1、PDF外文：http:/ AcascadediterativeFouriertransformalgorithm foroptical securityapplications Abstract: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 corr
2、elator 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. Compu
3、ter 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 stra
4、tegy may reduce the risk of being intruded. Key words: Opticalsecurityoptical encryptioncascaded iterativeFouriertransformalgorithm 1.Introduction Optical techniques have shown great potential in the field of information security applications. Recently Rfrgier and Javidi proposed a novel doubl
5、e-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 optica
6、l 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 Four
7、ier 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 &nbs
8、p;(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 lockwhile the retrieved phase expjp(x, y) serves as the key of the security system. To reconstruct the origin
9、al 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. However, because the key expjp(x, y) contains informat
10、ion 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 diff
11、erent 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
12、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 mult
13、iple-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 no
14、t 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 significan
15、tly 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 o
16、f 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
17、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 and the corresponding discuss are presented in Section 3. 2. Cascaded It
18、erative Fourier Transform (CIFT) Algorithm Consider the operation of the encryption system with the help of a 4-f correlator as shown in Fig.1, the phase masks placed in the input and the Fourier planes are denoted as and respectively, where (x, y) and (u, v) represent the space and the freque
19、ncy coordinate, respectively. Once the system is illuminated with a monochromatic plane wave, a target image f(x,y)(an image to be decrypted or verified) is expected to obtain at the output plane. The phase-masks andcontain the information of f(x,y), that is,f(x,y)is encoded into these phase-masks.
20、The encoding process is the optimization of the two phase-distributions. It is somewhat similar with the problems of the image reconstruction and the phase retrieval, which can be solved with the POCS algorithm. However, the present problem comes down to the phase retrieval in three (or more, in gen
21、eral) planes along the propagation direction. So the conventional POCS algorithm should be modified for this application. The cascaded iteration Fourier transform (CIFT) algorithm begins with the initialization of the phase-distributions of the masks. Suppose the iteration process reach
22、es the kthiteration (k = 1, 2, 3, ), and the phase -distributions in the input and the Fourier plane are represented as and , respectively. Then an estimation of the target image is obtained at the output of the correlator defined by where FT and IFT denote the Fourier transform and the
23、 inverse Fourier transform, respectively.Iffk(x,y)satisfies the convergent criterion, the iteration process stops, and and are the optimized distributions. Otherwise, the fk(x,y) is modified to satisfy the target image constraint as follows Then the modified function is transformed backward t
24、o generate both of the phase-distributions as follows where ang denotes the phase extraction function. Then k is replaced by k+1 for the next iteration. It is shown in Eqs. 3(a) and 3(b) that both of the phase-distributions are modified in every iteration, accorded to the estimation of the ta
25、rget image in the present iteration. It ensures he algorithm converges with much faster speed and more consistent for the phase-masks. In general, the convergent criterion can be the MSE or the correlation coefficient between the iterated and the target image, which are defined by where M*N is the size of the image, and E denotes the mean of the image.
