Fast and accurate algorithm for the computation of complex linear canonical transforms
| Autor: | Haldun M. Ozaktas, Aykut Koc, Lambertus Hesselink |
|---|---|
| Přispěvatelé: | Haldun M. Özaktaş |
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
Computer science
Gaussian Computation Fast Fourier transform Lossless Space-bandwidth product Fractional Fourier transforms Linear canonical transform symbols.namesake Bandwidth Graded index Number of samples Optical systems Input sample Paraxial optical systems Fast Fourier transforms Eigenvalues and eigenfunctions Free space Lossy systems Numerical analysis Complex parameter Thin lens Complex number Linear canonical transformation Binary logarithm Atomic and Molecular Physics and Optics matrix Phase systems Electronic Optical and Magnetic Materials Fourier transform Gaussians Gaussian apertures Input-output symbols Mathematical transformations Computer Vision and Pattern Recognition Numerical computations Algorithm Algorithms |
| Zdroj: | Journal of the Optical Society of America A: Optics and Image Science, and Vision |
| Popis: | 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 approximately 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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