19 September 2014 Unitary implementation of the discrete two-dimensional non-separable linear canonical transform
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The continuous linear canonical transforms is known to describes wave field propagation through paraxial (quadratic phase) optical systems. Digital algorithms to numerically calculate the LCT are therefore important in modelling field propagation through first order optical systems and are also of interest for many purely digital signal processing applications. Significantly the continuous LCTs are unitary, but discretization can destroy this property resulting in a loss of conservative properties. Previously we presented a sufficient condition on the sampling rates chosen during discretization to ensure that digital implementations of the 1D and 2D separable LCTs were unitary. In this paper we extend our analysis to discuss the cases of the 2D non-separable LCT which are used to describe non-orthogonal, nonaxially symmetric and anamorphic systems. We also examine the consequences of ours results.
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Liang Zhao, Liang Zhao, John J. Healy, John J. Healy, John T. Sheridan, John T. Sheridan, "Unitary implementation of the discrete two-dimensional non-separable linear canonical transform", Proc. SPIE 9216, Optics and Photonics for Information Processing VIII, 921610 (19 September 2014); doi: 10.1117/12.2060984; https://doi.org/10.1117/12.2060984

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