Abstract

Interference-based optical encryption schemes have an inherent silhouette problem due to the equipollent nature of the phase-only masks (POMs) generated using an analytical method. One of the earlier methods suggested that removing the problem by use of exchanging process between two masks increases the computational load. This shortcoming is overcome with a noniterative method using the jigsaw transformation (JT) in a single step, with improved security because the inverse JT of these masks, along with correct permutation keys that are necessary to decrypt the original image. The stringent alignment requirement of the POMs in two different arms during the experiment is removed with an alternative method using a single spatial light modulator. Experimental results are provided to demonstrate the decryption process with the proposed method.

© 2011 Optical Society of America

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References

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    [CrossRef]

2010 (6)

Y. Han and Y. Zhang, “Optical image encryption based on two beams’ interference,” Opt. Commun. 283, 1690–1692(2010).
[CrossRef]

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (2010).
[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).
[CrossRef]

N. Zhu, Y. Wang, J. Liu, and J. Xie, “Holographic projection based on interference and analytical algorithm,” Opt. Commun. 283, 4969–4971 (2010),
[CrossRef]

L. Chen, D. Zhao, and F. Ge., “Gray images embedded in a color image and encrypted with FRFT and Region shift encoding methods,” Opt. Commun. 283, 2043–2049 (2010).
[CrossRef]

C-H. Niu, X-L. Wang, N-G. Lv, Z-H. Zhou, and X-Y. Li, “An encryption method with multiple encrypted keys based on interference principle,” Opt. Express 18, 7827–7834 (2010).
[CrossRef] [PubMed]

2009 (10)

N. Zhu, Y. Wang, J. Liu, J. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17, 13418–13428 (2009).
[CrossRef] [PubMed]

H-E. Hwang, H. T. Chang, and W-N. Lie, “Fast double-phase retrieval in Fresnel domain using modified Gerchberg-Saxton algorithm for lensless optical security systems,” Opt. Express 17, 13700–13710 (2009).
[CrossRef] [PubMed]

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1, 589–636 (2009).
[CrossRef]

Z. Liu, Q. Li, J. Dai, X. Zhao, Z. Sun, S. Liu, and M. A. Ahmad, “Image encryption based on random scrambling of the amplitude and phase in the frequency domain,” Opt. Eng. 48, 087005 (2009).
[CrossRef]

Y-R. Piao, D-H. Shin, and E-S. Kim, “Robust image encryption by combined use of integral imaging and pixel scrambling techniques,” Opt. Lasers Eng. 47, 1273–1281 (2009).
[CrossRef]

B. Wang and Y. Zhang, “Double images hiding based on optics interference,” Proc. SPIE 7512, 751207 (2009).
[CrossRef]

B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
[CrossRef]

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

Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A: Pure Appl. Opt. 11, 125406 (2009).
[CrossRef]

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

2008 (3)

P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmann’s second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
[CrossRef]

X-F. Meng, L-H. Cai, X-F. Xu, S-L. Yang, X-X. Shen, G-Y. Dong, and H. Zhang, “Full-phase image encryption by two-step phase-shifting interferometry,” Optik (Jena) 119, 434–440(2008).
[CrossRef]

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

2007 (1)

Y-Y. Wang, Y-R. Wang, Y. Wang, H-J. Li, and W-J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761–765 (2007).
[CrossRef]

2006 (2)

2005 (2)

B. M. Hennelly and J. T. Sheridan, “Optical encryption and the space bandwidth product,” Opt. Commun. 247, 291–305(2005).
[CrossRef]

J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499(2005).
[CrossRef]

2004 (3)

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

G. Situ and J. Zhang, “A lenseless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 115–122 (2004).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Random phase and jigsaw transform in the Fresnel domain,” Opt. Eng. 43, 2239–2249 (2004).
[CrossRef]

2003 (4)

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571 (2003).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Jena) 114, 251–265(2003).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[CrossRef]

B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28, 269–271 (2003).
[CrossRef] [PubMed]

2000 (1)

1996 (1)

R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Ahmad, M. A.

Z. Liu, Q. Li, J. Dai, X. Zhao, Z. Sun, S. Liu, and M. A. Ahmad, “Image encryption based on random scrambling of the amplitude and phase in the frequency domain,” Opt. Eng. 48, 087005 (2009).
[CrossRef]

Alfalou, A.

Brosseau, C.

Cai, L-H.

X-F. Meng, L-H. Cai, X-F. Xu, S-L. Yang, X-X. Shen, G-Y. Dong, and H. Zhang, “Full-phase image encryption by two-step phase-shifting interferometry,” Optik (Jena) 119, 434–440(2008).
[CrossRef]

Cai, L-Z.

Chang, H. T.

Chatwin, C.

R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Chen, L.

L. Chen, D. Zhao, and F. Ge., “Gray images embedded in a color image and encrypted with FRFT and Region shift encoding methods,” Opt. Commun. 283, 2043–2049 (2010).
[CrossRef]

Chen, W.

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (2010).
[CrossRef]

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

Dai, J.

Z. Liu, Q. Li, J. Dai, X. Zhao, Z. Sun, S. Liu, and M. A. Ahmad, “Image encryption based on random scrambling of the amplitude and phase in the frequency domain,” Opt. Eng. 48, 087005 (2009).
[CrossRef]

Dong, G-Y.

X-F. Meng, L-H. Cai, X-F. Xu, S-L. Yang, X-X. Shen, G-Y. Dong, and H. Zhang, “Full-phase image encryption by two-step phase-shifting interferometry,” Optik (Jena) 119, 434–440(2008).
[CrossRef]

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, 3289–3297 (2006).
[CrossRef] [PubMed]

Dong, Z.

Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A: Pure Appl. Opt. 11, 125406 (2009).
[CrossRef]

Fu, Y.

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (2010).
[CrossRef]

Ge, F.

L. Chen, D. Zhao, and F. Ge., “Gray images embedded in a color image and encrypted with FRFT and Region shift encoding methods,” Opt. Commun. 283, 2043–2049 (2010).
[CrossRef]

Han, P.

Han, Y.

Y. Han and Y. Zhang, “Optical image encryption based on two beams’ interference,” Opt. Commun. 283, 1690–1692(2010).
[CrossRef]

Hennelly, B.

Hennelly, B. M.

B. M. Hennelly and J. T. Sheridan, “Optical encryption and the space bandwidth product,” Opt. Commun. 247, 291–305(2005).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Random phase and jigsaw transform in the Fresnel domain,” Opt. Eng. 43, 2239–2249 (2004).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Jena) 114, 251–265(2003).
[CrossRef]

Hwang, H-E.

Javidi, B.

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

Joseph, J.

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).
[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmann’s second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[CrossRef]

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571 (2003).
[CrossRef]

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

Kim, E-S.

Y-R. Piao, D-H. Shin, and E-S. Kim, “Robust image encryption by combined use of integral imaging and pixel scrambling techniques,” Opt. Lasers Eng. 47, 1273–1281 (2009).
[CrossRef]

Kumar, P.

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).
[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmann’s second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
[CrossRef]

Li, H-J.

Y-Y. Wang, Y-R. Wang, Y. Wang, H-J. Li, and W-J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761–765 (2007).
[CrossRef]

Li, J.

J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499(2005).
[CrossRef]

Li, Q.

Z. Liu, Q. Li, J. Dai, X. Zhao, Z. Sun, S. Liu, and M. A. Ahmad, “Image encryption based on random scrambling of the amplitude and phase in the frequency domain,” Opt. Eng. 48, 087005 (2009).
[CrossRef]

Li, X-Y.

Lie, W-N.

Liu, J.

N. Zhu, Y. Wang, J. Liu, and J. Xie, “Holographic projection based on interference and analytical algorithm,” Opt. Commun. 283, 4969–4971 (2010),
[CrossRef]

N. Zhu, Y. Wang, J. Liu, J. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17, 13418–13428 (2009).
[CrossRef] [PubMed]

Liu, S.

Z. Liu, Q. Li, J. Dai, X. Zhao, Z. Sun, S. Liu, and M. A. Ahmad, “Image encryption based on random scrambling of the amplitude and phase in the frequency domain,” Opt. Eng. 48, 087005 (2009).
[CrossRef]

Liu, Z.

Z. Liu, Q. Li, J. Dai, X. Zhao, Z. Sun, S. Liu, and M. A. Ahmad, “Image encryption based on random scrambling of the amplitude and phase in the frequency domain,” Opt. Eng. 48, 087005 (2009).
[CrossRef]

Lu, H.

J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499(2005).
[CrossRef]

Lv, N-G.

Ma, Y.

J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499(2005).
[CrossRef]

Matoba, O.

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

Meng, X-F.

X-F. Meng, L-H. Cai, X-F. Xu, S-L. Yang, X-X. Shen, G-Y. Dong, and H. Zhang, “Full-phase image encryption by two-step phase-shifting interferometry,” Optik (Jena) 119, 434–440(2008).
[CrossRef]

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, 3289–3297 (2006).
[CrossRef] [PubMed]

Millan, M. S.

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

Nishchal, N. K.

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[CrossRef]

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571 (2003).
[CrossRef]

Niu, C-H.

Nomura, T.

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

Perez-Cabre, E.

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

Piao, Y-R.

Y-R. Piao, D-H. Shin, and E-S. Kim, “Robust image encryption by combined use of integral imaging and pixel scrambling techniques,” Opt. Lasers Eng. 47, 1273–1281 (2009).
[CrossRef]

Quan, C.

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (2010).
[CrossRef]

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

Shen, X-X.

X-F. Meng, L-H. Cai, X-F. Xu, S-L. Yang, X-X. Shen, G-Y. Dong, and H. Zhang, “Full-phase image encryption by two-step phase-shifting interferometry,” Optik (Jena) 119, 434–440(2008).
[CrossRef]

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, 3289–3297 (2006).
[CrossRef] [PubMed]

Sheridan, J. T.

B. M. Hennelly and J. T. Sheridan, “Optical encryption and the space bandwidth product,” Opt. Commun. 247, 291–305(2005).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Random phase and jigsaw transform in the Fresnel domain,” Opt. Eng. 43, 2239–2249 (2004).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Jena) 114, 251–265(2003).
[CrossRef]

B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28, 269–271 (2003).
[CrossRef] [PubMed]

Shin, D-H.

Y-R. Piao, D-H. Shin, and E-S. Kim, “Robust image encryption by combined use of integral imaging and pixel scrambling techniques,” Opt. Lasers Eng. 47, 1273–1281 (2009).
[CrossRef]

Singh, K.

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).
[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmann’s second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[CrossRef]

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571 (2003).
[CrossRef]

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

Situ, G.

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

G. Situ and J. Zhang, “A lenseless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 115–122 (2004).
[CrossRef]

Song, X.

J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499(2005).
[CrossRef]

Sun, W-J.

Y-Y. Wang, Y-R. Wang, Y. Wang, H-J. Li, and W-J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761–765 (2007).
[CrossRef]

Sun, Z.

Z. Liu, Q. Li, J. Dai, X. Zhao, Z. Sun, S. Liu, and M. A. Ahmad, “Image encryption based on random scrambling of the amplitude and phase in the frequency domain,” Opt. Eng. 48, 087005 (2009).
[CrossRef]

Tay, C. J.

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (2010).
[CrossRef]

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

Unnikrishnan, G.

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571 (2003).
[CrossRef]

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

Wang, B.

Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A: Pure Appl. Opt. 11, 125406 (2009).
[CrossRef]

B. Wang and Y. Zhang, “Double images hiding based on optics interference,” Proc. SPIE 7512, 751207 (2009).
[CrossRef]

B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
[CrossRef]

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

Wang, R. K.

R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Wang, X-L.

Wang, Y.

N. Zhu, Y. Wang, J. Liu, and J. Xie, “Holographic projection based on interference and analytical algorithm,” Opt. Commun. 283, 4969–4971 (2010),
[CrossRef]

N. Zhu, Y. Wang, J. Liu, J. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17, 13418–13428 (2009).
[CrossRef] [PubMed]

Y-Y. Wang, Y-R. Wang, Y. Wang, H-J. Li, and W-J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761–765 (2007).
[CrossRef]

Wang, Y-R.

Y-Y. Wang, Y-R. Wang, Y. Wang, H-J. Li, and W-J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761–765 (2007).
[CrossRef]

Wang, Y-Y.

Y-Y. Wang, Y-R. Wang, Y. Wang, H-J. Li, and W-J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761–765 (2007).
[CrossRef]

Watson, I. A.

R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Xie, J.

N. Zhu, Y. Wang, J. Liu, and J. Xie, “Holographic projection based on interference and analytical algorithm,” Opt. Commun. 283, 4969–4971 (2010),
[CrossRef]

N. Zhu, Y. Wang, J. Liu, J. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17, 13418–13428 (2009).
[CrossRef] [PubMed]

Xu, X-F.

X-F. Meng, L-H. Cai, X-F. Xu, S-L. Yang, X-X. Shen, G-Y. Dong, and H. Zhang, “Full-phase image encryption by two-step phase-shifting interferometry,” Optik (Jena) 119, 434–440(2008).
[CrossRef]

Yang, S-L.

X-F. Meng, L-H. Cai, X-F. Xu, S-L. Yang, X-X. Shen, G-Y. Dong, and H. Zhang, “Full-phase image encryption by two-step phase-shifting interferometry,” Optik (Jena) 119, 434–440(2008).
[CrossRef]

Yang, X-L.

Zhang, H.

N. Zhu, Y. Wang, J. Liu, J. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17, 13418–13428 (2009).
[CrossRef] [PubMed]

X-F. Meng, L-H. Cai, X-F. Xu, S-L. Yang, X-X. Shen, G-Y. Dong, and H. Zhang, “Full-phase image encryption by two-step phase-shifting interferometry,” Optik (Jena) 119, 434–440(2008).
[CrossRef]

Zhang, J.

G. Situ and J. Zhang, “A lenseless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 115–122 (2004).
[CrossRef]

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

Zhang, Y.

Y. Han and Y. Zhang, “Optical image encryption based on two beams’ interference,” Opt. Commun. 283, 1690–1692(2010).
[CrossRef]

B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
[CrossRef]

B. Wang and Y. Zhang, “Double images hiding based on optics interference,” Proc. SPIE 7512, 751207 (2009).
[CrossRef]

Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A: Pure Appl. Opt. 11, 125406 (2009).
[CrossRef]

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

Zhao, D.

L. Chen, D. Zhao, and F. Ge., “Gray images embedded in a color image and encrypted with FRFT and Region shift encoding methods,” Opt. Commun. 283, 2043–2049 (2010).
[CrossRef]

Zhao, J.

J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499(2005).
[CrossRef]

Zhao, X.

Z. Liu, Q. Li, J. Dai, X. Zhao, Z. Sun, S. Liu, and M. A. Ahmad, “Image encryption based on random scrambling of the amplitude and phase in the frequency domain,” Opt. Eng. 48, 087005 (2009).
[CrossRef]

Zhou, Z-H.

Zhu, N.

N. Zhu, Y. Wang, J. Liu, and J. Xie, “Holographic projection based on interference and analytical algorithm,” Opt. Commun. 283, 4969–4971 (2010),
[CrossRef]

N. Zhu, Y. Wang, J. Liu, J. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17, 13418–13428 (2009).
[CrossRef] [PubMed]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

J. Opt. (1)

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption based on interference under convergent random illumination,” J. Opt. 12, 095402 (2010).
[CrossRef]

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

Y. Zhang, B. Wang, and Z. Dong, “Enhancement of image hiding by exchanging two phase masks,” J. Opt. A: Pure Appl. Opt. 11, 125406 (2009).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (8)

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

L. Chen, D. Zhao, and F. Ge., “Gray images embedded in a color image and encrypted with FRFT and Region shift encoding methods,” Opt. Commun. 283, 2043–2049 (2010).
[CrossRef]

Y. Han and Y. Zhang, “Optical image encryption based on two beams’ interference,” Opt. Commun. 283, 1690–1692(2010).
[CrossRef]

N. Zhu, Y. Wang, J. Liu, and J. Xie, “Holographic projection based on interference and analytical algorithm,” Opt. Commun. 283, 4969–4971 (2010),
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Optical encryption and the space bandwidth product,” Opt. Commun. 247, 291–305(2005).
[CrossRef]

J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499(2005).
[CrossRef]

G. Situ and J. Zhang, “A lenseless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 115–122 (2004).
[CrossRef]

B. Wang and Y. Zhang, “Double images hiding based on optical interference,” Opt. Commun. 282, 3439–3443 (2009).
[CrossRef]

Opt. Eng. (6)

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Double random phase encryption with in-plane rotation of a modified Lohmann’s second-type system in the anamorphic fractional Fourier domain,” Opt. Eng. 47, 117001 (2008).
[CrossRef]

R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571 (2003).
[CrossRef]

Z. Liu, Q. Li, J. Dai, X. Zhao, Z. Sun, S. Liu, and M. A. Ahmad, “Image encryption based on random scrambling of the amplitude and phase in the frequency domain,” Opt. Eng. 48, 087005 (2009).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Random phase and jigsaw transform in the Fresnel domain,” Opt. Eng. 43, 2239–2249 (2004).
[CrossRef]

Opt. Express (3)

Opt. Laser Technol. (1)

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (2010).
[CrossRef]

Opt. Lasers Eng. (2)

Y-R. Piao, D-H. Shin, and E-S. Kim, “Robust image encryption by combined use of integral imaging and pixel scrambling techniques,” Opt. Lasers Eng. 47, 1273–1281 (2009).
[CrossRef]

Y-Y. Wang, Y-R. Wang, Y. Wang, H-J. Li, and W-J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761–765 (2007).
[CrossRef]

Opt. Lett. (4)

Optik (Jena) (2)

X-F. Meng, L-H. Cai, X-F. Xu, S-L. Yang, X-X. Shen, G-Y. Dong, and H. Zhang, “Full-phase image encryption by two-step phase-shifting interferometry,” Optik (Jena) 119, 434–440(2008).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Jena) 114, 251–265(2003).
[CrossRef]

Proc. IEEE (1)

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

Proc. SPIE (1)

B. Wang and Y. Zhang, “Double images hiding based on optics interference,” Proc. SPIE 7512, 751207 (2009).
[CrossRef]

Other (1)

B.Javidi, ed., Optical and Digital Techniques for Information Security (Springer-Verlag, 2005).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

(a) Flow chart for the generation of jigsaw transformed POMs of the proposed encryption scheme with the analytic process; I ( u , v ) , input image; R ( u , v ) ,RPM; R 1 J and R 2 J , jigsaw transformed POMs obtained after analytical process. (b) Decryption process.

Fig. 2
Fig. 2

(a) Gray scale input image. (b) Symmetric jigsaw transformed image, block size 64 × 64 pixels. (c) Asymmetric jigsaw transformed image, block size 128 × 32 pixels, (d) 1D asymmetric jigsaw transformed image; block size 32 × 512 pixels.

Fig. 3
Fig. 3

Phase distribution of the jigsaw transformed POMs, (a)  R 1 J and (b)  R 2 J , decrypted image retrieved from the individual jjigsaw transformed mask, (c) using R 1 J and (d) using R 2 J .

Fig. 4
Fig. 4

Decrypted image (a) using both jigsaw transformed masks, (b) using both inverse jigsaw transformed masks, (c) using both inverse jigsaw transformed masks with a wrong key.

Fig. 5
Fig. 5

RE between the decrypted image obtained from a single symmetric jigsaw transformed phase mask R 1 symm J , and the original image, as a function of the number of the blocks.

Fig. 6
Fig. 6

Decrypted image retrieved from the individual symmetric jigsaw transformed mask (a) using R 1 symm J with a block size of 1 × 1 pixels and (b) using R 1 symm J with a block size of 256 × 256 pixels.

Fig. 7
Fig. 7

RE between the decrypted image obtained from a single asymmetric jigsaw transformed phase mask R 1 asymm J , and the original image, as a function of the number of blocks.

Fig. 8
Fig. 8

Decrypted image retrieved from the individual asymmetric jigsaw transformed mask (a) using R 1 asymm J with a block size of 1 × 2 pixels and (b) using R 1 asymm J with a block size of 256 × 512 pixels.

Fig. 9
Fig. 9

RE between the decrypted image obtained from a single 1D asymmetric block-based jigsaw transformed phase mask R 1 1 - D J , and the original image, as a function of the number of blocks.

Fig. 10
Fig. 10

Decrypted image retrieved from the individual 1D asymmetric block-based jigsaw transformed mask R 1 1 - D J with a block size of 1 × 512 pixels.

Fig. 11
Fig. 11

Schematic diagram of the optical setup: Laser: solid state frequency-doubled Nd:YAG laser of a wavelength 532 nm , beam expander. BE, beam expander; P, polarizer; L, FT lens of focal length 50 cm .

Fig. 12
Fig. 12

Experimental results: FT of the resultant phase obtained from numerical summation of the POMs. (a)  R 1 and R 2 , (b)  R 1 e and R 2 e after 50 exchanges, (c)  R 1 e and R 2 e after 100 exchanges, (d)  R 1 J and R 2 J with 4 × 4 elemental block size, (e) inverse jigsaw transformation of R 1 J and R 2 J with a correct key, and (f) inverse jigsaw transformation of R 1 J and R 2 J with a wrong key.

Equations (10)

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I d ( u , v ) = I ( u , v ) R ( u , v ) ,
I d ( u , v ) = FT [ R 1 ( x , y ) ] + FT [ R 2 ( x , y ) ] ,
R 1 ( x , y ) + R 2 ( x , y ) = FT 1 [ I d ( u , v ) ] ,
R 1 ( x , y ) + R 2 ( x , y ) = D ( x , y ) ,
( D ( x , y ) R 1 ( x , y ) ) ( D ( x , y ) R 1 ( x , y ) ) * = 1.
r 1 = arg ( D ( x , y ) ) arccos ( abs ( D ( x , y ) / 2 ) ) and r 2 = arg ( D ( x , y ) R 1 ( x , y ) ) ,
R 1 J ( x , y ) = JT 1 [ R 1 ( x , y ) ] ,
R 2 J ( x , y ) = JT 1 [ R 2 ( x , y ) ] .
I e ( u , v ) = FT [ { R 1 ( x , y ) + R 2 ( x , y ) } ] .
RE = n = 1 N m = 1 M | | D ( x d , y d ) | | O ( x d , y d ) | | 2 n = 1 N m = 1 M | | O ( x d , y d ) | | 2 ,

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