英文文献及翻译级联迭代傅里叶变换算法在光学安全中的应用.docx

1、英文文献及翻译级联迭代傅里叶变换算法在光学安全中的应用A cascaded iterative Fourier transform algorithmfor 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 o

2、f 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

3、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-ass

4、ignment 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 n

5、ovel 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

6、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 c

7、orrelator. 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

8、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,

9、 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 information of the image f(x, y) and the lock expjb(u, v),

10、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 suc

11、h 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 ke

12、ys. 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

13、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 recover

14、ed 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

15、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

16、 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

17、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 Iterative Fourier Transform (CIFT) Algorithm Consider the operation of the encr

18、yption 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 asand respectively, where (x, y) and (u, v) represent the space and the frequency coordinate, respectively. Once the system is illuminated with a monochromatic pl

19、ane wave, a target image f(x,y)(an image to be decrypted or verified) is expected to obtain at the output plane. The phase-masksand contain the information of f(x,y), that is,f(x,y)is encoded into these phase-masks. The encoding process is the optimization of the two phase-distributions. It is somew

20、hat 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 general) planes along the propagation direction. So the conventional POCS algorithm sho

21、uld 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 reaches the kth iteration (k = 1, 2, 3, ), and the phase-distributions in the input and the Fourier pl

22、ane 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 inverse Fourier transform, respectively.If fk(x,y)satisfies the convergent criterion, the iteration process s

23、tops, 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 to generate both of the phase-distributions as follows where ang denotes the phase extraction function. Then k is rep

24、laced 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 target image in the present iteration. It ensures he algorithm converges with much faster speed and more consistent for the p

25、hase-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. The convergent behavior of this algorithm is similar to that of the

26、conventional POCS. That is, the MSE reduces rapidly in the foremost few iterations, then it keeps reducing slowly till it reaches the minimum. Correspondingly, the correlation coefficient is expected to increase rapidly at first and keep increasing slowly till the stopping criterion is satisfied. In

27、 decryption, the determined phase-masks and (the keys or essentially, the encrypted images) are placed in the input and the Fourier plane, respectively, and then transformed into the output plane through the correlation defined by Eq. (1). The modulus of the output is the decrypted image. The CIFT a

28、lgorithm retains the property of the conventional iteration algorithm, that is, the final phase-distributions of the masks are determined by the initializations of them. Therefore different initializations will result in different distributions of and . The target image cannot be decrypted if the ke

29、ys mismatch (that is, the keys were generated from the different iteration process). In practical system, the phases of the masks are quantized to finite levels, which might reduce the solution space and introduce noise to the recovered image. To compensate the loss of the quality, the target image

30、can be encoded into more phase-masks to provide additional freedom for solutions searching, which means to encrypt the image with a multi-stages (cascaded) correlator. From the point of view of security, this strategy significantly enlarges the key space (because more keys were generated), and makes

31、 the intrusion more difficult. Generally, the t-stages correlation is defined asfor t is even, or for t is odd, where the matrix I(x, y) represents the input plane wave, and the superscript i (i=1, 2, , t) denotes the serial number of the masks in the system. The phase-distributions of these masks m

32、ay be deduced by analogous analysis for Eq. 3. 3. Computer simulation In this section we numerically demonstrate our general concept.A jet plane image of the size 128 128 with 256 grayscale is used as the target image as shown in Fig. 2. The sizes of both phase-masks are same as the target image. And we suppose the optical system is illuminated by a plane wave with the amplitude equating to 1. The algorithm starts with the random initialization of the two phase-masks. Then the phase functions are transformed forward and backward alternatively through th