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Optics Letters

Optics Letters


  • Editor: Anthony J. Campillo
  • Vol. 30, Iss. 24 — Dec. 15, 2005
  • pp: 3302–3304

Alternative representation of the linear canonical integral transform

Tatiana Alieva and Martin J. Bastiaans  »View Author Affiliations

Optics Letters, Vol. 30, Issue 24, pp. 3302-3304 (2005)

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Starting with the Iwasawa-type decomposition of a first-order optical system (or ABCD system) as a cascade of a lens, a magnifier, and an orthosymplectic system (a system that is both symplectic and orthogonal), a further decomposition of the orthosymplectic system in the form of a separable fractional Fourier transformer embedded between two spatial-coordinate rotators is proposed. The resulting decomposition of the entire first-order optical system then shows a physically attractive representation of the linear canonical integral transformation, which, in contrast to Collins integral, is valid for any ray transformation matrix.

© 2005 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
(080.2730) Geometric optics : Matrix methods in paraxial optics
(120.4820) Instrumentation, measurement, and metrology : Optical systems

ToC Category:
Fourier Optics and Optical Signal Processing

Tatiana Alieva and Martin J. Bastiaans, "Alternative representation of the linear canonical integral transform," Opt. Lett. 30, 3302-3304 (2005)

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