Abstract

We implement an optical encryption system based on double-random phase encoding of the data at the input and the Fourier planes. In our method we decrypt the image by generating a conjugate of the encrypted image through phase conjugation in a photorefractive crystal. The use of phase conjugation results in near-diffraction-limited imaging. Also, the key that is used during encryption can also be used for decrypting the data, thereby alleviating the need for using a conjugate of the key. The effect of a finite space–bandwidth product of the random phase mask on the encryption system’s performance is discussed. A theoretical analysis is given of the sensitivity of the system to misalignment errors of a Fourier plane random phase mask.

© 1998 Optical Society of America

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References

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  1. B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
    [CrossRef]
  2. P. Réfrégier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
    [CrossRef] [PubMed]
  3. B. Javidi, G. S. Zhang, J. Li, “Encrypted optical memory using double-random phase encoding,” Appl. Opt. 36, 1054–1058 (1997).
    [CrossRef] [PubMed]
  4. B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
    [CrossRef]
  5. L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
    [CrossRef]
  6. E. L. Kral, J. F. Walkup, M. O. Hagler, “Correlation properties of random phase diffusers for multiplex holography,” Appl. Opt. 21, 1281–1290 (1982).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993), Chap. 4.
  9. L. Solymar, D. J. Webb, A. Grunnet-Jepson, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).
  10. J. Joseph, K. Singh, P. K. C. Pillai, “A new phase conjugate scheme for one way imaging through phase distorting media,” Appl. Phys. B. 51, 219–221 (1990).
    [CrossRef]
  11. J. Widjaja, Y. Tomita, “Optical triple-in digital logic using nonlinear optical four-wave mixing,” Appl. Opt. 34, 5074–5076 (1995).
    [CrossRef] [PubMed]
  12. A. D. Meigs, B. E. A. Saleh, “Spatial fidelity of photorefractive image correlators,” IEEE J. Quantum Electron. 30, 3025–3032 (1994).
    [CrossRef]
  13. P. Xie, J.-H. Dai, P.-Y. Wang, H.-J. Zhang, “Spatial fidelity of externally pumped phase conjugation in photorefractive crystals,” J. Opt. Soc. Am. B 14, 852–859 (1997).
    [CrossRef]
  14. J. Joseph, K. Singh, P. K. C. Pillai, “Crystal orientation dependence of SNR for signal beam amplification in photorefractive BaTiO3,” Opt. Laser Technol. 23, 237–240 (1991).
    [CrossRef]

1997 (2)

1996 (2)

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[CrossRef]

1995 (2)

1994 (2)

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

A. D. Meigs, B. E. A. Saleh, “Spatial fidelity of photorefractive image correlators,” IEEE J. Quantum Electron. 30, 3025–3032 (1994).
[CrossRef]

1991 (1)

J. Joseph, K. Singh, P. K. C. Pillai, “Crystal orientation dependence of SNR for signal beam amplification in photorefractive BaTiO3,” Opt. Laser Technol. 23, 237–240 (1991).
[CrossRef]

1990 (1)

J. Joseph, K. Singh, P. K. C. Pillai, “A new phase conjugate scheme for one way imaging through phase distorting media,” Appl. Phys. B. 51, 219–221 (1990).
[CrossRef]

1982 (1)

1977 (1)

Dai, J.-H.

Grunnet-Jepson, A.

L. Solymar, D. J. Webb, A. Grunnet-Jepson, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).

Hagler, M. O.

Horner, J. L.

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Javidi, B.

B. Javidi, G. S. Zhang, J. Li, “Encrypted optical memory using double-random phase encoding,” Appl. Opt. 36, 1054–1058 (1997).
[CrossRef] [PubMed]

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

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

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Joseph, J.

J. Joseph, K. Singh, P. K. C. Pillai, “Crystal orientation dependence of SNR for signal beam amplification in photorefractive BaTiO3,” Opt. Laser Technol. 23, 237–240 (1991).
[CrossRef]

J. Joseph, K. Singh, P. K. C. Pillai, “A new phase conjugate scheme for one way imaging through phase distorting media,” Appl. Phys. B. 51, 219–221 (1990).
[CrossRef]

Kral, E. L.

Krile, T. F.

Li, J.

B. Javidi, G. S. Zhang, J. Li, “Encrypted optical memory using double-random phase encoding,” Appl. Opt. 36, 1054–1058 (1997).
[CrossRef] [PubMed]

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

Marks, R. J.

Meigs, A. D.

A. D. Meigs, B. E. A. Saleh, “Spatial fidelity of photorefractive image correlators,” IEEE J. Quantum Electron. 30, 3025–3032 (1994).
[CrossRef]

Neto, L. G.

L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[CrossRef]

Pillai, P. K. C.

J. Joseph, K. Singh, P. K. C. Pillai, “Crystal orientation dependence of SNR for signal beam amplification in photorefractive BaTiO3,” Opt. Laser Technol. 23, 237–240 (1991).
[CrossRef]

J. Joseph, K. Singh, P. K. C. Pillai, “A new phase conjugate scheme for one way imaging through phase distorting media,” Appl. Phys. B. 51, 219–221 (1990).
[CrossRef]

Réfrégier, P.

Saleh, B. E. A.

A. D. Meigs, B. E. A. Saleh, “Spatial fidelity of photorefractive image correlators,” IEEE J. Quantum Electron. 30, 3025–3032 (1994).
[CrossRef]

Sheng, Y.

L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[CrossRef]

Singh, K.

J. Joseph, K. Singh, P. K. C. Pillai, “Crystal orientation dependence of SNR for signal beam amplification in photorefractive BaTiO3,” Opt. Laser Technol. 23, 237–240 (1991).
[CrossRef]

J. Joseph, K. Singh, P. K. C. Pillai, “A new phase conjugate scheme for one way imaging through phase distorting media,” Appl. Phys. B. 51, 219–221 (1990).
[CrossRef]

Solymar, L.

L. Solymar, D. J. Webb, A. Grunnet-Jepson, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).

Tomita, Y.

Walkup, J. F.

Wang, P.-Y.

Webb, D. J.

L. Solymar, D. J. Webb, A. Grunnet-Jepson, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).

Widjaja, J.

Xie, P.

Yeh, P.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993), Chap. 4.

Zhang, G.

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

Zhang, G. S.

Zhang, H.-J.

Appl. Opt. (4)

Appl. Phys. B. (1)

J. Joseph, K. Singh, P. K. C. Pillai, “A new phase conjugate scheme for one way imaging through phase distorting media,” Appl. Phys. B. 51, 219–221 (1990).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. D. Meigs, B. E. A. Saleh, “Spatial fidelity of photorefractive image correlators,” IEEE J. Quantum Electron. 30, 3025–3032 (1994).
[CrossRef]

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

Opt. Eng. (3)

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[CrossRef]

Opt. Laser Technol. (1)

J. Joseph, K. Singh, P. K. C. Pillai, “Crystal orientation dependence of SNR for signal beam amplification in photorefractive BaTiO3,” Opt. Laser Technol. 23, 237–240 (1991).
[CrossRef]

Opt. Lett. (1)

Other (2)

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993), Chap. 4.

L. Solymar, D. J. Webb, A. Grunnet-Jepson, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram illustrating the principle of the encryption system: R, reference beam; R*, beam counterpropagating to the reference beam; I, encrypted-image-bearing beam; I*, phase conjugate of the encrypted-image-bearing beam; PR, photorefractive crystal.

Fig. 2
Fig. 2

Schematic diagram of the experimental setup: BE, beam expander; M’s, mirrors; BS’s, beam splitters; o, object transparency; R, S, random phase masks; L1–L3, lenses; PRC, photorefractive crystal; IP, image-processing system; S′, shutter.

Fig. 3
Fig. 3

(a) Image to be encrypted, (b) encrypted image captured through CCD2 in the experimental setup, (c) decrypted image, and (d) decryption when a wrong key is used.

Equations (14)

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ψ x ,   y = o x ,   y R x ,   y S x ,   y ,
O x ,   y = o * x ,   y R * x ,   y S x ,   y   *   S x ,   y ,
O x ,   y = o x ,   y R * x ,   y S x ,   y   *   S x ,   y ,
ψ x ,   y = j = 1 L o j x ,   y R j x ,   y S j x ,   y ,
O i x ,   y = j = 1 L o j x ,   y R j * x ,   y S j x ,   y   *   S i x ,   y ,
P ϕ = 1 / M   ϕ k = 0 ,   2 π / M ,   4 π / M , ,   2 π M - 1 / M = 0     otherwise .
ξ x = S 1 x   *   S 1 x , = k = 0 N - 1 kD k + 1 D exp i 2 π α x d α = ND   sinc NDx exp i π NDx , N ,   | ξ x | δ x .
ξ x = k = 0 N - 1 kD kD + d   ϕ k exp i 2 π α x d α + k = 0 N - 1 kD + d k + 1 D exp i 2 π α x d α , ξ x = N D - d sinc D - d x sinc NDx sinc Dx × exp i π ND + d x + d   sinc dx exp i π dx × k = 0 N - 1   ϕ k exp i 2 π kDx .
n 2 x ¯ = d 2 sinc 2 dx × k 1 = 0 N - 1 k 2 = 0 N - 1 ϕ k 1 ϕ * k 2 exp i 2 π k 1 - k 2 Dx ¯ , n 2 x ¯ = d 2 sinc 2 dx k 1 = k 2 = 0 N - 1   ϕ k 1 ϕ * k 1 + k 1 - k 2 = 1 N - 1 ϕ k 1 ϕ * k 2 exp i 2 π | k 1 - k 2 | Dx ¯ = d 2 sinc 2 dx N + k 1 - k 2 = 1 N - 1 cos | k 1 - k 2 | Dx + ϕ ¯ ,
n 2 x ¯ = Nd 2   sinc 2 dx .
SNR = N D - d 2 / d 2 .
ξ x = k = 0 N - 1 kD k + 1 D   ϕ k exp i 2 π α x d α , = D   sinc Dx k = 0 N - 1   ϕ k exp i 2 π kDx .
n 2 x ¯ = D 2 sinc 2 Dx × k 1 = 0 N - 1 k 2 = 0 N - 1 ϕ k 1 ϕ * k 2 exp i 2 π k 1 - k 2 Dx ¯ , n 2 x ¯ = D 2 sinc 2 Dx k 1 = k 2 = 0 N - 1   ϕ k 1 ϕ * k 1 + k 1 - k 2 = 1 N - 1 ϕ k 1 ϕ * k 2 exp i 2 π | k 1 - k 2 | Dx ¯ .
n 2 x ¯ = ND 2   sinc 2 Dx .

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