Abstract

A novel technique for multiplexing complex images is proposed in which each image may be demultiplexed only if a set of random encryption keys is known. The technique utilizes the ability of the double random phase encoding method to spread a signals’ energy in both the space and the spatial frequency domains in a controlled manner. To multiplex, images are independently encrypted with different phase keys and then superimposed by recording sequentially on the same material. Each image is extracted by using the particular key associated with it. During decryption the energy from the other images is further spread, making it possible to minimize its effects by using suitable filters. Wigner analysis is applied to the technique, and numerical results are presented.

© 2007 Optical Society of America

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References

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2006 (3)

G. Situ and J. J. Zhang, J. Opt. A, Pure Appl. Opt. 8, 391 (2006).
[CrossRef]

T. Nomura, E. Nitanai, T. Numata, and B. Javidi, Opt. Eng. 45, 1 (2006).
[CrossRef]

O. Matoba, Y. Yokohama, M. Miura, K. Nitta, and T. Yoshimura, Appl. Opt. 45, 3270 (2006).
[CrossRef] [PubMed]

2004 (2)

W. C. Su and C. H. Lin, Appl. Opt. 43, 2298 (2004).
[CrossRef] [PubMed]

L. Hesselink, S. S. Orlov, and M. C. Bashaw, Proc. IEEE 92, 1231 (2004).
[CrossRef]

2003 (2)

B. M. Hennelly and J. T. Sheridan, Optik (Stuttgart) 114, 251 (2003).
[CrossRef]

B. Hennelly and J. T. Sheridan, Opt. Lett. 28, 269 (2003).
[CrossRef] [PubMed]

2001 (1)

1999 (1)

1997 (1)

1995 (2)

1982 (1)

1977 (1)

Bashaw, M. C.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, Proc. IEEE 92, 1231 (2004).
[CrossRef]

J. F. Heanue, M. C. Bashaw, and L. Hesselink, Appl. Opt. 34, 6021 (1995).
[CrossRef]

Caulfield, H. J.

H. J. Caulfield, D. Psaltis, and G. Sincerbox, Holographic Data Storage (Springer-Verlag, 2000).

Hagler, M. O.

Heanue, J. F.

Hennelly, B.

Hennelly, B. M.

B. M. Hennelly and J. T. Sheridan, Optik (Stuttgart) 114, 251 (2003).
[CrossRef]

Hesselink, L.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, Proc. IEEE 92, 1231 (2004).
[CrossRef]

J. F. Heanue, M. C. Bashaw, and L. Hesselink, Appl. Opt. 34, 6021 (1995).
[CrossRef]

Javidi, B.

Kral, E. L.

Krile, T. F.

Kuroda, K.

Li, J.

Lin, C. H.

Marks, R. J.

Matoba, O.

Miura, M.

Nitanai, E.

T. Nomura, E. Nitanai, T. Numata, and B. Javidi, Opt. Eng. 45, 1 (2006).
[CrossRef]

Nitta, K.

Nomura, T.

T. Nomura, E. Nitanai, T. Numata, and B. Javidi, Opt. Eng. 45, 1 (2006).
[CrossRef]

Numata, T.

T. Nomura, E. Nitanai, T. Numata, and B. Javidi, Opt. Eng. 45, 1 (2006).
[CrossRef]

Orlov, S. S.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, Proc. IEEE 92, 1231 (2004).
[CrossRef]

Psaltis, D.

H. J. Caulfield, D. Psaltis, and G. Sincerbox, Holographic Data Storage (Springer-Verlag, 2000).

Refregier, P.

Sheridan, J. T.

B. Hennelly and J. T. Sheridan, Opt. Lett. 28, 269 (2003).
[CrossRef] [PubMed]

B. M. Hennelly and J. T. Sheridan, Optik (Stuttgart) 114, 251 (2003).
[CrossRef]

Shimura, T.

Sincerbox, G.

H. J. Caulfield, D. Psaltis, and G. Sincerbox, Holographic Data Storage (Springer-Verlag, 2000).

Situ, G.

G. Situ and J. J. Zhang, J. Opt. A, Pure Appl. Opt. 8, 391 (2006).
[CrossRef]

Su, W. C.

Tan, X.

Walkup, J. F.

Yokohama, Y.

Yoshimura, T.

Zhang, G.

Zhang, J. J.

G. Situ and J. J. Zhang, J. Opt. A, Pure Appl. Opt. 8, 391 (2006).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Wigner volumes at different planes in the multiplexing and demultiplexing process. E n , energy density.

Fig. 2
Fig. 2

Decryption–demultiplexing scheme.

Fig. 3
Fig. 3

Images before and after we multiplex and demultiplex.

Tables (1)

Tables Icon

Table 1 Quantifying the Spreading

Equations (5)

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ψ { u ( x ) } ( x , k x ) = u ( x ϵ 2 ) u * ( x + ϵ 2 ) e i 2 π k x ϵ d ϵ ,
u ( x ) 0 , x > W , u ( x ) e i 2 π k x x d x 0 , k x > B .
E = ψ { u ( x ) } ( x , k x ) d x d k x .
ψ { u ( x ) v ( x ) } ( x , k x ) = ψ { u ( x ) } ( x , k x k ) ψ { v ( x ) } ( x , k x ) d k .
E ( Width x ) ( Width y ) ( Width k x ) ( Width k y ) .

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