Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a = 1. An optical interpretation is provided in terms of quadratic graded index media and discussed from both wave and ray viewpoints. Several mathematical properties are derived.
© 1993 Optical Society of America
Original Manuscript: November 30, 1992
Manuscript Accepted: March 1, 1993
Published: September 1, 1993
David Mendlovic and Haldun M. Ozaktas, "Fractional Fourier transforms and their optical implementation: I," J. Opt. Soc. Am. A 10, 1875-1881 (1993)