基于双随机相位编码的图像隐藏技术研究
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摘要
数千年来,信息在人类社会进步和发展中发挥了重要作用。当今,伴随着信息时代的到来,特别是80年代以来,随着计算机和网络技术的兴起与发展,信息安全问题日益凸显。基于信息光学理论的光学信息安全技术是近20年来信息安全领域内兴起的一个重要课题。当前,随着光电技术的不断进步,光学信息安全技术不断拓展、快速发展,在安全认证、图像加密和图像隐藏等方面不断涌现出新方法、新技术,促使人们对这些新的研究课题进行深入细致地探讨。
本文围绕双随机相位编码技术,将光学和数字技术相结合,研究了基于光学信息理论“双随机相位编码”技术的二元、灰度及彩色图像隐藏方法。
第一章,综述了信息安全问题的理论基础、重点介绍了信息隐藏技术及其研究现状；综述了光学信息安全技术的发展概述,介绍了目前国内外的相关领域研究现状,指出了本论文研究的目的和意义；对光信息安全技术的理论基础如透镜的傅立叶变换性质、全息技术、联合变换相关器和相位恢复算法理论和研究方法作了归纳介绍。
第二章,提出了基于联合变换相关器和全息技术的傅立叶域二元图像隐藏(水印)理论。利用联合变换相关器对隐藏(水印)图像进行加密,以联合功率谱的形式记录了加密信息,通过加性嵌入方式实现了加密图像傅立叶域隐藏。提出了结合图像特征的预处理方法,通过图像预处理的方法有效地降低了恢复图像中的交叉噪声,提高了恢复图像质量。该系统克服了光路对准、制作共轭相位密钥的问题,并能有效抵抗剪切、滤波和噪声等各类攻击。
第三章,提出了一种基于无透镜联合变换相关器和相移干涉技术的双图像隐藏技术。该技术利用无透镜联合变换相关器实现图像的加密,并以二步相移干涉光强的形式记录加密结果,提出了双图像分割和相位调制技术以实现双图像的隐藏。该系统结构简单、信息容量小、并能有效抑制和克服交叉噪声对恢复图像的干扰。
第四章,提出了一种基于Arnold变换和分数傅立叶域迭代恢复算法的彩色图像隐藏技术。根据RGB三基色原理,将彩色图像分解成R、G和B三个分量,利用Arnold变换实现多通道单分量置乱,由分数傅立叶域迭代恢复算法进一步对置乱分量进行加密；然后结合邻域相减技术将加密结果嵌入宿主图像的蓝色通道,实现了彩色图像的隐藏。
第五章,提出了一种基于混合记录技术的多幅彩色图像隐藏技术。该技术利用并行多通道混合记录,将RGB三通道信息记录在一幅灰度图像上,然后通过Arnold变换和菲涅耳域迭代恢复算法实现彩色图像的置乱、加密,将多个加密复光场的相位分布函数提取出来进行叠加,得到一个加密结果。该方法通过数值与光学技术结合的方法实现了单通道彩色图像处理,大大简化了系统结构,同时能有效去除恢复图像间的交叉噪声。
最后,总结了本论文已经完成的工作和主要创新点,并提出对未来工作的展望。
Information is powerful, mankind has had this knowledge for millennia. Nowdays, in this information age, especially in the mid-80s, with the advent of the computer and the internet, information security is becoming more and more important. Optical security technique based on the Fourier optics has become one of the most important issues in information security domain. With the advance of high performance CCD cameras and spatial light modulators (SLM), optical information security technique has developed rapidly and becomes more and more attractive for optical realization of security certificate, information encoding and information hiding. Various kinds of optical security techniques and systems have been proposed to solve the problem of security in the transmission of information, these excellent results will push us to take more further and detailed study to find more powerful system on this topic.
In this thesis, optical processing procedure and digital technique are used, the optical image hiding techniques for binary, gray and color image hiding based on the double random phase encoding (DRPE) are proposed. The major contributions of this thesis are summarized as follows:
This thesis begins by summarizing an overall rationale and development of the information security, and by focusing on the characteristics of information hiding in Chapter1. The classification and development of the optical security techniques are also presented in this part. The purpose and significance of this thesis are pointed out. The rationale of optical security such as:the Fourier transform characteristics of lens, optical hologram technique, the joint transform corrlator and the phase retrieval algorithm are also introduced in this part.
Chapter2will follow with a discussion of the proposed system for the binary image hiding. In this Chapter, based on the joint transform correlator architecture and holographic technique a new method for image hiding is presented. A hidden image encrypted by joint transform correlator architecture is embedded in the Fourier hologram of the host image. Inverse Fourier transform can be used to get the watermarked image, and joint transform correlator architecture is used to decode the hidden image from the watermarked hologram. Unlike other watermarking technique, by information prochoosing, noise added to the recovered hidden image by the host can be reduced. And unlike other watermarking systems based on double random phase encryption, no conjugate key is used to recover the hidden image. The robustness of the proposed system for resisting of attacks such as occlusion, noise and filtering are also introduced.
In Chapter3, based on the joint Fresnel transform correlator, a new system for double images hiding is presented. By this security system, dual secret images are encrypted and recorded as intensity patterns employing phase-shifting interference technology. To improve the system security, a dual images hiding method is used. By digital means, the deduced encryption complex distribution is divided into two subparts. For each image, only one subpart is reserved and modulated by a phase factor. Then these modified results are combined together and embedded into the host image. By the phase modulation, the cross talk caused by images superposition can be reduced for their spatial parallel separation.
Chapter4details the thesis of hiding a color image into another color image. In this part, a new method is proposed for color image hiding and extracting by use of phase retrieval algorithm in fractional Fourier transform domain and Arnold transform. Based on a cascaded phase iterative FRFT algorithm, the3-channel (R, G and B) of the secret color image permuted by ART are encrypted. Then the encoded information is embedded in Blue-channel (B-channel) of the enlarged color host image. The random phase mask, the wavelength, transform parameters are provided as keys for decryption.
In Chapter5, we propose a new method for multiple color images hiding by using of triplets recombination. In this proposed technique, triplet (R, G and B) components of the secret color image is recorded simultaneously as a real and positive gray image exploiting parallel multi-wavelength recording technology. Arnold transform and phase retrieval algorithm adapted to Fresnel transform domain are used to encode the parallel hybrid result. By using of the proposed technique, each color image is encrypted into a pure phase distribution and combined by superposition. Phase modulation is introduced to eliminate the cross-talk caused by multiple images superposition. The wavelength, transform parameters are provided as keys to enhance the system security.
Finally, we summarize the main conclusions in this thesis and anticipate a more efficient, reliable and significant work would be done in the future for the optical security applications.
本文围绕双随机相位编码技术,将光学和数字技术相结合,研究了基于光学信息理论“双随机相位编码”技术的二元、灰度及彩色图像隐藏方法。
第一章,综述了信息安全问题的理论基础、重点介绍了信息隐藏技术及其研究现状；综述了光学信息安全技术的发展概述,介绍了目前国内外的相关领域研究现状,指出了本论文研究的目的和意义；对光信息安全技术的理论基础如透镜的傅立叶变换性质、全息技术、联合变换相关器和相位恢复算法理论和研究方法作了归纳介绍。
第二章,提出了基于联合变换相关器和全息技术的傅立叶域二元图像隐藏(水印)理论。利用联合变换相关器对隐藏(水印)图像进行加密,以联合功率谱的形式记录了加密信息,通过加性嵌入方式实现了加密图像傅立叶域隐藏。提出了结合图像特征的预处理方法,通过图像预处理的方法有效地降低了恢复图像中的交叉噪声,提高了恢复图像质量。该系统克服了光路对准、制作共轭相位密钥的问题,并能有效抵抗剪切、滤波和噪声等各类攻击。
第三章,提出了一种基于无透镜联合变换相关器和相移干涉技术的双图像隐藏技术。该技术利用无透镜联合变换相关器实现图像的加密,并以二步相移干涉光强的形式记录加密结果,提出了双图像分割和相位调制技术以实现双图像的隐藏。该系统结构简单、信息容量小、并能有效抑制和克服交叉噪声对恢复图像的干扰。
第四章,提出了一种基于Arnold变换和分数傅立叶域迭代恢复算法的彩色图像隐藏技术。根据RGB三基色原理,将彩色图像分解成R、G和B三个分量,利用Arnold变换实现多通道单分量置乱,由分数傅立叶域迭代恢复算法进一步对置乱分量进行加密；然后结合邻域相减技术将加密结果嵌入宿主图像的蓝色通道,实现了彩色图像的隐藏。
第五章,提出了一种基于混合记录技术的多幅彩色图像隐藏技术。该技术利用并行多通道混合记录,将RGB三通道信息记录在一幅灰度图像上,然后通过Arnold变换和菲涅耳域迭代恢复算法实现彩色图像的置乱、加密,将多个加密复光场的相位分布函数提取出来进行叠加,得到一个加密结果。该方法通过数值与光学技术结合的方法实现了单通道彩色图像处理,大大简化了系统结构,同时能有效去除恢复图像间的交叉噪声。
最后,总结了本论文已经完成的工作和主要创新点,并提出对未来工作的展望。
Information is powerful, mankind has had this knowledge for millennia. Nowdays, in this information age, especially in the mid-80s, with the advent of the computer and the internet, information security is becoming more and more important. Optical security technique based on the Fourier optics has become one of the most important issues in information security domain. With the advance of high performance CCD cameras and spatial light modulators (SLM), optical information security technique has developed rapidly and becomes more and more attractive for optical realization of security certificate, information encoding and information hiding. Various kinds of optical security techniques and systems have been proposed to solve the problem of security in the transmission of information, these excellent results will push us to take more further and detailed study to find more powerful system on this topic.
In this thesis, optical processing procedure and digital technique are used, the optical image hiding techniques for binary, gray and color image hiding based on the double random phase encoding (DRPE) are proposed. The major contributions of this thesis are summarized as follows:
This thesis begins by summarizing an overall rationale and development of the information security, and by focusing on the characteristics of information hiding in Chapter1. The classification and development of the optical security techniques are also presented in this part. The purpose and significance of this thesis are pointed out. The rationale of optical security such as:the Fourier transform characteristics of lens, optical hologram technique, the joint transform corrlator and the phase retrieval algorithm are also introduced in this part.
Chapter2will follow with a discussion of the proposed system for the binary image hiding. In this Chapter, based on the joint transform correlator architecture and holographic technique a new method for image hiding is presented. A hidden image encrypted by joint transform correlator architecture is embedded in the Fourier hologram of the host image. Inverse Fourier transform can be used to get the watermarked image, and joint transform correlator architecture is used to decode the hidden image from the watermarked hologram. Unlike other watermarking technique, by information prochoosing, noise added to the recovered hidden image by the host can be reduced. And unlike other watermarking systems based on double random phase encryption, no conjugate key is used to recover the hidden image. The robustness of the proposed system for resisting of attacks such as occlusion, noise and filtering are also introduced.
In Chapter3, based on the joint Fresnel transform correlator, a new system for double images hiding is presented. By this security system, dual secret images are encrypted and recorded as intensity patterns employing phase-shifting interference technology. To improve the system security, a dual images hiding method is used. By digital means, the deduced encryption complex distribution is divided into two subparts. For each image, only one subpart is reserved and modulated by a phase factor. Then these modified results are combined together and embedded into the host image. By the phase modulation, the cross talk caused by images superposition can be reduced for their spatial parallel separation.
Chapter4details the thesis of hiding a color image into another color image. In this part, a new method is proposed for color image hiding and extracting by use of phase retrieval algorithm in fractional Fourier transform domain and Arnold transform. Based on a cascaded phase iterative FRFT algorithm, the3-channel (R, G and B) of the secret color image permuted by ART are encrypted. Then the encoded information is embedded in Blue-channel (B-channel) of the enlarged color host image. The random phase mask, the wavelength, transform parameters are provided as keys for decryption.
In Chapter5, we propose a new method for multiple color images hiding by using of triplets recombination. In this proposed technique, triplet (R, G and B) components of the secret color image is recorded simultaneously as a real and positive gray image exploiting parallel multi-wavelength recording technology. Arnold transform and phase retrieval algorithm adapted to Fresnel transform domain are used to encode the parallel hybrid result. By using of the proposed technique, each color image is encrypted into a pure phase distribution and combined by superposition. Phase modulation is introduced to eliminate the cross-talk caused by multiple images superposition. The wavelength, transform parameters are provided as keys to enhance the system security.
Finally, we summarize the main conclusions in this thesis and anticipate a more efficient, reliable and significant work would be done in the future for the optical security applications.
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4. G. Situ and J. Zhang, "Double random-phase encoding in the Fresnel domain," Opt. Lett.29,1584-1586(2004).
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6. T.Nomura and B. Javidi, "Optical encryption using a joint transform correlator architecture," Opt. Eng.39,2031-2035(2000).
7. S. Kishk and B. Javidi, "Information hiding technique with double phase encoding," Appl. Opt.41,5462-5470(2002).
8. N. Takai and Y. Mifune, "Digital watermarking by a holographic technique," Appl. Opt.41,865-873(2002).
9. H.T. Chang and C.L. Tsan, "Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain," Appl. Opt.44,6211-6219 (2005).
10. Y. Shi, G. Situ and J. Zhang, "Optical image hiding in the Fresnel domain," J. Opt. A:Pure Appl. Opt.8,569-577(2007).
U.S. Kishk and B. Javidi, "Watermarking of three-dimensional objects by digital holography," Opt. Lett.28,167-169(2003).
12. Y. Shi, G. Situ and J. Zhang, "Multiple-image hiding in the Fresnel domain," Opt. Lett.32,1914-1916(2007).
13. M. He, Q. Tan, L. Cao, Q. He and G. Jin, "Security enhanced optical encryption system by random phase key and permutation key," Opt. Exp.17,22462-22473 (2009).
14. H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen and G. Y. Dong, "Image watermarking based on an iterative phase retrieval algorithm and sine-cosine modulation in the discrete-cosine-transform domain," Opt. Commun. 278,257-263(2007).
15. D. Abookasis, O. Arazi, J. Rosen and B. Javidi, "Security optical systems based on joint transform correlator with significant output images," Opt. Eng.40, 1584-1589(2001).
16. H. T. Chang and C. T. Chen, "Enhanced optical image verification based on joint transform correlator adopting Fourier hologram," Opt. Rev.11,165-169(2004).
17. C. L. Mela and C. Iemmi, "Optical encryption using phase-shifting interferometry in a joint transform correlator," Opt. Lett.31,2562-2564(2006).
18. O. Matoba and B. Javidi, "Optical retrieval of encrypted digital holograms for secure real-time display," Opt. Lett.27,321-323(2002).
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1. P. Refregier and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett.20,767-769 (1995).
2. B. Javidi, "Security information with optical technology," Phys. Today.50,27-32 (1997).
3. G. Unnikrishnan, J. Joseph and K. Singh, "Optical encryption by double-random phase encoding in the fractional Fourier domain," Opt. Lett.25,887-889(2000).
4. G. Situ and J. Zhang, "Double random-phase encoding in the Fresnel domain," Opt. Lett.29,1584-1586(2004).
5. B. Javidi and Takanori Nomura, "Securing information by use of digital holography," Opt. Lett.25,28-30(2000).
6. E. Tajahuerce, O. Matoba, S. Verrall and B. Javidi, "Optoelectronic information encryption with phase-shifting interferometry," Appl. Opt.39,2313-2320(2000).
7. S. Kishk and B. Javidi, "Information hiding technique with double phase encoding," Appl. Opt.41,5462-5470(2002).
8. N. Takai and Y. Mifune, "Digital watermarking by a holographic technique," Appl. Opt.41,865-873(2002).
9. S. Kishk and B. Javidi, "Watermarking of three-dimensional objects by digital holography," Opt. Lett.28,167-169(2003).
10. H. Chang and C. Tsan, "Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain," Appl. Opt.44,6211-6219 (2005).
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17. H. T. Chang and C. T. Chen, "Enhanced optical image verification based on joint transform correlator adopting Fourier hologram," Opt. Rev.11,165-169(2004).
18. D. Abookasis, O. Montal, O. Aramson and J. Rosen, "Watermarks encrypted in a concealogram and deciphered by a modified joint-transform correlator," Appl. Opt.55,3019-3023(2005).
19. X. Shi and D. Zhao, "Image hiding in Fourier domain by use of joint transform correlator architecture and holographic technique," Appl. Opt.50, 766-773(2011).
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23. W.Qin, X.Peng, X.Meng and B. Gao, "Vulnerability to chosen-plaintext attack of optoelectronic information encryption with phase-shifting interferometry," Opt. Eng.50,065601-1-065601-5(2011).
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1. P. Refregier and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett.20,767-769(1995).
2. B. Javidi, "Security information with optical technology," Phys. Today 50,27-32 (1997).
3. G. Unnikrishnan, J. Joseph and K. Singh, "Optical encryption by double-random phase encoding in the fractional Fourier domain," Opt. Lett.25,887-889(2000).
4. G. Situ and J. Zhang, "Double random-phase encoding in the Fresnel domain," Opt. Lett.29,1584-1586(2004).
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7. S. Kishk and B. Javidi, "Information hiding technique with double phase encoding," Appl. Opt.41,5462-5470(2002).
8. H.T. Chang and C.L. Tsan, "Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain," Appl. Opt.44,6211-6219 (2005).
9. H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen and G. Y. Dong, "Image watermarking based on an iterative phase retrieval algorithm and sine-cosine modulation in the discrete-cosine-transform domain," Opt. Commun. 278,257-263(2007).
10. Y. Shi, G. Situ and J. Zhang, "Multiple-image hiding in the Fresnel domain," Opt. Lett.32,1914-1916(2007).
11. G. Situ and J. Zhang, "Image hiding with computer-generated phase codes for optical authentication," Opt. Commun.245,55-65(2005).
12. M. He, Q. Tan, L. Cao, Q. He and G. Jin, "Security enhanced optical encryption system by random phase key and permutation key," Opt. Exp.17,22462-22473 (2009).
13.X. Zhou and J. G. Chen, "Information hiding based on double-random phase encoding technology," J. Mod. Opt.53,1777-1783(2006).
14. L. Chen and D. Zhao, "Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms," Opt. Exp.14, 8552-8560(2006).
15. L. Chen and D. Zhao, "Color information processing (coding and synthesis) with fractional Fourier transforms and digital holography" Opt. Exp 15,16080-16089 (2007).
16. F. Ge, L. Chen and D. Zhao, "A half-blind color image hiding and encryption method in fractional Fourier domains", Opt. Commun.281,4254-4260(2008).
17. Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin and S. Liu, "Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains." Opt. Commun.284,123-128(2011).
18. W. Chen, C. Quan and C. J. Tay. "Optical color image encryption based on Arnold transform and interference method." Opt. Commun.282, 3680-3685(2009).
19. Y. Li, K. Kreske and J. Rosen, "Security and encryption optical systems based on a correlator with significant output images," Appl. Opt.39,5295-5301(2000).
20. Z. Liu and S. Liu, "Double image encryption based on iterative fractional fractional Fourier transform." Opt. Commun.275,324-329(2007).
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28. X. Shi and D. Zhao, "Color image hiding based on the phase retrieval technique and Arnold transform," Appl. Opt.50,2134-2139(2011).
1. P. Refregier and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett.20,767-769(1995).
2. B. Javidi, "Security information with optical technology," Phys. Today 50,27-32 (1997).
3. G. Unnikrishnan, J. Joseph and K. Singh, "Optical encryption by double-random phase encoding in the fractional Fourier domain," Opt. Lett.25,887-889(2000).
4. G. Situ and J. Zhang, "Double random-phase encoding in the Fresnel domain," Opt. Lett.29,1584-1586(2004).
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9. Y. Shi, G. Situ and J. Zhang, "Multiple-image hiding in the Fresnel domain," Opt. Lett.32,1914-1916(2007).
10. Z. Liu and S. Liu, "Double image encryption based on iterative fractional fractional Fourier transform," Opt. Commun.275,324-329(2007).
11. H. T. Chang, W. C. Lu and C. J. Kuo, "Multiple-phase retrieval for optical security systems by use of random-phase encoding," Appl. Opt.41, 4825-4834(2002).
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14. M. He, Q. Tan, L. Cao, Q. He and G. Jin, "Security enhanced optical encryption system by random phase key and permutation key," Opt. Exp.17,22462-22473 (2009).
15. S. Kishk and B. Javidi, "Information hiding technique with double phase encoding," Appl. Opt.41,5462-5470(2002).
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17. H.T. Chang and C.L. Tsan, "Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain," Appl. Opt.44,6211-6219 (2005).
18. S. Zhang and M. Karim, "Color image encryption using double random phase encoding," Micr. and Opt. Tech. Lett.21,318-322(1999).
19. L. Chen and D. Zhao, "Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms," Opt. Exp.14, 8552-8560(2006).
20. W. Chen, C. Quan and C. J. Tay, "Optical color image encryption based on Arnold transform and interference method," Opt. Commun.282, 3680-3685(2009).
21. X. Shi and D. Zhao, "Color image hiding based on the phase retrieval technique and Arnold transform," Appl. Opt.50,2134-2139(2011).
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4. G. Situ and J. Zhang, "Double random-phase encoding in the Fresnel domain," Opt. Lett.29,1584-1586(2004).
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8. N. Takai and Y. Mifune, "Digital watermarking by a holographic technique," Appl. Opt.41,865-873(2002).
9. H.T. Chang and C.L. Tsan, "Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain," Appl. Opt.44,6211-6219 (2005).
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16. H. T. Chang and C. T. Chen, "Enhanced optical image verification based on joint transform correlator adopting Fourier hologram," Opt. Rev.11,165-169(2004).
17. C. L. Mela and C. Iemmi, "Optical encryption using phase-shifting interferometry in a joint transform correlator," Opt. Lett.31,2562-2564(2006).
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1. P. Refregier and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett.20,767-769 (1995).
2. B. Javidi, "Security information with optical technology," Phys. Today.50,27-32 (1997).
3. G. Unnikrishnan, J. Joseph and K. Singh, "Optical encryption by double-random phase encoding in the fractional Fourier domain," Opt. Lett.25,887-889(2000).
4. G. Situ and J. Zhang, "Double random-phase encoding in the Fresnel domain," Opt. Lett.29,1584-1586(2004).
5. B. Javidi and Takanori Nomura, "Securing information by use of digital holography," Opt. Lett.25,28-30(2000).
6. E. Tajahuerce, O. Matoba, S. Verrall and B. Javidi, "Optoelectronic information encryption with phase-shifting interferometry," Appl. Opt.39,2313-2320(2000).
7. S. Kishk and B. Javidi, "Information hiding technique with double phase encoding," Appl. Opt.41,5462-5470(2002).
8. N. Takai and Y. Mifune, "Digital watermarking by a holographic technique," Appl. Opt.41,865-873(2002).
9. S. Kishk and B. Javidi, "Watermarking of three-dimensional objects by digital holography," Opt. Lett.28,167-169(2003).
10. H. Chang and C. Tsan, "Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain," Appl. Opt.44,6211-6219 (2005).
11. X. Meng, L. Cai, X. Xu, X. Yang, X. Shen, G. Dong and Y. Wang, "Two-step phase-shifting interferometry and its application in image encryption," Opt. Lett. 31,1414-1426(2006).
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16. D. Abookasis, O. Arazi, J. Rosen and B. Javidi, "Security optical systems based on a joint transform correlator with significant output images," Opt. Eng.40, 1584-1589(2001).
17. H. T. Chang and C. T. Chen, "Enhanced optical image verification based on joint transform correlator adopting Fourier hologram," Opt. Rev.11,165-169(2004).
18. D. Abookasis, O. Montal, O. Aramson and J. Rosen, "Watermarks encrypted in a concealogram and deciphered by a modified joint-transform correlator," Appl. Opt.55,3019-3023(2005).
19. X. Shi and D. Zhao, "Image hiding in Fourier domain by use of joint transform correlator architecture and holographic technique," Appl. Opt.50, 766-773(2011).
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21. C. Mela and C. Iemmi, "Optical encryption using phase-shifting interferometry in a joint transform correlator," Opt. Lett.31,2562-2564(2006).
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1. P. Refregier and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett.20,767-769(1995).
2. B. Javidi, "Security information with optical technology," Phys. Today 50,27-32 (1997).
3. G. Unnikrishnan, J. Joseph and K. Singh, "Optical encryption by double-random phase encoding in the fractional Fourier domain," Opt. Lett.25,887-889(2000).
4. G. Situ and J. Zhang, "Double random-phase encoding in the Fresnel domain," Opt. Lett.29,1584-1586(2004).
5. T. Nomura and B. Javidi, "Optical encryption using a joint transform correlator architecture," Opt. Eng.39,2031-2035(2000).
6. X. Peng, Z. Cui and T. Tan, "Information encryption with virtual-optics imaging system," Opt Commun.212,235-45(2002).
7. S. Kishk and B. Javidi, "Information hiding technique with double phase encoding," Appl. Opt.41,5462-5470(2002).
8. H.T. Chang and C.L. Tsan, "Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain," Appl. Opt.44,6211-6219 (2005).
9. H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen and G. Y. Dong, "Image watermarking based on an iterative phase retrieval algorithm and sine-cosine modulation in the discrete-cosine-transform domain," Opt. Commun. 278,257-263(2007).
10. Y. Shi, G. Situ and J. Zhang, "Multiple-image hiding in the Fresnel domain," Opt. Lett.32,1914-1916(2007).
11. G. Situ and J. Zhang, "Image hiding with computer-generated phase codes for optical authentication," Opt. Commun.245,55-65(2005).
12. M. He, Q. Tan, L. Cao, Q. He and G. Jin, "Security enhanced optical encryption system by random phase key and permutation key," Opt. Exp.17,22462-22473 (2009).
13.X. Zhou and J. G. Chen, "Information hiding based on double-random phase encoding technology," J. Mod. Opt.53,1777-1783(2006).
14. L. Chen and D. Zhao, "Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms," Opt. Exp.14, 8552-8560(2006).
15. L. Chen and D. Zhao, "Color information processing (coding and synthesis) with fractional Fourier transforms and digital holography" Opt. Exp 15,16080-16089 (2007).
16. F. Ge, L. Chen and D. Zhao, "A half-blind color image hiding and encryption method in fractional Fourier domains", Opt. Commun.281,4254-4260(2008).
17. Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin and S. Liu, "Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains." Opt. Commun.284,123-128(2011).
18. W. Chen, C. Quan and C. J. Tay. "Optical color image encryption based on Arnold transform and interference method." Opt. Commun.282, 3680-3685(2009).
19. Y. Li, K. Kreske and J. Rosen, "Security and encryption optical systems based on a correlator with significant output images," Appl. Opt.39,5295-5301(2000).
20. Z. Liu and S. Liu, "Double image encryption based on iterative fractional fractional Fourier transform." Opt. Commun.275,324-329(2007).
21. H. T. Chang, W. C. Lu and C. J. Kuo, "Multiple-phase retrieval for optical security systems by use of random-phase encoding," Appl. Opt.41, 4825-4834(2002).
22. X. Meng, L. Cai, X. Yang, X. Shen and G. Dong, "Information security system by iterative multiple-phase retrieval and pixel random permutation," Appl. Opt.45, 3289-3297(2006).
23. W. Chen, X. Chen, A. Anand and B. Javidi, "Optical encryption using multiple intensity samplingsin the axial domain," J. Opt. Soc. Am. A.30,806-812(2013).
24. W. Chen, X. Chen, A. Anand and C. Sheppard, "Optical image encryption based on diffractive imaging," Opt. Lett.35,3817-3819(2010).
25. W. Chen, X. Chen, A. Anand and C. Sheppard, "Optical color-image encryption and synthesis using coherent diffractive imaging in the Fresnel domain," Opt. Exp. 20,3853-3865(2012).
26. J. R. Fienup, "Phase retrieval algorithm:a comparison," Appl. Opt.22,2758-2769 (1982).
27. Z. Zalevsky, D. Mendlovic and R. Dorsch, "Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain," Opt. Lett.21,842-844(1996).
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