Abstract

The mismatch in the number of degrees of freedom supported by volume holograms and the boundary fields that control them limits the dynamic range of recorded holograms. For holograms controlled by using fractal sampling grids, the maximum dynamic range falls inversely with the minimum number of exposures needed to record the hologram, the rank of the hologram. In adaptive holography, feedback between coupled holograms prevents the dynamic range from decreasing faster than the fundamental limit. If the control problem is overcome, the maximum dynamic range that a hologram can support falls inversely with the square root of the rank. In principle, holograms in which the dynamic range falls inversely with the square root of the rank can be recorded by using cross-spectrally coherent polychromatic pulses.

© 1992 Optical Society of America

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  1. P. J. van Heerden, “Theory of optical information storage in solids,” Appl. Opt. 2, 393–400 (1963).
    [CrossRef]
  2. A. Kozma, E. S. Barrekette, eds., Special issue on optical storage of digital data, Appl. Opt.13, (4) (1974).
    [CrossRef]
  3. N. H. Farhat, D. Psaltis, A. Prata, E. Paek, “Optical implementation of the Hopfield model,” Appl. Opt. 24, 1469–1475 (1985).
    [CrossRef] [PubMed]
  4. D. Z. Anderson, “Coherent optical eigenstate memory,” Opt. Lett. 11, 56–58 (1986).
    [CrossRef] [PubMed]
  5. D. Psaltis, D. J. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
    [CrossRef]
  6. D. Psaltis, D. J. Brady, X.-G. Gu, S. Lin, “Holography in artificial neural networks,” Nature (London) 343, 325–330 (1990).
    [CrossRef]
  7. G. Carpenter, S. Grossberg, eds., special issue on neural networks, Appl. Opt.26(23) (1987).
  8. A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–224 (1990).
    [CrossRef]
  9. E. S. Maniloff, K. M. Johnson, “Dynamic holographic interconnects using static holograms,” Opt. Eng. 29, 225–229 (1990).
    [CrossRef]
  10. M. Cabrera, J. Y. Jezequel, J. C. Andre, “Three-dimensional machining by laser photopolymerization,” in Lasers in Polymer Science Technology (CRC, Boca Raton, Fla., 1990), pp. 73–95.
  11. S. Hunter, F. Kiamilev, S. Esener, D. A. Parthenopoulos, P. M. Rentzepis, “Potentials of 2-photon based 3-D optical memories for high-performance computing,” Appl. Opt. 29, 2058–2066 (1990).
    [CrossRef] [PubMed]
  12. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
    [CrossRef]
  13. D. L. Staebler, Second International Conference on Electro-Photography (Society for Imaging Science and Technology, Chicago, Ill., 1974), p. 210.
  14. K. Bløtekjaer, “Limitations on holographic storage capacity of photochromic and photorefractive media,” Appl. Opt. 18, 57–67 (1979).
    [CrossRef] [PubMed]
  15. R. A. Bartolini, A. Bloom, J. S. Escher, “Volume holographic recording characteristics of an organic medium,” Appl. Opt. 15, 1261–1265 (1976).
    [CrossRef] [PubMed]
  16. T. Todorov, L. Nikolova, N. Tomova, V. Dragostinova, “Photoinduced anisotropy in rigid dye solutions for transient polarization holography,” IEEE J. Quantum Electron. QE-22, 1262–1267 (1986).
    [CrossRef]
  17. P. Gunter, J.-P. Huignard, eds., Photorefractive Materials and Their Applications I and II (Springer-Verlag, Berlin, 1989), Vols. I and II.
  18. W. J. Tomlinson, E. A. Chandross, “Organic photochemical refractive-index image recording systems,” Adv. Photochem. 12, 201–281 (1980).
    [CrossRef]
  19. I.-C. Khoo, R. Nomarndin, “The mechanism and dynamics of transient thermal gradient diffraction in pneumatic liquid crystal films,” IEEE J. Quantum Electron. QE-21, 329–335 (1985).
    [CrossRef]
  20. J. H. Wendorff, M. Eich, “Nonlinear optical phenomena in liquid crystalline side chain polymers,” Mol. Cryst. Liq. Cryst. 169, 133–166 (1989).
    [CrossRef]
  21. H. Lee, X. G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal crosstalk,” J. Appl. Phys. 65, 2191–2194 (1989).
    [CrossRef]
  22. D. Psaltis, X. G. Gu, D. Brady, “Holographic implementations of neural networks,” in An Introduction to Neural and Electronic Networks, S. F. Zornetzer, J. L. Davis, C. Lau, eds. (Academic, New York, 1989), pp. 339–348.
  23. See, for example, C.-T. Chen, Linear System Theory and Design (Holt, Rinehart & Winston, New York, 1984), p. 569.
  24. N. V. Kuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–956 (1979).
    [CrossRef]
  25. W. J. Burke, P. Sheng, “Crosstalk noise from multiple thick phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
    [CrossRef]
  26. D. J. Brady, “Photorefractive volume holography in artificial neural networks,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1990).
  27. J. E. Ford, S. H. Lee, Y. Fainman, “Application of photo-refractive crystals to optical interconnection,” in Digital Optical Computing II, R. Arrathoon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1215, 155–163 (1990).
    [CrossRef]
  28. F. Mok, M. Tackitt, H. M. Stoll, “Massively parallel optical template matcher/correlator,” in Optical Society of America 1990 Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 211 (A).
  29. F. Mok, M. Tackitt, H. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3crystal,” Opt. Lett. 16, 605–608 (1991).
    [CrossRef] [PubMed]
  30. D. J. Brady, K. Hsu, D. Psaltis, “Periodically refreshed multiply exposed photorefractive holograms,” Opt. Lett. 15, 817–820 (1990).
    [CrossRef] [PubMed]
  31. J. Hong, P. Yeh, D. Psaltis, D. J. Brady, “Diffraction efficiency of strong volume holograms,” Opt. Lett. 15, 344–346 (1990).
    [CrossRef] [PubMed]
  32. R. A. Bartolini, A. Bloom, J. S. Escher, “Multiple storage of holograms in an organic medium,” Appl. Phys. Lett. 28, 506–508 (1976).
    [CrossRef]
  33. J. M. Heaton, L. Solymar, “Transient energy transfer during hologram formation in photorefractive crystals,” Opt. Acta 32, 397–400 (1985).
    [CrossRef]
  34. D. J. Brady, D. Psaltis, “Perceptron learning in optical neural computers,” in Optical Computing: Proceedings of the 34th Scottish Universities Summer School in Physics, B. S. Wherrett, F. A. P. Tooley, eds. (Edinburgh U. Press, Edinburgh, Scotland, 1988), pp. 251–265.
  35. H. Yoshinaga, K. Kitayama, T. Hara, “Experimental learning in an optical perceptronlike neural network,” Opt. Lett. 14, 716–718 (1989).
    [CrossRef] [PubMed]
  36. E. G. Paek, J. R. Wullert, J. S. Patel, “Holographic implementation of a learning machine based on a multicategory perceptron algorithm,” Opt. Lett. 14, 1303–1305 (1989).
    [CrossRef] [PubMed]
  37. D. Z. Anderson, M. C. Erie, “Resonator memories and optical novelty filters,” Opt. Eng. 26, 434–444 (1987).
    [CrossRef]
  38. P. Saari, R. Kaarli, A. Rebane, “Picosecond time- and space-domain holography by photochemical hole burning,” J. Opt. Soc. Am. B 3, 527–533 (1986).
    [CrossRef]

1991

1990

D. J. Brady, K. Hsu, D. Psaltis, “Periodically refreshed multiply exposed photorefractive holograms,” Opt. Lett. 15, 817–820 (1990).
[CrossRef] [PubMed]

J. Hong, P. Yeh, D. Psaltis, D. J. Brady, “Diffraction efficiency of strong volume holograms,” Opt. Lett. 15, 344–346 (1990).
[CrossRef] [PubMed]

D. Psaltis, D. J. Brady, X.-G. Gu, S. Lin, “Holography in artificial neural networks,” Nature (London) 343, 325–330 (1990).
[CrossRef]

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–224 (1990).
[CrossRef]

E. S. Maniloff, K. M. Johnson, “Dynamic holographic interconnects using static holograms,” Opt. Eng. 29, 225–229 (1990).
[CrossRef]

S. Hunter, F. Kiamilev, S. Esener, D. A. Parthenopoulos, P. M. Rentzepis, “Potentials of 2-photon based 3-D optical memories for high-performance computing,” Appl. Opt. 29, 2058–2066 (1990).
[CrossRef] [PubMed]

1989

J. H. Wendorff, M. Eich, “Nonlinear optical phenomena in liquid crystalline side chain polymers,” Mol. Cryst. Liq. Cryst. 169, 133–166 (1989).
[CrossRef]

H. Lee, X. G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal crosstalk,” J. Appl. Phys. 65, 2191–2194 (1989).
[CrossRef]

H. Yoshinaga, K. Kitayama, T. Hara, “Experimental learning in an optical perceptronlike neural network,” Opt. Lett. 14, 716–718 (1989).
[CrossRef] [PubMed]

E. G. Paek, J. R. Wullert, J. S. Patel, “Holographic implementation of a learning machine based on a multicategory perceptron algorithm,” Opt. Lett. 14, 1303–1305 (1989).
[CrossRef] [PubMed]

1988

1987

D. Z. Anderson, M. C. Erie, “Resonator memories and optical novelty filters,” Opt. Eng. 26, 434–444 (1987).
[CrossRef]

1986

P. Saari, R. Kaarli, A. Rebane, “Picosecond time- and space-domain holography by photochemical hole burning,” J. Opt. Soc. Am. B 3, 527–533 (1986).
[CrossRef]

D. Z. Anderson, “Coherent optical eigenstate memory,” Opt. Lett. 11, 56–58 (1986).
[CrossRef] [PubMed]

T. Todorov, L. Nikolova, N. Tomova, V. Dragostinova, “Photoinduced anisotropy in rigid dye solutions for transient polarization holography,” IEEE J. Quantum Electron. QE-22, 1262–1267 (1986).
[CrossRef]

1985

N. H. Farhat, D. Psaltis, A. Prata, E. Paek, “Optical implementation of the Hopfield model,” Appl. Opt. 24, 1469–1475 (1985).
[CrossRef] [PubMed]

I.-C. Khoo, R. Nomarndin, “The mechanism and dynamics of transient thermal gradient diffraction in pneumatic liquid crystal films,” IEEE J. Quantum Electron. QE-21, 329–335 (1985).
[CrossRef]

J. M. Heaton, L. Solymar, “Transient energy transfer during hologram formation in photorefractive crystals,” Opt. Acta 32, 397–400 (1985).
[CrossRef]

1980

W. J. Tomlinson, E. A. Chandross, “Organic photochemical refractive-index image recording systems,” Adv. Photochem. 12, 201–281 (1980).
[CrossRef]

1979

K. Bløtekjaer, “Limitations on holographic storage capacity of photochromic and photorefractive media,” Appl. Opt. 18, 57–67 (1979).
[CrossRef] [PubMed]

N. V. Kuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–956 (1979).
[CrossRef]

1977

W. J. Burke, P. Sheng, “Crosstalk noise from multiple thick phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

1976

R. A. Bartolini, A. Bloom, J. S. Escher, “Volume holographic recording characteristics of an organic medium,” Appl. Opt. 15, 1261–1265 (1976).
[CrossRef] [PubMed]

R. A. Bartolini, A. Bloom, J. S. Escher, “Multiple storage of holograms in an organic medium,” Appl. Phys. Lett. 28, 506–508 (1976).
[CrossRef]

1969

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

1963

Anderson, D. Z.

D. Z. Anderson, M. C. Erie, “Resonator memories and optical novelty filters,” Opt. Eng. 26, 434–444 (1987).
[CrossRef]

D. Z. Anderson, “Coherent optical eigenstate memory,” Opt. Lett. 11, 56–58 (1986).
[CrossRef] [PubMed]

Andre, J. C.

M. Cabrera, J. Y. Jezequel, J. C. Andre, “Three-dimensional machining by laser photopolymerization,” in Lasers in Polymer Science Technology (CRC, Boca Raton, Fla., 1990), pp. 73–95.

Bartolini, R. A.

R. A. Bartolini, A. Bloom, J. S. Escher, “Volume holographic recording characteristics of an organic medium,” Appl. Opt. 15, 1261–1265 (1976).
[CrossRef] [PubMed]

R. A. Bartolini, A. Bloom, J. S. Escher, “Multiple storage of holograms in an organic medium,” Appl. Phys. Lett. 28, 506–508 (1976).
[CrossRef]

Bloom, A.

R. A. Bartolini, A. Bloom, J. S. Escher, “Multiple storage of holograms in an organic medium,” Appl. Phys. Lett. 28, 506–508 (1976).
[CrossRef]

R. A. Bartolini, A. Bloom, J. S. Escher, “Volume holographic recording characteristics of an organic medium,” Appl. Opt. 15, 1261–1265 (1976).
[CrossRef] [PubMed]

Bløtekjaer, K.

Brady, D.

D. Psaltis, X. G. Gu, D. Brady, “Holographic implementations of neural networks,” in An Introduction to Neural and Electronic Networks, S. F. Zornetzer, J. L. Davis, C. Lau, eds. (Academic, New York, 1989), pp. 339–348.

Brady, D. J.

D. J. Brady, K. Hsu, D. Psaltis, “Periodically refreshed multiply exposed photorefractive holograms,” Opt. Lett. 15, 817–820 (1990).
[CrossRef] [PubMed]

D. Psaltis, D. J. Brady, X.-G. Gu, S. Lin, “Holography in artificial neural networks,” Nature (London) 343, 325–330 (1990).
[CrossRef]

J. Hong, P. Yeh, D. Psaltis, D. J. Brady, “Diffraction efficiency of strong volume holograms,” Opt. Lett. 15, 344–346 (1990).
[CrossRef] [PubMed]

D. Psaltis, D. J. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
[CrossRef]

D. J. Brady, “Photorefractive volume holography in artificial neural networks,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1990).

D. J. Brady, D. Psaltis, “Perceptron learning in optical neural computers,” in Optical Computing: Proceedings of the 34th Scottish Universities Summer School in Physics, B. S. Wherrett, F. A. P. Tooley, eds. (Edinburgh U. Press, Edinburgh, Scotland, 1988), pp. 251–265.

Burke, W. J.

W. J. Burke, P. Sheng, “Crosstalk noise from multiple thick phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

Cabrera, M.

M. Cabrera, J. Y. Jezequel, J. C. Andre, “Three-dimensional machining by laser photopolymerization,” in Lasers in Polymer Science Technology (CRC, Boca Raton, Fla., 1990), pp. 73–95.

Chandross, E. A.

W. J. Tomlinson, E. A. Chandross, “Organic photochemical refractive-index image recording systems,” Adv. Photochem. 12, 201–281 (1980).
[CrossRef]

Dragostinova, V.

T. Todorov, L. Nikolova, N. Tomova, V. Dragostinova, “Photoinduced anisotropy in rigid dye solutions for transient polarization holography,” IEEE J. Quantum Electron. QE-22, 1262–1267 (1986).
[CrossRef]

Eich, M.

J. H. Wendorff, M. Eich, “Nonlinear optical phenomena in liquid crystalline side chain polymers,” Mol. Cryst. Liq. Cryst. 169, 133–166 (1989).
[CrossRef]

Erie, M. C.

D. Z. Anderson, M. C. Erie, “Resonator memories and optical novelty filters,” Opt. Eng. 26, 434–444 (1987).
[CrossRef]

Escher, J. S.

R. A. Bartolini, A. Bloom, J. S. Escher, “Multiple storage of holograms in an organic medium,” Appl. Phys. Lett. 28, 506–508 (1976).
[CrossRef]

R. A. Bartolini, A. Bloom, J. S. Escher, “Volume holographic recording characteristics of an organic medium,” Appl. Opt. 15, 1261–1265 (1976).
[CrossRef] [PubMed]

Esener, S.

Fainman, Y.

J. E. Ford, S. H. Lee, Y. Fainman, “Application of photo-refractive crystals to optical interconnection,” in Digital Optical Computing II, R. Arrathoon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1215, 155–163 (1990).
[CrossRef]

Farhat, N. H.

Ford, J. E.

J. E. Ford, S. H. Lee, Y. Fainman, “Application of photo-refractive crystals to optical interconnection,” in Digital Optical Computing II, R. Arrathoon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1215, 155–163 (1990).
[CrossRef]

Gu, X. G.

H. Lee, X. G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal crosstalk,” J. Appl. Phys. 65, 2191–2194 (1989).
[CrossRef]

D. Psaltis, X. G. Gu, D. Brady, “Holographic implementations of neural networks,” in An Introduction to Neural and Electronic Networks, S. F. Zornetzer, J. L. Davis, C. Lau, eds. (Academic, New York, 1989), pp. 339–348.

Gu, X.-G.

D. Psaltis, D. J. Brady, X.-G. Gu, S. Lin, “Holography in artificial neural networks,” Nature (London) 343, 325–330 (1990).
[CrossRef]

Habiby, S. F.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–224 (1990).
[CrossRef]

Hara, T.

Heaton, J. M.

J. M. Heaton, L. Solymar, “Transient energy transfer during hologram formation in photorefractive crystals,” Opt. Acta 32, 397–400 (1985).
[CrossRef]

Hong, J.

Hsu, K.

Hubbard, W. M.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–224 (1990).
[CrossRef]

Hunter, S.

Jezequel, J. Y.

M. Cabrera, J. Y. Jezequel, J. C. Andre, “Three-dimensional machining by laser photopolymerization,” in Lasers in Polymer Science Technology (CRC, Boca Raton, Fla., 1990), pp. 73–95.

Johnson, K. M.

E. S. Maniloff, K. M. Johnson, “Dynamic holographic interconnects using static holograms,” Opt. Eng. 29, 225–229 (1990).
[CrossRef]

Kaarli, R.

Khoo, I.-C.

I.-C. Khoo, R. Nomarndin, “The mechanism and dynamics of transient thermal gradient diffraction in pneumatic liquid crystal films,” IEEE J. Quantum Electron. QE-21, 329–335 (1985).
[CrossRef]

Kiamilev, F.

Kitayama, K.

Kuktarev, N. V.

N. V. Kuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–956 (1979).
[CrossRef]

Lee, H.

H. Lee, X. G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal crosstalk,” J. Appl. Phys. 65, 2191–2194 (1989).
[CrossRef]

Lee, S. H.

J. E. Ford, S. H. Lee, Y. Fainman, “Application of photo-refractive crystals to optical interconnection,” in Digital Optical Computing II, R. Arrathoon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1215, 155–163 (1990).
[CrossRef]

Lin, S.

D. Psaltis, D. J. Brady, X.-G. Gu, S. Lin, “Holography in artificial neural networks,” Nature (London) 343, 325–330 (1990).
[CrossRef]

Maniloff, E. S.

E. S. Maniloff, K. M. Johnson, “Dynamic holographic interconnects using static holograms,” Opt. Eng. 29, 225–229 (1990).
[CrossRef]

Markov, V. B.

N. V. Kuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–956 (1979).
[CrossRef]

Marrakchi, A.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–224 (1990).
[CrossRef]

Mok, F.

F. Mok, M. Tackitt, H. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3crystal,” Opt. Lett. 16, 605–608 (1991).
[CrossRef] [PubMed]

F. Mok, M. Tackitt, H. M. Stoll, “Massively parallel optical template matcher/correlator,” in Optical Society of America 1990 Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 211 (A).

Nikolova, L.

T. Todorov, L. Nikolova, N. Tomova, V. Dragostinova, “Photoinduced anisotropy in rigid dye solutions for transient polarization holography,” IEEE J. Quantum Electron. QE-22, 1262–1267 (1986).
[CrossRef]

Nomarndin, R.

I.-C. Khoo, R. Nomarndin, “The mechanism and dynamics of transient thermal gradient diffraction in pneumatic liquid crystal films,” IEEE J. Quantum Electron. QE-21, 329–335 (1985).
[CrossRef]

Odulov, S. G.

N. V. Kuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–956 (1979).
[CrossRef]

Paek, E.

Paek, E. G.

Parthenopoulos, D. A.

Patel, J. S.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–224 (1990).
[CrossRef]

E. G. Paek, J. R. Wullert, J. S. Patel, “Holographic implementation of a learning machine based on a multicategory perceptron algorithm,” Opt. Lett. 14, 1303–1305 (1989).
[CrossRef] [PubMed]

Prata, A.

Psaltis, D.

D. Psaltis, D. J. Brady, X.-G. Gu, S. Lin, “Holography in artificial neural networks,” Nature (London) 343, 325–330 (1990).
[CrossRef]

D. J. Brady, K. Hsu, D. Psaltis, “Periodically refreshed multiply exposed photorefractive holograms,” Opt. Lett. 15, 817–820 (1990).
[CrossRef] [PubMed]

J. Hong, P. Yeh, D. Psaltis, D. J. Brady, “Diffraction efficiency of strong volume holograms,” Opt. Lett. 15, 344–346 (1990).
[CrossRef] [PubMed]

H. Lee, X. G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal crosstalk,” J. Appl. Phys. 65, 2191–2194 (1989).
[CrossRef]

D. Psaltis, D. J. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
[CrossRef]

N. H. Farhat, D. Psaltis, A. Prata, E. Paek, “Optical implementation of the Hopfield model,” Appl. Opt. 24, 1469–1475 (1985).
[CrossRef] [PubMed]

D. Psaltis, X. G. Gu, D. Brady, “Holographic implementations of neural networks,” in An Introduction to Neural and Electronic Networks, S. F. Zornetzer, J. L. Davis, C. Lau, eds. (Academic, New York, 1989), pp. 339–348.

D. J. Brady, D. Psaltis, “Perceptron learning in optical neural computers,” in Optical Computing: Proceedings of the 34th Scottish Universities Summer School in Physics, B. S. Wherrett, F. A. P. Tooley, eds. (Edinburgh U. Press, Edinburgh, Scotland, 1988), pp. 251–265.

Rebane, A.

Rentzepis, P. M.

Saari, P.

Sheng, P.

W. J. Burke, P. Sheng, “Crosstalk noise from multiple thick phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

Solymar, L.

J. M. Heaton, L. Solymar, “Transient energy transfer during hologram formation in photorefractive crystals,” Opt. Acta 32, 397–400 (1985).
[CrossRef]

Soskin, M. S.

N. V. Kuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–956 (1979).
[CrossRef]

Staebler, D. L.

D. L. Staebler, Second International Conference on Electro-Photography (Society for Imaging Science and Technology, Chicago, Ill., 1974), p. 210.

Stoll, H. M.

F. Mok, M. Tackitt, H. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3crystal,” Opt. Lett. 16, 605–608 (1991).
[CrossRef] [PubMed]

F. Mok, M. Tackitt, H. M. Stoll, “Massively parallel optical template matcher/correlator,” in Optical Society of America 1990 Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 211 (A).

Tackitt, M.

F. Mok, M. Tackitt, H. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3crystal,” Opt. Lett. 16, 605–608 (1991).
[CrossRef] [PubMed]

F. Mok, M. Tackitt, H. M. Stoll, “Massively parallel optical template matcher/correlator,” in Optical Society of America 1990 Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 211 (A).

Todorov, T.

T. Todorov, L. Nikolova, N. Tomova, V. Dragostinova, “Photoinduced anisotropy in rigid dye solutions for transient polarization holography,” IEEE J. Quantum Electron. QE-22, 1262–1267 (1986).
[CrossRef]

Tomlinson, W. J.

W. J. Tomlinson, E. A. Chandross, “Organic photochemical refractive-index image recording systems,” Adv. Photochem. 12, 201–281 (1980).
[CrossRef]

Tomova, N.

T. Todorov, L. Nikolova, N. Tomova, V. Dragostinova, “Photoinduced anisotropy in rigid dye solutions for transient polarization holography,” IEEE J. Quantum Electron. QE-22, 1262–1267 (1986).
[CrossRef]

van Heerden, P. J.

Vinetskii, V. L.

N. V. Kuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–956 (1979).
[CrossRef]

Wagner, K.

Wendorff, J. H.

J. H. Wendorff, M. Eich, “Nonlinear optical phenomena in liquid crystalline side chain polymers,” Mol. Cryst. Liq. Cryst. 169, 133–166 (1989).
[CrossRef]

Wolf, E.

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

Wullert, J. R.

Yeh, P.

Yoshinaga, H.

Adv. Photochem.

W. J. Tomlinson, E. A. Chandross, “Organic photochemical refractive-index image recording systems,” Adv. Photochem. 12, 201–281 (1980).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

R. A. Bartolini, A. Bloom, J. S. Escher, “Multiple storage of holograms in an organic medium,” Appl. Phys. Lett. 28, 506–508 (1976).
[CrossRef]

Ferroelectrics

N. V. Kuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–956 (1979).
[CrossRef]

IEEE J. Quantum Electron.

T. Todorov, L. Nikolova, N. Tomova, V. Dragostinova, “Photoinduced anisotropy in rigid dye solutions for transient polarization holography,” IEEE J. Quantum Electron. QE-22, 1262–1267 (1986).
[CrossRef]

I.-C. Khoo, R. Nomarndin, “The mechanism and dynamics of transient thermal gradient diffraction in pneumatic liquid crystal films,” IEEE J. Quantum Electron. QE-21, 329–335 (1985).
[CrossRef]

J. Appl. Phys.

W. J. Burke, P. Sheng, “Crosstalk noise from multiple thick phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

H. Lee, X. G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal crosstalk,” J. Appl. Phys. 65, 2191–2194 (1989).
[CrossRef]

J. Opt. Soc. Am. B

Mol. Cryst. Liq. Cryst.

J. H. Wendorff, M. Eich, “Nonlinear optical phenomena in liquid crystalline side chain polymers,” Mol. Cryst. Liq. Cryst. 169, 133–166 (1989).
[CrossRef]

Nature (London)

D. Psaltis, D. J. Brady, X.-G. Gu, S. Lin, “Holography in artificial neural networks,” Nature (London) 343, 325–330 (1990).
[CrossRef]

Opt. Acta

J. M. Heaton, L. Solymar, “Transient energy transfer during hologram formation in photorefractive crystals,” Opt. Acta 32, 397–400 (1985).
[CrossRef]

Opt. Commun.

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

Opt. Eng.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–224 (1990).
[CrossRef]

E. S. Maniloff, K. M. Johnson, “Dynamic holographic interconnects using static holograms,” Opt. Eng. 29, 225–229 (1990).
[CrossRef]

D. Z. Anderson, M. C. Erie, “Resonator memories and optical novelty filters,” Opt. Eng. 26, 434–444 (1987).
[CrossRef]

Opt. Lett.

Other

A. Kozma, E. S. Barrekette, eds., Special issue on optical storage of digital data, Appl. Opt.13, (4) (1974).
[CrossRef]

M. Cabrera, J. Y. Jezequel, J. C. Andre, “Three-dimensional machining by laser photopolymerization,” in Lasers in Polymer Science Technology (CRC, Boca Raton, Fla., 1990), pp. 73–95.

G. Carpenter, S. Grossberg, eds., special issue on neural networks, Appl. Opt.26(23) (1987).

D. L. Staebler, Second International Conference on Electro-Photography (Society for Imaging Science and Technology, Chicago, Ill., 1974), p. 210.

P. Gunter, J.-P. Huignard, eds., Photorefractive Materials and Their Applications I and II (Springer-Verlag, Berlin, 1989), Vols. I and II.

D. Psaltis, X. G. Gu, D. Brady, “Holographic implementations of neural networks,” in An Introduction to Neural and Electronic Networks, S. F. Zornetzer, J. L. Davis, C. Lau, eds. (Academic, New York, 1989), pp. 339–348.

See, for example, C.-T. Chen, Linear System Theory and Design (Holt, Rinehart & Winston, New York, 1984), p. 569.

D. J. Brady, “Photorefractive volume holography in artificial neural networks,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1990).

J. E. Ford, S. H. Lee, Y. Fainman, “Application of photo-refractive crystals to optical interconnection,” in Digital Optical Computing II, R. Arrathoon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1215, 155–163 (1990).
[CrossRef]

F. Mok, M. Tackitt, H. M. Stoll, “Massively parallel optical template matcher/correlator,” in Optical Society of America 1990 Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 211 (A).

D. J. Brady, D. Psaltis, “Perceptron learning in optical neural computers,” in Optical Computing: Proceedings of the 34th Scottish Universities Summer School in Physics, B. S. Wherrett, F. A. P. Tooley, eds. (Edinburgh U. Press, Edinburgh, Scotland, 1988), pp. 251–265.

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Figures (11)

Fig. 1
Fig. 1

System for recording a volume hologram.

Fig. 2
Fig. 2

Geometry of the control signals on the wave normal surface.

Fig. 3
Fig. 3

System for constructing and monitoring holographic linear transformations.

Fig. 4
Fig. 4

Plot of [tn/τ(n)] versus exposure number. Plots are shown for values of F(α)/(α) from 0 to 1000. The data were calculated by using a numerical solution to Eq. (51).

Fig. 5
Fig. 5

Photograph of light diffracted from each of 111 gratings recorded in sequence. Each spot corresponds to the signal diffracted by a single grating.

Fig. 6
Fig. 6

Relative diffraction efficiency per grating versus the number of exposures for the data of Fig. 5.

Fig. 7
Fig. 7

System for periodically refreshing adaptive volume holograms.

Fig. 8
Fig. 8

System for maintaining adaptively recorded holograms, using continuous feedback.

Fig. 9
Fig. 9

Reconstruction of multiple independent images, using a unidirectional polychromatic probe.

Fig. 10
Fig. 10

3-D wave-normal shell for polychromatically controlled volume holograms.

Fig. 11
Fig. 11

System for periodically refreshing volume holograms, using polychromatic light.

Equations (97)

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R N g N 1 + N 2 .
d A ( r , t ) d t = A 0 E 0 [ E 1 · E 2 * + E 1 * · E 2 ] ,
A ( r , t ) = n A n ( t ) exp ( j K n · r ) ,
E 1 ( r , t ) = n 1 = - N 1 / 2 N 1 / 2 n 2 = - N 2 / 2 N 2 / 2 E n 1 n 2 1 ( t ) exp ( - j ω 0 t ) × exp ( j k n 1 n 2 1 · r ) ,
E 2 ( r , t ) = n 1 = - N 1 / 2 N 1 / 2 n 2 = - N 2 / 2 N 2 / 2 E n 1 n 2 2 ( t ) exp ( - j ω 0 t ) × exp ( j k n 1 n 2 2 · r ) ,
k n 1 n 2 1 k 0 { [ cos ( θ ) - n 1 Δ θ sin ( θ ) ] z ^ + [ sin ( θ ) + n 1 Δ θ cos ( θ ) ] x ^ + n 2 Δ ϕ sin ( θ ) y ^ } ,
k n 1 n 2 2 k 0 { [ cos ( θ ) - n 1 Δ θ sin ( θ ) ] z ^ + [ sin ( θ ) + n 1 Δ θ cos ( θ ) ] x ^ + n 2 Δ ϕ sin ( θ ) y ^ } .
d A n d t = A 0 E 0 [ n 1 , n 2 E n 1 , n 2 1 ( t ) E n 1 , n 2 2 * ( t ) ] ,
[ K n - ( k n 1 n 2 1 - k n 1 n 2 2 ) i ] < π L i ,
k n 1 n 2 - k n 1 n 2 = k 0 { ( n 1 + n 1 ) Δ θ sin θ z ^ + [ 2 sin θ + ( n 1 - n 1 ) Δ θ cos θ ] x ^ + ( n 2 - n 2 ) Δ ϕ sin θ y ^ } .
Δ θ sin θ λ L z ,
Δ θ cos θ λ L x ,
Δ ϕ sin θ λ L y .
N 1 2 N 2 V λ 3 sin θ .
d A n d t = A 0 E 0 [ n 2 = - N 2 / 2 N 2 / 2 E n 1 , n 2 1 ( t ) E n 1 , n 2 2 * ( t ) ] ,
E n 1 , n 2 1 ( t ) = E n 1 , n 2 1 ( i )             for j < i t j < t < j i t j ,
E n 1 , n 2 2 ( t ) = E n 1 , n 2 2 ( i )             for j < i t j < t < j i t j ,
A n = i = 1 N e n 2 = - N 2 / 2 N 2 / 2 A 0 t i E 0 E n 1 , n 2 1 ( i ) E n 1 , n 2 2 * ( i ) + A n ( 0 ) ,
W ¯ = i = 1 N e A 0 t i E 0 E 1 ( i ) E 2 ( i ) + W ¯ ( 0 ) .
W ¯ = Γ n = 1 R β n u n v n ,
n = 1 R β n = 1.
W ¯ = A 0 i = 1 N e t i E 1 ( i ) E 2 ( i ) t = 1 N e t i [ E 1 ( i ) E 1 ( i ) + E 2 ( i ) E 2 ( i ) ] ,
E 1 ( n ) = n R s n n u n , E 2 ( n ) = n R r n n v n .
W ¯ = A 0 n = 1 N e n R n R t n s n n r n n * u n v n * m N e m R t m [ ( r m m 2 + s m m 2 ) ] .
u p W ¯ v p = Γ β p .
u p W ¯ v p = A 0 n = 1 N e t n s n p r n p * m N e m R t m [ ( r m m 2 + s m m 2 ) ] .
β p Γ = A 0 n = 1 N e t n s n p r n p * m N e m R t m [ ( r m m 2 + s m m 2 ) ] .
Γ = A 0 m = 1 N e m = 1 R t m s m m r m m * m N e m R t m [ ( r m m 2 + s m m 2 ) ]
Γ = A 0 2 .
W ¯ = A 0 2 n = 1 R β n u n v n ,
η ψ = ψ W ¯ T W ¯ ψ ψ ψ = Γ 2 n β n 2 ψ v n 2 ψ ψ .
η ψ = A 0 2 4 R β n 2 s n 2 R s n 2 .
η n = A 0 2 4 β n 2 A 0 2 4 R 2 .
d A ( r , t ) d t = { A 0 / E 0 E 1 ( r , t ) + E 2 ( r , t ) 2 for A < A 0 0 otherwise .
A ( r , N e ) = A 0 E 0 i = 1 N e t i E 1 ( r , i ) + E 2 ( r , i ) 2 ,
Q = i = 1 N e t i E 1 ( r , i ) + E 2 ( r , i ) 2 E 0 1
Q = i = 1 N e t i [ E 1 ( i ) E 1 ( i ) + E 2 ( i ) E 2 ( i ) ] E 0 .
i = 1 N e τ i = 1 ,
t 0 < E 0 i = 1 N e τ i [ E 1 ( i ) E 1 ( i ) + E 2 ( i ) E 2 ( i ) ] .
A ( r , N e ) A 0 i = 1 N e τ i E 1 ( r , i ) + E 2 ( r , i ) 2 i = 1 N e τ i [ E 1 ( i ) E 1 ( i ) + E 2 ( i ) E 2 ( i ) ] .
d A n d t = A 0 α E n 1 , n 2 1 ( t ) E n 1 , n 2 2 * ( t ) - A n τ ,
τ ( t ) = α [ E 1 ( t ) E 1 ( t ) + E 2 ( t ) E 2 ( t ) ] .
d W ¯ d t = A 0 α E 1 ( t ) E 2 ( t ) - W ¯ ( t ) τ ( t ) .
W ¯ ( N e ) = A 0 n = 1 N e exp [ - n > n t n / τ ( n ) ] { 1 - exp [ - t n / τ ( n ) ] } [ E 1 ( n ) E 1 ( n ) + E 2 ( n ) E 2 ( n ) ] × E 2 ( n ) E 2 ( n ) .
W ¯ ( R ) = A 0 γ n = 1 R λ n E 1 ( n ) E 2 ( n ) ,
t 1 τ ( 1 ) = - log ( 1 - χ ) ,
t n τ ( n ) = log ( λ 1 I 1 + χ i = 2 n λ i I i λ 1 I 1 + χ i = 2 n - 1 λ i I i ) ,
γ = χ λ 1 I 1 + χ i = 2 N e λ i I i
f n = exp ( j ξ n ) exp [ - n > n t n / τ ( n ) ] { 1 - exp [ - t n / τ ( n ) ] } [ E 1 ( n ) E 1 ( n ) + E 2 ( n ) E 2 ( n ) ] .
W ¯ = A 0 n = 1 N e f n E 1 ( n ) E 2 ( n ) .
f n + 1 f n = λ n + 1 λ n .
R [ t n τ ( n ) ] = log ( λ 1 I 1 + χ i = 2 n λ i I i λ 1 I 1 + χ i = 2 n - 1 λ i I i ) .
n = n + 1 N e R [ t n τ ( n ) ] = log ( λ 1 I 1 + χ i = 2 N e λ i I i λ 1 I 1 + χ i = 2 n λ i I i ) .
f n = exp ( j ξ n ) I n exp { - j n > n F [ t n τ ( n ) ] } × ( λ 1 I 1 + χ i = 2 n λ i I i ) { 1 - exp [ - t n / τ ( n ) ] } λ 1 I i + χ i = 2 N e λ i I i .
t n τ ( n ) = exp { - j tan - 1 [ F ( α ) R ( α ) ] } { 1 + [ F ( α ) R ( α ) ] 2 } 1 / 2 × log ( λ 1 I 1 + χ i = 2 n λ i I i λ 1 I 1 + χ i = 2 n - 1 λ i I i )
f n { 1 + [ F ( α ) R ( α ) ] 2 } 1 / 2 χ λ n λ i I i + χ i = 2 N e λ i I i ,
ξ n = F ( α ) R ( α ) log ( λ 1 I 1 + χ i = 2 n λ i I i λ 1 I 1 + χ i = 2 n - 1 λ i I i ) + tan - 1 [ F ( α ) R ( α ) ] .
γ { 1 + [ F ( α ) R ( α ) ] 2 } 1 / 2 χ λ 1 I 1 + χ i = 2 R λ i I i .
F ( α ) R ( α ) = 1 2 | ( γ r e μ ) 1 / 2 - ( e μ γ r ) 1 / 2 | ,
w i j = | n β n φ i u n v n ν j | .
W ¯ = A 0 n = 1 D 0 n = 1 D i w n n φ n ν n m = 1 D 0 m = 1 D i 2 w m m ,
Γ = A 0 m = 1 D 0 m = 1 D i 2 w m m = A 0 2 [ m = 1 D 0 m = 1 D i n = 1 r β n φ i u n v n ν j ] - 1 .
n = 1 D 0 φ n φ n = I ,
n = 1 D i ν n ν n = I ,
n D 0 u n φ n φ n u n = 1 , n D i v n ν n ν n v n = 1
Γ A 0 2 D 0 D i = A 0 2 N e .
W ¯ 0 = Γ 0 n = 1 R β n u n ν n .
E p 2 = C W ¯ 0 ν p = C Γ 0 β p u p .
W ¯ c = C A 0 Γ 0 n = 1 R β n u n ν n N 1 + C 2 Γ 0 2 n = 1 R β n 2 = Γ c n = 1 R β n u n ν n .
Γ c = A 0 2 ( N 1 n = 1 N e β n 2 ) 1 / 2 ,
C = 1 Γ 0 ( N 1 n = 1 N e β n 2 ) 1 / 2 .
Γ c A 0 2 ( R N 1 ) 1 / 2 .
E 1 ( r , t ) = n = 1 N e E 1 n ( r , t ) exp ( - j ω n t ) , E 2 ( r , t ) = n = 2 N e E 2 n ( r , t ) exp ( - j ω n t ) .
A ( r , T ) = A 0 E 0 0 T E 1 ( r , t ) + E 2 ( r , t ) 2 d t .
A ( r ) = A 0 T E 0 n = 1 N e E 1 n ( r ) + E 2 n ( r ) 2 ,
E 1 n ( r , t ) = f ( t ) E 1 n ( r ) , E 2 n ( r , t ) = f ( t ) E 2 n ( r ) ,
f ( t ) = n = 1 p ( t - n t r )
ω n = ω 0 + n Δ ω .
A ( r , T ) = A 0 E 0 n = 1 N e n = 1 N e [ E 1 n ( r ) + E 2 n ( r ) ] · [ E 1 n * ( r ) + E 2 n * ( r ) ] × 0 T exp [ - j ( n - n ) Δ ω t ] f ( t ) 2 d t .
A ( r , T ) = A 0 T t δ E 0 t r | n = 1 N e E 1 n ( r ) + E 2 n ( r ) | 2 .
T < E 0 t r t δ 1 n = 1 N e E 1 n ( r ) 2 + E 2 n ( r ) 2 ,
A ( r , T ) = A 0 | n = 1 N e E 1 n ( r ) + E 2 n ( r ) | 2 n = 1 N e E 1 n ( r ) 2 + E 2 n ( r ) 2 .
E 1 ( r , t ) = E r f ( t ) exp [ j ( k r · r - ω r t ) ] .
E 2 ( r , t ) = n = 1 N e n 1 = - N 1 / 2 N 1 / 2 n 2 = - N 2 / 2 N 2 / 2 E n 1 n 2 2 n f ( t ) exp ( - j ω n t ) × exp ( j k n 1 n 2 2 n · r ) ,
k n 1 n 2 2 n ω n μ 0 { [ cos ( θ ) - n 1 Δ θ sin ( θ ) ] z ^ + [ sin ( θ ) + n 1 Δ θ cos ( θ ) ] x ^ + n 2 Δ ϕ sin ( θ ) y ^ } .
A n = A 0 E r · E p 1 p 2 2 p * E r 2 + n = 1 N e n 1 = - N 1 / 2 N 1 / 2 n 2 = - N 2 / 2 N 2 / 2 E n 1 n 2 2 n 2 ,
K n = k r - k p 1 p 2 2 p .
E r 2 = n = 1 N e n 1 = - N 1 / 2 N 1 / 2 n 2 = - N 2 / 2 N 2 / 2 E n 1 n 2 2 n 2 ,
A n = A 0 E p 1 p 2 2 p 2 ( n = 1 N e n 1 = - N 1 / 2 N 1 / 2 n 2 = - N 2 / 2 N 2 / 2 E n 1 n 2 2 n 2 ) 1 / 2 .
w i j = Γ n = 1 R β n φ i u n v n ν j .
i = 1 D 0 j = 1 D i w i j 2 = Γ 2 i = 1 D 0 j = 1 D i n = 1 R n = 1 R β n β n u n φ i × φ i u n v n ν j ν j v n .
w i j 2 = Γ 2 n = 1 R β n 2 D i D 0 .
Γ = A 0 2 R
k n 1 n 2 2 n - k n 1 n 2 2 n > π L ,
Δ ω > π ω k 0 L ,
t δ 1 N e Δ ω < L N e c π ,
t δ 10 - 13 s .

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