Abstract

A secure holographic memory system that uses fully phase encryption is presented. Two-dimensional arrays of data are phase encoded. Each array is then transformed into a stationary white-noise-like pattern by use of a random-phase mask located at the input plane and another at the Fourier plane. This encrypted information is then stored holographically in a photorefractive LiNbO3:Fe crystal. The original phase-encoded data can be recovered, by use of the two random-phase masks, with a phase-conjugate readout beam. This phase information can then be converted back to intensity information with an interferometer. Recording multiple images by use of angular multiplexing is demonstrated. The influence of a limited system bandwidth on the quality of reconstructed data is evaluated numerically. These computer simulation results show that a fully phase-based encryption system generally performs better than an amplitude-based encryption system when the system bandwidth is limited by a moderate amount.

© 2000 Optical Society of America

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1999 (3)

1998 (3)

1997 (4)

1996 (2)

1995 (2)

1993 (2)

1992 (1)

1991 (1)

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

1989 (1)

H. Lee, X. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2194 (1989).
[CrossRef]

1982 (1)

1974 (1)

Allison, D. B.

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

Bashaw, M. C.

Bollaro, F.

Brangaccio, D. J.

Bruning, H.

Chipman, R. A.

D’Nelly, K. G.

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

Davis, J. A.

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

Denz, C.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Gallagher, J. E.

Goudail, F.

Gu, X.

H. Lee, X. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2194 (1989).
[CrossRef]

Guibert, L.

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

Heanue, J. F.

Herriott, D. R.

Hesselink, L.

Ina, H.

Javidi, B.

Joesph, J.

Kang, Y. H.

Kim, K. H.

Kobayashi, S.

Lai, S.

S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2740–2742 (1996).
[CrossRef]

Lee, B.

Lee, H.

H. Lee, X. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2194 (1989).
[CrossRef]

Leyva, V.

Li, J.

Luo, Z.

Matoba, O.

Mok, F. H.

F. H. Mok, “Angle-multiplexed storage of 5000 holograms in lithium niobate,” Opt. Lett. 11, 915–917 (1993).
[CrossRef]

Moreno, I.

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

Pauliat, G.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Pezzaniti, J. L.

Psaltis, D.

H. Lee, X. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2194 (1989).
[CrossRef]

Rakuljic, G. A.

Réfrégier, P.

Roosen, G.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Rosenfeld, D. P.

Sayano, K.

Sergent, A.

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

Singh, K.

Takeda, M.

Towghi, N.

Tschudi, T.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Unnikrishnan, G.

White, A. D.

Yamaguchi, I.

Yariv, A.

Zhang, G.

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

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

Zhang, T.

Zhao, F.

Appl. Opt. (5)

J. Appl. Phys. (1)

H. Lee, X. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2194 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Opt. Eng. (3)

S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2740–2742 (1996).
[CrossRef]

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

Opt. Lett. (8)

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the proposed secure memory system with a phase-encoded input.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

(a) Original binary data to be displayed on the phase-only SLM, (b) intensity distribution of phase-encoded data, (c) encrypted information obtained by use of double random-phase masks at the input and the Fourier planes.

Fig. 4
Fig. 4

Decrypted information: (a) amplitude of the decrypted information without the interferometer, (b) amplitude of the decrypted information with the interferometer, (c) decrypted information when the random-phase mask at the Fourier plane is moved by 0.1 mm, and (d) decrypted information when the random-phase mask at the input plane is moved by 0.1 mm.

Fig. 5
Fig. 5

Decrypted information that was recorded by angular multiplexing.

Fig. 6
Fig. 6

Computer simulation used to investigate the influence of limited bandwidth on the quality of decrypted information: (a) encryption and (b) decryption with a limited aperture at the Fourier plane.

Fig. 7
Fig. 7

Mean squared error obtained with fully phase-based and amplitude-based decryption as a function of the proportion of the Fourier plane that is blocked.

Fig. 8
Fig. 8

Example of part of the input data and decrypted data when each pixel has a size of 16 × 16 cells and 61% of the Fourier plane is blocked: (a) input data, (b) fully phase-based decrypted information, and (c) amplitude-based decrypted information.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

Ψξ, η=Fexpjπox, ym1x, yM2ξ, η,
|Ψξ, η+Rξ, η|2.
ψx, y=exp-jπox, ym1*x, y m2x, y  m2x, ym1x, y,
Ux, y=|exp-jπox, y+expjπφ|2=2+2 cos πox, y+φ.
Ux, y=4ox, y=10ox, y=0.
sx, y=sx, yexp-j2πh1x, y m2x, y  ax, y m2*x, yexpj2πh1x, y,
Erra=m=1Mn=1Non, m-|sn, m|2M×N,
Errp=m=1Mn=1Non, m-argsn, m/π2M×N.

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