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.
© 2005 Optical Society of America
Soo-Chang Pei and Jian-Jiun Ding, "Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms," J. Opt. Soc. Am. A 22, 460-474 (2005)