Eigenfunctions of the canonical transform and the self-imaging problems in optical system
نویسندگان
چکیده
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. In this paper, we will derive the eigenfunctions of AFT. The eigenfunctions seems hard to be derived, but since AFT can be represented by the time-frequency matrix (TF matrix), so we can just use the matrix operations to derive its eigenfunctions. Then, because many optical systems can be represented as a special case of AFT, so the eigenfunctions of the AFT are just the light distributions that will cause the selfimaging phenomena for some optical system. We will use the eigenfunctions we derive to discuss the self-imaging phenomena.
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