Abstract

A method for optical image hiding and for optical image encryption and hiding in the Fresnel domain via completely optical means is proposed, which encodes original object image into the encrypted image and then embeds it into host image in our modified Mach-Zehnder interferometer architecture. The modified Mach-Zehnder interferometer not only provides phase shifts to record complex amplitude of final encrypted object image on CCD plane but also introduces host image into reference path of the interferometer to hide it. The final encrypted object image is registered as interference patterns, which resemble a Fresnel diffraction pattern of the host image, and thus the secure information is imperceptible to unauthorized receivers. The method can simultaneously realize image encryption and image hiding at a high speed in pure optical system. The validity of the method and its robustness against some common attacks are investigated by numerical simulations and experiments.

© 2014 Optical Society of America

1. Introduction

Image security has become increasingly important with the greater need for image sharing in many image application areas. Since the optical image encryption method was first proposed [1], many optical encryption methods have been developed successively [220]. However, the study of image security includes not only image encryption but also image hiding and watermarking [21, 22]. Image encryption involves encoding the data itself to make it secret, without hiding its existence, therefore, the encrypted image is a garbled map. Obviously, the garbled map involving the secret image is easy to cause the attacker's attention. On the other hand, image hiding and watermarking techniques embed the secret information (or the watermark) into a host image and retain it in its original form to hide the existence of the secret data, which can achieve secure message storage and transmission to avoid the attention of eavesdroppers. Nowadays, with the two combined image security techniques, a large number of research works have been conducted to get higher security and unnoticeable characteristics to unauthorized users in the digital domain [2331]. Recently some researchers combined optical encryption technique with hiding technique to further enhance data security, but the reported approaches all first realize optical encryption, and then transform the encrypted image to digital data, finally complete image hiding through electronic means [2328]. That is to say, these methods perform image encryption and image hiding in serial mode and realize image hiding through electronic means. Although some papers are classified in the optical image hiding field, they actually relate to image encryption and not to the hiding technology mentioned above [32, 33]. In this paper, optical image encryption and hiding can be simultaneously realized in a pure optical system, which increases the security of the secret image and takes use of the advantages of optical information processing technique. The addition of optical image hiding technology to optical image encryption doesn’t increase the complexity of the encryption system, but just introduces a host image into the reference path of the interferometer, which is usually used for optical image encryption task, to perform image hiding. In addition, the introduction of host image can increase the key space of the secure system and further enhance the security of optical image encryption.

A completely optical scheme for image hiding and for image encryption and hiding is presented in this paper, based on phase-shifting interferometry and double random phase encoding (DRPE) [1] in our modified Mach-Zehnder interferometer. An object image is placed in one path of the interferometer, and host image is located in the other path of it. The object image is encrypted to a white-sense stationary noise pattern by using DRPE method in the object beam path. Afterwards, the white-sense stationary noise pattern can be interfered with the complex amplitude diffracted by the host image to produce interference patterns. Finally the object image is encrypted and embedded into the host image in the Fresnel domain. The resulting three interference fringes recorded by a CCD camera, together with complex distribution information of the host image, they are all processed to yield the complex amplitude distribution of the encrypted object field. Then, the distribution is inverse Fresnel transformed to reconstruct the original object with corresponding optical system parameters through digital or optical means. The encrypted and hidden image can be easily transmitted through ordinary digital communication channels, and less attention will be paid by attackers to the secure image. Meanwhile, compared our method’s encryption effect with DRPE method, the introduction of host image can enhance the encryption effect. The principles, numerical simulations and experimental results are described as follows.

2. Fundamental principles

2.1 Optical image encryption and hiding

The image encryption and hiding system is shown in Fig. 1. A laser beam is divided into an object beam and a reference beam. The object beam first illuminates an object image that is used for encryption and hiding, and then passes through two random phase masks R1 and R2 to carry out encryption by using DRPE method. In the other arm, the reference beam is modulated by our assigned host image and no longer the traditional reference beam in Mach-Zehnder interferometer. The reference beam first illuminates the piezoelectric transducer mirror (PZT), which is capable of phase shifting, and then passes through the host image. After two images experiencing Fresnel diffraction, the diffraction waves are registered as interference patterns on a CCD plane, which resemble a Fresnel diffraction pattern of the host image. By adjusting the intensity ratio of two paths via NDF1 and NDF2, different embedded levels for image hiding can be achieved.

 

Fig. 1 Scheme of optical image encryption and hiding. BE, beam expander; L, lens; BS, beam splitter; M, mirror; NDF, neutral density filters; R, random phase plate; PZT, piezoelectric transducer mirror; Oe, object image; Oh, host image.

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Supposing that the illuminate light amplitudes in the object and reference path are constant C1, C2 respectively, the transmittances of object image and host image are O(x0,y0) and h(x0',y0') respectively, the complex amplitude transmittances of random phase plates R1 and R2 areexp[i2πp(x0,y0)]andexp[i2πq(x0,y0)] respectively, where p(x0,y0) and q(x0,y0) are two independent white noises uniformly distributed in [0, 1]. The distance between plates R1 and R2 is z1, that between R2 and CCD is z2, and that between Oh and CCD is z3.The object image is first encrypted using DRPE in the Fresnel field, so one of complex distribution on CCD plane coming from O(x0,y0), R1 and R2 can be described as

ψ0(ξ,η)=A(ξ,η)exp(iϕ(ξ,η))=FrtZ2{FrtZ1{C1×O(x0,y0)×exp[i2πp(x0,y0)]}×exp[i2πq(x1,y1)]},
where Frt denotes Fresnel transform, and the other diffracted by the host image is represented by
ψh(ξ,η;ϕR)=Ah(ξ,η)exp[iϕh(ξ,η)]exp(iϕR)=FrtZ3{C2exp(iϕR)h(x0',y0')}(ϕR=0,π2,π),
where ϕR represents the stepped phase modulated by PZT. When two diffraction waves ψ0(ξ,η)and ψh(ξ,η;ϕR)appears on CCD plane, coherent interference occurs to embed the encrypted noise-like image into the Fresnel diffraction image of host image. That is to say, the system performs optical image hiding in the Fresnel domain according to image hiding theory [21]. Therefore, the resulting intensity patterns that will be recorded by a CCD camera can be expressed as

I(ξ,η;ϕR)=|ψ0(ξ,η)+ψh(ξ,η;ϕR)|2=A(ξ,η)2+Ah(ξ,η)2+2A(ξ,η)Ah(ξ,η)cos[ϕh(ξ,η)+ϕR-ϕ(ξ,η)].

By adjusting the intensity ratio of two paths via NDF in the modified Mach-Zehnder interferometer, different embedded levels for image hiding can be achieved. The finally aim is to obtain interferograms, that look like the Fresnel diffraction image of host image, for implementing image hiding well in the Fresnel transform domain, which is shown in Fig. 3(a) and Fig. 3(b). Until now, the system has accomplished optical image encryption and hiding simultaneously.

2.2 Image recovery and decryption

By sending the three-step phase-shifting interferograms I(ξ,η;ϕR), random phase plates R1, R2 and the complex distribution of host image on CCD plane, together with the parameters of optical setup shown in Fig. 1, one user can successfully complete the retrieval of the original object image. First we can calculate the phase ϕ(ξ,η) and amplitude A(ξ,η) of the encrypted image on CCD plane according to Eq. (3) as follows:

ϕ(ξ,η)=tan12I(ξ,η;π/2)I(ξ,η;0)I(ξ,η;π)I(ξ,η;0)I(ξ,η;π)+ϕh(ξ,η),
A(ξ,η)={[I(ξ,η;0)I(ξ,η;π)]2+[2I(ξ,η;π/2)I(ξ,η;0)I(ξ,η;π)]2}1/24Ah(ξ,η),
where the host image diffraction distribution ϕh(ξ,η), Ah(ξ,η) on CCD plane can be obtained ahead of time using phase-shifting interferometry without the object image and random phase plates in Fig. 1 setup. In the process, the encrypted image can be recovered from the hidden image I(ξ,η;ϕR).

Once the encrypted image information A(ξ,η) and ϕ(ξ,η) are known, in addition to random phase masks z1,z2 and λ, we can digitally or optically retrieve the original object image from the encrypted image as

O'(x0,y0)=IFrtZ1{IFrtZ2{A(ξ,η)exp(jϕ(ξ,η)}×exp[i2πq(x1,y1)]}×exp[i2πp(x0,y0)],
where IFrt denotes inverse Fresnel transform.

From the above mentioned, we can see that this method can further enhance the security of optical image encryption when introducing host image into our system because the diffraction distribution of host image Ah(ξ,η), ϕh(ξ,η) can serve as the keys.

If the random phase plates R1 and R2 be removed from the scheme of optical image encryption and hiding in Fig. 1, the system can realize optical image hiding in pure optical means. Optical image hiding method is similar to the above and the expressions for optical image hiding just remove the effects of the random phase plates R1 and R2 in the aforementioned formulas. The delivered intensity patterns recorded on CCD are also similar to Fresnel holograms of the host image. Therefore, the principle of optical image hiding is no longer restated.

3. Computer simulations and experimental results

3.1 Experimental results for optical image hiding

In the experiment, the largest number of pixels for a DAHENG MVC-1000 type CCD is 1280(H) by 1024(V) with a pixel size of 5.2μm×5.2μm, and the largest number of pixels of a HOLOEYE LC 2002 type spatial light modulator (SLM) is 800(H) by 600(V) with a pixel pitch of 32μm. The size of the host image “C” is 0.4cm×0.3cm, and the size of the “sunshape” object coming from Microsoft Office 2003 used for hiding is 0.5568cm×0.5952cm. The wavelength of the He-Ne laser is 632.8 nm and the light amplitude ratio between the object beam and reference beam is 0.1:1. The stepped phase shifts in optical image hiding system are introduced by λ/2 wave plate and λ/4 wave plate. The recording distances of object image and host image are 0.768 m and 1.004 m respectively. The experimental results for optical image hiding in a modified Mach-Zehnder interferometer are shown in Fig. 2. Figure 2(a) shows one of the interferograms of the host image and Fig. 2(b) shows one of the interferograms from when the hidden images have been hidden in the host image. This illustration shows that the secret image can be embedded into the host image without destroying the original host's form and the existence of the data can be hidden in the Fresnel domain. Figure 2(c) shows the recovered original image from when the phase information ϕhof the host image is used, and Fig. 2(d) shows the larger version of Fig. 2(c). The experimental results show that this optical image hiding method is performed by using a completely optical scheme in the Fresnel domain, and a hidden image can be reconstructed with a specified algorithm.

 

Fig. 2 Experimental results. (a) One of the interferograms of the host image and (b) one of the interferograms from when the hidden image has been embedded into the host image; (c) retrieved image from when the phase information ϕhof the host image is used; and (d) the larger version of (c).

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3.2 Computer simulations for optical image encryption and hiding

Limited by the optical encryption devices and equipment, we cannot conduct the entire experiment with the simple experimental platform, so we use computer simulations to verify the feasibility of this method like general verification method of other papers [1619]. The original object images used to be encrypted and hidden are shown in Figs. 4(a) and 5(a), the host image is shown in Fig. 3(c), all at size of 256×256 pixels. The wavelength of the He-Ne laser is 632.8 nm and the light amplitude ratio between the object beam and reference beam is 0.000001:1. The first diffraction distance of the object image z1 is 0.1 m, and the second diffraction distance of the object image z2 is 0.2 m. The diffraction distance of the host image z3 is 0.3 m. After conducting optical image encryption and hiding on the object images, we can obtain the three interferograms that appear like on-axis holograms of the host image, one of these three interferograms for Figs. 4(a) and 5(a) is in turn shown in Figs. 4(b) and 5(b). Figures 4(c) and 5(c) show the recovered object images for Figs. 4(a) and 5(a) when only using the phase information ϕ(ξ,η) of the complex diffraction field of the encrypted object image. Once the diffraction distribution ϕh(ξ,η),Ah(ξ,η) of the host image is calculated using phase-shifting interferometry, the perfect recovered image could be gotten according to Eqs. (4), (5), and (6). Figures 4(e) and 5(e) show the perfect recovered images for Figs. 4(a) and 5(a). Figures 4(d) and 5(d) illustrate that the original object image cannot retrieved without the phase information ϕh(ξ,η) of the host image. The simulation results show that this optical image encryption and hiding method is performed by using a completely optical scheme in the Fresnel domain. The encrypted and hidden image can be easily transmitted through ordinary digital communication channels, and less attention will be paid by attackers to the secure image. Meanwhile, compared our method’s encryption effect with DRPE method, the introduction of host image can further enhance the encryption effect of our system because the diffraction distribution of the host image can serve as the keys.

 

Fig. 3 Interferograms after performing optical image encryption and hiding with different embedded levels and host image. (a) The interferogram when the light amplitude ratio of theobject beam and reference beam is 0.00001:1; (b) the interferogram when the light amplitude ratio of the object beam and reference beam is 0.000001:1;(c) host image.

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Fig. 4 Results with a binary image. (a) Binary image; (b) one of three interferograms for (a) after performing optical image encryption and hiding; (c) retrieved image only using the phase information ϕh(ξ,η) of the host image; (d) retrieved image when the phase information ϕh(ξ,η) of the host image is not used; (e) retrieved image when the amplitude A(ξ,η) and phase information ϕ(ξ,η) are all used to recover the original image.

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Fig. 5 Similar results as in Fig. 4 but with a gray-level image.

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4. Robustness of optical image encryption and hiding

A series of computer simulations have been carried out to investigate the robustness of our proposed method. First, we cut the three recorded interferograms by 25% respectively, and one of the cut interferograms and the corresponding retrieved object image are shown in Fig. 6. Second, the white additive Gaussian noise of zero-mean with a standard deviation of 0.1 is added to the three interferograms respectively, and one of the noise-added interferograms and the corresponding retrieved object image are shown in Fig. 7. Third, we test the effect of filtering the recorded interferograms in spatial domain, and a low-pass Gaussian filter and a high-pass Gaussian filter both with 3×3 window size and a standard deviation of 0.5 are applied here. One of the filtered interferograms and the corresponding retrieved object images in the two cases are shown in Fig. 8 and Fig. 9 respectively. Fourth, we apply JPEG compression on the interferograms with the compression ratio parameter q = 99% and one of the compressed interferograms and the corresponding retrieved object image are shown in Fig. 10. Lastly, we rotate all the three interferograms anticlockwise by 0.2 degree. One of the rotated interferograms and the corresponding retrieved object image are shown in Fig. 11. These results obviously prove that the method is robust to the various common distortions and attacks.

 

Fig. 6 Robustness of this method against occlusion attack. (a) One of the three interferograms cut by 25% for Fig. 5(a); (b) the corresponding retrieved object image.

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Fig. 7 Robustness of this method against noise attack. (a) One of the three interferograms for Fig. 5(a) distorted by zero-mean white additive Gaussian noise with a standard deviation of 0.1; (b) the corresponding retrieved object image.

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Fig. 8 Robustness of this method against low-pass filter attack. (a) One of the three interferograms for Fig. 5(a) filtered by a low-pass Gaussian filter with 3×3 window size and a standard deviation of 0.5; (b) the corresponding retrieved object image.

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Fig. 9 Robustness of this method against high-pass Gaussian filter attack. (a) One of the three interferograms for Fig. 5(a) filtered by a high-pass Gaussian filter with 3×3 window size and a standard deviation of 0.5; (b) the corresponding retrieved object image.

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Fig. 10 Robustness of this method against JPEG compression attack. (a) One of the three interferograms for Fig. 5(a) compressed with the compression ratio parameter q = 99%; (b) the corresponding retrieved object image.

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Fig. 11 Robustness of this method against rotation attack. (a) One of the three interferograms for Fig. 5(a) rotated anticlockwise by 0.2 degree; (b) the corresponding recovered object image.

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To evaluate the impact of various common distortions and attacks on the retrieved image, the correlation coefficient (CC) is introduced for comparing the retrieved image with the original one, which is defined as

CC=COV[O'(x0,y0),O(x0,y0)]σOσO',
where O'(x0,y0) and O(x0,y0) stand for the retrieved image and the original image respectively, σO and σO' are the standard deviations of O'(x0,y0) and O(x0,y0), and COV[O'(x0,y0),O(x0,y0)] is the covariance of the two corresponding images.

The curves of the CCs versus different intensity of the above distortions and attacks are shown in Fig. 12. The CCs versus the low-pass filter’s window size and the high-pass filter’s window size are shown in Fig. 12(a) and Fig. 12(b) respectively. As shown, the curve in Fig. 12(a) drops down sharply first, but after the filter’s window size increasing to 2×2pixels, the CC retains throughout a constant with respect to different window size of the filters; while the curve in Fig. 12(b) gradually ascends with the increasing high-pass filter’s window size. This indicates that the low frequency information in the interferograms is more useful to the reconstruction of the original image than the high frequency information.

 

Fig. 12 The curves of CCs versus different intensity of some common image distortions and attacks. (a) Low-pass Gaussian filter attack; (b) high-pass Gaussian filter attack; (c) JPEG compression attack; (d) rotation attack.

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Figure 12(c) presents the variation of the CC versus the image compression ratio. We easily notice that the increasing compression ratio results in the curve going up, for the less damage to interferograms can be induced in the compression operation with smaller compression ratio.

The curve shown in the Fig. 12(d) presents the CC versus the rotation angle, which declines gradually with the rotation angle increasing. And the CC value corresponding to 0.6 degree rotation angle has been near zero. It implies that the method is very sensitive to the rotation distortion of the interferograms.

From all the above curves of CCs, we can conclude that the presented optical image encryption and hiding method is robust to the above various common attacks, and it is more sensitive to the JPEG compression and the rotation attacks than other attacks. Because the CCs drop down to a small value (less than 0.2) due to relatively slight attack in these two cases; while the CCs under the both filter attacks are all larger than 0.7 regardless of any attack intensity.

We have also made the same evaluations with the binary image, and the results are similar to those obtained from the gray-level image, but the CCs with the binary image are obviously higher than it with the gray-level image under every attack.

5 Conclusions

In summary, the method for optical image hiding and for optical image encryption and hiding is presented in this paper, and a fully optical scheme of our method is demonstrated in a modified Mach-Zehnder interferometer. The encrypted and hidden data, which are registered as Fresnel holograms, are obtained by three-step phase-shifting interferometry in a modified Mach-Zehnder interferometer; finally, the original object image was digitally or optically retrieved via inverse Fresnel transform after the complex distribution of the encrypted image (or the original object image) on CCD plane is calculated with the specified recovery algorithm. The effectiveness and robustness of the method is verified by numerical simulations and experimental results. This technique allows for high-speed image hiding and image encryption and hiding through completely optical means; and this method can further enhance the security of optical image encryption when introducing optical image hiding because the delivered intensity patterns are not noise-like patterns in single optical encryption that attract eavesdroppers, but they are similar to Fresnel holograms of the host image in our method. So it is expected to be widely used for image encryption, watermarks, image/video secure transmission, and future all-optical transmission system. For example, this method can be used for real-time video security transmission and naked-eye 3D Television, etc. Moreover, the technique can combine with other phase-shifting holography and optical encryption method to get wide range of applications and probably superior performance. For example, the method can be combined with color holographic techniques to achieve color images encryption and hiding.

Acknowledgments

This work was supported by the Project of Department of Education of Guangdong Province, China (Research on method and application of compressive imaging with coherent light illumination). The authors wish to express their deepest thanks to the editor and reviewers for giving us constructive suggestions that have helped us both in the English accuracy and in the depth of discussion to improve the quality of this paper.

References and links

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4. X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31(10), 1414–1416 (2006). [CrossRef]   [PubMed]  

5. N. Singh and A. Sinha, “Optical image encryption using fractional Fourier transform and chaos,” Opt. Lasers Eng. 46(2), 117–123 (2008). [CrossRef]  

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References

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  1. P. Refregier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).
    [CrossRef] [PubMed]
  2. B. Javidi, T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25(1), 28–30 (2000).
    [CrossRef] [PubMed]
  3. G. Unnikrishnan, J. Joseph, K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25(12), 887–889 (2000).
    [CrossRef] [PubMed]
  4. X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, Y. R. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31(10), 1414–1416 (2006).
    [CrossRef] [PubMed]
  5. N. Singh, A. Sinha, “Optical image encryption using fractional Fourier transform and chaos,” Opt. Lasers Eng. 46(2), 117–123 (2008).
    [CrossRef]
  6. W. Chen, X. D. Chen, C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35(22), 3817–3819 (2010).
    [CrossRef] [PubMed]
  7. P. Kumar, J. Joseph, K. Singh, “Optical image encryption using a jigsaw transform for silhouette removal in interference-based methods and decryption with a single spatial light modulator,” Appl. Opt. 50(13), 1805–1811 (2011).
    [CrossRef] [PubMed]
  8. Y. Zhang, B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33(21), 2443–2445 (2008).
    [CrossRef] [PubMed]
  9. J. Li, T. Zheng, Q. Z. Liu, R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285(7), 1704–1709 (2012).
    [CrossRef]
  10. Y. S. Zhang, D. Xiao, “Double optical image encryption using discrete Chirikov standard map and chaos- based fractional random transform,” Opt. Lasers Eng. 51(4), 472–480 (2013).
    [CrossRef]
  11. Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38(9), 1425–1427 (2013).
    [CrossRef] [PubMed]
  12. J. Zang, Z. Xie, Y. Zhang, “Optical image encryption with spatially incoherent illumination,” Opt. Lett. 38(8), 1289–1291 (2013).
    [CrossRef] [PubMed]
  13. A. Alfalou, C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1(3), 589–636 (2009).
    [CrossRef]
  14. A. Alfalou, C. Brosseau, N. Abdallah, M. Jridi, “Assessing the performance of a method of simultaneous compression and encryption of multiple images and its resistance against various attacks,” Opt. Express 21(7), 8025–8043 (2013).
    [CrossRef] [PubMed]
  15. A. Alfalou, C. Brosseau, N. Abdallah, M. Jridi, “Simultaneous fusion, compression, and encryption of multiple images,” Opt. Express 19(24), 24023–24029 (2011).
    [CrossRef] [PubMed]
  16. W. Liu, Z. Liu, S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm,” Opt. Lett. 38(10), 1651–1653 (2013).
    [CrossRef] [PubMed]
  17. N. Zhu, Y. T. Wang, J. Liu, J. H. Xie, H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17(16), 13418–13424 (2009).
    [CrossRef] [PubMed]
  18. R. Tao, Y. Xin, Y. Wang, “Double image encryption based on random phase encoding in the fractional Fourier domain,” Opt. Express 15(24), 16067–16079 (2007).
    [CrossRef] [PubMed]
  19. A. Alfalou, C. Brosseau, “Exploiting root-mean-square time-frequency structure for multiple-image optical compression and encryption,” Opt. Lett. 35(11), 1914–1916 (2010).
    [CrossRef] [PubMed]
  20. W. Chen, X. Chen, C. J. R. Sheppard, “Optical color-image encryption and synthesis using coherent diffractive imaging in the Fresnel domain,” Opt. Express 20(4), 3853–3865 (2012).
    [CrossRef] [PubMed]
  21. F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding - a survey,” Proc. IEEE 87(7), 1062–1078 (1999).
    [CrossRef]
  22. I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking (Academic, 2001).
  23. S. Kishk, B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41(26), 5462–5470 (2002).
    [CrossRef] [PubMed]
  24. N. Takai, Y. Mifune, “Digital watermarking by a holographic technique,” Appl. Opt. 41(5), 865–873 (2002).
    [CrossRef] [PubMed]
  25. S. Kishk, B. Javidi, “Watermarking of three-dimensional objects by digital holography,” Opt. Lett. 28(3), 167–169 (2003).
    [CrossRef] [PubMed]
  26. H. T. Chang, C. L. Tsan, “Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain,” Appl. Opt. 44(29), 6211–6219 (2005).
    [CrossRef] [PubMed]
  27. M. Z. He, L. Z. Cai, Q. Liu, X. L. Yang, “Phase-only encryption and watermarking based on phase-shifting interferometry,” Appl. Opt. 44(13), 2600–2606 (2005).
    [CrossRef] [PubMed]
  28. F. Ge, L. F. Chen, D. M. Zhao, “A half-blind color image hiding and encryption method in fractional Fourier domains,” Opt. Commun. 281(17), 4254–4260 (2008).
    [CrossRef]
  29. X. P. Zhang, Reversible data hiding in encrypted image,” IEEE Signal Proc. Let. 18, 255–258 (2011). http://www.sciencedirect.com/science/article/pii/S0165168413002417 - item1#item1
  30. C. H. Chuang, Y. L. Chen, “Steganographic optical image encryption system based on reversible data hiding and double random phase encoding,” Opt. Eng. 52(2), 028201 (2013).
    [CrossRef]
  31. W. M. Zhang, K. Ma, N. Yu, “Reversibility improved data hiding in encrypted images,” Signal Process. 94, 118–127 (2014).
    [CrossRef]
  32. Y. Shi, G. Situ, J. Zhang, “Optical image hiding in the Fresnel domain,” J. Opt. A, Pure Appl. Opt. 8(6), 569–577 (2006).
    [CrossRef]
  33. Y. Shi, G. Situ, J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32(13), 1914–1916 (2007).
    [CrossRef] [PubMed]

2014 (1)

W. M. Zhang, K. Ma, N. Yu, “Reversibility improved data hiding in encrypted images,” Signal Process. 94, 118–127 (2014).
[CrossRef]

2013 (6)

2012 (2)

W. Chen, X. Chen, C. J. R. Sheppard, “Optical color-image encryption and synthesis using coherent diffractive imaging in the Fresnel domain,” Opt. Express 20(4), 3853–3865 (2012).
[CrossRef] [PubMed]

J. Li, T. Zheng, Q. Z. Liu, R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285(7), 1704–1709 (2012).
[CrossRef]

2011 (2)

2010 (2)

2009 (2)

2008 (3)

Y. Zhang, B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33(21), 2443–2445 (2008).
[CrossRef] [PubMed]

N. Singh, A. Sinha, “Optical image encryption using fractional Fourier transform and chaos,” Opt. Lasers Eng. 46(2), 117–123 (2008).
[CrossRef]

F. Ge, L. F. Chen, D. M. Zhao, “A half-blind color image hiding and encryption method in fractional Fourier domains,” Opt. Commun. 281(17), 4254–4260 (2008).
[CrossRef]

2007 (2)

2006 (2)

2005 (2)

2003 (1)

2002 (2)

2000 (2)

1999 (1)

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding - a survey,” Proc. IEEE 87(7), 1062–1078 (1999).
[CrossRef]

1995 (1)

Abdallah, N.

Alfalou, A.

Anderson, R. J.

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding - a survey,” Proc. IEEE 87(7), 1062–1078 (1999).
[CrossRef]

Brosseau, C.

Cai, L. Z.

Chang, H. T.

Chen, L. F.

F. Ge, L. F. Chen, D. M. Zhao, “A half-blind color image hiding and encryption method in fractional Fourier domains,” Opt. Commun. 281(17), 4254–4260 (2008).
[CrossRef]

Chen, W.

Chen, X.

Chen, X. D.

Chen, Y. L.

C. H. Chuang, Y. L. Chen, “Steganographic optical image encryption system based on reversible data hiding and double random phase encoding,” Opt. Eng. 52(2), 028201 (2013).
[CrossRef]

Chuang, C. H.

C. H. Chuang, Y. L. Chen, “Steganographic optical image encryption system based on reversible data hiding and double random phase encoding,” Opt. Eng. 52(2), 028201 (2013).
[CrossRef]

Dong, G. Y.

Gao, Q.

Ge, F.

F. Ge, L. F. Chen, D. M. Zhao, “A half-blind color image hiding and encryption method in fractional Fourier domains,” Opt. Commun. 281(17), 4254–4260 (2008).
[CrossRef]

He, M. Z.

Javidi, B.

Joseph, J.

Jridi, M.

Kishk, S.

Kuhn, M. G.

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding - a survey,” Proc. IEEE 87(7), 1062–1078 (1999).
[CrossRef]

Kumar, P.

Li, H.

Li, J.

J. Li, T. Zheng, Q. Z. Liu, R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285(7), 1704–1709 (2012).
[CrossRef]

Li, R.

J. Li, T. Zheng, Q. Z. Liu, R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285(7), 1704–1709 (2012).
[CrossRef]

Li, T.

Liu, J.

Liu, Q.

Liu, Q. Z.

J. Li, T. Zheng, Q. Z. Liu, R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285(7), 1704–1709 (2012).
[CrossRef]

Liu, S.

Liu, W.

Liu, Z.

Ma, K.

W. M. Zhang, K. Ma, N. Yu, “Reversibility improved data hiding in encrypted images,” Signal Process. 94, 118–127 (2014).
[CrossRef]

Meng, X. F.

Mifune, Y.

Nomura, T.

Petitcolas, F. A. P.

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding - a survey,” Proc. IEEE 87(7), 1062–1078 (1999).
[CrossRef]

Refregier, P.

Shen, X. X.

Sheppard, C. J. R.

Shi, Y.

Singh, K.

Singh, N.

N. Singh, A. Sinha, “Optical image encryption using fractional Fourier transform and chaos,” Opt. Lasers Eng. 46(2), 117–123 (2008).
[CrossRef]

Sinha, A.

N. Singh, A. Sinha, “Optical image encryption using fractional Fourier transform and chaos,” Opt. Lasers Eng. 46(2), 117–123 (2008).
[CrossRef]

Situ, G.

Y. Shi, G. Situ, J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32(13), 1914–1916 (2007).
[CrossRef] [PubMed]

Y. Shi, G. Situ, J. Zhang, “Optical image hiding in the Fresnel domain,” J. Opt. A, Pure Appl. Opt. 8(6), 569–577 (2006).
[CrossRef]

Takai, N.

Tao, R.

Tsan, C. L.

Unnikrishnan, G.

Wang, B.

Wang, Y.

Wang, Y. R.

Wang, Y. T.

Xiao, D.

Y. S. Zhang, D. Xiao, “Double optical image encryption using discrete Chirikov standard map and chaos- based fractional random transform,” Opt. Lasers Eng. 51(4), 472–480 (2013).
[CrossRef]

Xie, J. H.

Xie, Z.

Xin, Y.

Xu, X. F.

Yang, X. L.

Yu, N.

W. M. Zhang, K. Ma, N. Yu, “Reversibility improved data hiding in encrypted images,” Signal Process. 94, 118–127 (2014).
[CrossRef]

Zang, J.

Zhang, H.

Zhang, J.

Y. Shi, G. Situ, J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32(13), 1914–1916 (2007).
[CrossRef] [PubMed]

Y. Shi, G. Situ, J. Zhang, “Optical image hiding in the Fresnel domain,” J. Opt. A, Pure Appl. Opt. 8(6), 569–577 (2006).
[CrossRef]

Zhang, S.

Zhang, W. M.

W. M. Zhang, K. Ma, N. Yu, “Reversibility improved data hiding in encrypted images,” Signal Process. 94, 118–127 (2014).
[CrossRef]

Zhang, Y.

Zhang, Y. S.

Y. S. Zhang, D. Xiao, “Double optical image encryption using discrete Chirikov standard map and chaos- based fractional random transform,” Opt. Lasers Eng. 51(4), 472–480 (2013).
[CrossRef]

Zhao, D. M.

F. Ge, L. F. Chen, D. M. Zhao, “A half-blind color image hiding and encryption method in fractional Fourier domains,” Opt. Commun. 281(17), 4254–4260 (2008).
[CrossRef]

Zheng, T.

J. Li, T. Zheng, Q. Z. Liu, R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285(7), 1704–1709 (2012).
[CrossRef]

Zhu, N.

Adv. Opt. Photon. (1)

Appl. Opt. (5)

J. Opt. A, Pure Appl. Opt. (1)

Y. Shi, G. Situ, J. Zhang, “Optical image hiding in the Fresnel domain,” J. Opt. A, Pure Appl. Opt. 8(6), 569–577 (2006).
[CrossRef]

Opt. Commun. (2)

J. Li, T. Zheng, Q. Z. Liu, R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285(7), 1704–1709 (2012).
[CrossRef]

F. Ge, L. F. Chen, D. M. Zhao, “A half-blind color image hiding and encryption method in fractional Fourier domains,” Opt. Commun. 281(17), 4254–4260 (2008).
[CrossRef]

Opt. Eng. (1)

C. H. Chuang, Y. L. Chen, “Steganographic optical image encryption system based on reversible data hiding and double random phase encoding,” Opt. Eng. 52(2), 028201 (2013).
[CrossRef]

Opt. Express (5)

Opt. Lasers Eng. (2)

N. Singh, A. Sinha, “Optical image encryption using fractional Fourier transform and chaos,” Opt. Lasers Eng. 46(2), 117–123 (2008).
[CrossRef]

Y. S. Zhang, D. Xiao, “Double optical image encryption using discrete Chirikov standard map and chaos- based fractional random transform,” Opt. Lasers Eng. 51(4), 472–480 (2013).
[CrossRef]

Opt. Lett. (12)

B. Javidi, T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25(1), 28–30 (2000).
[CrossRef] [PubMed]

G. Unnikrishnan, J. Joseph, K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25(12), 887–889 (2000).
[CrossRef] [PubMed]

P. Refregier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).
[CrossRef] [PubMed]

X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, Y. R. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31(10), 1414–1416 (2006).
[CrossRef] [PubMed]

Y. Shi, G. Situ, J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32(13), 1914–1916 (2007).
[CrossRef] [PubMed]

A. Alfalou, C. Brosseau, “Exploiting root-mean-square time-frequency structure for multiple-image optical compression and encryption,” Opt. Lett. 35(11), 1914–1916 (2010).
[CrossRef] [PubMed]

W. Chen, X. D. Chen, C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35(22), 3817–3819 (2010).
[CrossRef] [PubMed]

Y. Zhang, B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33(21), 2443–2445 (2008).
[CrossRef] [PubMed]

S. Kishk, B. Javidi, “Watermarking of three-dimensional objects by digital holography,” Opt. Lett. 28(3), 167–169 (2003).
[CrossRef] [PubMed]

J. Zang, Z. Xie, Y. Zhang, “Optical image encryption with spatially incoherent illumination,” Opt. Lett. 38(8), 1289–1291 (2013).
[CrossRef] [PubMed]

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38(9), 1425–1427 (2013).
[CrossRef] [PubMed]

W. Liu, Z. Liu, S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm,” Opt. Lett. 38(10), 1651–1653 (2013).
[CrossRef] [PubMed]

Proc. IEEE (1)

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding - a survey,” Proc. IEEE 87(7), 1062–1078 (1999).
[CrossRef]

Signal Process. (1)

W. M. Zhang, K. Ma, N. Yu, “Reversibility improved data hiding in encrypted images,” Signal Process. 94, 118–127 (2014).
[CrossRef]

Other (2)

X. P. Zhang, Reversible data hiding in encrypted image,” IEEE Signal Proc. Let. 18, 255–258 (2011). http://www.sciencedirect.com/science/article/pii/S0165168413002417 - item1#item1

I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking (Academic, 2001).

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Figures (12)

Fig. 1
Fig. 1

Scheme of optical image encryption and hiding. BE, beam expander; L, lens; BS, beam splitter; M, mirror; NDF, neutral density filters; R, random phase plate; PZT, piezoelectric transducer mirror; Oe, object image; Oh, host image.

Fig. 2
Fig. 2

Experimental results. (a) One of the interferograms of the host image and (b) one of the interferograms from when the hidden image has been embedded into the host image; (c) retrieved image from when the phase information ϕ h of the host image is used; and (d) the larger version of (c).

Fig. 3
Fig. 3

Interferograms after performing optical image encryption and hiding with different embedded levels and host image. (a) The interferogram when the light amplitude ratio of the object beam and reference beam is 0.00001:1; (b) the interferogram when the light amplitude ratio of the object beam and reference beam is 0.000001:1;(c) host image.

Fig. 4
Fig. 4

Results with a binary image. (a) Binary image; (b) one of three interferograms for (a) after performing optical image encryption and hiding; (c) retrieved image only using the phase information ϕ h (ξ,η) of the host image; (d) retrieved image when the phase information ϕ h (ξ,η) of the host image is not used; (e) retrieved image when the amplitude A(ξ,η) and phase information ϕ(ξ,η) are all used to recover the original image.

Fig. 5
Fig. 5

Similar results as in Fig. 4 but with a gray-level image.

Fig. 6
Fig. 6

Robustness of this method against occlusion attack. (a) One of the three interferograms cut by 25% for Fig. 5(a); (b) the corresponding retrieved object image.

Fig. 7
Fig. 7

Robustness of this method against noise attack. (a) One of the three interferograms for Fig. 5(a) distorted by zero-mean white additive Gaussian noise with a standard deviation of 0.1; (b) the corresponding retrieved object image.

Fig. 8
Fig. 8

Robustness of this method against low-pass filter attack. (a) One of the three interferograms for Fig. 5(a) filtered by a low-pass Gaussian filter with 3×3 window size and a standard deviation of 0.5; (b) the corresponding retrieved object image.

Fig. 9
Fig. 9

Robustness of this method against high-pass Gaussian filter attack. (a) One of the three interferograms for Fig. 5(a) filtered by a high-pass Gaussian filter with 3×3 window size and a standard deviation of 0.5; (b) the corresponding retrieved object image.

Fig. 10
Fig. 10

Robustness of this method against JPEG compression attack. (a) One of the three interferograms for Fig. 5(a) compressed with the compression ratio parameter q = 99%; (b) the corresponding retrieved object image.

Fig. 11
Fig. 11

Robustness of this method against rotation attack. (a) One of the three interferograms for Fig. 5(a) rotated anticlockwise by 0.2 degree; (b) the corresponding recovered object image.

Fig. 12
Fig. 12

The curves of CCs versus different intensity of some common image distortions and attacks. (a) Low-pass Gaussian filter attack; (b) high-pass Gaussian filter attack; (c) JPEG compression attack; (d) rotation attack.

Equations (7)

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ψ 0 (ξ,η)=A(ξ,η)exp(iϕ(ξ,η)) =Fr t Z 2 { Fr t Z 1 { C 1 ×O( x 0 , y 0 )×exp[i2πp( x 0 , y 0 )] }×exp[i2πq( x 1 , y 1 )] },
ψ h (ξ,η; ϕ R )= A h (ξ,η)exp[i ϕ h (ξ,η)]exp(i ϕ R ) =Fr t Z 3 { C 2 exp(i ϕ R )h( x 0 ' , y 0 ' ) } ( ϕ R =0, π 2 ,π),
I(ξ,η; ϕ R )= | ψ 0 (ξ,η)+ ψ h (ξ,η; ϕ R ) | 2 =A (ξ,η) 2 + A h (ξ,η) 2 +2A(ξ,η) A h (ξ,η)cos[ ϕ h (ξ,η)+ ϕ R -ϕ(ξ,η)].
ϕ(ξ,η)= tan 1 2I(ξ,η;π/ 2)I(ξ,η;0)I(ξ,η;π) I(ξ,η;0)I(ξ,η;π) + ϕ h (ξ,η),
A(ξ,η)= { [I(ξ,η;0)I(ξ,η;π)] 2 +[2I(ξ,η;π/ 2)I(ξ,η;0)I(ξ,η;π) ] 2 } 1/2 4 A h (ξ,η) ,
O ' ( x 0 , y 0 )=IFr t Z 1 { IFr t Z 2 { A(ξ,η)exp(jϕ(ξ,η) }×exp[i2πq( x 1 , y 1 )] }×exp[i2πp( x 0 , y 0 )],
CC= COV[O'( x 0 , y 0 ),O( x 0 , y 0 )] σ O σ O' ,

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