Fast and accurate algorithm for the computation of complex linear canonical transforms

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buir.contributor.authorHaldun M. Özaktaş
dc.citation.epage1908en_US
dc.citation.issueNumber9en_US
dc.citation.spage1896en_US
dc.citation.volumeNumber27en_US
dc.contributor.authorKoç A.
dc.contributor.authorÖzaktaş, Haldun M.
dc.contributor.authorHesselink, L.
dc.date.accessioned2016-02-08T09:57:14Z
dc.date.available2016-02-08T09:57:14Z
dc.date.issued2010-08-05en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractA fast and accurate algorithm is developed for the numerical computation of the family of complex linear canonical transforms (CLCTs), which represent the input-output relationship of complex quadratic-phase systems. Allowing the linear canonical transform parameters to be complex numbers makes it possible to represent paraxial optical systems that involve complex parameters. These include lossy systems such as Gaussian apertures, Gaussian ducts, or complex graded-index media, as well as lossless thin lenses and sections of free space and any arbitrary combinations of them. Complex-ordered fractional Fourier transforms (CFRTs) are a special case of CLCTs, and therefore a fast and accurate algorithm to compute CFRTs is included as a special case of the presented algorithm. The algorithm is based on decomposition of an arbitrary CLCT matrix into real and complex chirp multiplications and Fourier transforms. The samples of the output are obtained from the samples of the input in ∼N log N time, where N is the number of input samples. A space-bandwidth product tracking formalism is developed to ensure that the number of samples is information-theoretically sufficient to reconstruct the continuous transform, but not unnecessarily redundant.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T09:57:14Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2010en
dc.identifier.doi10.1364/JOSAA.27.001896en_US
dc.identifier.issn1084-7529
dc.identifier.urihttp://hdl.handle.net/11693/22227
dc.language.isoEnglishen_US
dc.publisherOptical Society of Americaen_US
dc.relation.isversionofhttp://dx.doi.org/10.1364/JOSAA.27.001896en_US
dc.source.titleJournal of the Optical Society of America A: Optics and Image Science, and Visionen_US
dc.subjectAlgorithmsen_US
dc.subjectBandwidthen_US
dc.subjectEigenvalues and eigenfunctionsen_US
dc.subjectFast Fourier transformsen_US
dc.subjectOptical systemsen_US
dc.subjectComplex numberen_US
dc.subjectComplex parameteren_US
dc.subjectFractional Fourier transformsen_US
dc.subjectFree spaceen_US
dc.subjectGaussian aperturesen_US
dc.subjectGaussiansen_US
dc.subjectGraded indexen_US
dc.subjectInput sampleen_US
dc.subjectInput-outputen_US
dc.subjectLinear canonical transformen_US
dc.subjectLosslessen_US
dc.subjectLossy systemsen_US
dc.subjectmatrixen_US
dc.subjectNumber of samplesen_US
dc.subjectNumerical computationsen_US
dc.subjectParaxial optical systemsen_US
dc.subjectPhase systemsen_US
dc.subjectSpace-bandwidth producten_US
dc.subjectThin lensen_US
dc.subjectMathematical transformationsen_US
dc.titleFast and accurate algorithm for the computation of complex linear canonical transformsen_US
dc.typeArticleen_US

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