Constraints to solve parallelogram grid problems in 2D non separable linear canonical transform

Liang Zhao; John J. Healy; Inbarasan Muniraj; Xiao-Guang Cui; Ra'ed Malallah; James P. Ryle; John T. Sheridan

doi:10.1117/12.2265862

31 May 2017 Constraints to solve parallelogram grid problems in 2D non separable linear canonical transform

Liang Zhao, John J. Healy, Inbarasan Muniraj, Xiao-Guang Cui, Ra'ed Malallah, James P. Ryle, John T. Sheridan

Proceedings Volume 10233, Holography: Advances and Modern Trends V; 102331V (2017) https://doi.org/10.1117/12.2265862
Event: SPIE Optics + Optoelectronics, 2017, Prague, Czech Republic

Abstract

The 2D non-separable linear canonical transform (2D-NS-LCT) can model a range of various paraxial optical systems. Digital algorithms to evaluate the 2D-NS-LCTs are important in modeling the light field propagations and also of interest in many digital signal processing applications. In [Zhao 14] we have reported that a given 2D input image with rectangular shape/boundary, in general, results in a parallelogram output sampling grid (generally in an affine coordinates rather than in a Cartesian coordinates) thus limiting the further calculations, e.g. inverse transform. One possible solution is to use the interpolation techniques; however, it reduces the speed and accuracy of the numerical approximations. To alleviate this problem, in this paper, some constraints are derived under which the output samples are located in the Cartesian coordinates. Therefore, no interpolation operation is required and thus the calculation error can be significantly eliminated.

Citation Download Citation

Liang Zhao, John J. Healy, Inbarasan Muniraj, Xiao-Guang Cui, Ra'ed Malallah, James P. Ryle, and John T. Sheridan "Constraints to solve parallelogram grid problems in 2D non separable linear canonical transform", Proc. SPIE 10233, Holography: Advances and Modern Trends V, 102331V (31 May 2017); https://doi.org/10.1117/12.2265862

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