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An optical encryption method of multiple-image based on spatial angle multiplexing and double random phase encoding is proposed in this paper. In the encryption process, firstly the original images are modulated by random phase in Fresnel transform with different diffraction distances. Secondly, the modulated images are coherently superposed with reference beams which have different spatial angles and random phases, to generate interference fringes. Finally, the interference fringes from different directions are superposed to form a compound encrypted image. In the decryption process, the compound image is placed in a spatial filtering and Fresnel diffraction system, and the decrypted images are obtained after implementing the different phase keys’ demodulation and Fresnel diffraction with correct distance. This method encrypts multiple images into a single gray-scale image, which is easy to save and transmit. The double random phases are placed in object light and reference light respectively, which reduces the complexity of the encryption system and overcomes the difficulty of pixel-by-pixel alignment of random phase keys in traditional decryption experiment. At the same time, the multiplexing capacity of the proposed encryption system is analyzed, and the result shows that the system has sufficient encryption capacity. So the proposed method possesses the characteristics of high storage efficiency, simple calculation and strong anti-noise ability, and thus can encrypt multiple images simultaneously. In this paper, the encryption effect is evaluated by correlation coefficient, while the effectiveness and security are verified by simulation experiment.
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Keywords:
- multiple-image encryption /
- spatial angle multiplexing /
- digital holography /
- interference encryption
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Google Scholar
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Google Scholar
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Google Scholar
[15] Shao Z, Shu H, Wu J, Dong Z, Coatrieux G 2014 Opt. Express 22 4932
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[21] Javidi B, Carnicer A, Yamaguchi M, Nomura T, Pérez-Cabré E, Millán M S, Nishchal N K, Torroba R, Barrera J F, He W, Peng X, Stern A, Rivenson Y, Alfalou A, Brosseau C, Guo C, Sheridan J T, Situ G, Naruse M, Matsumoto T, Juvells L, Tajahuerce E, Lancis J, Chen W, Chen X, Pinkse P W, Mosk A P, Markman A 2016 J. Opt. 18 083001
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图 1 多图像光学加密系统(SLM是空间光调制器,
$f$ 是透镜焦距,${z_i}$ 是菲涅耳衍射距离,$R(\theta )$ 表示CCD旋转后与x轴的夹角,${\alpha _i}$ 是物光O与参考光R的夹角)Figure 1. Optical setup of multiple-image encryption process. SLM is spatial light modulator,
$f$ is focal length,${z_i}$ is the distance of Fresnel diffraction,$R(\theta )$ is the rotation angle of CCD,${\alpha _i}$ is angle between object light O and reference light R.
图 2 (a)−(h) 8幅待加密图像
Figure 2. (a)−(h) Multiple-image to be encrypted.
图 3 (a)—(h)8幅原始图像对应的加密干涉条纹
Figure 3. (a)－(h) Encrypted interference fringes corresponding to 8 original images.
图 4 加密结果图
Figure 4. Encrypted image.
图 5 多图像解密系统
Figure 5. Decryption system of multiple-image.
图 6 (a)
$p_2^* $ 为解密密钥时频谱图, 其中F1—F8为相应的滤波器; (b)${p_2}$ 为解密密钥时频谱图Figure 6. (a) Decrypted spectrum with right key
$p_2^ * $ , where F1－F8 are filters; (b) decrypted spectrum with key${p_2}$ .
图 7 (a)—(h) 8个图像的正确密钥解密结果
Figure 7. (a)－(h) 8 Decrypted images with all right keys.
图 8 (a)随机相位密钥
$p_2^ * $ 错误时原始图“A”解密结果; (a')随机相位密钥$p_2^ * $ 错误且无滤波器时原始图“A”解密结果; (b)随机相位密钥$p_2^ * $ 错误时原始图“光”解密结果; (b')随机相位密钥$p_2^ * $ 错误且无滤波器时原始图“光”解密结果Figure 8. Decrypted results with wrong key
$p_2^ * $ : (a) For original image “A”; (a') for original image “A” without filter; (b) for original image “光”; (b') for original image “光” without filter.
图 9 (a)波长
$\lambda = 633$ nm其他密钥正确时原始图“B”的解密图像; (b)原始图“学”的解密图像Figure 9. Decrypted results with wrong key
$\lambda = 633$ nm: (a) For original image “B”; (b) for original image “学”.
图 10 当
${p_1}$ 的动态范围为${\text{0—π}}$ 时原始图“息”的CC随菲涅耳衍射距离${z_8}$ 的变化Figure 10. The
$CC$ dependence on${z_8}$ when the dynamic range of${p_1}$ is 0－π.
图 11 当
${p_1}$ 的动态范围为${\text{0—1.5π}}$ 时原始图“息”的$CC$ 随菲涅耳衍射距离${z_8}$ 的变化Figure 11. The
$CC$ dependence on${z_8}$ when the dynamic range of${p_1}$ is 0－1.5π. -
[1] Refregier P, Javidi B 1995 Opt. Lett. 20 767
Google Scholar
[2] Liu Z, Chen H, Blondel W, Shen Z, Liu S 2018 Opt. Lasers Eng. 105 1
[3] Chen L, Zhao D 2006 Opt. Express 14 8552
Google Scholar
[4] Zhao D, Li X, Chen L 2008 Opt. Commun. 281 5326
[5] Xu S J, Wang J Z, Yang S X 2008 Chin. Phys. B 17 4027
Google Scholar
[6] Borujeni S E, Eshghi M 2013 J. Telecommun. Syst. 52 525
[7] Toto-Arellano N, Rodriguez-Zurita G, Meneses-Fabian C, Vazquez-Castillo J 2008 Opt. Express 16 19330
Google Scholar
[8] Nomura T, Javidi B 2000 Opt. Eng. 39 2031
Google Scholar
[9] Shi Y S, Li T, Wang Y L, Gao Q K, Zhang S G, Li H F 2013 Opt. Lett. 38 1425
Google Scholar
[10] Gopinathan U, Naughton T, Sheridan J 2006 Appl. Opt. 45 5693
Google Scholar
[11] Javidi B, Nomura T 2000 Opt. Lett. 25 28
Google Scholar
[12] 席思星, 于娜娜, 王晓雷, 朱巧芬, 董昭, 王微, 刘秀红, 王华英 2019 物理学报 68 110502
Google Scholar
Xi S X, Yu N N, Wang X L, Zhu Q F, Dong Z, Wang W, Liu X H, Wang H Y 2019 Acta. Phys. Sin. 68 110502
Google Scholar
[13] Li X, Meng X, Yang X, Wang Y, Yin Y, Peng X, He W, Dong G, Chen H 2018 Opt. Lasers Eng. 102 106
[14] Xiao D, Li X, Liu S, Wang Q 2018 Opt. Commun. 410 488
Google Scholar
[15] Shao Z, Shu H, Wu J, Dong Z, Coatrieux G 2014 Opt. Express 22 4932
Google Scholar
[16] Situ G, Zhang J 2005 Opt. Lett. 30 1306
Google Scholar
[17] Xu D, Lu M, Jia C, Hu Z 2017 J. Russ. Laser Res. 38 285
Google Scholar
[18] Deepan B, Quan C, Wang Y, Tay C 2014 Appl. Opt. 53 4539
Google Scholar
[19] Tang Z, Song J, Zhang X 2016 Opt. Lasers Eng. 80 1
[20] Kong D, Shen X, Xu Q, Wang X, Guo H 2013 Appl. Opt. 52 2619
Google Scholar
[21] Javidi B, Carnicer A, Yamaguchi M, Nomura T, Pérez-Cabré E, Millán M S, Nishchal N K, Torroba R, Barrera J F, He W, Peng X, Stern A, Rivenson Y, Alfalou A, Brosseau C, Guo C, Sheridan J T, Situ G, Naruse M, Matsumoto T, Juvells L, Tajahuerce E, Lancis J, Chen W, Chen X, Pinkse P W, Mosk A P, Markman A 2016 J. Opt. 18 083001
Google Scholar
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