Abstract

A novel optical image encryption scheme based on interference is proposed. The original image is digitally encoded into one phase-only mask by employing an improved Gerchberg-Saxton phase retrieval algorithm together with another predefined random phase mask which serves as the encryption key. The decryption process can be implemented optically based on Michelson interferometer by using the same key. The scheme can be regarded as a stream-cipher-like encryption system, the encryption and decryption keys are the same, however the operations are different. The position coordinates and light wavelength can also be used as additional keys during the decryption. Numerical simulations have demonstrated the validity and robustness of the proposed method.

© 2011 Optical Society of America

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  1. P. Refregier, and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
    [CrossRef] [PubMed]
  2. D. S. Monaghan, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Key-space analysis of double random phase encryption technique,” Appl. Opt. 46, 6641–6647 (2007).
    [CrossRef] [PubMed]
  3. B. Javidi, G. Zhang, and J. Li, “Encrypted optical memory using double-random phase encoding,” Opt. Eng. 36, 1054–1058 (1997).
  4. O. Matoba, and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
    [CrossRef]
  5. 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, 1644–1646 (2005).
    [CrossRef] [PubMed]
  6. X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31, 1044–1046 (2006).
    [CrossRef] [PubMed]
  7. S. Liu, Q. Mi, and B. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244 (2001).
    [CrossRef]
  8. Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
    [CrossRef]
  9. X. Wang, and D. Zhao, “Image encryption based on anamorphic fractional Fourier transform and three-step phase-shifting interferometry,” Opt. Commun. 268, 240–244 (2006).
    [CrossRef]
  10. Z. Liu, and S. Liu, “Random fractional Fourier transform,” Opt. Lett. 32, 2088–2090 (2007).
    [CrossRef] [PubMed]
  11. L. Chen, and D. Zhao, “Optical image encryption with Hartley transforms,” Opt. Lett. 31, 3438–3440 (2006).
    [CrossRef] [PubMed]
  12. H. Kim, D. H. Kim, and Y. Lee, “Encryption of digital hologram of 3-d object by virtual optics,” Opt. Express 12,Q14912–4921 (2004).
    [CrossRef] [PubMed]
  13. Z. Liu, and S. Liu, “Randomization of the Fourier transform,” Opt. Lett. 32, 478–480 (2007).
    [CrossRef] [PubMed]
  14. Z. Liu, and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
    [CrossRef]
  15. G. Situ, and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
    [CrossRef] [PubMed]
  16. H. Li, and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281, 5745–5749 (2008).
    [CrossRef]
  17. 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]
  18. Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).
    [CrossRef]
  19. Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).
    [CrossRef]
  20. Y. Zhang, and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
    [CrossRef] [PubMed]
  21. M. Madjarova, M. Kakuta, M. Yamaguchi, and N. Ohyama, “Optical implementation of the stream cipher based on the irreversible cellular automata algorithm,” Opt. Lett. 22, 1624–1626 (1997).
    [CrossRef]
  22. J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 38, 47–54 (1999).
    [CrossRef]
  23. J. W. Han, S. Lee, and E. S. Kim, “Optical key bit stream generator,” Opt. Eng. 38, 33–38 (1999).
    [CrossRef]
  24. S. Zhang, and R. Karim, “High-security optical integrated stream ciphers,” Opt. Eng. 38, 20–24 (1999).
    [CrossRef]
  25. T. Sasaki, H. Togo, J. Tanida, and Y. Ichioka, “Stream cipher based on pseudorandom number generation with optical affine transformation,” Appl. Opt. 39, 2340–2346 (2000).
    [CrossRef]
  26. 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).
  27. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]

2009

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).
[CrossRef]

2008

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

H. Li, and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281, 5745–5749 (2008).
[CrossRef]

2007

Z. Liu, and S. Liu, “Random fractional Fourier transform,” Opt. Lett. 32, 2088–2090 (2007).
[CrossRef] [PubMed]

Z. Liu, and S. Liu, “Randomization of the Fourier transform,” Opt. Lett. 32, 478–480 (2007).
[CrossRef] [PubMed]

Z. Liu, and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

D. S. Monaghan, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Key-space analysis of double random phase encryption technique,” Appl. Opt. 46, 6641–6647 (2007).
[CrossRef] [PubMed]

2006

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

L. Chen, and D. Zhao, “Optical image encryption with Hartley transforms,” Opt. Lett. 31, 3438–3440 (2006).
[CrossRef] [PubMed]

X. Wang, and D. Zhao, “Image encryption based on anamorphic fractional Fourier transform and three-step phase-shifting interferometry,” Opt. Commun. 268, 240–244 (2006).
[CrossRef]

2005

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]

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, 1644–1646 (2005).
[CrossRef] [PubMed]

2004

H. Kim, D. H. Kim, and Y. Lee, “Encryption of digital hologram of 3-d object by virtual optics,” Opt. Express 12,Q14912–4921 (2004).
[CrossRef] [PubMed]

2002

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

2001

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

2000

T. Sasaki, H. Togo, J. Tanida, and Y. Ichioka, “Stream cipher based on pseudorandom number generation with optical affine transformation,” Appl. Opt. 39, 2340–2346 (2000).
[CrossRef]

1999

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 38, 47–54 (1999).
[CrossRef]

J. W. Han, S. Lee, and E. S. Kim, “Optical key bit stream generator,” Opt. Eng. 38, 33–38 (1999).
[CrossRef]

S. Zhang, and R. Karim, “High-security optical integrated stream ciphers,” Opt. Eng. 38, 20–24 (1999).
[CrossRef]

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

1997

B. Javidi, G. Zhang, and J. Li, “Encrypted optical memory using double-random phase encoding,” Opt. Eng. 36, 1054–1058 (1997).

M. Madjarova, M. Kakuta, M. Yamaguchi, and N. Ohyama, “Optical implementation of the stream cipher based on the irreversible cellular automata algorithm,” Opt. Lett. 22, 1624–1626 (1997).
[CrossRef]

1995

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

1982

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

1972

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).

Ahmad, M. A.

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).
[CrossRef]

Arcos, S.

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, 1644–1646 (2005).
[CrossRef] [PubMed]

Cai, L. 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]

Carnicer, A.

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, 1644–1646 (2005).
[CrossRef] [PubMed]

Chen, L.

L. Chen, and D. Zhao, “Optical image encryption with Hartley transforms,” Opt. Lett. 31, 3438–3440 (2006).
[CrossRef] [PubMed]

Dai, J.

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).
[CrossRef]

Fienup, J. R.

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

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).

Gopinathan, U.

D. S. Monaghan, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Key-space analysis of double random phase encryption technique,” Appl. Opt. 46, 6641–6647 (2007).
[CrossRef] [PubMed]

Han, J. W.

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 38, 47–54 (1999).
[CrossRef]

J. W. Han, S. Lee, and E. S. Kim, “Optical key bit stream generator,” Opt. Eng. 38, 33–38 (1999).
[CrossRef]

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]

Ichioka, Y.

T. Sasaki, H. Togo, J. Tanida, and Y. Ichioka, “Stream cipher based on pseudorandom number generation with optical affine transformation,” Appl. Opt. 39, 2340–2346 (2000).
[CrossRef]

Javidi, B.

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

B. Javidi, G. Zhang, and J. Li, “Encrypted optical memory using double-random phase encoding,” Opt. Eng. 36, 1054–1058 (1997).

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

Juvells, I.

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, 1644–1646 (2005).
[CrossRef] [PubMed]

Kakuta, M.

M. Madjarova, M. Kakuta, M. Yamaguchi, and N. Ohyama, “Optical implementation of the stream cipher based on the irreversible cellular automata algorithm,” Opt. Lett. 22, 1624–1626 (1997).
[CrossRef]

Karim, R.

S. Zhang, and R. Karim, “High-security optical integrated stream ciphers,” Opt. Eng. 38, 20–24 (1999).
[CrossRef]

Kim, D. H.

H. Kim, D. H. Kim, and Y. Lee, “Encryption of digital hologram of 3-d object by virtual optics,” Opt. Express 12,Q14912–4921 (2004).
[CrossRef] [PubMed]

Kim, E. S.

J. W. Han, S. Lee, and E. S. Kim, “Optical key bit stream generator,” Opt. Eng. 38, 33–38 (1999).
[CrossRef]

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 38, 47–54 (1999).
[CrossRef]

Kim, H.

H. Kim, D. H. Kim, and Y. Lee, “Encryption of digital hologram of 3-d object by virtual optics,” Opt. Express 12,Q14912–4921 (2004).
[CrossRef] [PubMed]

Lee, S.

J. W. Han, S. Lee, and E. S. Kim, “Optical key bit stream generator,” Opt. Eng. 38, 33–38 (1999).
[CrossRef]

Lee, Y.

H. Kim, D. H. Kim, and Y. Lee, “Encryption of digital hologram of 3-d object by virtual optics,” Opt. Express 12,Q14912–4921 (2004).
[CrossRef] [PubMed]

Li, H.

H. Li, and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281, 5745–5749 (2008).
[CrossRef]

Li, J.

B. Javidi, G. Zhang, and J. Li, “Encrypted optical memory using double-random phase encoding,” Opt. Eng. 36, 1054–1058 (1997).

Li, Q.

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).
[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.

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).
[CrossRef]

Z. Liu, and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

Z. Liu, and S. Liu, “Randomization of the Fourier transform,” Opt. Lett. 32, 478–480 (2007).
[CrossRef] [PubMed]

Z. Liu, and S. Liu, “Random fractional Fourier transform,” Opt. Lett. 32, 2088–2090 (2007).
[CrossRef] [PubMed]

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

Liu, Z.

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).
[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

Z. Liu, and S. Liu, “Random fractional Fourier transform,” Opt. Lett. 32, 2088–2090 (2007).
[CrossRef] [PubMed]

Z. Liu, and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

Z. Liu, and S. Liu, “Randomization of the Fourier transform,” Opt. Lett. 32, 478–480 (2007).
[CrossRef] [PubMed]

Madjarova, M.

M. Madjarova, M. Kakuta, M. Yamaguchi, and N. Ohyama, “Optical implementation of the stream cipher based on the irreversible cellular automata algorithm,” Opt. Lett. 22, 1624–1626 (1997).
[CrossRef]

Matoba, O.

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

Meng, X. F.

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.

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

Monaghan, D. S.

D. S. Monaghan, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Key-space analysis of double random phase encryption technique,” Appl. Opt. 46, 6641–6647 (2007).
[CrossRef] [PubMed]

Montes-Usategui, M.

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, 1644–1646 (2005).
[CrossRef] [PubMed]

Naughton, T. J.

D. S. Monaghan, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Key-space analysis of double random phase encryption technique,” Appl. Opt. 46, 6641–6647 (2007).
[CrossRef] [PubMed]

Ohyama, N.

M. Madjarova, M. Kakuta, M. Yamaguchi, and N. Ohyama, “Optical implementation of the stream cipher based on the irreversible cellular automata algorithm,” Opt. Lett. 22, 1624–1626 (1997).
[CrossRef]

Park, C. S.

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 38, 47–54 (1999).
[CrossRef]

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, 1044–1046 (2006).
[CrossRef] [PubMed]

Refregier, P.

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

Ryu, D. H.

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 38, 47–54 (1999).
[CrossRef]

Sasaki, T.

T. Sasaki, H. Togo, J. Tanida, and Y. Ichioka, “Stream cipher based on pseudorandom number generation with optical affine transformation,” Appl. Opt. 39, 2340–2346 (2000).
[CrossRef]

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).

Sheridan, J. T.

D. S. Monaghan, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Key-space analysis of double random phase encryption technique,” Appl. Opt. 46, 6641–6647 (2007).
[CrossRef] [PubMed]

Situ, G.

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

Sun, X.

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).
[CrossRef]

Z. Liu, Q. Li, J. Dai, X. Sun, S. Liu, and M. A. Ahmad, “A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains,” Opt. Commun. 282, 1536–1540 (2009).
[CrossRef]

Tanida, J.

T. Sasaki, H. Togo, J. Tanida, and Y. Ichioka, “Stream cipher based on pseudorandom number generation with optical affine transformation,” Appl. Opt. 39, 2340–2346 (2000).
[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]

Togo, H.

T. Sasaki, H. Togo, J. Tanida, and Y. Ichioka, “Stream cipher based on pseudorandom number generation with optical affine transformation,” Appl. Opt. 39, 2340–2346 (2000).
[CrossRef]

Wang, B.

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

Wang, X.

X. Wang, and D. Zhao, “Image encryption based on anamorphic fractional Fourier transform and three-step phase-shifting interferometry,” Opt. Commun. 268, 240–244 (2006).
[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.

H. Li, and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281, 5745–5749 (2008).
[CrossRef]

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, 1044–1046 (2006).
[CrossRef] [PubMed]

Yamaguchi, M.

M. Madjarova, M. Kakuta, M. Yamaguchi, and N. Ohyama, “Optical implementation of the stream cipher based on the irreversible cellular automata algorithm,” Opt. Lett. 22, 1624–1626 (1997).
[CrossRef]

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, 1044–1046 (2006).
[CrossRef] [PubMed]

Zhang, G.

B. Javidi, G. Zhang, and J. Li, “Encrypted optical memory using double-random phase encoding,” Opt. Eng. 36, 1054–1058 (1997).

Zhang, J.

G. Situ, and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
[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, 1044–1046 (2006).
[CrossRef] [PubMed]

Zhang, S.

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Figures (6)

Fig. 1
Fig. 1

The flowchart of the optical process of our algorithm. Two incident light beams, which are modulated by phase only masks POM1 and POM2 respectively, propagate to the output plane and interfere with each other to construct the original image.

Fig. 2
Fig. 2

Flowchart of the proposed phase retrieval algorithm.

Fig. 3
Fig. 3

Schematic illustration of the optical decryption setup.

Fig. 4
Fig. 4

Encryption results: (a) the primary image for encryption, (b) decryption result with right keys. The phase distributions of (c) POM1 and (d) POM2.

Fig. 5
Fig. 5

The NMSE curves of recovered images with the change of: (a) l2, (b) λ. The attached drawings is retrieved with parameters of a small value shifting when NMSE≈ 0.2 as the red lines indicates.

Fig. 6
Fig. 6

The noise-attack test: (a) dependence of NMSE on the change of noise intensity, the attach image is retrieved from POM2 with noise intensity of 15(dB), (b)dependence of NMSE on the change of missing data, the attach image is retrieved from POM2 when 1/16 of the mask POM2 is blocked.

Tables (1)

Tables Icon

Table 1 Convergence speed of the phase retrieval algorithm

Equations (9)

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f ( x , y ) = I ( x , y ) .
f ( x , y ) exp [ i φ ( x , y ) ] = f 1 ( x , y ) exp [ i φ 1 ( x , y ) ] + f 2 ( x , y ) exp [ i φ 2 ( x , y ) ] = exp [ i ϕ 1 ( x , y ) ] h ( x , y , l 1 ) + exp [ i ϕ 2 ( x , y ) ] h ( x , y , l 2 ) .
h ( x , y , l ) = exp ( 2 i π l / λ ) i λ l exp [ i π λ l ( x 2 + y 2 ) ] ,
exp [ i ϕ 2 ( x 2 , y 2 ) ] = 1 { { f 2 ( x , y ) exp [ i φ 2 ( x , y ) ] } { h ( x , y , l 2 ) } } ,
f 2 ( k ) exp [ i φ 2 ( k ) ] = f exp [ i φ ( k ) ] f 1 exp [ i φ 1 ] ,
g ( k ) exp [ i ϕ 2 ( k ) ] = 1 { { f 2 ( k ) exp [ i φ 2 ( k ) ] } { h ( x , y , l 2 ) } } ,
f 2 ( k + 1 ) exp [ i φ 2 ( k + 1 ) ] = exp [ i ϕ 2 ( k ) ] h ( x , y , l 2 ) ,
f ( k + 1 ) exp [ i φ ( k + 1 ) ] = f 1 exp ( i φ 1 ) + f 2 ( k + 1 ) exp [ i φ 2 ( k + 1 ) ] .
NMSE = m = 1 N n = 1 N | | f ( k ) ( m , n ) | | f ( m , n ) | | 2 m = 1 N n = 1 N | f ( m , n ) | 2 ,

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