Abstract

We investigate the shift-tolerance property of the decrypting phase mask in an optical double-random phase-encoding encryption system. A simple method for improving the shift tolerance of the phase mask is proposed. We demonstrate how the robustness to data loss of the encrypted image extends the shift tolerance of the decrypting phase mask. The signal-to-noise ratio is calculated. Both a computer simulation and an experiment are presented.

© 2000 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. J. Rodolfo, H. Rabenbach, J.-P. Huignard, “Performance of a photorefractive joint transform correlator for fingerprint identification,” Opt. Eng. 34, 1166–1171 (1995).
    [CrossRef]
  3. P. Réfrégier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
    [CrossRef] [PubMed]
  4. L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
    [CrossRef]
  5. S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2470–2472 (1996).
    [CrossRef]
  6. 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]
  7. B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double random phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
    [CrossRef]
  8. B. Javidi, A. Sergent, E. Ahouzi, “Performance of double random phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
    [CrossRef]
  9. B. Javidi, E. Ahouzi, “Optical security system with Fourier plane encoding,” Appl. Opt. 37, 6247–6255 (1998).
    [CrossRef]
  10. O. Matoba, B. Javidi, “Encrypted optical storage with angular multiplexing,” Appl. Opt. 38, 7288–7293 (1999).
    [CrossRef]
  11. G. Unnikrishnan, J. Joseph, K. Singh, “Optical encryption system that uses phase conjugation in a photorefractive crystal,” Appl. Opt. 37, 8181–8186 (1998).
    [CrossRef]

1999 (1)

1998 (3)

1997 (1)

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

1996 (3)

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

S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2470–2472 (1996).
[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]

1995 (2)

J. Rodolfo, H. Rabenbach, J.-P. Huignard, “Performance of a photorefractive joint transform correlator for fingerprint identification,” Opt. Eng. 34, 1166–1171 (1995).
[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]

1994 (1)

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

Ahouzi, E.

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double random phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

B. Javidi, E. Ahouzi, “Optical security system with Fourier plane encoding,” Appl. Opt. 37, 6247–6255 (1998).
[CrossRef]

Guibert, L.

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

Horner, J. L.

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

Huignard, J.-P.

J. Rodolfo, H. Rabenbach, J.-P. Huignard, “Performance of a photorefractive joint transform correlator for fingerprint identification,” Opt. Eng. 34, 1166–1171 (1995).
[CrossRef]

Javidi, B.

O. Matoba, B. Javidi, “Encrypted optical storage with angular multiplexing,” Appl. Opt. 38, 7288–7293 (1999).
[CrossRef]

B. Javidi, E. Ahouzi, “Optical security system with Fourier plane encoding,” Appl. Opt. 37, 6247–6255 (1998).
[CrossRef]

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double random phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

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

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.

Lai, S.

S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2470–2472 (1996).
[CrossRef]

Li, J.

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]

Matoba, O.

Neto, L. G.

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

Rabenbach, H.

J. Rodolfo, H. Rabenbach, J.-P. Huignard, “Performance of a photorefractive joint transform correlator for fingerprint identification,” Opt. Eng. 34, 1166–1171 (1995).
[CrossRef]

Réfrégier, P.

Rodolfo, J.

J. Rodolfo, H. Rabenbach, J.-P. Huignard, “Performance of a photorefractive joint transform correlator for fingerprint identification,” Opt. Eng. 34, 1166–1171 (1995).
[CrossRef]

Sergent, A.

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double random phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

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

Unnikrishnan, G.

Zhang, G.

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

Appl. Opt. (3)

Opt. Eng. (7)

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

J. Rodolfo, H. Rabenbach, J.-P. Huignard, “Performance of a photorefractive joint transform correlator for fingerprint identification,” Opt. Eng. 34, 1166–1171 (1995).
[CrossRef]

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

S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2470–2472 (1996).
[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]

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

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double random phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

Opt. Lett. (1)

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of the optical double-random phase-encoding encryption system: (a) encryption setup, (b) decryption setup.

Fig. 2
Fig. 2

(a) Original binary image of character E, (b) double-random phase-encrypted image of character E, (c) half the encrypted image is blocked, (d) 3/4 the encrypted image is blocked, (e) 7/8 the encrypted image is blocked.

Fig. 3
Fig. 3

(a), (b), (c), and (d) are decrypted images of Figs. 2(b), 2(c), 2(d), and 2(e), respectively, while the decrypting key is placed at the matching position.

Fig. 4
Fig. 4

(a), (b), (c), and (d) are decrypted images of Figs. 2(b), 2(c), 2(d), and 2(e), respectively, while the decrypting key is shifted for one pixel transversely.

Fig. 5
Fig. 5

(a), (b), (c), and (d) are decrypted images of Figs. 2(b), 2(c), 2(d), and 2(e), respectively, while the decrypting key is shifted for two pixel transversely.

Fig. 6
Fig. 6

(a), (b), (c), and (d) are decrypted images of Figs. 2(b), 2(c), 2(d), and 2(e), respectively, while the decrypting key is shifted for three pixel transversely.

Fig. 7
Fig. 7

Experimental setup: M, mirror; BS, beam splitter; SF, spatial filter; PH, pinhole; D, power detector; CL, collimating lens; GG, ground glass; FL, Fourier lens; S, shutter.

Fig. 8
Fig. 8

Experimental results. Circles, measured data when all the encrypted data recorded in the crystal were used for decryption. Squares, measured data when half the crystal surface is blocked. Solid and dashed curves, normalized intensity of point source predicted by Eq. (8) when all and half the encrypted data, respectively, are used.

Fig. 9
Fig. 9

Experimental setup for measuring the effective pixel size of the ground glass. The LiNbO3 crystal is placed closely behind the ground glass. Experimental setup: M, mirror; BS, beam splitter; SF, spatial filter; PH, pinhole; D, power detector; CL, collimating lens; GG, ground glass; S, shutter.

Fig. 10
Fig. 10

Normalized diffraction intensity with respect to the displacement of the ground glass when the LiNbO3 crystal is placed closely behind the ground glass to record the index gratings.

Equations (10)

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qx=fxexpi2πϕx * hx,
Qu, Δ=Duexpi2πΨu-Ψu-Δ/λf,
SNR=ND-Δ2/Δ2,
qx=n=0M-1 fnexpi2πϕnhx-n,
qxrectxΩ=n=0M-1fnexpi2πϕn×hx-n * rectxΩ=n=0M-1fnexpi2πϕnexp-i2πnu×expi2πΨu * Ω sincΩu=n=0M-1Ωfnexpi2πϕn×ξ=0N-1exp-i2πnξ×expi2πΨξsincΩu-ξ,
qxrectxΩ=n=0M-1Ωfnexpi2πϕnsincΩΔλfexp-i2πnu-Δλfexpi2πΨu-Δλf+Ωfnexpi2πϕnξu-Δ/λfN-1exp-i2πnξexpi2πΨξsincΩu-ξ=n=0M-1Ωfnexpi2πϕnsincΩΔλfexp-i2πnu-Δλfexpi2πΨu-Δλf+Ru, n.
fdx=n=0M-1Ω sincΩΔλffnexpi2πϕn×exp-i2πΔλf nδx-n+rx, n=Ω sincΩΔλffxexpi2πϕx×exp-i2πΔλf x+n=0M-1 rx, n,
|fdx|2=Ω2 sinc2ΩΔλf|fx|2+n=0M-1 rx, n,
|fdx|2=Ω2|fx|2+n=0M-1 rx, n.
SNR=NΩ2 sinc2ΩΔ/λfMΩ-Ω2 sinc2ΩΔ/λf.

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