Fast and accurate algorithm for the computation of complex linear canonical transforms
Author
Koç A.
Haldun M. Özaktaş
Hesselink, L.
Date
2010-08-05Source Title
Journal of the Optical Society of America A: Optics and Image Science, and Vision
Print ISSN
1084-7529
Publisher
Optical Society of America
Volume
27
Issue
9
Pages
1896 - 1908
Language
English
Type
ArticleItem Usage Stats
128
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Abstract
A 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.
Keywords
AlgorithmsBandwidth
Eigenvalues and eigenfunctions
Fast Fourier transforms
Optical systems
Complex number
Complex parameter
Fractional Fourier transforms
Free space
Gaussian apertures
Gaussians
Graded index
Input sample
Input-output
Linear canonical transform
Lossless
Lossy systems
matrix
Number of samples
Numerical computations
Paraxial optical systems
Phase systems
Space-bandwidth product
Thin lens
Mathematical transformations
Permalink
http://hdl.handle.net/11693/22227Published Version (Please cite this version)
http://dx.doi.org/10.1364/JOSAA.27.001896Collections
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