A self-Fourier function (SFF), according to Caola [ J. Phys. A 24, L1143 ( 1991)], is a function that is its own Fourier transform. The Gaussian and Dirac combs are well-known examples. Many more SFF’s have been discovered recently by Caola. This discovery might bear some fruit in optics, since the Fourier transform is perhaps the most important theoretical tool in wave optics. We show that Caola discovered all SFF’s. Furthermore, we study other self-transform functions, which are also tied to some transformations that play a role in coherent optics.
© 1992 Optical Society of America
Original Manuscript: January 23, 1992
Revised Manuscript: April 6, 1992
Manuscript Accepted: May 8, 1992
Published: November 1, 1992
Adolf W. Lohmann and David Mendlovic, "Self-Fourier objects and other self-transform objects," J. Opt. Soc. Am. A 9, 2009-2012 (1992)