The scaled fractional Fourier transform is suggested and is implemented optically by one lens for different values of φ and output scale. In addition, physically it relates the FRT with the general lens transform—the optical diffraction between two asymmetrically positioned planes before and after a lens.
© 1997 Optical Society of America
Jianwen Hua, Liren Liu, and Guoqiang Li, "Scaled fractional Fourier transform and its optical implementation," Appl. Opt. 36, 8490-8492 (1997)