Eigenfunctions of the offset Fourier, fractional Fourier, and linear canonical transforms
Journal
Journal of the Optical Society of America A: Optics and Image Science, and Vision
Journal Volume
20
Journal Issue
3
Pages
522-532
Date Issued
2003
Author(s)
Abstract
The offset Fourier transform (offset FT), offset fractional Fourier transform (offset FRFT), and offset linear canonical transform (offset LCT) are the space-shifted and frequency-modulated versions of the original transforms. They are more general and flexible than the original ones. We derive the eigenfunctions and the eigenvalues of the offset FT, FRFT, and LCT. We can use their eigenfunctions to analyze the self-imaging phenomena of the optical system with free spaces and the media with the transfer function exp[j(h 2x2 + h1x + h0)] (such as lenses and shifted lenses). Their eigenfunctions are also useful for resonance phenomena analysis, fractal theory development, and phase retrieval. © 2003 Optical Society of America.
Other Subjects
Eigenvalues and eigenfunctions; Fourier transforms; Optical transfer function; Linear canonical transforms (LCT); Optical systems
Type
journal article
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