THE FRACTIONAL FOURIER-TRANSFORM IN OPTICAL PROPAGATION PROBLEMS - COMMENT

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 interpret ation of the FRT given recently in a paper by Alieva et al, is not phy sically appropriate. We then show how those integral transformations c an be treated in a unified way within the framework of the special aff ine Fourier transformation. Finally the multidimensional FRT presented in the above paper is further generalized to allow n independent frac tional degrees.