A numerical algorithm based on a single fast Fourier transform is proposed. Its precision and calculation efficiency show better performance than those of previously published algorithms. It is also shown that if specific conditions are met, the numerical calculations of two successive fractional Fourier transforms produce results that are similar to the analytical solution.
© 1998 Optical Society of America
(070.2590) Fourier optics and signal processing : ABCD transforms
Original Manuscript: October 22, 1997
Revised Manuscript: February 25, 1998
Manuscript Accepted: April 23, 1998
Published: August 1, 1998
Francisco J. Marinho and Luı́s M. Bernardo, "Numerical calculation of fractional Fourier transforms with a single fast-Fourier-transform algorithm," J. Opt. Soc. Am. A 15, 2111-2116 (1998)