We have investigated the multiplicity and complexity in eigenvalues of the fractional Fourier transform and found that the ambiguity of the eigenvalues may indicate randomness. We have therefore proposed a method to randomize the Fourier transform. Such a random Fourier transform can be applied in the field of image encryption and decryption.
© 2007 Optical Society of America
Fourier Optics and Optical Signal Processing
Original Manuscript: October 12, 2006
Revised Manuscript: November 13, 2006
Manuscript Accepted: November 20, 2006
Published: February 2, 2007
Zhengjun Liu and Shutian Liu, "Randomization of the Fourier transform," Opt. Lett. 32, 478-480 (2007)