Abstract

We show that multiple secure data recording under a wavelength multiplexing technique is possible in a joint transform correlator (JTC) arrangement. We evaluate both the performance of the decrypting procedure and the influence of the input image size when decrypting with a wavelength different from that employed in the encryption step. This analysis reveals that the wavelength is a valid parameter to conduct image multiplexing encoding with the JTC architecture. In addition, we study the influence of the minimum wavelength change that prevents decoding cross talk. Computer simulations confirm the performance of the proposed technique.

© 2009 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2008 (1)

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Code retrieval via undercover multiplexing,” Optik (Jena) 119, 139-142 (2008).

2006 (3)

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encryption-decryption via lateral shifting of a random phase mask,” Opt. Commun. 259, 532-536 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33(2006).
[CrossRef]

2005 (1)

2004 (2)

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584-1586 (2004).
[CrossRef] [PubMed]

B. M. Hennelly and J. T. Sheridan, “Random phase and jigsaw encryption in the Fresnel domain,” Opt. Eng. 43, 2239-2249(2004).
[CrossRef]

2003 (1)

B. M. Hennelly and J. B. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Jena) 114, 251-265(2003).

2000 (8)

1999 (1)

O. Matoba and B. Javidi, “Encrypted optical storage with wavelength-key and random phase codes,” Appl. Opt. 38, 6785-6790 (1999).

1995 (2)

1993 (2)

Barrera, J. F.

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Code retrieval via undercover multiplexing,” Optik (Jena) 119, 139-142 (2008).

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encryption-decryption via lateral shifting of a random phase mask,” Opt. Commun. 259, 532-536 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33(2006).
[CrossRef]

Bashaw, M. C.

Bolognini, N.

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Code retrieval via undercover multiplexing,” Optik (Jena) 119, 139-142 (2008).

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encryption-decryption via lateral shifting of a random phase mask,” Opt. Commun. 259, 532-536 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33(2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

Chiou, A. E. T.

Heanue, J. F.

Henao, R.

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Code retrieval via undercover multiplexing,” Optik (Jena) 119, 139-142 (2008).

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encryption-decryption via lateral shifting of a random phase mask,” Opt. Commun. 259, 532-536 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33(2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

Hennelly, B. M.

B. M. Hennelly and J. T. Sheridan, “Random phase and jigsaw encryption in the Fresnel domain,” Opt. Eng. 43, 2239-2249(2004).
[CrossRef]

B. M. Hennelly and J. B. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Jena) 114, 251-265(2003).

Hesselink, L.

Javidi, B.

Joseph, J.

Kuroda, K.

Li, H.-Y. S.

Matoba, O.

Mok, F. H.

Nomura, T.

Opt, Appl.

O. Matoba and B. Javidi, “Encrypted optical storage with wavelength-key and random phase codes,” Appl. Opt. 38, 6785-6790 (1999).

Psaltis, D.

Qiao, Y.

Refregier, P.

Sheridan, J. B.

B. M. Hennelly and J. B. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Jena) 114, 251-265(2003).

Sheridan, J. T.

B. M. Hennelly and J. T. Sheridan, “Random phase and jigsaw encryption in the Fresnel domain,” Opt. Eng. 43, 2239-2249(2004).
[CrossRef]

Shimura, T.

Singh, K.

Situ, G.

Su, W.

Sun, C.

Tajahuerce, E.

Tan, X.

Tebaldi, M.

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Code retrieval via undercover multiplexing,” Optik (Jena) 119, 139-142 (2008).

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encryption-decryption via lateral shifting of a random phase mask,” Opt. Commun. 259, 532-536 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33(2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

Torroba, R.

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Code retrieval via undercover multiplexing,” Optik (Jena) 119, 139-142 (2008).

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encryption-decryption via lateral shifting of a random phase mask,” Opt. Commun. 259, 532-536 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33(2006).
[CrossRef]

Unnikrishnan, G.

Verrall, S. C.

Wang, B.

Zhang, J.

Appl. Opt. (7)

Opt. Commun. (3)

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encryption-decryption via lateral shifting of a random phase mask,” Opt. Commun. 259, 532-536 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33(2006).
[CrossRef]

Opt. Eng. (2)

B. M. Hennelly and J. T. Sheridan, “Random phase and jigsaw encryption in the Fresnel domain,” Opt. Eng. 43, 2239-2249(2004).
[CrossRef]

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031-2035 (2000).
[CrossRef]

Opt. Lett. (6)

Optik (Jena) (2)

B. M. Hennelly and J. B. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Jena) 114, 251-265(2003).

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Code retrieval via undercover multiplexing,” Optik (Jena) 119, 139-142 (2008).

Other (1)

O. Matoba and B. Javidi, “Encrypted optical storage with wavelength-key and random phase codes,” Appl. Opt. 38, 6785-6790 (1999).

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Figures (5)

Fig. 1
Fig. 1

JTC scheme used in the proposal: (a) write-in step and (b) read-out step, where L is a lens, f is the focal length ( f = 5 cm ), and g ( x ) and r ( x ) are random-phase masks.

Fig. 2
Fig. 2

Results showing the reconstruction of the encrypted input data, the word CIOP, for different input pixel size and for a read-out wavelength shifted with respect to that used in the write-in step. The MSE value is listed for the shifted wavelength reconstruction cases.

Fig. 3
Fig. 3

MSE in terms of the read-out wavelengths. Note that the write-in wavelength is 640 nm .

Fig. 4
Fig. 4

Multiplexing decrypted images, each one reading out with the wavelength as they were encrypted.

Fig. 5
Fig. 5

One channel recovered image sequences that correspond to encrypted N input images. The input image size is 400 × 400 pixels.

Equations (10)

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JPS ( ν ) = | F [ r ( x a ) g ( x a ) + h ( x b ) ] | 2 = | R ( ν ) G ( ν ) | 2 + 1 + [ R ( ν ) G ( ν ) ] * H ( ν ) exp [ 2 i π ( b a ) ν ] + [ R ( ν ) G ( ν ) ] H * ( ν ) exp [ 2 i π ( a b ) ν ] ,
JPS ( x ) = [ r ( x ) g ( x ) ] [ r ( x ) g ( x ) ] + δ ( x ) + h ( x ) [ r ( x ) g ( x ) ] δ ( x b + a ) + [ r ( x ) g ( x ) ] h ( x ) δ ( x a + b ) ,
M ( ν ) = JPS ( ν ) H ( ν ) exp [ 2 π i b ν ] = | R ( ν ) G ( ν ) | 2 H ( ν ) exp [ 2 π i b ν ] + H ( ν ) exp [ 2 π i b ν ] + [ R ( ν ) G ( ν ) ] * H ( ν ) H ( ν ) exp [ 2 π i ( 2 b a ) ν ] + R ( ν ) G ( ν ) exp [ 2 π i a ν ] .
m ( x ) = h ( x ) [ r ( x ) g ( x ) ] [ r ( x ) g ( x ) ] δ ( x b ) + h ( x ) δ ( x b ) + h ( x ) h ( x ) [ r ( x ) g ( x ) ] δ ( x 2 b a ) + r ( x ) g ( x ) δ ( x a ) .
IR ( x , x 0 , f , λ + Δ λ ) = exp [ 2 π i f / ( λ + Δ λ ) ] i ( λ + Δ λ ) f exp { i π ( λ + Δ λ ) f [ x x 0 ] 2 } ,
1 λ + Δ λ = 1 λ Δ λ λ 2 .
W ( ν ) = K ( ν ) exp [ 2 π i ( Φ ( η ν ) Φ ( ν ) ) ] ,
w ( x ) = r ( x ) g ( x ) F [ exp [ 2 π i ( Φ ( η ν ) Φ ( ν ) ) ] ] ,
g ^ i ( x ) = g i ( x ) + n ( x ) ,
n ( x ) = j = 1 N w j ( x , λ i + Δ λ i j ) , i = 1 N ,

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