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J Opt Soc Am A Opt Image Sci Vis. 2005 Mar;22(3):460-74.

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

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Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan 10617.


Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.


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