Eigenfunctions of the canonical transform and the self-imaging problems in optical system
Journal
ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Journal Volume
1
Pages
73-76
Date Issued
2000-06
Date
2000-06
Author(s)
Abstract
The affine Fourier transform (AFT) also called as the canonical transform. It generalizes the fractional Fourier transform (FRFT), Fresnel transform, scaling operation, etc., and is a very useful tool for signal processing. We derive the eigenfunctions of the AFT. The eigenfunctions seems hard to be derived, but since the AFT can be represented by the time-frequency matrix (TF matrix), we can use the matrix operations to derive its eigenfunctions. Then, because many optical systems can be represented as a special case of the AFT, the eigenfunctions of the AFT are just the light distributions that will cause the self-imaging phenomena for some optical systems. We use the eigenfunctions we derive to discuss the self-imaging phenomena. © 2000 IEEE.
Other Subjects
Affine transforms; Eigenvalues and eigenfunctions; Optical systems; Eigenvalues and eigenfunctions; Imaging techniques; Light scattering; Matrix algebra; Optical instrument lenses; Optical systems; Refractive index; Wave propagation; Affine Fourier transforms; Canonical transform; Fractional Fourier transforms; Fresnel transform; Light distribution; Matrix operations; Self imaging; Time frequency; Signal processing; Fourier transforms; Affine fourier transform; Fractional fourier transform; Fresnel transform
Type
journal article
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