外文翻譯---級(jí)聯(lián)迭代傅里葉變換算法在光學(xué)安全中的應(yīng)用（英文）

1、A cascaded iterative Fourier transform algorithm for optical security applicationsGuohai Situ, Jingjuan ZhangDepartment of Physics, Graduate School of the Chinese Academy of Sciences, P.O. Box 3908, Beijing, 100039, Chin

2、aAbstract: A cascaded iterative Fourier transform (CIFT) al- gorithm 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 respe

3、ctively, in order to implement the optical encryption or authenticity verifica- tion. Compared with previous methods, the proposed algo- rithm employs an improved searching strategy: modifying the phase-distributions of

4、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

5、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 securi

6、ty – optical encryption – cascaded iterative Fourier transform algorithm1. IntroductionOptical techniques have shown great potential in the field of information security applications. Recently Re ´- fre ´gier a

7、nd Javidi [1] proposed a novel double-ran- dom-phase encoding technique, which encodes a pri- mary image into a stationary white noise. This technique was also used to encrypt information in the fractional Fourier domain

8、 [2, 3] and to store encrypted information holographically [4, 5]. Phase encoding techniques were also proposed for optical authenticity verification [6–8]. Wang et al. [9] and Li et al. [10] proposed another method for

9、optical encryption and authenticity verifi- cation. Unlike the techniques mentioned above, this method encrypts information completely into a phase mask, which is located in either the input or the Four- ier domain of a

10、4-f correlator. For instance, given the predefinitions of a significant image fðx; yÞ as the de- sired output and a phase-distribution exp fibðu; vÞg in the Fourier domain, it’s easy to optimize the o

11、ther phase function exp fipðx; yÞÞg with a modified projec-tion onto constraint sets (POCS) algorithm [10]. There- fore the image fðx; yÞ is encoded successfully into exp fipðx; yÞg wit

12、h the aid of exp fibðu; vÞg. In other words, the fixed phase exp fibðu; vÞg serves as the lock while the retrieved phase exp fipðx; yÞg serves as the key of the security system. To reconstru

13、ct the original information, the phase functions exp fipðx; yÞg and exp fibðu; vÞg must match and be located in the input and the Fourier plane respectively. Abookasis et al. [11] implemented this sch

14、eme with a joint transform correlator for optical verification. However, because the key exp fipðx; yÞg contains information of the image fðx; yÞ and the lock exp fibðu; vÞg, and the 4-f cor

15、relator 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 sys- tem uses only one loc

16、k for different image. In order to increase the secure level of such system, one ap- proach is to use different lock function for different image. Enlarging the key space is another approach to increase the secure level.

17、 It can be achieved by en- crypting images in the fractional Fourier domain; as a result, the scale factors and the transform order offer additional keys [2, 3]. On the other hand, note that the phase-mask serves as the

18、key of the system, enlar- ging 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. [12] have pro- posed a multiple-phases retrieval algorit

19、hm and de- monstrated 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 constr

20、aint in each iteration. As a result, the masks are not so con- sistent and may affect the quality of the recovered im- age. In the present paper, we propose a modified POCS algorithm that adjusts the distributions of bot

21、h 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 becau

22、se of the co-adjusting of the two masks during the iteration process. When the iteration process is finished, the tar-Guohai Situ, Jingjuan Zhang, A cascaded iterative Fourier transform algorithm for optical security app

23、lications 473International Journal for Light and Electron Optics0030-4026/03/114/10-473 $ 15.00/0Received 1 July 2003; accepted 12 October 2003.Correspondence to: G. Situ E-mail: ghsitu@mails.gscas.ac.cnOptik 114, No. 10

24、 (2003) 473–477 http://www.elsevier-deutschland.de/ijleoventional iteration algorithm, that is, the final phase- distributions of the masks are determined by the initia- lizations of them. Therefore different initializat

25、ions will result in different distributions of foptðx; yÞ and woptðu; vÞ. The target image cannot be descrypted if the keys mismatch (that is, the keys were generated from the different iteration proc

26、ess). In practical system, the phases of the masks are quantized to finite levels, which might reduce the solu- tion space and introduce noise to the recovered image. To compensate the loss of the quality, the target ima

27、ge can be encoded into more phase-masks to provide ad- ditional freedom for solutions searching, which means to encrypt the image with a multi-stages (cascaded) correlator. From the point of view of security, this strat-

28、 egy significantly enlarges the key space (because more keys were generated), and makes the intrusion more difficult. Generally, the t-stages correlation is defined asf 0ðx; yÞ ¼ IFT fFT f. . . IFT fFT fex

29、p ½i2pfð1Þ ðx; yÞ?g? exp ½i2pwð2Þðu; vÞ?g . . . exp ½i2pfðt?1Þðx; yÞ?g? exp ½i2pwðtÞðu; vÞ?g ; ð5aÞfor t is ev

30、en, orf 0ðx; yÞ ¼ IFT fFT f. . . IFT fFT fIðx; yÞg? exp ½i2pwð1Þðu; vÞ?g . . . exp ½i2pfðt?1Þðx; yÞ?g? exp ½i2pwðtÞðu; vÞ

31、;?g ; ð5bÞfor t is odd, where the matrix Iðx; yÞ represents the input plane wave, and the superscript i ði ¼ 1; 2; . . . ; tÞ denotes the serial number of the masks in the system. The p

32、hase-distributions of these masks may be de- duced by analogous analysis for eq. 3.3. Computer simulationIn this section we numerically demonstrate our gen- eral concept. A jet plane image of the size 128 ? 128 with 256

33、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 opti- cal system is illuminated by a plane wave with the amplitude equating to 1. T

34、he algorithm starts with the random initialization of the two phase-masks. Then the phase functions are transformed forward and backward alternatively through the correlation defined by eqs. (1)–(3). The algorithm conver

35、ges very fast. The correlation coefficient reaches 0.99 after about 3 iterations, then it keeps increasing slowly and finally reaches 1 within 20 iterations, cor- respondingly, the intensity distribution of the re- triev

36、ed image is extremely close to that of the target image. Rigorously, the correlation coefficient does converge but not equate to 1 no matter how many iterations the algorithm runs because no analytic so-lutions for eq. (

37、1) can be found. Here we say it REACHES 1 just because the difference between the two images is beyond the limitation of the repre- sentational precision of the digital computer. Actu- ally, the CIFT algorithm retains th

38、e error-reducing property of the conventional POCS algorithm. The MSE keeps reducing till the local (but not global) minimum is reached. One interesting character of the CIFT algorithm is that arbitrary initializations c

39、an generate recovered images with almost same quality, and result in different distributions for the masks, as shown in fig. 3. Therefore the optimized phase-masks can be used as the keys of the security system. Only two

40、 phase-masks, which match each other and are located in the appropriate planes of the 4-f architecture, respectively, can recover the tar- get image. Otherwise, the output is meaningless. On the other hand, the keys exp

41、½i2pfoptðx; yÞ? and exp ½i2pwoptðu; vÞ?, are phase-only functions, and have ran- dom-like distributions as well. These characters may introduce a high level of security because they offer a

42、property of anti-counterfeiting. Another secure advan- tage of the CIFT algorithm arises in the application of authenticity verification. Instead of detecting a single correlation peak, the verification system based on t

43、he CIFT algorithm detects a significant output to deter- mine whether or not to verify the input. So it is impos- sible to cause a false verification by directly illuminat- ing the output plane bypassing the correlator b

44、ecause the intruder cannot generate the same pattern at the output without the knowledge of the correct phase-dis- tributions. This is especially useful in the applications where high security is necessary. For the sake

45、of secur- ity, the two masks are expected assigning to two per- sons, respectively. Therefore, the verification can be performed only under the authorizations of them both. If higher security is required, more phase-mask

46、s can be retrieved and assigned to more authorities so as to diminish the risk of being stolen of the keys. To compare with previous methods, the CIFT algo- rithm and the previous methods are investigated under the same

47、initial conditions. Let Algorithm A, B, C and D denote the methods presented in refs. [9], [10], [12] and the algorithm proposed in the present paper, re- spectively. Algorithm A and B merely modify the dis- tribution of