Alternative representation of the linear canonical integral transform

T. Alieva, M.J. Bastiaans

Research output: Contribution to journalArticleAcademicpeer-review

38 Citations (Scopus)

Abstract

Starting with the Iwasawa decomposition of a first-order optical system (or ABCD-system) as a cascade of a lens, a magnifier, and an ortho-symplectic system (a system that is both symplectic and orthogonal), a further decomposition of the ortho-symplectic system in the form of a separable fractional Fourier transformer embedded in 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.
Original languageEnglish
Pages (from-to)3302-3304
Number of pages3
JournalOptics Letters
Volume30
Issue number24
DOIs
Publication statusPublished - 2005

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integral transformations
decomposition
magnification
transformers
rays
cascades
lenses

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Alternative representation of the linear canonical integral transform. / Alieva, T.; Bastiaans, M.J.

In: Optics Letters, Vol. 30, No. 24, 2005, p. 3302-3304.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Alieva, T.

AU - Bastiaans, M.J.

PY - 2005

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N2 - Starting with the Iwasawa decomposition of a first-order optical system (or ABCD-system) as a cascade of a lens, a magnifier, and an ortho-symplectic system (a system that is both symplectic and orthogonal), a further decomposition of the ortho-symplectic system in the form of a separable fractional Fourier transformer embedded in 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.

AB - Starting with the Iwasawa decomposition of a first-order optical system (or ABCD-system) as a cascade of a lens, a magnifier, and an ortho-symplectic system (a system that is both symplectic and orthogonal), a further decomposition of the ortho-symplectic system in the form of a separable fractional Fourier transformer embedded in 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.

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DO - 10.1364/OL.30.003302

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