河南科技大学本科毕业设计（论文）11A cascaded iterative Fourier transform algorithm for optical security applicationsAbstract:A cascaded iterative Fourier transform (CIFT) algorithm is presented for optical security applications. Two phase-masks are designed and located in the input and the Fourier domains of a 4-f correlator respectively, in order to implement the optical encryption or authenticity verification. Compared with previous methods, the proposed algorithm employs an improved searching strategy: modifying the phase-distributions of both masks synchronously as well as enlarging the searching space. Computer simulations show that the algorithm results in much faster convergence and better image quality for the recovered image. Each of these masks is assigned to different person. Therefore, the decrypted image can be obtained only when all these masks are under authorization. This key-assignment strategy may reduce the risk of being intruded.Key words: Optical security optical encryption cascaded iterative Fourier transform algorithm1. IntroductionOptical techniques have shown great potential in the field of information security applications. Recently Rfrgier and Javidi proposed a novel double-random-phase encoding technique, which encodes a primary image into a stationary white noise. This technique was also used to encrypt information in the fractional Fourier domain and to store encrypted information holographically. Phase encoding techniques were also proposed for optical authenticity verification. Wang et al and Li et al proposed another method for optical encryption and authenticity verification. Unlike the techniques mentioned above, this method encrypts information completely into a phase mask, which is located in either the input or the Fourier domain of a 4-f correlator. For instance, given the predefinitions of a significant image f(x, y) as the desired output and a phase-distribution expjb(u, v) in the Fourier domain, its easy to optimize the other phase function expjp(x, y) with a modified projection onto constraint sets (POCS) algorithm 10. Therefore the image f(x, y) is encoded successfully into expjp(x, y) with the aid of expjb(u, v). In other words, the fixed phase expjb(u, v) serves as the lock while the retrieved phase expjp(x, y) serves as the key of the security system. To reconstruct the original information, the phase functions expjp(x, y) and expjb(u, v) must match and be located in the input and the Fourier plane respectively. Abookasis et al implemented this scheme with a joint transform correlator for optical verification. 河南科技大学本科毕业设计（论文）22However, because the key expjp(x, y) contains information of the image f(x, y) and the lock expjb(u, v), and the 4-f correlator has a character of linearity, it is possible for the intruder to find out the phase-distribution of the lock function by statistically analyzing the random characters of the keys if the system uses only one lock for different image. In order to increase the secure level of such system, one approach is to use different lock function for different image. Enlarging the key space is another approach to increase the secure level. It can be achieved by encrypting images in the fractional Fourier domain; as a result, the scale factors and the transform order offer additional keys. On the other hand, note that the phase-mask serves as the key of the system, enlarging the key space can be achieved by encoding the target image into two or more phase masks with a modified POCS algorithm. Chang et al have proposed a multiple-phases retrieval algorithm and demonstrated that an optical security system based on it has higher level of security and higher quality for the decrypted image. However, this algorithm retrieves only one phase-distribution with a phase constraint in each iteration. As a result, the masks are not so consistent and may affect the quality of the recovered image. In the present paper, we propose a modified POCS algorithm that adjusts the distributions of both phase-masks synchronously in each iteration. As a result, the convergent speed of the iteration process is expected to significantly increase. And the target image with much higher quality is expected to recover because of the co-adjusting of the two masks during the iteration process. When the iteration process is finished, the target image is encoded into the phase-masks successfully. Each of these masks severs as the key of the security system and part of the encrypted image itself as well. Moreover, the algorithm can be extended to generate multiple phase-masks for arbitrary stages correlator. To acquire the maximum security, each key is assigned to different authority so that the decryption cannot be performed but being authorized by all of them. This key-assignment scheme is especially useful for military and government applications. The algorithm description is presented in Section 2. Computer simulation of this algorithm