Abstract

Several respected colleges and anonymous reviewers asked us: is the fractional Fourier transform (FRT) more than a modified Fresnel transform (FRS)? Our answer is yes, the FRT is in our opinion a worthy addition to the class of transformations in optics. To understand our belief it might be useful to re call, why we invented the optical FRT, actually twice, at first in the context of GRIN fiber optics (1) and then as a linear centerpiece to sketch how the FRT could have been invented as a special case of A. E. siegman's integral transform, or as a special case of J. Shamir's operator optics. Those two authors could have invented easily the FRT, if the need to do so had arisen. We mention those two almost-inventions in order to present family features of various optical transforms. Furthermore, this sideline of our arguments is useful as preparation for answering the question; which one of all those transforms is most fundamental? We will propose four criteria for measuring the fundamentality. In our opinion, all four criteria are subjective in nature. In other words, a statement like: transform A is merely a modification of transform B, has no universal validity.

© 1995 Optical Society of America