Fast numerical algorithm for the linear canonical transform

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dc.contributor.author Hennelly, Bryan M.
dc.contributor.author Sheridan, John T.
dc.date.accessioned 2011-12-01T11:27:06Z
dc.date.available 2011-12-01T11:27:06Z
dc.date.copyright 2005 Optical Society of America en
dc.date.issued 2005-05-01
dc.identifier.citation Journal of the Optical Society of America A en
dc.identifier.issn 1084-7529
dc.identifier.issn 1520-8532
dc.identifier.uri http://hdl.handle.net/10197/3368
dc.description.abstract The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the area of optical signal processing) to calculate the discrete FT, FRT, and FST. All of these algorithms are based on the use of the fast Fourier transform (FFT). In this paper we develop theory for the discrete linear canonical transform (DLCT), which is to the LCT what the discrete Fourier transform (DFT) is to the FT. We then derive the fast linear canonical transform (FLCT), an N log N algorithm for its numerical implementation by an approach similar to that used in deriving the FFT from the DFT. Our algorithm is significantly different from the FFT, is based purely on the properties of the LCT, and can be used for FFT, FRT, and FST calculations and, in the most general case, for the rapid calculation of the effect of any QPS. en
dc.description.sponsorship Science Foundation Ireland en
dc.description.sponsorship Irish Research Council for Science, Engineering and Technology en
dc.format.extent 194995 bytes
dc.format.extent 1072 bytes
dc.format.mimetype application/pdf
dc.format.mimetype text/plain
dc.language.iso en en
dc.publisher Optical Society of America en
dc.rights This paper was published in Journal of the Optical Society of America A and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/abstract.cfm?URI=JOSAA-22-5-928. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law. en
dc.subject.lcsh Contact transformations en
dc.subject.lcsh Optical data processing en
dc.subject.lcsh Image processing--Digital techniques en
dc.subject.lcsh Fourier transform optics en
dc.title Fast numerical algorithm for the linear canonical transform en
dc.type Journal Article en
dc.internal.availability Full text available en
dc.internal.webversions Publisher's version en
dc.internal.webversions http://dx.doi.org/10.1364/JOSAA.22.000928 en
dc.status Not peer reviewed en
dc.identifier.volume 22 en
dc.identifier.issue 5 en
dc.identifier.startpage 928 en
dc.identifier.endpage 937 en
dc.identifier.doi 10.1364/JOSAA.22.000928
dc.neeo.contributor Hennelly|Bryan M.|aut| en
dc.neeo.contributor Sheridan|John T.|aut| en
dc.description.othersponsorship Enterprise Ireland en
dc.description.admin da, pe, la, sp, ke, ab, is, en - kpw24/11/11 en


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