Eigenfunctions and self-imaging phenomena of the two-dimensional nonseparable linear canonical transform | Zendy

Jian–Jiun Ding | Zendy; SooChang Pei | Zendy

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Eigenfunctions and self-imaging phenomena of the two-dimensional nonseparable linear canonical transform

Author(s) -

Jian–Jiun Ding,

SooChang Pei

Publication year - 2011

Publication title -

journal of the optical society of america a

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.803

H-Index - 158

eISSN - 1520-8532

pISSN - 1084-7529

DOI - 10.1364/josaa.28.000082

Subject(s) - eigenfunction , fractional fourier transform , fourier transform , generalization , work (physics) , image (mathematics) , mathematics , mathematical analysis , physics , computer science , fourier analysis , eigenvalues and eigenvectors , quantum mechanics , artificial intelligence

The two-dimensional (2D) nonseparable linear canonical transform (NSLCT) is a generalization of the fractional Fourier transform (FRFT) and the LCT. It is useful in signal analysis and optics. The eigenfunctions of both the FRFT and the LCT have been derived. In this paper, we extend the previous work and derive the eigenfunctions of the 2D NSLCT. Although the 2D NSLCT is very complicated and has 16 parameters, with the proposed methods, we can successfully find the eigenfunctions of the 2D NSLCT in all cases. Since many optical systems can be represented by the 2D NSLCT, our results are useful for analyzing the self-imaging phenomena of optical systems.

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