Abstract

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.

© 2011 Optical Society of America

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