Optical image encryption based on double phase encoding with fractional Fourier transform

A fractional Fourier domain double phase encoding method is proposed for the optical image encryption system. The encryption technique adopts two stages of fractional Fourier transforms with the conventional random phase encoding in both of the original image plane and the fractional Fourier domain. Numerical simulations show that the proposed technique is as efficient as the conventional Fourier domain random phase encoding. However, with the additional degrees of freedom provided by the fractional Fourier transform, the numbers of security keys can be increased from two to four. That makes the encrypted image more difficult to be decrypted by an unauthorized person.