Abstract

We propose a method of wavelength multiplexing based on a modified Gerchberg–Saxton algorithm (MGSA) and a cascaded phase modulation scheme in the Fresnel transform domain to reduce the cross talk in the multiple-image-encryption framework. First, each plain image is encoded to a complex function by using the MGSA. Next, the phase components of the created complex functions are multiplexed with different wavelength parameters, and then they are modulated before being combined together as a phase-only function, which is recorded in the first phase-only mask (POM). Finally, the second POM is generated by applying the MGSA again on the amplitude derived from the summation of the total created complex functions. Simulation results show that the cross talk between multiplexed images has been significantly reduced compared with an existing similar method. Therefore, the multiplexing capacity in encrypting multiple gray-scale images can be increased accordingly.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. G. H. Lin, H. T. Chang, W. N. Lai, and C. H. Chuang, “Public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
    [CrossRef]
  4. R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
    [CrossRef]
  5. Y. C. Chang, H. T. Chang, and C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
    [CrossRef]
  6. H. T. Chang, “Image encryption using separate amplitude-based virtual image and iteratively retrieved phase information,” Opt. Eng. 40, 2165–2171 (2001).
    [CrossRef]
  7. G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
    [CrossRef] [PubMed]
  8. H. E. Hwang and P. Han, “Fast algorithm of phase masks for image encryption in the Fresnel domain,” J. Opt. Soc. Am. A 23, 1870–1874 (2006).
    [CrossRef]
  9. G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain B,” Opt. Lett. 25, 887–889 (2000).
    [CrossRef]
  10. S. T. Liu, Q. L. Mi, and B. H. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244 (2001).
    [CrossRef]
  11. Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
    [CrossRef]
  12. G. Situ and J. Zhang, “A cascaded iterative Fourier transform algorithm for optical security applications,” Optik 114, 473–477 (2003).
    [CrossRef]
  13. Y. Li, K. Kreske, and J. Rosen, “Security and encryption optical systems based on a correlator with significant output images,” Appl. Opt. 39, 5295–5301 (2000).
    [CrossRef]
  14. 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, 4815–4834 (2002).
    [CrossRef]
  15. G. Situ and J. Zhang, “A lensless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 115–122 (2004).
    [CrossRef]
  16. M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
    [CrossRef]
  17. B. M. Hennelly, T. J. Naughton, J. McDonald, J. T. Sheridan, G. Unnikrishnan, D. P. Kelly, and B. Javidi, “Spread-space spread-spectrum technique for secure multiplexing,” Opt. Lett. 32, 1060–1066 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  19. G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
    [CrossRef] [PubMed]
  20. G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A: Pure Appl. Opt. 8, 391–397 (2006).
    [CrossRef]
  21. H. E. Hwang, H. T. Chang, and W. N. Lie, “Multiple-image encryption and multiplexing using modified Gerchberg–Saxton algorithm and phase modulation in Fresnel transform domain,” Opt. Lett. 34, 3917–3919 (2009).
    [CrossRef] [PubMed]
  22. 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]
  23. R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).
  24. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  25. H. E. Hwang and P. Han, “Signal reconstruction algorithm based on a single intensity in the Fresnel domain,” Opt. Express 15, 3766–3776 (2007).
    [CrossRef] [PubMed]
  26. M. Paturzo, P. Memmolo, L. Miccio, A. Finizio, P. Ferrarro, A. Tulino, and B. Javidi, “Numerical multiplexing and demultiplexing of digital holographic information for remote reconstruction in amplitude and phase,” Opt. Lett. 33, 2629–2631 (2008).
    [CrossRef] [PubMed]
  27. X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070–1075 (2007).
    [CrossRef]
  28. N. K. Nishchal and T. J. Naughton, “Flexible optical encryption with multiple users and multiple security levels,” Opt. Commun. 284, 735–739 (2011).
    [CrossRef]

2011 (1)

N. K. Nishchal and T. J. Naughton, “Flexible optical encryption with multiple users and multiple security levels,” Opt. Commun. 284, 735–739 (2011).
[CrossRef]

2009 (2)

2008 (2)

2007 (3)

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

B. M. Hennelly, T. J. Naughton, J. McDonald, J. T. Sheridan, G. Unnikrishnan, D. P. Kelly, and B. Javidi, “Spread-space spread-spectrum technique for secure multiplexing,” Opt. Lett. 32, 1060–1066 (2007).
[CrossRef] [PubMed]

H. E. Hwang and P. Han, “Signal reconstruction algorithm based on a single intensity in the Fresnel domain,” Opt. Express 15, 3766–3776 (2007).
[CrossRef] [PubMed]

2006 (2)

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A: Pure Appl. Opt. 8, 391–397 (2006).
[CrossRef]

H. E. Hwang and P. Han, “Fast algorithm of phase masks for image encryption in the Fresnel domain,” J. Opt. Soc. Am. A 23, 1870–1874 (2006).
[CrossRef]

2005 (2)

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
[CrossRef]

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

2004 (3)

G. Situ and J. Zhang, “A lensless 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]

Y. C. Chang, H. T. Chang, and C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
[CrossRef]

2003 (2)

G. H. Lin, H. T. Chang, W. N. Lai, and C. H. Chuang, “Public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

G. Situ and J. Zhang, “A cascaded iterative Fourier transform algorithm for optical security applications,” Optik 114, 473–477 (2003).
[CrossRef]

2002 (3)

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
[CrossRef]

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, 4815–4834 (2002).
[CrossRef]

C. H. Yeh, H. T. Chang, H. C. Chien, and C. J. Kuo, “Design of cascaded phase keys for hierarchical security system,” Appl. Opt. 41, 6128–6134 (2002).
[CrossRef] [PubMed]

2001 (2)

H. T. Chang, “Image encryption using separate amplitude-based virtual image and iteratively retrieved phase information,” Opt. Eng. 40, 2165–2171 (2001).
[CrossRef]

S. T. Liu, Q. L. Mi, and B. H. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244 (2001).
[CrossRef]

2000 (2)

1996 (1)

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

1995 (1)

1972 (1)

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

1971 (1)

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Amaya, D.

Bolognini, N.

Cai, L. Z.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
[CrossRef]

Chang, H. T.

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

Y. C. Chang, H. T. Chang, and C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
[CrossRef]

G. H. Lin, H. T. Chang, W. N. Lai, and C. H. Chuang, “Public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

C. H. Yeh, H. T. Chang, H. C. Chien, and C. J. Kuo, “Design of cascaded phase keys for hierarchical security system,” Appl. Opt. 41, 6128–6134 (2002).
[CrossRef] [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, 4815–4834 (2002).
[CrossRef]

H. T. Chang, “Image encryption using separate amplitude-based virtual image and iteratively retrieved phase information,” Opt. Eng. 40, 2165–2171 (2001).
[CrossRef]

Chang, Y. C.

Y. C. Chang, H. T. Chang, and C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
[CrossRef]

Chatwin, C.

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

Cheng, X. C.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Chien, H. C.

Chuang, C. H.

G. H. Lin, H. T. Chang, W. N. Lai, and C. H. Chuang, “Public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

Dong, G. Y.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Ferrarro, P.

Finizio, A.

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 35, 237–246 (1972).

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Han, P.

He, M. Z.

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
[CrossRef]

Hennelly, B. M.

Hwang, H. E.

Javidi, B.

Joseph, J.

Kelly, D. P.

Kreske, K.

Kuo, C. J.

Y. C. Chang, H. T. Chang, and C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
[CrossRef]

C. H. Yeh, H. T. Chang, H. C. Chien, and C. J. Kuo, “Design of cascaded phase keys for hierarchical security system,” Appl. Opt. 41, 6128–6134 (2002).
[CrossRef] [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, 4815–4834 (2002).
[CrossRef]

Lai, W. N.

G. H. Lin, H. T. Chang, W. N. Lai, and C. H. Chuang, “Public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

Li, Y.

Lie, W. N.

Lin, G. H.

G. H. Lin, H. T. Chang, W. N. Lai, and C. H. Chuang, “Public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

Liu, Q.

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
[CrossRef]

Liu, S. T.

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, 4815–4834 (2002).
[CrossRef]

McDonald, J.

Memmolo, P.

Meng, X. F.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
[CrossRef]

Mi, Q. L.

Miccio, L.

Naughton, T. J.

Nishchal, N. K.

N. K. Nishchal and T. J. Naughton, “Flexible optical encryption with multiple users and multiple security levels,” Opt. Commun. 284, 735–739 (2011).
[CrossRef]

Paturzo, M.

Refregier, P.

Rosen, J.

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 35, 237–246 (1972).

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Shen, X. X.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Sheridan, J. T.

Singh, K.

Situ, G.

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A: Pure Appl. Opt. 8, 391–397 (2006).
[CrossRef]

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

G. Situ and J. Zhang, “A lensless 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]

G. Situ and J. Zhang, “A cascaded iterative Fourier transform algorithm for optical security applications,” Optik 114, 473–477 (2003).
[CrossRef]

Tanno, N.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
[CrossRef]

Tebaldi, M.

Torroba, R.

Tulino, A.

Unnikrishnan, G.

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. C.

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
[CrossRef]

Wang, Y. R.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070–1075 (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]

Xu, X. F.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Yang, X. L.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Yeh, C. H.

Zhang, H.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

Zhang, J.

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A: Pure Appl. Opt. 8, 391–397 (2006).
[CrossRef]

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

G. Situ and J. Zhang, “A lensless 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]

G. Situ and J. Zhang, “A cascaded iterative Fourier transform algorithm for optical security applications,” Optik 114, 473–477 (2003).
[CrossRef]

Zhang, Y.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
[CrossRef]

Zheng, C. H.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
[CrossRef]

Zhu, B. H.

Appl. Opt. (4)

J. Opt. A: Pure Appl. Opt. (2)

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A: Pure Appl. Opt. 8, 391–397 (2006).
[CrossRef]

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 9, 1070–1075 (2007).
[CrossRef]

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

Opt. Commun. (5)

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
[CrossRef]

Y. C. Chang, H. T. Chang, and C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
[CrossRef]

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

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
[CrossRef]

N. K. Nishchal and T. J. Naughton, “Flexible optical encryption with multiple users and multiple security levels,” Opt. Commun. 284, 735–739 (2011).
[CrossRef]

Opt. Eng. (3)

H. T. Chang, “Image encryption using separate amplitude-based virtual image and iteratively retrieved phase information,” Opt. Eng. 40, 2165–2171 (2001).
[CrossRef]

G. H. Lin, H. T. Chang, W. N. Lai, and C. H. Chuang, “Public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (8)

M. Paturzo, P. Memmolo, L. Miccio, A. Finizio, P. Ferrarro, A. Tulino, and B. Javidi, “Numerical multiplexing and demultiplexing of digital holographic information for remote reconstruction in amplitude and phase,” Opt. Lett. 33, 2629–2631 (2008).
[CrossRef] [PubMed]

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

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

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

S. T. Liu, Q. L. Mi, and B. H. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244 (2001).
[CrossRef]

B. M. Hennelly, T. J. Naughton, J. McDonald, J. T. Sheridan, G. Unnikrishnan, D. P. Kelly, and B. Javidi, “Spread-space spread-spectrum technique for secure multiplexing,” Opt. Lett. 32, 1060–1066 (2007).
[CrossRef] [PubMed]

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

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

Optik (3)

G. Situ and J. Zhang, “A cascaded iterative Fourier transform algorithm for optical security applications,” Optik 114, 473–477 (2003).
[CrossRef]

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

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

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Figures (8)

Fig. 1
Fig. 1

(a) The flow chart of the GSA is used for performing phase retrieval if their intensities at their respective optical planes are known. (b) Flow chart of a MGSA.

Fig. 2
Fig. 2

Optical multiple-image encryption setup by wavelength multiplexing based on cascaded POMs in the FrT domain.

Fig. 3
Fig. 3

Block diagram of the proposed multiple-image encryption and wavelength multiplexing.

Fig. 4
Fig. 4

Nine test gray-scale images used in the proposed multiple-image multiplexing encryption.

Fig. 5
Fig. 5

Noiselike POF recorded in (a)  POM 1 and (b)  POM 2 .

Fig. 6
Fig. 6

(a) Entire decrypted image with the wavelength λ 3 = 460 nm in the reconstruction plane. (b) Enlarged decrypted image g ^ 3 λ ( x 1 , y 1 ) corresponding to the original image g 3 ( x 1 , y 1 ) in Fig. 6a. (c) Entire decrypted image with a wavelength of λ 6 = 520 nm in the reconstruction plane. (d) Enlarged decrypted image g ^ 6 λ ( x 1 , y 1 ) corresponding to the original image g 6 ( x 1 , y 1 ) in Fig. 6c.

Fig. 7
Fig. 7

(a) Nine test binary images used in the proposed multiple-image multiplexing encryption method. (b) The original binary image g 3 ( x 1 , y 1 ) . (c) The entire decrypted binary image with a wavelength of λ 3 = 460 nm in the reconstruction plane. (d) The enlarged decrypted binary image g ^ 3 λ ( x 1 , y 1 ) corresponding to the original binary image g 3 ( x 1 , y 1 ) in Fig. 7c. (e) The original binary image g 6 ( x 1 , y 1 ) . (f) The entire decrypted binary image with a wavelength of λ 6 = 5 20 nm in the reconstruction plane. (g) The enlarged decrypted binary image g ^ 6 λ ( x 1 , y 1 ) corresponding to the original binary image g 6 ( x 1 , y 1 ) in Fig. 7f.

Fig. 8
Fig. 8

Comparison between the proposed and Situ’s [19] methods in terms of the correlation coefficient.

Equations (7)

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FrT { H ( x 2 , y 2 ) exp [ j ψ h ( x 2 , y 2 ) ] ; λ ; z } = exp ( j 2 π z λ ) j λ z H ( x 2 , y 2 ) exp [ j ψ h ( x 2 , y 2 ) ] exp { j π λ z [ ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 ] } d x 2 d y 2 = T ^ ( x 1 , y 1 ) exp [ j ψ G ( x 1 , y 1 ) ] ,
FrT { exp [ j ψ λ n ( x 1 , y 1 ) ] ; λ n ; z 1 } = g ^ n λ ( x 0 , y 0 ) exp [ j ψ g ^ n λ ( x 0 , y 0 ) ] ,
FrT { exp [ j ψ λ n ( x 1 , y 1 ) ] ; λ n ; z 1 } = g ^ n λ ( x 0 μ 0 , y 0 ν 0 ) exp [ j ω ( x 0 , y 0 ) ] ,
ψ λ n ( x 1 , y 1 ) = ψ λ n ( x 1 , y 1 ) + 2 π ( μ n x 1 + ν n y 1 ) λ n z 1 ,
A T λ ( x 1 , y 1 ) exp [ j ψ T λ ( x 1 , y 1 ) ] = n = 1 N exp [ j ψ λ n ( x 1 , y 1 ) ] ,
FrT { exp [ j ϕ ( x 2 , y 2 ) ] ; λ n ; z n } = A ^ T λ ( x 1 , y 1 ) exp [ j φ ( x 1 , y 1 ) ] ,
| FrT ( FrT { exp [ j ϕ ( x 2 , y 2 ) ] ; λ n ; z n } exp [ j φ ( x 1 , y 1 ) + j ψ T λ ( x 1 , y 1 ) ] ; λ n ; z 1 ) | = | FrT { A ^ T λ ( x 1 , y 1 ) exp [ j φ ( x 1 , y 1 ) ] exp [ j φ ( x 1 , y 1 ) + j ψ T λ ( x 1 , y 1 ) ] ; λ n ; z 1 } | = | FrT { A ^ T λ ( x 1 , y 1 ) exp [ j ψ T λ ( x 1 , y 1 ) ] ; λ n ; z 1 } | = | FrT { n = 1 N exp [ j ψ λ n ( x 1 , y 1 ) + j 2 π ( μ n x 1 + ν n y 1 ) λ n z ] ; λ n ; z 1 } | = | FrT { n = 1 N exp [ j ψ λ n ( x 1 , y 1 ) ] ; λ n ; z 1 } | = | g ^ n λ ( x 0 μ n , y 0 ν n ) exp [ j ω ( x 0 , y 0 ) ] + n λ n ( x 0 , y 0 ) | g ^ n λ ( x 0 μ n , y 0 ν n ) + | n λ n ( x 0 , y 0 ) | ,

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