Abstract

A new approach to self-aligning unsupervised optical learning based on the competitive learning algorithm and adaptive holographic interconnections is introduced. A volume hologram is used to diffract the light from an input spatial light modulator so that it focuses upon a custom winner-take-all very-large-scale-integrated circuit liquid-crystal spatial light modulator. The units that receive the most light switch to a reflective state, and the light reflected from the winning pixels interferes in the volume of the dynamic hologram with the phase conjugate of the input pattern in order to add an outer-product perturbation to the current holographic interconnection. As a set of input patterns is cycled through many times, the system learns to diffract the light from a particular input class upon a self-organized set of detectors that recognize similar input patterns without the aid of a teacher or any required alignment. Beam-propagation simulations are used to show that the holographic optical learning network faithfully reproduces the behavior of the ideal competitive learning algorithm. A winner-take-all detector/modulator device containing a total of 576 optical neurons grouped into 31 separate competitive patches in the required sparse-grid topology has been successfully fabricated, and experimental results are presented.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Hong, D. Psaltis, “Storage capacity of holographic associative memories,” Opt. Lett. 11, 812–814 (1986).
    [CrossRef] [PubMed]
  2. B. H. Soffer, G. J. Dunning, Y. Owechko, E. Marom, “Associative holographic memory with feedback using phase conjugate mirrors,” Opt. Lett. 11, 118–120 (1986).
    [CrossRef] [PubMed]
  3. E. G. Paek, D. Psaltis, “Optical associative memory using Fourier transform holograms,” Opt. Eng. 26, 428–433 (1987).
  4. J. Jang, S. Jung, S. Lee, S. Shin, “Optical implementation of the Hopfield model for two-dimensional associative memory,” Opt. Lett. 13, 248–260 (1988).
    [CrossRef] [PubMed]
  5. J. Shamir, H. Caulfield, R. Johnson, “Massive holographic interconnections and their limitations,” Appl. Opt. 28, 311–324 (1989).
    [CrossRef] [PubMed]
  6. G. Y. Sirat, A. D. Maruani, R. C. Chevallier, “Frequency multiplexed raster neural networks. 1. Theory,” Appl. Opt. 28, 1429–1435 (1989).
    [CrossRef] [PubMed]
  7. K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 26, 5061–5076 (1987).
    [CrossRef] [PubMed]
  8. M. Kranzdorf, B. J. Bigner, L. Zhang, K. M. Johnson, “Optical connectionist machine with polarization based bipolar weight values,” Opt. Eng. 28, 844–848 (1989).
  9. T. Lu, F. T. S. Yu, D. A. Gregory, “Self-organizing optical neural network for unsupervised learning,” Opt. Eng. 29, 1107–1113 (1990).
    [CrossRef]
  10. M. Ishikawa, N. Mukohzaka, H. Toyoda, Y. Suzuki, “Experimental studies on learning capabilities of optical associative memory,” Appl. Opt. 29, 289–295 (1990).
    [CrossRef] [PubMed]
  11. D. Psaltis, N. Farhat, “Optical information processing based on an associative memory model of neural nets with thresholding and feedback,” Opt. Lett. 10, 98–100 (1985).
    [CrossRef]
  12. R. A. Athale, H. H. Szu, C. B. Friedlander, “Optical implementation of associative memory with controllable nonlinearity in the correlation domain,” Opt. Lett. 11, 482–484 (1986).
    [CrossRef] [PubMed]
  13. 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]
  14. Y. Owechko, “Optoelectronic resonator neural networks,” Appl. Opt. 26, 5104–5111 (1987).
    [CrossRef] [PubMed]
  15. K. Hsu, D. Brady, D. Psaltis, “Experimental demonstration of optical neural computers,” in Neural Information Processing Systems, D. Anderson, ed. (American Institute of Physics, New York, 1988), pp. 377–386.
  16. C. H. Wang, B. K. Jenkins, “Subtracting incoherent optical neuron model: analysis, experiment, and applications,” Appl. Opt. 29, 2171–2186 (1990).
    [CrossRef] [PubMed]
  17. I. Shariv, O. Gila, A. A. Friesem, “All-optical bipolar neural network with polarization-modulating neurons,” Opt. Lett. 16, 1692–1694 (1991).
    [CrossRef] [PubMed]
  18. D. Z. Anderson, “Coherent optical eigenstate memory,” Opt. Lett. 11, 45–47 (1986).
    [CrossRef]
  19. A. Yariv, S.-K. Kwong, “Associative memories based on message-bearing optical modes in phase-conjugate resonators,” Opt. Lett. 11, 186–188 (1986).
    [CrossRef] [PubMed]
  20. G. J. Dunning, E. Marom, Y. Owechko, B. H. Soffer, “All-optical associative memory with shift invariance and multiple-image recall,” Opt. Lett. 12, 346–348 (1987).
    [CrossRef] [PubMed]
  21. L.-S. Lee, M. H. Stoll, M. C. Tackitt, “Continuous-time optical neural network associative memory,” Opt. Lett. 14, 162–164 (1989).
    [CrossRef] [PubMed]
  22. A. L. Lentine, H. S. Hinton, D. Miller, J. E. Henry, J. E. Cunningham, L. Chirovsky, “Symmetric self-electro-optic effect device: optical set-reset latch,” Appl. Phys. Lett. 52, 1419–1421 (1988).
    [CrossRef]
  23. J. Pankove, C. Radehaus, K. Wagner, “Winner-take-all neural net with memory,” Electron. Lett. 26, 349–350 (1990).
    [CrossRef]
  24. D. A. Jared, K. M. Johnson, “Optically addressed thresholding very-large-scale-integration/liquid-crystal spatial light modulators,” Opt. Lett. 16, 967–969 (1991).
    [CrossRef] [PubMed]
  25. T. Slagle, K. Wagner, “Winner-take-all spatial light modulator,” Opt. Lett. 17, 1164–1166 (1992).
    [CrossRef] [PubMed]
  26. K. Wagner, T. Slagle, “Competitive optical learning with winner-take-all modulators,” in Optical Computing, Vol. 6 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 280–283.
  27. V. V. Voronov, I. R. Dorosh, Y. S. Kuz’minov, N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
    [CrossRef]
  28. H. Lee, X. G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2194 (1989).
    [CrossRef]
  29. H. Lee, “Volume holographic global and local interconnecting patterns with maximal capacity and minimal first-order crosstalk,” Appl. Opt. 28, 5312–5316 (1989).
    [CrossRef] [PubMed]
  30. D. Psaltis, D. Brady, X. Gu, S. Lin, “Holography in artificial neural networks,” Nature (London) 343, 325–330 (1990).
    [CrossRef]
  31. D. E. Rumelhart, D. Zipser, “Feature discovery by competitive learning,” Cognit. Sci. 9, 75–112 (1985).
    [CrossRef]
  32. S. Grossberg, “Competitive learning, from interactive activation to adaptive resonance,” Cognit. Sci. 11, 23–63 (1987).
    [CrossRef]
  33. C. von der Malsburg, “Self-organization of orientation sensitive cells in the striate cortex,” Kybernetik 14, 85–100 (1973).
    [CrossRef] [PubMed]
  34. T. W. Ryan, “The resonance correlation network,” in Proceedings of the Second IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), Vol. I, pp. I-673–I-680.
  35. G. A. Carpenter, S. Grossberg, “Art 2: self-organization of stable category recognition codes for analog input patterns,” Appl. Opt. 26, 4919–4930 (1987).
    [CrossRef] [PubMed]
  36. B. Kosko, “Stochastic competitive learning,” IEEE Trans. Neural Net. 2, 522–529 (1991).
    [CrossRef]
  37. M. Lemmon, B. V. K. V. Kumar, “Competitive learning with generalized winner-take-all activation,” IEEE Trans. Neural Net. 3, 167–175 (1992).
    [CrossRef]
  38. T. Kohonen, Self-Organization and Associative Memory (Springer-Verlag, New York, 1984).
  39. K. Wagner, R. Feinleib, “Competitive optoelectronic learning network,” in Neural Network Models for Optical Computing, R. A. Athale, J. Davis, eds., Proc. Soc. Photo-Opt. Instrum. Eng.882, 162–172 (1988).
  40. M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi-two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
    [CrossRef]
  41. Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
  42. V. N. Blaschuk, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, B. Y. ZePDovich, “Wavefront reversal with angular tilting-theory and experiment for the four-wave mixing,” Opt. Commun. 31, 383–387 (1979).
    [CrossRef]
  43. J. H. Hong, S. Campbell, P. Yeh, “Optical pattern classifier with perceptron learning,” Appl. Opt. 29, 3019–3025 (1990).
    [CrossRef] [PubMed]
  44. K. Kitayama, H. Yoshinaga, T. Hara, “Experiments of learning in optical perceptron-like and multilayer neural networks,” in Proceedings of the Third International Joint Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1989), Vol. 2, pp. 465–471.
    [CrossRef]
  45. M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Phhotorefractive Crystals in Coherent Optical Systems (Springer-Verlag, New York, 1991).
  46. L. Cheng, P. Yeh, “Cross-polarization beam coupling in photorefractive GaAs crystals,” Opt. Lett. 13, 50–52 (1988).
    [CrossRef] [PubMed]
  47. T. Y. Chang, A. E. Chiou, P. Yeh, “Cross-polarization photorefractive two-beam coupling in gallium arsenide,” J. Opt. Soc. Am. B 5, 1724–1729 (1988).
    [CrossRef]
  48. H. J. Mager, O. Wess, W. Waidelich, “Sequential associative information storage and reconstruction in a holographic circuit,” Opt. Commun. 9, 156–160 (1973).
    [CrossRef]
  49. H. Lee, “Cross-talk effects in multiplexed volume holograms,” Opt. Lett. 13, 874–876 (1988).
    [CrossRef] [PubMed]
  50. D. J. Brady, “Photorefractive volume holography in artificial neural networks,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1990).
  51. C. X.-G. Gu, “Optical neural networks using volume holograms,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1990).
  52. L. K. Cotter, T. J. Drabik, R. J. Dillon, M. A. Handschy, “Ferroelectric-liquid-crystal/silicon-integrated-circuit spatial light modulator,” Opt. Lett. 15, 291–293 (1990).
    [CrossRef] [PubMed]
  53. D. R. Pape, “Multichannel Bragg cells: design, performance, and applications,” Opt. Eng. 31, 2148–2158 (1992).
    [CrossRef]
  54. B. E. Boser, E. Sackinger, J. Bromley, Y. LeCunn, R. Howard, L. Jackel, “An analog neural network processor and its application to high-speed character recognition,” in Proceedings of the Third International Joint Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1991), Vol. 1, pp. 415–420.
  55. T. Huang, K. Wagner, “Photoanisotropic incoherent-to-coherent optical converter,” Appl. Opt. (to be published).
  56. D. Psaltis, D. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
    [CrossRef]
  57. J. E. Ford, Y. Fainman, S. H. Lee, “Array interconnection by phase-coded optical correlation,” Opt. Lett. 15, 1089–1091 (1990).
    [CrossRef]
  58. C. G. Guest, R. TeKolste, “Designs and devices for optical bidirectional associative memories,” Appl. Opt. 26, 5055–5060 (1987).
    [CrossRef] [PubMed]
  59. Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, “Incremental recording for photorefractive hologram multiplexing,” Opt. Lett. 16, 1774–1776 (1991).
    [CrossRef] [PubMed]
  60. P. Gunter, J. Huignard, eds., Photorefractive Materials and Their Applications 1, Vol. 62 of Topics in Applied Physics (Springer-Verlag, New York, 1988); Photorefractive Materials and Their Applications 2, Vol 63 of Topics in Applied Physics (Springer-Verlag, New York, 1988).
    [CrossRef]
  61. D. Z. Anderson, R. Saxena, “Theory of multimode operation of a unidirectional ring oscillator having photorefractive gain: weak-field limit,” J. Opt. Soc. Am. B 4, 164–176 (1987).
    [CrossRef]
  62. C. Gu, P. Yeh, “Scattering due to randomly distributed charge particles in photorefractive crystals,” Opt. Lett. 16, 1572–1574 (1991).
    [CrossRef] [PubMed]
  63. T. Todorov, L. Nikolova, N. Tomov, V. Dragostinova, “Photoinduced anisotropy in rigid dye solutions for transient polarization holography,” IEEE J. Quantum Electron. QE-22, 1262–1267 (1986).
    [CrossRef]
  64. D. Haronian, A. Lewis, “Elements of a unique bacteriorhodopsin neural network architecture,” Appl. Op. 30, 597–608 (1991).
    [CrossRef]
  65. V. Y. Bazhenov, M. S. Soskin, V. B. Taranenko, M. V. Vasnetsov, “Biopolymers for real-time optical processing,” in Optical Processing and Computing, H. H. Arsenault, T. Szoplik, B. Macukow, eds. (Academic, New York, 1989), Chap. 4.
  66. J. J. A. Couture, R. A. Lessard, “Modulation transfer function measurements for thin layers of azo dyes in PVA matrix used as an optical recording material,” Appl. Opt. 27, 3368–3374 (1988).
    [CrossRef] [PubMed]
  67. T. Huang, K. Wagner, “Holographic diffraction in photoanisotropic organic materials,” J. Opt. Soc. Am. A 10, 306–315 (1993).
    [CrossRef]
  68. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and application of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
    [CrossRef]
  69. S. I. Stepanov, M. P. Petrov, “Degenerate four-wave mixing via shifted phase holograms in cubic photorefractive crystals,” Opt. Commun. 53, 64–69 (1985).
    [CrossRef]
  70. R. Rajbenbach, B. Imbert, J. P. Huignard, S. Mallick, “Near-infrared four-wave mixing with gain and self-starting oscillators with photorefractive gas,” Opt. Lett. 14, 78–80 (1989).
    [CrossRef] [PubMed]
  71. J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
    [CrossRef]
  72. R. V. Johnson, A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. 25, 235–249 (1986).
  73. C. W. Slinger, “Weighted volume interconnects for adaptive networks,” Opt. Comput. Process. 31, 219–232 (1991).
  74. B. K. Jenkins, A. R. Tanguay, “Photonic implementations of neural networks,” in Neural Networks for Signal Processing, B. Kosko, ed. (Prentice-Hall, Englewood Cliffs, N.J., 1992), Chap. 9, pp. 287–382.
  75. Topical Meeting Digest on Smart Pixels, IEEE Catalog 92TH0421-8 (Institute of Electrical and Electronics Engineers, New York, 1992).
  76. I. Underwood, D. G. Vass, R. M. Sillitto, “Evaluation of an nMOS VLSI array for an adaptive liquid-crystal spatial light modulator,” Proc. Inst. Electr. Eng. 133, 77–82 (1986).
  77. N. A. Clark, S. T. Lagerwall, “Submicrosecond bistable electro-optic switching in liquid crystals,” Appl. Phys. Lett. 36, 899–901 (1980).
    [CrossRef]
  78. D. J. McKnight, D. G. Vass, R. M. Sillitto, “Development of a spatial light modulator: a randomly addressed liquid-crystal-over-nMOS array,” Appl. Opt. 28, 4757–4761 (1989).
    [CrossRef] [PubMed]
  79. S. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, “One-dimensional silicon/PLZT spatial light modulators,” Opt. Eng. 26, 406–413 (1986).
  80. J. Lazzaro, S. Ryckebusch, M. A. Mahowald, C. A. Mead, “Winner-take-all networks of O(N) complexity,” in Advances in Neural Information Processing Systems 1, D. Touretzky, ed. (Kaufmann, Los Altos, Calif., 1989), pp. 703–711.
  81. C. Mead, “Adaptive retina,” in Analog VLSI Implementation of Neural SystemsC. Mead, ed. (Kluwer, Norwell, Mass., 1989), Chap. 10, pp. 239–246.
    [CrossRef]
  82. D. A. Jared, K. M. Johnson, “Ferroelectric liquid crystal spatial light modulators,” in Spatial Light Modulators and Applications III, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1150, pp. 46–60 (1990).
  83. E. B. Baum, D. Haussier, “What size net gives valid generalization,” Neural Computat. 1, 151–160 (1989).
    [CrossRef]

1993

1992

D. R. Pape, “Multichannel Bragg cells: design, performance, and applications,” Opt. Eng. 31, 2148–2158 (1992).
[CrossRef]

T. Slagle, K. Wagner, “Winner-take-all spatial light modulator,” Opt. Lett. 17, 1164–1166 (1992).
[CrossRef] [PubMed]

M. Lemmon, B. V. K. V. Kumar, “Competitive learning with generalized winner-take-all activation,” IEEE Trans. Neural Net. 3, 167–175 (1992).
[CrossRef]

1991

1990

L. K. Cotter, T. J. Drabik, R. J. Dillon, M. A. Handschy, “Ferroelectric-liquid-crystal/silicon-integrated-circuit spatial light modulator,” Opt. Lett. 15, 291–293 (1990).
[CrossRef] [PubMed]

J. H. Hong, S. Campbell, P. Yeh, “Optical pattern classifier with perceptron learning,” Appl. Opt. 29, 3019–3025 (1990).
[CrossRef] [PubMed]

J. E. Ford, Y. Fainman, S. H. Lee, “Array interconnection by phase-coded optical correlation,” Opt. Lett. 15, 1089–1091 (1990).
[CrossRef]

C. H. Wang, B. K. Jenkins, “Subtracting incoherent optical neuron model: analysis, experiment, and applications,” Appl. Opt. 29, 2171–2186 (1990).
[CrossRef] [PubMed]

T. Lu, F. T. S. Yu, D. A. Gregory, “Self-organizing optical neural network for unsupervised learning,” Opt. Eng. 29, 1107–1113 (1990).
[CrossRef]

M. Ishikawa, N. Mukohzaka, H. Toyoda, Y. Suzuki, “Experimental studies on learning capabilities of optical associative memory,” Appl. Opt. 29, 289–295 (1990).
[CrossRef] [PubMed]

J. Pankove, C. Radehaus, K. Wagner, “Winner-take-all neural net with memory,” Electron. Lett. 26, 349–350 (1990).
[CrossRef]

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi-two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[CrossRef]

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

1989

L.-S. Lee, M. H. Stoll, M. C. Tackitt, “Continuous-time optical neural network associative memory,” Opt. Lett. 14, 162–164 (1989).
[CrossRef] [PubMed]

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

H. Lee, “Volume holographic global and local interconnecting patterns with maximal capacity and minimal first-order crosstalk,” Appl. Opt. 28, 5312–5316 (1989).
[CrossRef] [PubMed]

J. Shamir, H. Caulfield, R. Johnson, “Massive holographic interconnections and their limitations,” Appl. Opt. 28, 311–324 (1989).
[CrossRef] [PubMed]

G. Y. Sirat, A. D. Maruani, R. C. Chevallier, “Frequency multiplexed raster neural networks. 1. Theory,” Appl. Opt. 28, 1429–1435 (1989).
[CrossRef] [PubMed]

M. Kranzdorf, B. J. Bigner, L. Zhang, K. M. Johnson, “Optical connectionist machine with polarization based bipolar weight values,” Opt. Eng. 28, 844–848 (1989).

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]

D. J. McKnight, D. G. Vass, R. M. Sillitto, “Development of a spatial light modulator: a randomly addressed liquid-crystal-over-nMOS array,” Appl. Opt. 28, 4757–4761 (1989).
[CrossRef] [PubMed]

E. B. Baum, D. Haussier, “What size net gives valid generalization,” Neural Computat. 1, 151–160 (1989).
[CrossRef]

R. Rajbenbach, B. Imbert, J. P. Huignard, S. Mallick, “Near-infrared four-wave mixing with gain and self-starting oscillators with photorefractive gas,” Opt. Lett. 14, 78–80 (1989).
[CrossRef] [PubMed]

1988

1987

1986

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

R. V. Johnson, A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. 25, 235–249 (1986).

S. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, “One-dimensional silicon/PLZT spatial light modulators,” Opt. Eng. 26, 406–413 (1986).

I. Underwood, D. G. Vass, R. M. Sillitto, “Evaluation of an nMOS VLSI array for an adaptive liquid-crystal spatial light modulator,” Proc. Inst. Electr. Eng. 133, 77–82 (1986).

D. Z. Anderson, “Coherent optical eigenstate memory,” Opt. Lett. 11, 45–47 (1986).
[CrossRef]

A. Yariv, S.-K. Kwong, “Associative memories based on message-bearing optical modes in phase-conjugate resonators,” Opt. Lett. 11, 186–188 (1986).
[CrossRef] [PubMed]

R. A. Athale, H. H. Szu, C. B. Friedlander, “Optical implementation of associative memory with controllable nonlinearity in the correlation domain,” Opt. Lett. 11, 482–484 (1986).
[CrossRef] [PubMed]

J. Hong, D. Psaltis, “Storage capacity of holographic associative memories,” Opt. Lett. 11, 812–814 (1986).
[CrossRef] [PubMed]

B. H. Soffer, G. J. Dunning, Y. Owechko, E. Marom, “Associative holographic memory with feedback using phase conjugate mirrors,” Opt. Lett. 11, 118–120 (1986).
[CrossRef] [PubMed]

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).

1985

D. E. Rumelhart, D. Zipser, “Feature discovery by competitive learning,” Cognit. Sci. 9, 75–112 (1985).
[CrossRef]

D. Psaltis, N. Farhat, “Optical information processing based on an associative memory model of neural nets with thresholding and feedback,” Opt. Lett. 10, 98–100 (1985).
[CrossRef]

S. I. Stepanov, M. P. Petrov, “Degenerate four-wave mixing via shifted phase holograms in cubic photorefractive crystals,” Opt. Commun. 53, 64–69 (1985).
[CrossRef]

1984

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and application of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

1980

N. A. Clark, S. T. Lagerwall, “Submicrosecond bistable electro-optic switching in liquid crystals,” Appl. Phys. Lett. 36, 899–901 (1980).
[CrossRef]

V. V. Voronov, I. R. Dorosh, Y. S. Kuz’minov, N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[CrossRef]

1979

V. N. Blaschuk, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, B. Y. ZePDovich, “Wavefront reversal with angular tilting-theory and experiment for the four-wave mixing,” Opt. Commun. 31, 383–387 (1979).
[CrossRef]

1976

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

1973

H. J. Mager, O. Wess, W. Waidelich, “Sequential associative information storage and reconstruction in a holographic circuit,” Opt. Commun. 9, 156–160 (1973).
[CrossRef]

C. von der Malsburg, “Self-organization of orientation sensitive cells in the striate cortex,” Kybernetik 14, 85–100 (1973).
[CrossRef] [PubMed]

Anderson, D. Z.

Athale, R. A.

Baum, E. B.

E. B. Baum, D. Haussier, “What size net gives valid generalization,” Neural Computat. 1, 151–160 (1989).
[CrossRef]

Bazhenov, V. Y.

V. Y. Bazhenov, M. S. Soskin, V. B. Taranenko, M. V. Vasnetsov, “Biopolymers for real-time optical processing,” in Optical Processing and Computing, H. H. Arsenault, T. Szoplik, B. Macukow, eds. (Academic, New York, 1989), Chap. 4.

Bigner, B. J.

M. Kranzdorf, B. J. Bigner, L. Zhang, K. M. Johnson, “Optical connectionist machine with polarization based bipolar weight values,” Opt. Eng. 28, 844–848 (1989).

Blaschuk, V. N.

V. N. Blaschuk, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, B. Y. ZePDovich, “Wavefront reversal with angular tilting-theory and experiment for the four-wave mixing,” Opt. Commun. 31, 383–387 (1979).
[CrossRef]

Boser, B. E.

B. E. Boser, E. Sackinger, J. Bromley, Y. LeCunn, R. Howard, L. Jackel, “An analog neural network processor and its application to high-speed character recognition,” in Proceedings of the Third International Joint Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1991), Vol. 1, pp. 415–420.

Brady, D.

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

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

K. Hsu, D. Brady, D. Psaltis, “Experimental demonstration of optical neural computers,” in Neural Information Processing Systems, D. Anderson, ed. (American Institute of Physics, New York, 1988), pp. 377–386.

Brady, D. J.

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

Bromley, J.

B. E. Boser, E. Sackinger, J. Bromley, Y. LeCunn, R. Howard, L. Jackel, “An analog neural network processor and its application to high-speed character recognition,” in Proceedings of the Third International Joint Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1991), Vol. 1, pp. 415–420.

Campbell, S.

Carpenter, G. A.

Caulfield, H.

Chang, T. Y.

Cheng, L.

Chevallier, R. C.

Chiou, A. E.

Chirovsky, L.

A. L. Lentine, H. S. Hinton, D. Miller, J. E. Henry, J. E. Cunningham, L. Chirovsky, “Symmetric self-electro-optic effect device: optical set-reset latch,” Appl. Phys. Lett. 52, 1419–1421 (1988).
[CrossRef]

Clark, N. A.

N. A. Clark, S. T. Lagerwall, “Submicrosecond bistable electro-optic switching in liquid crystals,” Appl. Phys. Lett. 36, 899–901 (1980).
[CrossRef]

Cotter, L. K.

Couture, J. J. A.

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and application of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

Cunningham, J. E.

A. L. Lentine, H. S. Hinton, D. Miller, J. E. Henry, J. E. Cunningham, L. Chirovsky, “Symmetric self-electro-optic effect device: optical set-reset latch,” Appl. Phys. Lett. 52, 1419–1421 (1988).
[CrossRef]

Dillon, R. J.

Dorosh, I. R.

V. V. Voronov, I. R. Dorosh, Y. S. Kuz’minov, N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[CrossRef]

Drabik, T. J.

L. K. Cotter, T. J. Drabik, R. J. Dillon, M. A. Handschy, “Ferroelectric-liquid-crystal/silicon-integrated-circuit spatial light modulator,” Opt. Lett. 15, 291–293 (1990).
[CrossRef] [PubMed]

S. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, “One-dimensional silicon/PLZT spatial light modulators,” Opt. Eng. 26, 406–413 (1986).

Dragostinova, V.

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

Dunning, G. J.

Esener, S.

S. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, “One-dimensional silicon/PLZT spatial light modulators,” Opt. Eng. 26, 406–413 (1986).

Fainman, Y.

Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, “Incremental recording for photorefractive hologram multiplexing,” Opt. Lett. 16, 1774–1776 (1991).
[CrossRef] [PubMed]

J. E. Ford, Y. Fainman, S. H. Lee, “Array interconnection by phase-coded optical correlation,” Opt. Lett. 15, 1089–1091 (1990).
[CrossRef]

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).

Farhat, N.

Feinleib, R.

K. Wagner, R. Feinleib, “Competitive optoelectronic learning network,” in Neural Network Models for Optical Computing, R. A. Athale, J. Davis, eds., Proc. Soc. Photo-Opt. Instrum. Eng.882, 162–172 (1988).

Feit, M. D.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Fischer, B.

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi-two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and application of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

Fleck, J. A.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Ford, J. E.

Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, “Incremental recording for photorefractive hologram multiplexing,” Opt. Lett. 16, 1774–1776 (1991).
[CrossRef] [PubMed]

J. E. Ford, Y. Fainman, S. H. Lee, “Array interconnection by phase-coded optical correlation,” Opt. Lett. 15, 1089–1091 (1990).
[CrossRef]

Friedlander, C. B.

Friesem, A. A.

Gila, O.

Gregory, D. A.

T. Lu, F. T. S. Yu, D. A. Gregory, “Self-organizing optical neural network for unsupervised learning,” Opt. Eng. 29, 1107–1113 (1990).
[CrossRef]

Grossberg, S.

G. A. Carpenter, S. Grossberg, “Art 2: self-organization of stable category recognition codes for analog input patterns,” Appl. Opt. 26, 4919–4930 (1987).
[CrossRef] [PubMed]

S. Grossberg, “Competitive learning, from interactive activation to adaptive resonance,” Cognit. Sci. 11, 23–63 (1987).
[CrossRef]

Gu, C.

Gu, C. X.-G.

C. X.-G. Gu, “Optical neural networks using volume holograms,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1990).

Gu, X.

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

Gu, X. G.

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

Guest, C. G.

Handschy, M. A.

Hara, T.

K. Kitayama, H. Yoshinaga, T. Hara, “Experiments of learning in optical perceptron-like and multilayer neural networks,” in Proceedings of the Third International Joint Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1989), Vol. 2, pp. 465–471.
[CrossRef]

Haronian, D.

D. Haronian, A. Lewis, “Elements of a unique bacteriorhodopsin neural network architecture,” Appl. Op. 30, 597–608 (1991).
[CrossRef]

Haussier, D.

E. B. Baum, D. Haussier, “What size net gives valid generalization,” Neural Computat. 1, 151–160 (1989).
[CrossRef]

Henry, J. E.

A. L. Lentine, H. S. Hinton, D. Miller, J. E. Henry, J. E. Cunningham, L. Chirovsky, “Symmetric self-electro-optic effect device: optical set-reset latch,” Appl. Phys. Lett. 52, 1419–1421 (1988).
[CrossRef]

Hinton, H. S.

A. L. Lentine, H. S. Hinton, D. Miller, J. E. Henry, J. E. Cunningham, L. Chirovsky, “Symmetric self-electro-optic effect device: optical set-reset latch,” Appl. Phys. Lett. 52, 1419–1421 (1988).
[CrossRef]

Hong, J.

Hong, J. H.

Howard, R.

B. E. Boser, E. Sackinger, J. Bromley, Y. LeCunn, R. Howard, L. Jackel, “An analog neural network processor and its application to high-speed character recognition,” in Proceedings of the Third International Joint Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1991), Vol. 1, pp. 415–420.

Hsu, K.

K. Hsu, D. Brady, D. Psaltis, “Experimental demonstration of optical neural computers,” in Neural Information Processing Systems, D. Anderson, ed. (American Institute of Physics, New York, 1988), pp. 377–386.

Huang, T.

T. Huang, K. Wagner, “Holographic diffraction in photoanisotropic organic materials,” J. Opt. Soc. Am. A 10, 306–315 (1993).
[CrossRef]

T. Huang, K. Wagner, “Photoanisotropic incoherent-to-coherent optical converter,” Appl. Opt. (to be published).

Huignard, J. P.

Imbert, B.

Ishikawa, M.

Jackel, L.

B. E. Boser, E. Sackinger, J. Bromley, Y. LeCunn, R. Howard, L. Jackel, “An analog neural network processor and its application to high-speed character recognition,” in Proceedings of the Third International Joint Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1991), Vol. 1, pp. 415–420.

Jang, J.

Jared, D. A.

D. A. Jared, K. M. Johnson, “Optically addressed thresholding very-large-scale-integration/liquid-crystal spatial light modulators,” Opt. Lett. 16, 967–969 (1991).
[CrossRef] [PubMed]

D. A. Jared, K. M. Johnson, “Ferroelectric liquid crystal spatial light modulators,” in Spatial Light Modulators and Applications III, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1150, pp. 46–60 (1990).

Jenkins, B. K.

C. H. Wang, B. K. Jenkins, “Subtracting incoherent optical neuron model: analysis, experiment, and applications,” Appl. Opt. 29, 2171–2186 (1990).
[CrossRef] [PubMed]

B. K. Jenkins, A. R. Tanguay, “Photonic implementations of neural networks,” in Neural Networks for Signal Processing, B. Kosko, ed. (Prentice-Hall, Englewood Cliffs, N.J., 1992), Chap. 9, pp. 287–382.

Johnson, K. M.

D. A. Jared, K. M. Johnson, “Optically addressed thresholding very-large-scale-integration/liquid-crystal spatial light modulators,” Opt. Lett. 16, 967–969 (1991).
[CrossRef] [PubMed]

M. Kranzdorf, B. J. Bigner, L. Zhang, K. M. Johnson, “Optical connectionist machine with polarization based bipolar weight values,” Opt. Eng. 28, 844–848 (1989).

D. A. Jared, K. M. Johnson, “Ferroelectric liquid crystal spatial light modulators,” in Spatial Light Modulators and Applications III, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1150, pp. 46–60 (1990).

Johnson, R.

Johnson, R. V.

R. V. Johnson, A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. 25, 235–249 (1986).

Jung, S.

Khomenko, A. V.

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Phhotorefractive Crystals in Coherent Optical Systems (Springer-Verlag, New York, 1991).

Kitayama, K.

K. Kitayama, H. Yoshinaga, T. Hara, “Experiments of learning in optical perceptron-like and multilayer neural networks,” in Proceedings of the Third International Joint Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1989), Vol. 2, pp. 465–471.
[CrossRef]

Klancnik, E.

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).

Kohonen, T.

T. Kohonen, Self-Organization and Associative Memory (Springer-Verlag, New York, 1984).

Kosko, B.

B. Kosko, “Stochastic competitive learning,” IEEE Trans. Neural Net. 2, 522–529 (1991).
[CrossRef]

Kranzdorf, M.

M. Kranzdorf, B. J. Bigner, L. Zhang, K. M. Johnson, “Optical connectionist machine with polarization based bipolar weight values,” Opt. Eng. 28, 844–848 (1989).

Kumar, B. V. K. V.

M. Lemmon, B. V. K. V. Kumar, “Competitive learning with generalized winner-take-all activation,” IEEE Trans. Neural Net. 3, 167–175 (1992).
[CrossRef]

Kuz’minov, Y. S.

V. V. Voronov, I. R. Dorosh, Y. S. Kuz’minov, N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[CrossRef]

Kwong, S.-K.

Lagerwall, S. T.

N. A. Clark, S. T. Lagerwall, “Submicrosecond bistable electro-optic switching in liquid crystals,” Appl. Phys. Lett. 36, 899–901 (1980).
[CrossRef]

Lazzaro, J.

J. Lazzaro, S. Ryckebusch, M. A. Mahowald, C. A. Mead, “Winner-take-all networks of O(N) complexity,” in Advances in Neural Information Processing Systems 1, D. Touretzky, ed. (Kaufmann, Los Altos, Calif., 1989), pp. 703–711.

LeCunn, Y.

B. E. Boser, E. Sackinger, J. Bromley, Y. LeCunn, R. Howard, L. Jackel, “An analog neural network processor and its application to high-speed character recognition,” in Proceedings of the Third International Joint Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1991), Vol. 1, pp. 415–420.

Lee, H.

Lee, L.-S.

Lee, S.

Lee, S. H.

Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, “Incremental recording for photorefractive hologram multiplexing,” Opt. Lett. 16, 1774–1776 (1991).
[CrossRef] [PubMed]

J. E. Ford, Y. Fainman, S. H. Lee, “Array interconnection by phase-coded optical correlation,” Opt. Lett. 15, 1089–1091 (1990).
[CrossRef]

S. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, “One-dimensional silicon/PLZT spatial light modulators,” Opt. Eng. 26, 406–413 (1986).

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).

Lemmon, M.

M. Lemmon, B. V. K. V. Kumar, “Competitive learning with generalized winner-take-all activation,” IEEE Trans. Neural Net. 3, 167–175 (1992).
[CrossRef]

Lentine, A. L.

A. L. Lentine, H. S. Hinton, D. Miller, J. E. Henry, J. E. Cunningham, L. Chirovsky, “Symmetric self-electro-optic effect device: optical set-reset latch,” Appl. Phys. Lett. 52, 1419–1421 (1988).
[CrossRef]

Lessard, R. A.

Lewis, A.

D. Haronian, A. Lewis, “Elements of a unique bacteriorhodopsin neural network architecture,” Appl. Op. 30, 597–608 (1991).
[CrossRef]

Lin, S.

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

Lu, T.

T. Lu, F. T. S. Yu, D. A. Gregory, “Self-organizing optical neural network for unsupervised learning,” Opt. Eng. 29, 1107–1113 (1990).
[CrossRef]

Ma, J.

Mager, H. J.

H. J. Mager, O. Wess, W. Waidelich, “Sequential associative information storage and reconstruction in a holographic circuit,” Opt. Commun. 9, 156–160 (1973).
[CrossRef]

Mahowald, M. A.

J. Lazzaro, S. Ryckebusch, M. A. Mahowald, C. A. Mead, “Winner-take-all networks of O(N) complexity,” in Advances in Neural Information Processing Systems 1, D. Touretzky, ed. (Kaufmann, Los Altos, Calif., 1989), pp. 703–711.

Mallick, S.

Mamaev, A. V.

V. N. Blaschuk, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, B. Y. ZePDovich, “Wavefront reversal with angular tilting-theory and experiment for the four-wave mixing,” Opt. Commun. 31, 383–387 (1979).
[CrossRef]

Marom, E.

Maruani, A. D.

McKnight, D. J.

Mead, C.

C. Mead, “Adaptive retina,” in Analog VLSI Implementation of Neural SystemsC. Mead, ed. (Kluwer, Norwell, Mass., 1989), Chap. 10, pp. 239–246.
[CrossRef]

Mead, C. A.

J. Lazzaro, S. Ryckebusch, M. A. Mahowald, C. A. Mead, “Winner-take-all networks of O(N) complexity,” in Advances in Neural Information Processing Systems 1, D. Touretzky, ed. (Kaufmann, Los Altos, Calif., 1989), pp. 703–711.

Miller, D.

A. L. Lentine, H. S. Hinton, D. Miller, J. E. Henry, J. E. Cunningham, L. Chirovsky, “Symmetric self-electro-optic effect device: optical set-reset latch,” Appl. Phys. Lett. 52, 1419–1421 (1988).
[CrossRef]

Morris, J. R.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Mukohzaka, N.

Nikolova, L.

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

Ophir, Y.

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi-two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[CrossRef]

Owechko, Y.

Paek, E. G.

Pankove, J.

J. Pankove, C. Radehaus, K. Wagner, “Winner-take-all neural net with memory,” Electron. Lett. 26, 349–350 (1990).
[CrossRef]

Pape, D. R.

D. R. Pape, “Multichannel Bragg cells: design, performance, and applications,” Opt. Eng. 31, 2148–2158 (1992).
[CrossRef]

Patel, J. S.

Petrov, M. P.

S. I. Stepanov, M. P. Petrov, “Degenerate four-wave mixing via shifted phase holograms in cubic photorefractive crystals,” Opt. Commun. 53, 64–69 (1985).
[CrossRef]

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Phhotorefractive Crystals in Coherent Optical Systems (Springer-Verlag, New York, 1991).

Pilipetsky, N. F.

V. N. Blaschuk, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, B. Y. ZePDovich, “Wavefront reversal with angular tilting-theory and experiment for the four-wave mixing,” Opt. Commun. 31, 383–387 (1979).
[CrossRef]

Psaltis, D.

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

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

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

E. G. Paek, D. Psaltis, “Optical associative memory using Fourier transform holograms,” Opt. Eng. 26, 428–433 (1987).

K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 26, 5061–5076 (1987).
[CrossRef] [PubMed]

J. Hong, D. Psaltis, “Storage capacity of holographic associative memories,” Opt. Lett. 11, 812–814 (1986).
[CrossRef] [PubMed]

D. Psaltis, N. Farhat, “Optical information processing based on an associative memory model of neural nets with thresholding and feedback,” Opt. Lett. 10, 98–100 (1985).
[CrossRef]

K. Hsu, D. Brady, D. Psaltis, “Experimental demonstration of optical neural computers,” in Neural Information Processing Systems, D. Anderson, ed. (American Institute of Physics, New York, 1988), pp. 377–386.

Radehaus, C.

J. Pankove, C. Radehaus, K. Wagner, “Winner-take-all neural net with memory,” Electron. Lett. 26, 349–350 (1990).
[CrossRef]

Rajbenbach, R.

Rumelhart, D. E.

D. E. Rumelhart, D. Zipser, “Feature discovery by competitive learning,” Cognit. Sci. 9, 75–112 (1985).
[CrossRef]

Ryan, T. W.

T. W. Ryan, “The resonance correlation network,” in Proceedings of the Second IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), Vol. I, pp. I-673–I-680.

Ryckebusch, S.

J. Lazzaro, S. Ryckebusch, M. A. Mahowald, C. A. Mead, “Winner-take-all networks of O(N) complexity,” in Advances in Neural Information Processing Systems 1, D. Touretzky, ed. (Kaufmann, Los Altos, Calif., 1989), pp. 703–711.

Sackinger, E.

B. E. Boser, E. Sackinger, J. Bromley, Y. LeCunn, R. Howard, L. Jackel, “An analog neural network processor and its application to high-speed character recognition,” in Proceedings of the Third International Joint Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1991), Vol. 1, pp. 415–420.

Sasaki, H.

Saxena, R.

Segev, M.

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi-two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[CrossRef]

Shamir, J.

Shariv, I.

Shin, S.

Shkunov, V. V.

V. N. Blaschuk, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, B. Y. ZePDovich, “Wavefront reversal with angular tilting-theory and experiment for the four-wave mixing,” Opt. Commun. 31, 383–387 (1979).
[CrossRef]

Sillitto, R. M.

D. J. McKnight, D. G. Vass, R. M. Sillitto, “Development of a spatial light modulator: a randomly addressed liquid-crystal-over-nMOS array,” Appl. Opt. 28, 4757–4761 (1989).
[CrossRef] [PubMed]

I. Underwood, D. G. Vass, R. M. Sillitto, “Evaluation of an nMOS VLSI array for an adaptive liquid-crystal spatial light modulator,” Proc. Inst. Electr. Eng. 133, 77–82 (1986).

Sirat, G. Y.

Slagle, T.

T. Slagle, K. Wagner, “Winner-take-all spatial light modulator,” Opt. Lett. 17, 1164–1166 (1992).
[CrossRef] [PubMed]

K. Wagner, T. Slagle, “Competitive optical learning with winner-take-all modulators,” in Optical Computing, Vol. 6 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 280–283.

Slinger, C. W.

C. W. Slinger, “Weighted volume interconnects for adaptive networks,” Opt. Comput. Process. 31, 219–232 (1991).

Soffer, B. H.

Soskin, M. S.

V. Y. Bazhenov, M. S. Soskin, V. B. Taranenko, M. V. Vasnetsov, “Biopolymers for real-time optical processing,” in Optical Processing and Computing, H. H. Arsenault, T. Szoplik, B. Macukow, eds. (Academic, New York, 1989), Chap. 4.

Stepanov, S. I.

S. I. Stepanov, M. P. Petrov, “Degenerate four-wave mixing via shifted phase holograms in cubic photorefractive crystals,” Opt. Commun. 53, 64–69 (1985).
[CrossRef]

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Phhotorefractive Crystals in Coherent Optical Systems (Springer-Verlag, New York, 1991).

Stoll, M. H.

Suzuki, Y.

Szu, H. H.

Tackitt, M. C.

Taketomi, Y.

Tanguay, A. R.

R. V. Johnson, A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. 25, 235–249 (1986).

B. K. Jenkins, A. R. Tanguay, “Photonic implementations of neural networks,” in Neural Networks for Signal Processing, B. Kosko, ed. (Prentice-Hall, Englewood Cliffs, N.J., 1992), Chap. 9, pp. 287–382.

Taranenko, V. B.

V. Y. Bazhenov, M. S. Soskin, V. B. Taranenko, M. V. Vasnetsov, “Biopolymers for real-time optical processing,” in Optical Processing and Computing, H. H. Arsenault, T. Szoplik, B. Macukow, eds. (Academic, New York, 1989), Chap. 4.

TeKolste, R.

Title, M. A.

S. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, “One-dimensional silicon/PLZT spatial light modulators,” Opt. Eng. 26, 406–413 (1986).

Tkachenko, N. V.

V. V. Voronov, I. R. Dorosh, Y. S. Kuz’minov, N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[CrossRef]

Todorov, T.

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

Tomov, N.

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

Toyoda, H.

Underwood, I.

I. Underwood, D. G. Vass, R. M. Sillitto, “Evaluation of an nMOS VLSI array for an adaptive liquid-crystal spatial light modulator,” Proc. Inst. Electr. Eng. 133, 77–82 (1986).

Vasnetsov, M. V.

V. Y. Bazhenov, M. S. Soskin, V. B. Taranenko, M. V. Vasnetsov, “Biopolymers for real-time optical processing,” in Optical Processing and Computing, H. H. Arsenault, T. Szoplik, B. Macukow, eds. (Academic, New York, 1989), Chap. 4.

Vass, D. G.

D. J. McKnight, D. G. Vass, R. M. Sillitto, “Development of a spatial light modulator: a randomly addressed liquid-crystal-over-nMOS array,” Appl. Opt. 28, 4757–4761 (1989).
[CrossRef] [PubMed]

I. Underwood, D. G. Vass, R. M. Sillitto, “Evaluation of an nMOS VLSI array for an adaptive liquid-crystal spatial light modulator,” Proc. Inst. Electr. Eng. 133, 77–82 (1986).

von der Malsburg, C.

C. von der Malsburg, “Self-organization of orientation sensitive cells in the striate cortex,” Kybernetik 14, 85–100 (1973).
[CrossRef] [PubMed]

Voronov, V. V.

V. V. Voronov, I. R. Dorosh, Y. S. Kuz’minov, N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[CrossRef]

Wagner, K.

T. Huang, K. Wagner, “Holographic diffraction in photoanisotropic organic materials,” J. Opt. Soc. Am. A 10, 306–315 (1993).
[CrossRef]

T. Slagle, K. Wagner, “Winner-take-all spatial light modulator,” Opt. Lett. 17, 1164–1166 (1992).
[CrossRef] [PubMed]

J. Pankove, C. Radehaus, K. Wagner, “Winner-take-all neural net with memory,” Electron. Lett. 26, 349–350 (1990).
[CrossRef]

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

K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 26, 5061–5076 (1987).
[CrossRef] [PubMed]

K. Wagner, T. Slagle, “Competitive optical learning with winner-take-all modulators,” in Optical Computing, Vol. 6 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 280–283.

K. Wagner, R. Feinleib, “Competitive optoelectronic learning network,” in Neural Network Models for Optical Computing, R. A. Athale, J. Davis, eds., Proc. Soc. Photo-Opt. Instrum. Eng.882, 162–172 (1988).

T. Huang, K. Wagner, “Photoanisotropic incoherent-to-coherent optical converter,” Appl. Opt. (to be published).

Waidelich, W.

H. J. Mager, O. Wess, W. Waidelich, “Sequential associative information storage and reconstruction in a holographic circuit,” Opt. Commun. 9, 156–160 (1973).
[CrossRef]

Wang, C. H.

Wang, J. H.

S. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, “One-dimensional silicon/PLZT spatial light modulators,” Opt. Eng. 26, 406–413 (1986).

Wess, O.

H. J. Mager, O. Wess, W. Waidelich, “Sequential associative information storage and reconstruction in a holographic circuit,” Opt. Commun. 9, 156–160 (1973).
[CrossRef]

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and application of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

Wullert, J. R.

Yariv, A.

A. Yariv, S.-K. Kwong, “Associative memories based on message-bearing optical modes in phase-conjugate resonators,” Opt. Lett. 11, 186–188 (1986).
[CrossRef] [PubMed]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and application of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

Yeh, P.

Yoshinaga, H.

K. Kitayama, H. Yoshinaga, T. Hara, “Experiments of learning in optical perceptron-like and multilayer neural networks,” in Proceedings of the Third International Joint Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1989), Vol. 2, pp. 465–471.
[CrossRef]

Yu, F. T. S.

T. Lu, F. T. S. Yu, D. A. Gregory, “Self-organizing optical neural network for unsupervised learning,” Opt. Eng. 29, 1107–1113 (1990).
[CrossRef]

ZePDovich, B. Y.

V. N. Blaschuk, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, B. Y. ZePDovich, “Wavefront reversal with angular tilting-theory and experiment for the four-wave mixing,” Opt. Commun. 31, 383–387 (1979).
[CrossRef]

Zhang, L.

M. Kranzdorf, B. J. Bigner, L. Zhang, K. M. Johnson, “Optical connectionist machine with polarization based bipolar weight values,” Opt. Eng. 28, 844–848 (1989).

Zipser, D.

D. E. Rumelhart, D. Zipser, “Feature discovery by competitive learning,” Cognit. Sci. 9, 75–112 (1985).
[CrossRef]

Appl. Op.

D. Haronian, A. Lewis, “Elements of a unique bacteriorhodopsin neural network architecture,” Appl. Op. 30, 597–608 (1991).
[CrossRef]

Appl. Opt.

C. G. Guest, R. TeKolste, “Designs and devices for optical bidirectional associative memories,” Appl. Opt. 26, 5055–5060 (1987).
[CrossRef] [PubMed]

J. J. A. Couture, R. A. Lessard, “Modulation transfer function measurements for thin layers of azo dyes in PVA matrix used as an optical recording material,” Appl. Opt. 27, 3368–3374 (1988).
[CrossRef] [PubMed]

H. Lee, “Volume holographic global and local interconnecting patterns with maximal capacity and minimal first-order crosstalk,” Appl. Opt. 28, 5312–5316 (1989).
[CrossRef] [PubMed]

J. H. Hong, S. Campbell, P. Yeh, “Optical pattern classifier with perceptron learning,” Appl. Opt. 29, 3019–3025 (1990).
[CrossRef] [PubMed]

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

J. Shamir, H. Caulfield, R. Johnson, “Massive holographic interconnections and their limitations,” Appl. Opt. 28, 311–324 (1989).
[CrossRef] [PubMed]

G. Y. Sirat, A. D. Maruani, R. C. Chevallier, “Frequency multiplexed raster neural networks. 1. Theory,” Appl. Opt. 28, 1429–1435 (1989).
[CrossRef] [PubMed]

K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 26, 5061–5076 (1987).
[CrossRef] [PubMed]

M. Ishikawa, N. Mukohzaka, H. Toyoda, Y. Suzuki, “Experimental studies on learning capabilities of optical associative memory,” Appl. Opt. 29, 289–295 (1990).
[CrossRef] [PubMed]

C. H. Wang, B. K. Jenkins, “Subtracting incoherent optical neuron model: analysis, experiment, and applications,” Appl. Opt. 29, 2171–2186 (1990).
[CrossRef] [PubMed]

Y. Owechko, “Optoelectronic resonator neural networks,” Appl. Opt. 26, 5104–5111 (1987).
[CrossRef] [PubMed]

G. A. Carpenter, S. Grossberg, “Art 2: self-organization of stable category recognition codes for analog input patterns,” Appl. Opt. 26, 4919–4930 (1987).
[CrossRef] [PubMed]

D. J. McKnight, D. G. Vass, R. M. Sillitto, “Development of a spatial light modulator: a randomly addressed liquid-crystal-over-nMOS array,” Appl. Opt. 28, 4757–4761 (1989).
[CrossRef] [PubMed]

Appl. Phys.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Appl. Phys. Lett.

A. L. Lentine, H. S. Hinton, D. Miller, J. E. Henry, J. E. Cunningham, L. Chirovsky, “Symmetric self-electro-optic effect device: optical set-reset latch,” Appl. Phys. Lett. 52, 1419–1421 (1988).
[CrossRef]

N. A. Clark, S. T. Lagerwall, “Submicrosecond bistable electro-optic switching in liquid crystals,” Appl. Phys. Lett. 36, 899–901 (1980).
[CrossRef]

Cognit. Sci.

D. E. Rumelhart, D. Zipser, “Feature discovery by competitive learning,” Cognit. Sci. 9, 75–112 (1985).
[CrossRef]

S. Grossberg, “Competitive learning, from interactive activation to adaptive resonance,” Cognit. Sci. 11, 23–63 (1987).
[CrossRef]

Electron. Lett.

J. Pankove, C. Radehaus, K. Wagner, “Winner-take-all neural net with memory,” Electron. Lett. 26, 349–350 (1990).
[CrossRef]

IEEE J. Quantum Electron.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and application of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

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

IEEE Trans. Neural Net.

B. Kosko, “Stochastic competitive learning,” IEEE Trans. Neural Net. 2, 522–529 (1991).
[CrossRef]

M. Lemmon, B. V. K. V. Kumar, “Competitive learning with generalized winner-take-all activation,” IEEE Trans. Neural Net. 3, 167–175 (1992).
[CrossRef]

J. Appl. Phys.

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

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Kybernetik

C. von der Malsburg, “Self-organization of orientation sensitive cells in the striate cortex,” Kybernetik 14, 85–100 (1973).
[CrossRef] [PubMed]

Nature (London)

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

Neural Computat.

E. B. Baum, D. Haussier, “What size net gives valid generalization,” Neural Computat. 1, 151–160 (1989).
[CrossRef]

Opt. Commun.

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi-two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[CrossRef]

V. N. Blaschuk, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, B. Y. ZePDovich, “Wavefront reversal with angular tilting-theory and experiment for the four-wave mixing,” Opt. Commun. 31, 383–387 (1979).
[CrossRef]

H. J. Mager, O. Wess, W. Waidelich, “Sequential associative information storage and reconstruction in a holographic circuit,” Opt. Commun. 9, 156–160 (1973).
[CrossRef]

S. I. Stepanov, M. P. Petrov, “Degenerate four-wave mixing via shifted phase holograms in cubic photorefractive crystals,” Opt. Commun. 53, 64–69 (1985).
[CrossRef]

Opt. Comput. Process.

C. W. Slinger, “Weighted volume interconnects for adaptive networks,” Opt. Comput. Process. 31, 219–232 (1991).

Opt. Eng.

R. V. Johnson, A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. 25, 235–249 (1986).

D. R. Pape, “Multichannel Bragg cells: design, performance, and applications,” Opt. Eng. 31, 2148–2158 (1992).
[CrossRef]

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).

M. Kranzdorf, B. J. Bigner, L. Zhang, K. M. Johnson, “Optical connectionist machine with polarization based bipolar weight values,” Opt. Eng. 28, 844–848 (1989).

T. Lu, F. T. S. Yu, D. A. Gregory, “Self-organizing optical neural network for unsupervised learning,” Opt. Eng. 29, 1107–1113 (1990).
[CrossRef]

E. G. Paek, D. Psaltis, “Optical associative memory using Fourier transform holograms,” Opt. Eng. 26, 428–433 (1987).

S. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, “One-dimensional silicon/PLZT spatial light modulators,” Opt. Eng. 26, 406–413 (1986).

Opt. Lett.

J. Jang, S. Jung, S. Lee, S. Shin, “Optical implementation of the Hopfield model for two-dimensional associative memory,” Opt. Lett. 13, 248–260 (1988).
[CrossRef] [PubMed]

J. Hong, D. Psaltis, “Storage capacity of holographic associative memories,” Opt. Lett. 11, 812–814 (1986).
[CrossRef] [PubMed]

B. H. Soffer, G. J. Dunning, Y. Owechko, E. Marom, “Associative holographic memory with feedback using phase conjugate mirrors,” Opt. Lett. 11, 118–120 (1986).
[CrossRef] [PubMed]

I. Shariv, O. Gila, A. A. Friesem, “All-optical bipolar neural network with polarization-modulating neurons,” Opt. Lett. 16, 1692–1694 (1991).
[CrossRef] [PubMed]

D. Z. Anderson, “Coherent optical eigenstate memory,” Opt. Lett. 11, 45–47 (1986).
[CrossRef]

A. Yariv, S.-K. Kwong, “Associative memories based on message-bearing optical modes in phase-conjugate resonators,” Opt. Lett. 11, 186–188 (1986).
[CrossRef] [PubMed]

G. J. Dunning, E. Marom, Y. Owechko, B. H. Soffer, “All-optical associative memory with shift invariance and multiple-image recall,” Opt. Lett. 12, 346–348 (1987).
[CrossRef] [PubMed]

L.-S. Lee, M. H. Stoll, M. C. Tackitt, “Continuous-time optical neural network associative memory,” Opt. Lett. 14, 162–164 (1989).
[CrossRef] [PubMed]

D. Psaltis, N. Farhat, “Optical information processing based on an associative memory model of neural nets with thresholding and feedback,” Opt. Lett. 10, 98–100 (1985).
[CrossRef]

R. A. Athale, H. H. Szu, C. B. Friedlander, “Optical implementation of associative memory with controllable nonlinearity in the correlation domain,” Opt. Lett. 11, 482–484 (1986).
[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]

D. A. Jared, K. M. Johnson, “Optically addressed thresholding very-large-scale-integration/liquid-crystal spatial light modulators,” Opt. Lett. 16, 967–969 (1991).
[CrossRef] [PubMed]

T. Slagle, K. Wagner, “Winner-take-all spatial light modulator,” Opt. Lett. 17, 1164–1166 (1992).
[CrossRef] [PubMed]

L. Cheng, P. Yeh, “Cross-polarization beam coupling in photorefractive GaAs crystals,” Opt. Lett. 13, 50–52 (1988).
[CrossRef] [PubMed]

J. E. Ford, Y. Fainman, S. H. Lee, “Array interconnection by phase-coded optical correlation,” Opt. Lett. 15, 1089–1091 (1990).
[CrossRef]

H. Lee, “Cross-talk effects in multiplexed volume holograms,” Opt. Lett. 13, 874–876 (1988).
[CrossRef] [PubMed]

R. Rajbenbach, B. Imbert, J. P. Huignard, S. Mallick, “Near-infrared four-wave mixing with gain and self-starting oscillators with photorefractive gas,” Opt. Lett. 14, 78–80 (1989).
[CrossRef] [PubMed]

C. Gu, P. Yeh, “Scattering due to randomly distributed charge particles in photorefractive crystals,” Opt. Lett. 16, 1572–1574 (1991).
[CrossRef] [PubMed]

Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, “Incremental recording for photorefractive hologram multiplexing,” Opt. Lett. 16, 1774–1776 (1991).
[CrossRef] [PubMed]

L. K. Cotter, T. J. Drabik, R. J. Dillon, M. A. Handschy, “Ferroelectric-liquid-crystal/silicon-integrated-circuit spatial light modulator,” Opt. Lett. 15, 291–293 (1990).
[CrossRef] [PubMed]

Proc. Inst. Electr. Eng.

I. Underwood, D. G. Vass, R. M. Sillitto, “Evaluation of an nMOS VLSI array for an adaptive liquid-crystal spatial light modulator,” Proc. Inst. Electr. Eng. 133, 77–82 (1986).

Sov. J. Quantum Electron.

V. V. Voronov, I. R. Dorosh, Y. S. Kuz’minov, N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[CrossRef]

Other

K. Hsu, D. Brady, D. Psaltis, “Experimental demonstration of optical neural computers,” in Neural Information Processing Systems, D. Anderson, ed. (American Institute of Physics, New York, 1988), pp. 377–386.

K. Wagner, T. Slagle, “Competitive optical learning with winner-take-all modulators,” in Optical Computing, Vol. 6 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 280–283.

T. W. Ryan, “The resonance correlation network,” in Proceedings of the Second IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), Vol. I, pp. I-673–I-680.

T. Kohonen, Self-Organization and Associative Memory (Springer-Verlag, New York, 1984).

K. Wagner, R. Feinleib, “Competitive optoelectronic learning network,” in Neural Network Models for Optical Computing, R. A. Athale, J. Davis, eds., Proc. Soc. Photo-Opt. Instrum. Eng.882, 162–172 (1988).

V. Y. Bazhenov, M. S. Soskin, V. B. Taranenko, M. V. Vasnetsov, “Biopolymers for real-time optical processing,” in Optical Processing and Computing, H. H. Arsenault, T. Szoplik, B. Macukow, eds. (Academic, New York, 1989), Chap. 4.

P. Gunter, J. Huignard, eds., Photorefractive Materials and Their Applications 1, Vol. 62 of Topics in Applied Physics (Springer-Verlag, New York, 1988); Photorefractive Materials and Their Applications 2, Vol 63 of Topics in Applied Physics (Springer-Verlag, New York, 1988).
[CrossRef]

B. K. Jenkins, A. R. Tanguay, “Photonic implementations of neural networks,” in Neural Networks for Signal Processing, B. Kosko, ed. (Prentice-Hall, Englewood Cliffs, N.J., 1992), Chap. 9, pp. 287–382.

Topical Meeting Digest on Smart Pixels, IEEE Catalog 92TH0421-8 (Institute of Electrical and Electronics Engineers, New York, 1992).

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

C. X.-G. Gu, “Optical neural networks using volume holograms,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1990).

B. E. Boser, E. Sackinger, J. Bromley, Y. LeCunn, R. Howard, L. Jackel, “An analog neural network processor and its application to high-speed character recognition,” in Proceedings of the Third International Joint Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1991), Vol. 1, pp. 415–420.

T. Huang, K. Wagner, “Photoanisotropic incoherent-to-coherent optical converter,” Appl. Opt. (to be published).

K. Kitayama, H. Yoshinaga, T. Hara, “Experiments of learning in optical perceptron-like and multilayer neural networks,” in Proceedings of the Third International Joint Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1989), Vol. 2, pp. 465–471.
[CrossRef]

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Phhotorefractive Crystals in Coherent Optical Systems (Springer-Verlag, New York, 1991).

J. Lazzaro, S. Ryckebusch, M. A. Mahowald, C. A. Mead, “Winner-take-all networks of O(N) complexity,” in Advances in Neural Information Processing Systems 1, D. Touretzky, ed. (Kaufmann, Los Altos, Calif., 1989), pp. 703–711.

C. Mead, “Adaptive retina,” in Analog VLSI Implementation of Neural SystemsC. Mead, ed. (Kluwer, Norwell, Mass., 1989), Chap. 10, pp. 239–246.
[CrossRef]

D. A. Jared, K. M. Johnson, “Ferroelectric liquid crystal spatial light modulators,” in Spatial Light Modulators and Applications III, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1150, pp. 46–60 (1990).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (21)

Fig. 1
Fig. 1

Architecture of the lensless self-aligning optical competitive learning system.

Fig. 2
Fig. 2

Competitive learning network with N inputs and M outputs, broken into two competitive WTA patches with m1 = 3 units in one and m2 = 2 units in the other.

Fig. 3
Fig. 3

(a) Undistorted input pattern vectors for the three classes, (b) magnitude of the weight matrix after 132 training epochs.

Fig. 4
Fig. 4

(a) Competitive learning algorithm learning curves from computer simulation, showing the magnitude of the inputs to the two-unit competitive array versus the training epoch number for noisy versions of the three patterns; (b) learning curves for the five-unit competitive array.

Fig. 5
Fig. 5

Same as Fig. 4(a) but with WTA modulation of the reflected input.

Fig. 6
Fig. 6

Fourier hologram competitive learning architecture with the inclusion of spatially separated modulators and detectors on the WTA device in order to achieve winning-unit power normalization and gain.

Fig. 7
Fig. 7

(a) Geometry of 4-f volume holographic recording with sparse grids to break the Bragg degeneracies of a volume holographic interconnection, (b) k-space (or momentum space) representation of Bragg matching with the sparse grids. FT lenses, Fourier-transform lenses.

Fig. 8
Fig. 8

Simulation of light from the input SLM propagating through the hologram and being imaged upon the phase-conjugate mirror by the two lenses in a 4-f configuration. After 400 pattern presentations, a small portion is diffracted toward the pixels in the WTA array, shown in the upper left.

Fig. 9
Fig. 9

Backward-propagating light from the phase-conjugate mirror interferes with the light from the winning pixels in the volume hologram to complete one outer-product holographic weight matrix perturbation.

Fig. 10
Fig. 10

(a) Optical-system-simulation learning curves for the two-unit competitive patch, showing WTA unit inputs for the three patterns over 133 training epochs, (b) learning curves for the five-unit competitive patch.

Fig. 11
Fig. 11

Final state of the index perturbation in the organic hologram reached after a successful learning sequence of 400 cycles.

Fig. 12
Fig. 12

Optical wave-vector space that shows the permitted propagating optical modes and the grating wave vectors formed between them: (a) self-aligned readout is accomplished by the beams propagating up (forward propagation) from the SLM, which are diffracted toward the WTA detectors; (b) recording is performed by the beams propagating down (backward propagation) from the PCM and WTA modulators; (c) grating wave-vector space showing the Kx and Kz component of each grating and its conjugate.

Fig. 13
Fig. 13

(a) Log of the Fourier transform of the final state reached by the holographic index perturbation after competitive learning, (b) linear scaling of a magnified version of one of the off-axis sidebands, showing the individual Fourier orders responsible for the learning.

Fig. 14
Fig. 14

Diagram of the VLSI/LC device: (a) external view, (b) cross section of an individual pixel.

Fig. 15
Fig. 15

Cross-sectional diagram of two units of a VLSI/LC WTA device.

Fig. 16
Fig. 16

Schematic diagram of one WTA unit.

Fig. 17
Fig. 17

VLSI circuit layout of two WTA units.

Fig. 18
Fig. 18

Photomicrographs of part of a fabricated chip showing coarse-array topology of the modulators and the detectors: (a) structure with the modulators directly on top of the detectors, (b) one row of the structure with the modulators adjacent to the detector and to the WTA circuitry.

Fig. 19
Fig. 19

Photomicrographs of a one-dimensional array showing optical WTA behavior: (a) array under uniform illumination, (b) array with additional illumination on the fifth unit.

Fig. 20
Fig. 20

Modulator voltage versus the ratio of the input optical intensities for different values of Vth: Vb = 1.0 V, Vth = 1.0 V (upper); Vb = 1.0 V, Vth = 1.2 V (lower).

Fig. 21
Fig. 21

Time response of an eight-unit WTA circuit with optical inputs and electrical outputs.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

p i = j N W i j x j = W i · x .
y i = { 1 for p i p i ( i M k + 1 , , M k + m k ) 0 otherwise .
Δ W i j = η x j y i ,
Δ W i j = η x j | x | y i α W i j ,
p ( j 1 , , j m ) = J ! m ! m J l = 1 J + 1 c l ! i = 1 m j i ! ,
P i = | j N W ˆ i j x ˆ j | 2 .
d W i j r d t = η cos ϕ x ˆ j | x | Y i α W i j r + σ r , d W i j r d t = η sin ϕ x ˆ j | x | Y i α W i j i + σ i .
B ( r ) = j M b j exp [ i Φ j ( r ) ] exp ( i ω t ) + c . c . ,
A * ( r ) = K N a k * exp [ i Ψ k ( r ) ] exp ( i ω t ) + c . c . ,
δ Δ n ( r ) = η Δ t ( A * B * + c . c . ) = η Δ t ( k N j M a k * b j * exp { i [ Φ j ( r ) Ψ k ( r ) ] } + c . c . ) .
A η Δ t ( A * B * ) = η Δ t { j M b j * exp [ i Φ j ( r ) ] exp ( i ω t ) + c . c . } × | k N a k | 2 .
Δ n ( r , t ) = η 0 t exp [ ( t t ) / τ ] A * ( r , t ) B * ( r , t ) d t η k N j M a k * b j * exp { i [ Φ j ( r ) Ψ k ( r ) ] } + c . c .
d Δ n ( r ) d t = η I I ( r , t ) α I I ( r , t ) Δ n ( r ) ,
η A 1 ( r , t ) A 2 * ( r , t ) exp { [ ( k 1 k 2 ) · r ] } α ( | A 1 ( r , t ) | 2 + | A 2 ( r , t ) | 2 ) Δ n ( r ) ,
d Δ n ( r ) d t = β I I ( r ) Δ n ( r ) τ ,
= β [ | A 1 ( r , t ) | 2 + | A 2 ( r , t ) | 2 + A 1 ( r , t ) A 2 * ( r , t ) exp [ i ( k 1 k 2 ) · r ] Δ n ( r ) τ ,

Metrics