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23 April 2019 A fast numerical algorithm for the 2D non-separable linear canonical transform based on a decomposition of the ABCD matrix
Liang Zhao, Min Wan, Qing Li, Sannuya Liu, John Sheridan, John Healy
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Proceedings Volume 11030, Holography: Advances and Modern Trends VI; 110301G (2019) https://doi.org/10.1117/12.2522839
Event: SPIE Optics + Optoelectronics, 2019, Prague, Czech Republic
Abstract
The two-dimensional non-separable linear canonical transform (2D-NS-LCT) can model a wide range of paraxial optical systems. Digital algorithms to calculate the 2D-NS-LCTs are of great interested in both light propagation modeling and digital signal processing. We have previously reported that the transform of a 2D image with rectangular sampling grid generally results in a parallelogram output sampling grid, thus complicating further calculations. One possible solution is to use interpolation techniques. However, it usually leads to poor calculation speed and reduced accuracy. To alleviate this problem, we previously proposed a unitary algorithm by choosing an advantageous sampling rate related to the system parameters. In this paper, a fast algorithm is further proposed based on a novel matrix decomposition, which can significantly improve the efficiency of the numerical approximations.
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Liang Zhao, Min Wan, Qing Li, Sannuya Liu, John Sheridan, and John Healy "A fast numerical algorithm for the 2D non-separable linear canonical transform based on a decomposition of the ABCD matrix", Proc. SPIE 11030, Holography: Advances and Modern Trends VI, 110301G (23 April 2019); https://doi.org/10.1117/12.2522839
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KEYWORDS
Systems modeling
Digital Light Processing
Digital signal processing
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