Secure optical encryption based on ghost imaging with fractional Fourier transform

Abstract In this paper, we propose an optical encryption scheme based on ghost imaging with fractional Fourier transform (FrFT). In the scheme, some special FrFT speckles with designed fractional orders are generated and used to illuminate an object, even the object is unknown, and the bucket detector without spatial resolution is then adopted to detect the signal. With the four-step or the three-step phase shift method, the image of the object can only be reconstructed by the authorized user who has the key, while the eavesdropper cannot recover the image. Importantly, the two FrFT parameters are used as the key, which can dramatically reduce the number of bits of the key transferred between authorized users comparing to existing optical encryption schemes based on CGI. In addition, the proposed scheme can be generalized in broadcast way for more authorized users, where each authorized user can obtain his own encrypted image. The experiment and numerical simulation results demonstrate the feasibility of the proposed scheme. The results also show that the image cannot be achieved when the fractional order gap between the IFrFT and the FrFT is greater than 0.4, even though the 100% FrFT speckles have been eavesdropped. It provides a promising imaging way for optical encryption.