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Although their mathematical forms apparently resemble each other, the diffraction integral and fractional Fourier transformation (FRT) have completely different physical meanings. This report shows than an interpretation of the FRT given in the paper of Alieva, Lopez, Agullo-Lopez, and Almeida [J. Mod. Opt. 41, 1037 (1994)] is not physically appropriate. It also shows how those integral transformations can be treated in a unified way within the framework of the special affine Fourier transformation (SAFT). Finally the multi-dimensional FRT presented in the above paper is further generalized to allow n independent fractional degrees.

Additional information

Authors: SHERIDAN J T, JRC Ispra (IT);COUTSOMITROS C T, JRC Ispra (IT);LUCIA A, JRC Ispra (IT);ABE S, Nihon University, College of Science and Technology, Chiba (JP)
Bibliographic Reference: EUR 16375 EN (1996) 13pp., FS, free of charge
Availability: Available from the Public Relations and Publications Unit, JRC Ispra, I-21020 Ispra (IT)
Record Number: 199610532 / Last updated on: 1996-05-13
Original language: en
Available languages: en