Similarity theorems for fractional Fourier transforms and fractional Hankel transforms

摘要

The significance of the similarity theorem for the fractional Fourier transform is discussed, and the properties of self-similar functions considered. The coucept of the fractional Hankel transform is developed for use in the analysis of diffraction and imaging in symmetrical optical systems. The particular case of Fresnel diffraction from a circular aperture is discussed and the effects of the similarity theorem are described.