Fractional Fourier transforms and their optical implementation: I

David Mendlovic, Haldun M. Ozaktas
1993 Optical Society of America. Journal A: Optics, Image Science, and Vision  
Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a = 1. An optical interpretation is provided in terms of quadratic graded index media and discussed from both wave and ray viewpoints. Several mathematical properties are derived.
doi:10.1364/josaa.10.001875 fatcat:fbsaboyb55g4fenk73eilywqbi