1 May 2014 Sampling of the two dimensional non-separable linear canonical transform
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The two-dimensional non-separable linear canonical transform (2D-NS-LCT) involves a significant generalization of the separable LCT (S-LCT), since it can represent orthogonal and non-orthogonal first order optical systems. Thus the availability of a discrete numerical approximation of the 2D-NS-LCT is important as it permits the modelling of a broad class of optical systems. The continuous 2D-NS-LCTs are unitary, but discretization can destroy this property. In this paper, we discuss the condition on the sampling chosen in the discretization, under which some special cases of the discrete 2D-NS-LCTs are unitary. The results presented here provide a basis for the discussion of the general condition for the discrete 2D-NS-LCT to be unitarity.
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Liang Zhao, Liang Zhao, John J. Healy, John J. Healy, John T. Sheridan, John T. Sheridan, "Sampling of the two dimensional non-separable linear canonical transform", Proc. SPIE 9131, Optical Modelling and Design III, 913112 (1 May 2014); doi: 10.1117/12.2052549; https://doi.org/10.1117/12.2052549

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