Previous generalizations of the fractional Fourier transform to two dimensions assumed separable kernels. We present a nonseparable definition for the two-dimensional fractional Fourier transform that includes the separable definition as a special case. Its digital and optical implementations are presented. The usefulness of the nonseparable transform is justified with an image-restoration example.
© 1998 Optical Society of America
Original Manuscript: December 4, 1997
Revised Manuscript: May 12, 1998
Published: August 10, 1998
Aysegul Sahin, M. Alper Kutay, and Haldun M. Ozaktas, "Nonseparable two-dimensional fractional Fourier transform," Appl. Opt. 37, 5444-5453 (1998)