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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. We point out that an interpretation of the FRT given in the paper of Alieva, Lopez, Agullo-Lopez, and Almeida (Journal of Modern Optics, Vol. 41 (1994) p. 1037) is not physically appropriate. We then show how those integral transformation 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: ABE S, Nihon University, College of Science and Technology, Chiba (JP);SHERIDAN J T, JRC Ispra (IT)
Bibliographic Reference: Article: Journal of Modern Optics (1996)
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