Abstract

We present the first, to our knowledge, demonstration of an encrypted optical storage based on double-random phase encoding by using angular multiplexing in a photorefractive material. Original two-dimensional data are encrypted by use of two random phase codes located in the input and the Fourier planes and are then stored holographically in a LiNbO3:Fe crystal. The retrieval of the original data can be achieved with a phase-conjugated readout scheme. We demonstrate the encryption and the decryption of multiple frames of two-dimensional digital data by using angular multiplexing. We also evaluate numerically the influence of the bandwidth of the optical system on the decrypted digital data. The bit error rate as a function of the optical system bandwidth is presented.

© 1999 Optical Society of America

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1999 (1)

1998 (2)

1997 (2)

1996 (2)

F. Zhao, K. Sayano, “Compact read-only memory with lensless phase-conjugate holograms,” Opt. Lett. 21, 1295–1297 (1996).
[CrossRef] [PubMed]

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

1995 (2)

1994 (2)

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

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

1993 (3)

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]

An, X.

Bashaw, M. C.

H. F. Heanue, M. C. Bashaw, L. Hesselink, “Encrypted holographic data storage based on orthogonal-phase-code multiplexing,” Appl. Opt. 34, 6012–6015 (1995).
[CrossRef] [PubMed]

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Bollaro, F.

Burr, G. W.

Chatwin, C. R.

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

Goudail, F.

Heanue, H. F.

Heanue, J. F.

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Hesselink, L.

H. F. Heanue, M. C. Bashaw, L. Hesselink, “Encrypted holographic data storage based on orthogonal-phase-code multiplexing,” Appl. Opt. 34, 6012–6015 (1995).
[CrossRef] [PubMed]

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

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.

Joseph, J.

Kang, Y. H.

Kim, K. H.

Lee, B.

Leyva, V.

Li, H.-Y.

Li, J.

Midwinter, J. E.

Mok, F. H.

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

Paek, E. G.

C. L. Wilson, C. I. Watson, E. G. Paek, “Combined optical neural network fingerprint matching,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 373–382 (1997).
[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]

Psaltis, D.

Qiao, Y.

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]

Sayano, K.

Selviah, D. R.

Singh, K.

Tao, S.

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.

Wang, R. K.

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

Watson, C. I.

C. L. Wilson, C. I. Watson, E. G. Paek, “Combined optical neural network fingerprint matching,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 373–382 (1997).
[CrossRef]

Watson, I. A.

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

Wilson, C. L.

C. L. Wilson, C. I. Watson, E. G. Paek, “Combined optical neural network fingerprint matching,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 373–382 (1997).
[CrossRef]

Yariv, A.

Zhang, G.

Zhao, F.

Appl. Opt. (5)

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

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. (2)

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

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

Opt. Lett. (6)

Science (1)

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Other (1)

C. L. Wilson, C. I. Watson, E. G. Paek, “Combined optical neural network fingerprint matching,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 373–382 (1997).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Illustration of the encrypted optical memory system with angular multiplexing: BS, beam splitter; L’s, lenses; FP, Fourier plane.

Fig. 2
Fig. 2

Experimental setup: RPM’s, random phase masks; BS’s, beam splitters; L’s, lenses; M’s, mirrors; BE, beam expander; SH’s, shutters; Ar+ laser, argon-ion laser; FP, Fourier plane.

Fig. 3
Fig. 3

Three original images to be encrypted.

Fig. 4
Fig. 4

Magnitude squared encrypted images.

Fig. 5
Fig. 5

Decrypted images obtained by use of the correct key, which is the same phase mask at the same location used in the recording process.

Fig. 6
Fig. 6

Reconstructed digital data of Fig. 5(b): (a) data where the intensity at each cell was calculated from Fig. 5(b), (b) the digitalized data by application of the computed threshold.

Fig. 7
Fig. 7

Decrypted images when the incorrect keys were used.

Fig. 8
Fig. 8

Illustration of the optical encrypted memory system with limited bandwidth in the Fourier plane.

Fig. 9
Fig. 9

Bit error rate as a function of the percentage of Fourier-plane blocking.

Equations (8)

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

Siν, η=Giν, ηHiν, η,
Giν, η=Fgix, yexp-jnix, y.
ϕν, η=i=1M |Siν, η+Riν, η|2,
six, y=gix, yexp-jnix, y Fexp-jhiν, η,
Siν, η=Gi*ν, ηHi*ν, ηKiν, η,
Kiν, η=exp-jkiν, η.
six, y=gi*x, yexpjnix, y  Cix, y,
Cix, y=Fexp-jhiν, η  Fexp-jtiν, η.

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