Publication: Alternative representation of the linear canonical integral transform
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2005-12-15
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Optical Society of America
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Abstract
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.
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© 2005 Optical Society of America. The Spanish Ministry of Education and Science is acknowledged for financial support through a “Ramon y Cajal” grant and projects TIC 2002-01846 (T. Alieva, talieva@fis.ucm.es) and SAB2004-0018 (M. J. Bastiaans, m.j.bastiaans@tue.nl).
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