1, 2007
  • pp: 3658–3665

Properties of the linear canonical integral transformation

Tatiana Alieva and Martin J. Bastiaans  »View Author Affiliations

JOSA A, Vol. 24, Issue 11, pp. 3658-3665 (2007)

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We provide a general expression and different classification schemes for the general two-dimensional canonical integral transformations that describe the propagation of coherent light through lossless first-order optical systems. Main theorems for these transformations, such as shift, scaling, derivation, etc., together with the canonical integral transforms of selected functions, are derived.

© 2007 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.4690) Fourier optics and signal processing : Morphological transformations
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(080.2730) Geometric optics : Matrix methods in paraxial optics
(110.6980) Imaging systems : Transforms
(120.4820) Instrumentation, measurement, and metrology : Optical systems
(350.6980) Other areas of optics : Transforms

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: May 4, 2007
Revised Manuscript: September 19, 2007
Manuscript Accepted: October 2, 2007
Published: October 30, 2007

Tatiana Alieva and Martin J. Bastiaans, "Properties of the linear canonical integral transformation," J. Opt. Soc. Am. A 24, 3658-3665 (2007)

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