Optical color-image encryption and synthesis using coherent diffractive imaging in the Fresnel domain

Wen Chen; Xudong Chen; Colin J. R. Sheppard

doi:10.1364/OE.20.003853

Optical color-image encryption and synthesis using coherent diffractive imaging in the Fresnel domain

Wen Chen, Xudong Chen, and Colin J. R. Sheppard

Optics Express
Vol. 20,
Issue 4,
pp. 3853-3865
(2012)
•https://doi.org/10.1364/OE.20.003853

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Wen Chen, Xudong Chen, and Colin J. R. Sheppard, "Optical color-image encryption and synthesis using coherent diffractive imaging in the Fresnel domain," Opt. Express 20, 3853-3865 (2012)

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Related Topics
Table of Contents Category
- Image Processing
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Optical security and encryption (060.4785)
- Pattern recognition, optical security and encryption (100.4998)
- Digital image processing (100.2000)
- Inverse problems (100.3190)
- Coherence imaging (110.1650)

About this Article
History
- Original Manuscript: October 25, 2011
- Revised Manuscript: December 7, 2011
- Manuscript Accepted: January 3, 2012
- Published: February 1, 2012

Accessible

Open Access

Abstract

We propose a new method using coherent diffractive imaging for optical color-image encryption and synthesis in the Fresnel domain. An optical multiple-random-phase-mask encryption system is applied, and a strategy based on lateral translations of a phase-only mask is employed during image encryption. For the decryption, an iterative phase retrieval algorithm is applied to extract high-quality decrypted color images from diffraction intensity maps (i.e., ciphertexts). In addition, optical color-image synthesis is also investigated based on coherent diffractive imaging. Numerical results are presented to demonstrate feasibility and effectiveness of the proposed method. Compared with conventional interference methods, coherent diffractive imaging approach may open up a new research perspective or can provide an effective alternative for optical color-image encryption and synthesis.

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References

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Publication

P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).
[Crossref] [PubMed]
B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
[Crossref]
O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]
T. J. Naughton, B. M. Hennelly, and T. Dowling, “Introducing secure modes of operation for optical encryption,” J. Opt. Soc. Am. A 25(10), 2608–2617 (2008).
[Crossref] [PubMed]
A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30(13), 1644–1646 (2005).
[Crossref] [PubMed]
X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31(8), 1044–1046 (2006).
[Crossref] [PubMed]
O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24(11), 762–764 (1999).
[Crossref] [PubMed]
G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29(14), 1584–1586 (2004).
[Crossref] [PubMed]
G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25(12), 887–889 (2000).
[Crossref] [PubMed]
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H. Li, “Image encryption based on gyrator transform and two-step phase-shifting interferometry,” Opt. Lasers Eng. 47(1), 45–50 (2009).
[Crossref]
Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49(29), 5632–5637 (2010).
[Crossref] [PubMed]
X. Peng, L. Yu, and L. Cai, “Double-lock for image encryption with virtual optical wavelength,” Opt. Express 10(1), 41–45 (2002).
[PubMed]
H. Kim, D. H. Kim, and Y. H. Lee, “Encryption of digital hologram of 3-D object by virtual optics,” Opt. Express 12(20), 4912–4921 (2004).
[Crossref] [PubMed]
L. Yu and L. Cai, “Multidimensional data encryption with digital holography,” Opt. Commun. 215(4-6), 271–284 (2003).
[Crossref]
B. Zhu, H. Zhao, and S. Liu, “Image encryption based on pure intensity random coding and digital holography technique,” Optik (Stuttg.) 114(2), 95–99 (2003).
[Crossref]
E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39(35), 6595–6601 (2000).
[Crossref] [PubMed]
X. Wang, D. Zhao, F. Jing, and X. Wei, “Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics,” Opt. Express 14(4), 1476–1486 (2006).
[Crossref] [PubMed]
S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microw. Opt. Technol. Lett. 21(5), 318–323 (1999).
[Crossref]
L. Chen and D. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Express 14(19), 8552–8560 (2006).
[Crossref] [PubMed]
G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30(11), 1306–1308 (2005).
[Crossref] [PubMed]
L. Chen and D. Zhao, “Color information processing (coding and synthesis) with fractional Fourier transforms and digital holography,” Opt. Express 15(24), 16080–16089 (2007).
[Crossref] [PubMed]
F. Mosso, M. Tebaldi, J. F. Barrera, N. Bolognini, and R. Torroba, “Pure optical dynamical color encryption,” Opt. Express 19(15), 13779–13786 (2011).
[Crossref] [PubMed]
S. Lai and M. A. Neifeld, “Digital wavefront reconstruction and its application to image encryption,” Opt. Commun. 178(4-6), 283–289 (2000).
[Crossref]
U. Schnars and W. Jüptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).
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]
R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).
J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
[Crossref] [PubMed]
F. C. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75(4), 043805 (2007).
[Crossref]
J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]
J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300(5624), 1419–1421 (2003).
[Crossref] [PubMed]
M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442(7098), 63–66 (2006).
[Crossref] [PubMed]
L. De Caro, C. Giannini, A. Cedola, D. Pelliccia, S. Lagomarsino, and W. Jark, “Phase retrieval in X-ray coherent Fresnel projection-geometry diffraction,” Appl. Phys. Lett. 90(4), 041105 (2007).
[Crossref]
I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100(15), 155503 (2008).
[Crossref] [PubMed]
J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
W. Chen and X. Chen, “Quantitative phase retrieval of a complex-valued object using variable function orders in the fractional Fourier domain,” Opt. Express 18(13), 13536–13541 (2010).
[Crossref] [PubMed]
W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18(26), 27095–27104 (2010).
[Crossref] [PubMed]
W. Chen and X. Chen, “Quantitative phase retrieval of complex-valued specimens based on noninterferometric imaging,” Appl. Opt. 50(14), 2008–2015 (2011).
[Crossref] [PubMed]
W. Chen and X. Chen, “Optical cryptography topology based on a three-dimensional particle-like distribution and diffractive imaging,” Opt. Express 19(10), 9008–9019 (2011).
[Crossref] [PubMed]
D. Wang, J. Zhao, F. Zhang, G. Pedrini, and W. Osten, “High-fidelity numerical realization of multiple-step Fresnel propagation for the reconstruction of digital holograms,” Appl. Opt. 47(19), D12–D20 (2008).
[Crossref] [PubMed]
W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13(7), 075404 (2011).
[Crossref]
K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields,” Opt. Express 17(22), 19662–19673 (2009).
[Crossref] [PubMed]
Original color image or plaintext (Peppers): http://sipi.usc.edu/database .
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(23), 4825–4834 (2002).
[Crossref] [PubMed]
X. F. Meng, L. Z. Cai, X. L. Yang, X. X. Shen, and G. Y. Dong, “Information security system by iterative multiple-phase retrieval and pixel random permutation,” Appl. Opt. 45(14), 3289–3297 (2006).
[Crossref] [PubMed]
X. Yong-Liang, Z. Xin, W. Qiong-Hua, Y. Sheng, and C. Yao-Yao, “Optical image encryption topology,” Opt. Lett. 34(20), 3223–3225 (2009).
[Crossref] [PubMed]
H. E. Hwang, H. T. Chang, and W. N. Lie, “Multiple-image encryption and multiplexing using a modified Gerchberg-Saxton algorithm and phase modulation in Fresnel-transform domain,” Opt. Lett. 34(24), 3917–3919 (2009).
[Crossref] [PubMed]
W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35(22), 3817–3819 (2010).
[Crossref] [PubMed]
J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662–1669 (1998).
[Crossref]
M. He, Q. Tan, L. Cao, Q. He, and G. Jin, “Security enhanced optical encryption system by random phase key and permutation key,” Opt. Express 17(25), 22462–22473 (2009).
[Crossref] [PubMed]
X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33(14), 1575–1577 (2008).
[Crossref] [PubMed]
P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase functions,” Opt. Lett. 34(3), 331–333 (2009).
[Crossref] [PubMed]
W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282(18), 3680–3685 (2009).
[Crossref]
X. Shi and D. Zhao, “Color image hiding based on the phase retrieval technique and Arnold transform,” Appl. Opt. 50(14), 2134–2139 (2011).
[Crossref] [PubMed]
W. Qin and X. Peng, “Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys,” J. Opt. A, Pure Appl. Opt. 11(7), 075402 (2009).
[Crossref]
G. Situ, U. Gopinathan, D. S. Monaghan, and J. T. Sheridan, “Cryptanalysis of optical security systems with significant output images,” Appl. Opt. 46(22), 5257–5262 (2007).
[Crossref] [PubMed]
U. Gopinathan, D. S. Monaghan, T. J. Naughton, and J. T. Sheridan, “A known-plaintext heuristic attack on the Fourier plane encryption algorithm,” Opt. Express 14(8), 3181–3186 (2006).
[Crossref] [PubMed]
W. McBride, N. L. O’Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr. A 61(3), 321–324 (2005).
[Crossref] [PubMed]
W. Chen, X. Chen, and C. J. R. Sheppard, “Optical double-image cryptography based on diffractive imaging with a laterally-translated phase grating,” Appl. Opt. 50(29), 5750–5757 (2011).
[Crossref] [PubMed]

2011 (6)

F. Mosso, M. Tebaldi, J. F. Barrera, N. Bolognini, and R. Torroba, “Pure optical dynamical color encryption,” Opt. Express 19(15), 13779–13786 (2011).
[Crossref] [PubMed]

W. Chen and X. Chen, “Quantitative phase retrieval of complex-valued specimens based on noninterferometric imaging,” Appl. Opt. 50(14), 2008–2015 (2011).
[Crossref] [PubMed]

W. Chen and X. Chen, “Optical cryptography topology based on a three-dimensional particle-like distribution and diffractive imaging,” Opt. Express 19(10), 9008–9019 (2011).
[Crossref] [PubMed]

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13(7), 075404 (2011).
[Crossref]

X. Shi and D. Zhao, “Color image hiding based on the phase retrieval technique and Arnold transform,” Appl. Opt. 50(14), 2134–2139 (2011).
[Crossref] [PubMed]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical double-image cryptography based on diffractive imaging with a laterally-translated phase grating,” Appl. Opt. 50(29), 5750–5757 (2011).
[Crossref] [PubMed]

2010 (4)

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

W. Chen and X. Chen, “Quantitative phase retrieval of a complex-valued object using variable function orders in the fractional Fourier domain,” Opt. Express 18(13), 13536–13541 (2010).
[Crossref] [PubMed]

W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18(26), 27095–27104 (2010).
[Crossref] [PubMed]

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49(29), 5632–5637 (2010).
[Crossref] [PubMed]

2009 (9)

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

H. Li, “Image encryption based on gyrator transform and two-step phase-shifting interferometry,” Opt. Lasers Eng. 47(1), 45–50 (2009).
[Crossref]

M. He, Q. Tan, L. Cao, Q. He, and G. Jin, “Security enhanced optical encryption system by random phase key and permutation key,” Opt. Express 17(25), 22462–22473 (2009).
[Crossref] [PubMed]

W. Qin and X. Peng, “Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys,” J. Opt. A, Pure Appl. Opt. 11(7), 075402 (2009).
[Crossref]

K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields,” Opt. Express 17(22), 19662–19673 (2009).
[Crossref] [PubMed]

X. Yong-Liang, Z. Xin, W. Qiong-Hua, Y. Sheng, and C. Yao-Yao, “Optical image encryption topology,” Opt. Lett. 34(20), 3223–3225 (2009).
[Crossref] [PubMed]

H. E. Hwang, H. T. Chang, and W. N. Lie, “Multiple-image encryption and multiplexing using a modified Gerchberg-Saxton algorithm and phase modulation in Fresnel-transform domain,” Opt. Lett. 34(24), 3917–3919 (2009).
[Crossref] [PubMed]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase functions,” Opt. Lett. 34(3), 331–333 (2009).
[Crossref] [PubMed]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282(18), 3680–3685 (2009).
[Crossref]

2008 (4)

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100(15), 155503 (2008).
[Crossref] [PubMed]

D. Wang, J. Zhao, F. Zhang, G. Pedrini, and W. Osten, “High-fidelity numerical realization of multiple-step Fresnel propagation for the reconstruction of digital holograms,” Appl. Opt. 47(19), D12–D20 (2008).
[Crossref] [PubMed]

X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33(14), 1575–1577 (2008).
[Crossref] [PubMed]

T. J. Naughton, B. M. Hennelly, and T. Dowling, “Introducing secure modes of operation for optical encryption,” J. Opt. Soc. Am. A 25(10), 2608–2617 (2008).
[Crossref] [PubMed]

2007 (4)

L. Chen and D. Zhao, “Color information processing (coding and synthesis) with fractional Fourier transforms and digital holography,” Opt. Express 15(24), 16080–16089 (2007).
[Crossref] [PubMed]

L. De Caro, C. Giannini, A. Cedola, D. Pelliccia, S. Lagomarsino, and W. Jark, “Phase retrieval in X-ray coherent Fresnel projection-geometry diffraction,” Appl. Phys. Lett. 90(4), 041105 (2007).
[Crossref]

F. C. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75(4), 043805 (2007).
[Crossref]

G. Situ, U. Gopinathan, D. S. Monaghan, and J. T. Sheridan, “Cryptanalysis of optical security systems with significant output images,” Appl. Opt. 46(22), 5257–5262 (2007).
[Crossref] [PubMed]

2006 (7)

U. Gopinathan, D. S. Monaghan, T. J. Naughton, and J. T. Sheridan, “A known-plaintext heuristic attack on the Fourier plane encryption algorithm,” Opt. Express 14(8), 3181–3186 (2006).
[Crossref] [PubMed]

X. F. Meng, L. Z. Cai, X. L. Yang, X. X. Shen, and G. Y. Dong, “Information security system by iterative multiple-phase retrieval and pixel random permutation,” Appl. Opt. 45(14), 3289–3297 (2006).
[Crossref] [PubMed]

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442(7098), 63–66 (2006).
[Crossref] [PubMed]

L. Chen and D. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Express 14(19), 8552–8560 (2006).
[Crossref] [PubMed]

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]

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31(8), 1044–1046 (2006).
[Crossref] [PubMed]

X. Wang, D. Zhao, F. Jing, and X. Wei, “Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics,” Opt. Express 14(4), 1476–1486 (2006).
[Crossref] [PubMed]

2005 (3)

A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30(13), 1644–1646 (2005).
[Crossref] [PubMed]

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30(11), 1306–1308 (2005).
[Crossref] [PubMed]

W. McBride, N. L. O’Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr. A 61(3), 321–324 (2005).
[Crossref] [PubMed]

2004 (2)

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29(14), 1584–1586 (2004).
[Crossref] [PubMed]

H. Kim, D. H. Kim, and Y. H. Lee, “Encryption of digital hologram of 3-D object by virtual optics,” Opt. Express 12(20), 4912–4921 (2004).
[Crossref] [PubMed]

2003 (3)

L. Yu and L. Cai, “Multidimensional data encryption with digital holography,” Opt. Commun. 215(4-6), 271–284 (2003).
[Crossref]

B. Zhu, H. Zhao, and S. Liu, “Image encryption based on pure intensity random coding and digital holography technique,” Optik (Stuttg.) 114(2), 95–99 (2003).
[Crossref]

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300(5624), 1419–1421 (2003).
[Crossref] [PubMed]

2002 (2)

X. Peng, L. Yu, and L. Cai, “Double-lock for image encryption with virtual optical wavelength,” Opt. Express 10(1), 41–45 (2002).
[PubMed]

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(23), 4825–4834 (2002).
[Crossref] [PubMed]

2000 (3)

E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39(35), 6595–6601 (2000).
[Crossref] [PubMed]

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

S. Lai and M. A. Neifeld, “Digital wavefront reconstruction and its application to image encryption,” Opt. Commun. 178(4-6), 283–289 (2000).
[Crossref]

1999 (3)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24(11), 762–764 (1999).
[Crossref] [PubMed]

S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microw. Opt. Technol. Lett. 21(5), 318–323 (1999).
[Crossref]

1998 (1)

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662–1669 (1998).
[Crossref]

1997 (1)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
[Crossref]

1995 (1)

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

1982 (1)

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
[Crossref] [PubMed]

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Allen, L. J.

Arcos, S.

Barrera, J. F.

F. Mosso, M. Tebaldi, J. F. Barrera, N. Bolognini, and R. Torroba, “Pure optical dynamical color encryption,” Opt. Express 19(15), 13779–13786 (2011).
[Crossref] [PubMed]

Bolognini, N.

F. Mosso, M. Tebaldi, J. F. Barrera, N. Bolognini, and R. Torroba, “Pure optical dynamical color encryption,” Opt. Express 19(15), 13779–13786 (2011).
[Crossref] [PubMed]

Bunk, O.

Cai, L.

L. Yu and L. Cai, “Multidimensional data encryption with digital holography,” Opt. Commun. 215(4-6), 271–284 (2003).
[Crossref]

X. Peng, L. Yu, and L. Cai, “Double-lock for image encryption with virtual optical wavelength,” Opt. Express 10(1), 41–45 (2002).
[PubMed]

Cai, L. Z.

Cao, L.

M. He, Q. Tan, L. Cao, Q. He, and G. Jin, “Security enhanced optical encryption system by random phase key and permutation key,” Opt. Express 17(25), 22462–22473 (2009).
[Crossref] [PubMed]

Carnicer, A.

Cedola, A.

Chang, H. T.

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(23), 4825–4834 (2002).
[Crossref] [PubMed]

Chapman, H. N.

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662–1669 (1998).
[Crossref]

Charalambous, P.

Chen, L.

L. Chen and D. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Express 14(19), 8552–8560 (2006).
[Crossref] [PubMed]

Chen, W.

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13(7), 075404 (2011).
[Crossref]

W. Chen and X. Chen, “Quantitative phase retrieval of complex-valued specimens based on noninterferometric imaging,” Appl. Opt. 50(14), 2008–2015 (2011).
[Crossref] [PubMed]

W. Chen and X. Chen, “Optical cryptography topology based on a three-dimensional particle-like distribution and diffractive imaging,” Opt. Express 19(10), 9008–9019 (2011).
[Crossref] [PubMed]

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

W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18(26), 27095–27104 (2010).
[Crossref] [PubMed]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282(18), 3680–3685 (2009).
[Crossref]

Chen, X.

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13(7), 075404 (2011).
[Crossref]

W. Chen and X. Chen, “Optical cryptography topology based on a three-dimensional particle-like distribution and diffractive imaging,” Opt. Express 19(10), 9008–9019 (2011).
[Crossref] [PubMed]

W. Chen and X. Chen, “Quantitative phase retrieval of complex-valued specimens based on noninterferometric imaging,” Appl. Opt. 50(14), 2008–2015 (2011).
[Crossref] [PubMed]

W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18(26), 27095–27104 (2010).
[Crossref] [PubMed]

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

Cheng, X. C.

David, C.

De Caro, L.

Dierolf, M.

Dong, G. Y.

Dowling, T.

T. J. Naughton, B. M. Hennelly, and T. Dowling, “Introducing secure modes of operation for optical encryption,” J. Opt. Soc. Am. A 25(10), 2608–2617 (2008).
[Crossref] [PubMed]

Fienup, J. R.

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
[Crossref] [PubMed]

Gao, M.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Giannini, C.

Gopinathan, U.

G. Situ, U. Gopinathan, D. S. Monaghan, and J. T. Sheridan, “Cryptanalysis of optical security systems with significant output images,” Appl. Opt. 46(22), 5257–5262 (2007).
[Crossref] [PubMed]

Gray, J.

Harder, R.

Hwang, H. E.

Jark, W.

Javidi, B.

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39(35), 6595–6601 (2000).
[Crossref] [PubMed]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24(11), 762–764 (1999).
[Crossref] [PubMed]

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
[Crossref]

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

Jefimovs, K.

Jin, G.

M. He, Q. Tan, L. Cao, Q. He, and G. Jin, “Security enhanced optical encryption system by random phase key and permutation key,” Opt. Express 17(25), 22462–22473 (2009).
[Crossref] [PubMed]

Jing, F.

Johnson, I.

Joseph, J.

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

Juvells, I.

Karim, M. A.

S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microw. Opt. Technol. Lett. 21(5), 318–323 (1999).
[Crossref]

Kim, D. H.

H. Kim, D. H. Kim, and Y. H. Lee, “Encryption of digital hologram of 3-D object by virtual optics,” Opt. Express 12(20), 4912–4921 (2004).
[Crossref] [PubMed]

Kim, H.

H. Kim, D. H. Kim, and Y. H. Lee, “Encryption of digital hologram of 3-D object by virtual optics,” Opt. Express 12(20), 4912–4921 (2004).
[Crossref] [PubMed]

Kirz, J.

Kumar, A.

Kumar, P.

Kuo, C. J.

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(23), 4825–4834 (2002).
[Crossref] [PubMed]

Lagomarsino, S.

Lai, S.

S. Lai and M. A. Neifeld, “Digital wavefront reconstruction and its application to image encryption,” Opt. Commun. 178(4-6), 283–289 (2000).
[Crossref]

Lee, Y. H.

H. Kim, D. H. Kim, and Y. H. Lee, “Encryption of digital hologram of 3-D object by virtual optics,” Opt. Express 12(20), 4912–4921 (2004).
[Crossref] [PubMed]

Li, H.

H. Li, “Image encryption based on gyrator transform and two-step phase-shifting interferometry,” Opt. Lasers Eng. 47(1), 45–50 (2009).
[Crossref]

Lie, W. N.

Lin, C.

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49(29), 5632–5637 (2010).
[Crossref] [PubMed]

Liu, S.

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49(29), 5632–5637 (2010).
[Crossref] [PubMed]

B. Zhu, H. Zhao, and S. Liu, “Image encryption based on pure intensity random coding and digital holography technique,” Optik (Stuttg.) 114(2), 95–99 (2003).
[Crossref]

Liu, Z.

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49(29), 5632–5637 (2010).
[Crossref] [PubMed]

Lu, W. C.

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(23), 4825–4834 (2002).
[Crossref] [PubMed]

Matoba, O.

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24(11), 762–764 (1999).
[Crossref] [PubMed]

Matsushima, K.

McBride, W.

Meng, X. F.

Miao, J.

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662–1669 (1998).
[Crossref]

Millan, M. Í. S.

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

Monaghan, D. S.

G. Situ, U. Gopinathan, D. S. Monaghan, and J. T. Sheridan, “Cryptanalysis of optical security systems with significant output images,” Appl. Opt. 46(22), 5257–5262 (2007).
[Crossref] [PubMed]

Montes-Usategui, M.

Mosso, F.

F. Mosso, M. Tebaldi, J. F. Barrera, N. Bolognini, and R. Torroba, “Pure optical dynamical color encryption,” Opt. Express 19(15), 13779–13786 (2011).
[Crossref] [PubMed]

Nagahara, L. A.

Naughton, T. J.

T. J. Naughton, B. M. Hennelly, and T. Dowling, “Introducing secure modes of operation for optical encryption,” J. Opt. Soc. Am. A 25(10), 2608–2617 (2008).
[Crossref] [PubMed]

Neifeld, M. A.

S. Lai and M. A. Neifeld, “Digital wavefront reconstruction and its application to image encryption,” Opt. Commun. 178(4-6), 283–289 (2000).
[Crossref]

Nomura, T.

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

Nugent, K. A.

O’Leary, N. L.

Osten, W.

F. C. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75(4), 043805 (2007).
[Crossref]

Pedrini, G.

F. C. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75(4), 043805 (2007).
[Crossref]

Pelliccia, D.

Peng, X.

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31(8), 1044–1046 (2006).
[Crossref] [PubMed]

X. Peng, L. Yu, and L. Cai, “Double-lock for image encryption with virtual optical wavelength,” Opt. Express 10(1), 41–45 (2002).
[PubMed]

Perez-Cabre, E.

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

Pfeifer, M. A.

Pfeiffer, F.

Qin, W.

Qiong-Hua, W.

X. Yong-Liang, Z. Xin, W. Qiong-Hua, Y. Sheng, and C. Yao-Yao, “Optical image encryption topology,” Opt. Lett. 34(20), 3223–3225 (2009).
[Crossref] [PubMed]

Quan, C.

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282(18), 3680–3685 (2009).
[Crossref]

Refregier, P.

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

Renker, D.

Robinson, I. K.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Sayre, D.

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662–1669 (1998).
[Crossref]

Shen, X. X.

Sheng, Y.

X. Yong-Liang, Z. Xin, W. Qiong-Hua, Y. Sheng, and C. Yao-Yao, “Optical image encryption topology,” Opt. Lett. 34(20), 3223–3225 (2009).
[Crossref] [PubMed]

Sheppard, C. J. R.

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

Sheridan, J. T.

G. Situ, U. Gopinathan, D. S. Monaghan, and J. T. Sheridan, “Cryptanalysis of optical security systems with significant output images,” Appl. Opt. 46(22), 5257–5262 (2007).
[Crossref] [PubMed]

Shi, X.

X. Shi and D. Zhao, “Color image hiding based on the phase retrieval technique and Arnold transform,” Appl. Opt. 50(14), 2134–2139 (2011).
[Crossref] [PubMed]

Shimobaba, T.

Singh, K.

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

Situ, G.

G. Situ, U. Gopinathan, D. S. Monaghan, and J. T. Sheridan, “Cryptanalysis of optical security systems with significant output images,” Appl. Opt. 46(22), 5257–5262 (2007).
[Crossref] [PubMed]

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30(11), 1306–1308 (2005).
[Crossref] [PubMed]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29(14), 1584–1586 (2004).
[Crossref] [PubMed]

Tajahuerce, E.

E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39(35), 6595–6601 (2000).
[Crossref] [PubMed]

Tan, Q.

M. He, Q. Tan, L. Cao, Q. He, and G. Jin, “Security enhanced optical encryption system by random phase key and permutation key,” Opt. Express 17(25), 22462–22473 (2009).
[Crossref] [PubMed]

Tay, C. J.

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282(18), 3680–3685 (2009).
[Crossref]

Tebaldi, M.

F. Mosso, M. Tebaldi, J. F. Barrera, N. Bolognini, and R. Torroba, “Pure optical dynamical color encryption,” Opt. Express 19(15), 13779–13786 (2011).
[Crossref] [PubMed]

Torroba, R.

F. Mosso, M. Tebaldi, J. F. Barrera, N. Bolognini, and R. Torroba, “Pure optical dynamical color encryption,” Opt. Express 19(15), 13779–13786 (2011).
[Crossref] [PubMed]

Unnikrishnan, G.

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

Vartanyants, I.

Vartanyants, I. A.

Wang, D.

Wang, X.

Wang, Y. R.

Wei, H.

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31(8), 1044–1046 (2006).
[Crossref] [PubMed]

Wei, X.

Williams, G. J.

Xin, Z.

X. Yong-Liang, Z. Xin, W. Qiong-Hua, Y. Sheng, and C. Yao-Yao, “Optical image encryption topology,” Opt. Lett. 34(20), 3223–3225 (2009).
[Crossref] [PubMed]

Xu, L.

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49(29), 5632–5637 (2010).
[Crossref] [PubMed]

Xu, X. F.

Yang, X. L.

Yao-Yao, C.

X. Yong-Liang, Z. Xin, W. Qiong-Hua, Y. Sheng, and C. Yao-Yao, “Optical image encryption topology,” Opt. Lett. 34(20), 3223–3225 (2009).
[Crossref] [PubMed]

Yong-Liang, X.

X. Yong-Liang, Z. Xin, W. Qiong-Hua, Y. Sheng, and C. Yao-Yao, “Optical image encryption topology,” Opt. Lett. 34(20), 3223–3225 (2009).
[Crossref] [PubMed]

Yu, B.

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31(8), 1044–1046 (2006).
[Crossref] [PubMed]

Yu, L.

L. Yu and L. Cai, “Multidimensional data encryption with digital holography,” Opt. Commun. 215(4-6), 271–284 (2003).
[Crossref]

X. Peng, L. Yu, and L. Cai, “Double-lock for image encryption with virtual optical wavelength,” Opt. Express 10(1), 41–45 (2002).
[PubMed]

Zhang, F.

Zhang, F. C.

F. C. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75(4), 043805 (2007).
[Crossref]

Zhang, H.

Zhang, J.

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30(11), 1306–1308 (2005).
[Crossref] [PubMed]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29(14), 1584–1586 (2004).
[Crossref] [PubMed]

Zhang, P.

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31(8), 1044–1046 (2006).
[Crossref] [PubMed]

Zhang, R.

Zhang, S. Q.

S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microw. Opt. Technol. Lett. 21(5), 318–323 (1999).
[Crossref]

Zhao, D.

X. Shi and D. Zhao, “Color image hiding based on the phase retrieval technique and Arnold transform,” Appl. Opt. 50(14), 2134–2139 (2011).
[Crossref] [PubMed]

L. Chen and D. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Express 14(19), 8552–8560 (2006).
[Crossref] [PubMed]

Zhao, H.

B. Zhu, H. Zhao, and S. Liu, “Image encryption based on pure intensity random coding and digital holography technique,” Optik (Stuttg.) 114(2), 95–99 (2003).
[Crossref]

Zhao, J.

Zhu, B.

B. Zhu, H. Zhao, and S. Liu, “Image encryption based on pure intensity random coding and digital holography technique,” Optik (Stuttg.) 114(2), 95–99 (2003).
[Crossref]

Zuo, J. M.

Acta Crystallogr. A (1)

Appl. Opt. (10)

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(23), 4825–4834 (2002).
[Crossref] [PubMed]

X. Shi and D. Zhao, “Color image hiding based on the phase retrieval technique and Arnold transform,” Appl. Opt. 50(14), 2134–2139 (2011).
[Crossref] [PubMed]

G. Situ, U. Gopinathan, D. S. Monaghan, and J. T. Sheridan, “Cryptanalysis of optical security systems with significant output images,” Appl. Opt. 46(22), 5257–5262 (2007).
[Crossref] [PubMed]

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49(29), 5632–5637 (2010).
[Crossref] [PubMed]

E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39(35), 6595–6601 (2000).
[Crossref] [PubMed]

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
[Crossref] [PubMed]

W. Chen and X. Chen, “Quantitative phase retrieval of complex-valued specimens based on noninterferometric imaging,” Appl. Opt. 50(14), 2008–2015 (2011).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

J. Opt. (1)

W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. 13(7), 075404 (2011).
[Crossref]

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

J. Opt. Soc. Am. A (2)

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662–1669 (1998).
[Crossref]

T. J. Naughton, B. M. Hennelly, and T. Dowling, “Introducing secure modes of operation for optical encryption,” J. Opt. Soc. Am. A 25(10), 2608–2617 (2008).
[Crossref] [PubMed]

Microw. Opt. Technol. Lett. (1)

S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microw. Opt. Technol. Lett. 21(5), 318–323 (1999).
[Crossref]

Nature (2)

Opt. Commun. (3)

S. Lai and M. A. Neifeld, “Digital wavefront reconstruction and its application to image encryption,” Opt. Commun. 178(4-6), 283–289 (2000).
[Crossref]

L. Yu and L. Cai, “Multidimensional data encryption with digital holography,” Opt. Commun. 215(4-6), 271–284 (2003).
[Crossref]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282(18), 3680–3685 (2009).
[Crossref]

Opt. Express (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. Express 17(25), 22462–22473 (2009).
[Crossref] [PubMed]

L. Chen and D. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Express 14(19), 8552–8560 (2006).
[Crossref] [PubMed]

F. Mosso, M. Tebaldi, J. F. Barrera, N. Bolognini, and R. Torroba, “Pure optical dynamical color encryption,” Opt. Express 19(15), 13779–13786 (2011).
[Crossref] [PubMed]

X. Peng, L. Yu, and L. Cai, “Double-lock for image encryption with virtual optical wavelength,” Opt. Express 10(1), 41–45 (2002).
[PubMed]

H. Kim, D. H. Kim, and Y. H. Lee, “Encryption of digital hologram of 3-D object by virtual optics,” Opt. Express 12(20), 4912–4921 (2004).
[Crossref] [PubMed]

W. Chen and X. Chen, “Optical cryptography topology based on a three-dimensional particle-like distribution and diffractive imaging,” Opt. Express 19(10), 9008–9019 (2011).
[Crossref] [PubMed]

W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18(26), 27095–27104 (2010).
[Crossref] [PubMed]

Opt. Lasers Eng. (1)

H. Li, “Image encryption based on gyrator transform and two-step phase-shifting interferometry,” Opt. Lasers Eng. 47(1), 45–50 (2009).
[Crossref]

Opt. Lett. (13)

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

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31(8), 1044–1046 (2006).
[Crossref] [PubMed]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24(11), 762–764 (1999).
[Crossref] [PubMed]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29(14), 1584–1586 (2004).
[Crossref] [PubMed]

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

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30(11), 1306–1308 (2005).
[Crossref] [PubMed]

X. Yong-Liang, Z. Xin, W. Qiong-Hua, Y. Sheng, and C. Yao-Yao, “Optical image encryption topology,” Opt. Lett. 34(20), 3223–3225 (2009).
[Crossref] [PubMed]

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

Optik (Stuttg.) (2)

B. Zhu, H. Zhao, and S. Liu, “Image encryption based on pure intensity random coding and digital holography technique,” Optik (Stuttg.) 114(2), 95–99 (2003).
[Crossref]

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Phys. Rev. A (1)

F. C. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75(4), 043805 (2007).
[Crossref]

Phys. Rev. Lett. (1)

Phys. Today (1)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
[Crossref]

Proc. IEEE (1)

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

Science (1)

Other (4)

U. Schnars and W. Jüptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

Original color image or plaintext (Peppers): http://sipi.usc.edu/database .

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Fig. 1 Schematic optical setup for multiple-random-phase-mask encryption based on lateral translations of a phase-only mask [39]: M, the phase-only mask; CCD, charge-coupled device. Three phase-only masks are used to illustrate the proposed method, and the application with fewer or more random phase-only masks is straightforward.

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Fig. 2 Schematic coordinate system for angular spectrum algorithm.

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Fig. 3 Optical setup for multiple-random-phase-mask encryptions using three channels.

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Fig. 4 Flow chart for retrieval algorithm at each channel during image decryption.

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Fig. 5 (a) An input color image (i.e., plaintext); (b) original and (c) the first laterally-translated phase-only masks M3; typical diffraction intensity maps (i.e., ciphertexts) at the (d) red, (e) green and (f) bluechannels.

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Fig. 6 (a) A relationship between the number of iterations and CC values using correct security keys at three channels (red color, red channel; green color, green channel; blue color, blue channel); decrypted images at (b) red, (c) green and (d) blue channels; (e) a decrypted color image after the incorporation.

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Fig. 7 Decrypted images with (a) a distance error of 2 mm for

z_{3}

at red channel; (b) a distance error of 2 mm for

z_{3}

at all three channels; (c) a wavelength error of 10 nm for

λ_{1};

(d) a wavelength error of 10 nm at all three channels; (e) a wrong phase-only mask M3 only at the red channel; (f) a wrong phase-only mask M3 at all three channels.

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Fig. 8 Information synthesis with addition operation: (a), (b) two input color images for addition operation; (c), (d) real and imaginary parts of the fused complex amplitude just before the M3 plane at red channel; (e), (f) relationships between iteration number and CC values using correct security keys for two input color images at three channels; (g) a fused color image decrypted at the output plane.

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Fig. 9 Information synthesis with subtraction operation: (a), (b) two input color images for subtraction operation; (c), (d) real and imaginary parts of the subtracted complex amplitude just before the M3 plane at red channel; (e), (f) relationships between the iteration number and CC values using correct security keys for two input color images at three channels; (g) the subtracted color image decrypted at the output plane.

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Equations (11)

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O (x_{1}, y_{1}) = \frac{j}{λ} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} O (ξ, η) M_{1} (ξ, η) \frac{\exp (- j k ρ)}{ρ} d ξ d η,

\begin{array}{l} O (x_{1}, y_{1}) = \frac{j}{λ z_{1}} \exp (- j \frac{2 π}{λ} z_{1}) \exp [- j \frac{π}{λ z_{1}} (x_{1}^{2} + y_{1}^{2})] \\ \times \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} O (ξ, η) M_{1} (ξ, η) \exp [- j \frac{π}{λ z_{1}} (ξ^{2} + η^{2})] \\ \times \exp [j \frac{2 π}{λ z_{1}} (x_{1} ξ + y_{1} η)] d ξ d η . \end{array}

O (x_{1}, y_{1}) = F T^{- 1} (ℑ (k_{ξ}, k_{η}; z_{1}) {F T [O (ξ, η) M_{1} (ξ, η)]}),

ℑ (k_{ξ}, k_{η}; z_{1}) = \exp (- j z_{1} k_{z}) = \exp (- j z_{1} \sqrt{k^{2} - k_{ξ}^{2} - k_{η}^{2}}),

ℑ (f_{ξ}, f_{η}; z_{1}) = {\begin{cases} \exp {- j k z_{1} {[1 - {(λ f_{ξ})}^{2} - {(λ f_{η})}^{2}]}^{1 / 2}} if {(f_{ξ}^{2} + f_{η}^{2})}^{1 / 2} < (1 / λ) \\ 0 Otherwise \end{cases},

ℑ (m, n; z_{1}) = \exp (- j k z_{1} {1 - {[\frac{λ (m - \frac{M}{2})}{M Δ ξ}]}^{2} - {[\frac{λ (n - \frac{N}{2})}{N Δ η}]}^{2}}^{1 / 2}),

I (μ, ν) = {| F W P_{z_{3}} {[F W P_{z_{2}} ({F W P_{z_{1}} [O (ξ, η) M_{1} (ξ, η)]} M_{2} (x_{1}, y_{1}))] M_{3} (x_{2}, y_{2})} |}^{2},

O' (ξ, η) = | F W P_{- z_{1}} ({F W P_{- z_{2}} [\bar{\bar{O_{n}^{4} (x_{2}, y_{2})}}]} {[M_{2} (x_{1}, y_{1})]}^{*}) | .

CC = [cov (O, O')] / (σ_{O} \times σ_{O'}),

O_{A d d}^{'} (ξ, η) = | F W P_{- z_{1}} ({F W P_{- z_{2}} [{\bar{\bar{O_{n}^{4} (x_{2}, y_{2})}}}^{(1)} + {\bar{\bar{O_{n}^{4} (x_{2}, y_{2})}}}^{(2)}]} {[M_{2} (x_{1}, y_{1})]}^{*}) |,

O_{S u b}^{'} (ξ, η) = | F W P_{- z_{1}} ({F W P_{- z_{2}} [{\bar{\bar{O_{n}^{4} (x_{2}, y_{2})}}}^{(1)} - {\bar{\bar{O_{n}^{4} (x_{2}, y_{2})}}}^{(2)}]} {[M_{2} (x_{1}, y_{1})]}^{*}) |,

Abstract

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