Abstract

We describe an encrypted optical memory that uses double-random phase encoding at the input plane and the Fourier plane. This technique allows the images to be stored as independent white complex stationary processes. Experimental results and computer simulations are presented.

© 1997 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. Ph. Refregier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
    [CrossRef] [PubMed]
  3. D. Psaltis, “Optical memory disks in optical information processing,” Appl. Opt. 29, 2038–2057 (1990).
    [CrossRef] [PubMed]
  4. M. A. Neifeld, D. Psaltis, “Programmable image associative memory using an optical disk and a photorefractive crystal,” Appl. Opt. 32, 4398–4409 (1993).
    [CrossRef] [PubMed]
  5. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967).
  6. E. N. Leith, J. Upatneiks, “Holograms: their properties and uses,” SPIE J. 4, 3–6 (1966).
  7. J. 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]
  8. A. Papoulis, Probability, Random Variable, and Stochastic Processes, 2nd ed. (McGraw-Hill, New York, 1984).
  9. R. J. Collier, B. Burckhardt, L. H. Lin, “Hologram recording materials,” in Optical Holography (Academic, New York, 1971), Chap. 10.

1995 (2)

1994 (1)

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

1993 (1)

1990 (1)

1966 (1)

E. N. Leith, J. Upatneiks, “Holograms: their properties and uses,” SPIE J. 4, 3–6 (1966).

Bashaw, M. C.

Burckhardt, B.

R. J. Collier, B. Burckhardt, L. H. Lin, “Hologram recording materials,” in Optical Holography (Academic, New York, 1971), Chap. 10.

Collier, R. J.

R. J. Collier, B. Burckhardt, L. H. Lin, “Hologram recording materials,” in Optical Holography (Academic, New York, 1971), Chap. 10.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967).

Heanue, J. F.

Hesselink, L.

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.

Ph. Refregier, 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]

Leith, E. N.

E. N. Leith, J. Upatneiks, “Holograms: their properties and uses,” SPIE J. 4, 3–6 (1966).

Lin, L. H.

R. J. Collier, B. Burckhardt, L. H. Lin, “Hologram recording materials,” in Optical Holography (Academic, New York, 1971), Chap. 10.

Neifeld, M. A.

Papoulis, A.

A. Papoulis, Probability, Random Variable, and Stochastic Processes, 2nd ed. (McGraw-Hill, New York, 1984).

Psaltis, D.

Refregier, Ph.

Upatneiks, J.

E. N. Leith, J. Upatneiks, “Holograms: their properties and uses,” SPIE J. 4, 3–6 (1966).

Appl. Opt. (3)

Opt. Eng. (1)

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

Opt. Lett. (1)

SPIE J. (1)

E. N. Leith, J. Upatneiks, “Holograms: their properties and uses,” SPIE J. 4, 3–6 (1966).

Other (3)

A. Papoulis, Probability, Random Variable, and Stochastic Processes, 2nd ed. (McGraw-Hill, New York, 1984).

R. J. Collier, B. Burckhardt, L. H. Lin, “Hologram recording materials,” in Optical Holography (Academic, New York, 1971), Chap. 10.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967).

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Figures (3)

Fig. 1
Fig. 1

Optical setup used to demonstrate the encrypted optical memory: CL, collimating lens; M, mirrors; BS, beam splitter; L, Fourier-transform lenses; S1, shutter.

Fig. 2
Fig. 2

Experimental results of encryption and decryption: (a) Images of E and Q used for encrypted memory. (b) Encrypted holographic optical memory with E and Q stored. Different masks are used for the encryption. (c) Decryption of E and Q from the memory shown in (b). The corresponding authorized codes are used for the decryption. (d) Decryption result when a wrong code is used.

Fig. 3
Fig. 3

Computer simulation for decrypting a memory where the image E is stored by use of 256 × 256 random phase codes. The image E is recovered when a different system bandwidth is used. (a) Original image of E. (b) Decrypted image of E with a system bandwidth of 200 × 200 pixels. (c) Decrypted image of E with a system bandwidth of 100 × 100 pixels. (d) Decrypted image of E with a system bandwidth of 50 × 50 pixels.

Equations (9)

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ϕx, y=i=1Mfix, yexpjnix, y*μix, y,
ϕξ=i=1Mfiξexpjniξ*μiξ,
fkξ=ϕξμkξ=fkξexpjnkξ+i=1ikMfiξ×expjniξ*μiξμkξ=fkξexpjnkξ+i=1ikMfiξexpjniξ*μiξ,
P=1Ni=1ikM ξ=0N-1 fiξ2=1NEtotal-Ek,
Ek=ξ=0N-1 fkξ2
Etotal=i=1M ξ=0N-1 fiξ2.
SNRkEnergy of the restored image EkEnergy of the noise overlapping the stored image fkξ.
SNRk=NEkNkEtotal-Ek.
SNRk=NNkM-1.

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