Abstract

We designed and built a high-capacity neural network based on volume holographic interconnections in a photorefractive crystal. We used this system to implement a Kohonen topological map. We describe and justify our optical setup and present some experimental results of self-organization in the learning database.

© 2001 Optical Society of America

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References

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  1. N. H. Farhat, D. Psaltis, A. Prata, E. Paek, “Optical implementation of the Hopfield model,” Appl. Opt. 24, 1469–1475 (1985).
    [CrossRef] [PubMed]
  2. J. H. Hong, S. Campbell, P. Yeh, “Optical pattern classifier with perceptron learning,” Appl. Opt. 29, 3019–3025 (1990).
    [CrossRef] [PubMed]
  3. Y. Owechko, “Optical implementation of back-propagation neural networks using cascaded-grating holography,” Int. J. Opt. Comput. 2, 201–231 (1991).
  4. J. Duvillier, M. Killinger, K. Heggarty, K. Yao, J. L. de Bougrenet de la Tocnaye, “All-optical implementation of a self-organizing map: a preliminary approach,” Appl. Opt. 33, 258–266 (1994).
    [CrossRef] [PubMed]
  5. M. Barge, K. Heggarty, Y. Idan, R. Chevallier, “64-channel correlator implementing a Kohonen-like neural network for handwritten-digit recognition,” Appl. Opt. 35, 4655–4665 (1996).
    [CrossRef] [PubMed]
  6. C. Berger, N. Collings, R. Völke, M. T. Gale, T. Hessler, “A microlens-array-based optical neural network application,” Pure Appl. Opt. 6, 683–689 (1997).
    [CrossRef]
  7. M. Saffman, D. Montgomery, A. A. Zozulya, D. Z. Anderson, “Topology-preserving mappings in a self-imaging photorefractively pumped ring resonator,” Chaos, Solitons Fractals4, 2077–2092 (1994).
    [CrossRef]
  8. P. Aing, G. Pauliat, G. Roosen, “Noise issues in holographic photorefractive interconnections: application to neural networks,” Opt. Commun. 143, 87–94 (1997).
    [CrossRef]
  9. Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
    [CrossRef]
  10. Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network (Erratum),” Opt. Commun. 135, 335 (1997).
    [CrossRef]
  11. G. W. Burr, S. Kobras, H. Hanssen, H. Coufal, “Content-addressable data storage by use of volume holograms,” Appl. Opt. 38, 6779–6784 (1999).
    [CrossRef]
  12. K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 26, 5061–5076 (1987).
    [CrossRef] [PubMed]
  13. G. A. Betzos, A. Lainé, P. A. Mitkas, “Improved associative recall of binary data in volume holographic memories,” Opt. Commun. 171, 37–44 (1999).
    [CrossRef]
  14. H.-Y. S. Li, Y. Qiao, D. Psaltis, “Optical network for real-time face recognition,” Appl. Opt. 32, 5026–5035 (1993).
    [CrossRef] [PubMed]
  15. K. Wagner, T. M. Slagle, “Optical competitive learning with VLSI/liquid-crystal winner-take-all modulators,” Appl. Opt. 32, 1408–1435 (1993).
    [CrossRef] [PubMed]
  16. F. H. Mok, H. M. Stoll, “Holographic inner-product processor for pattern recognition,” in Optical Pattern Recognition IV, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE1701, 312–322 (1992).
  17. X. An, D. Psaltis, G. W. Burr, “Thermal fixing of 10,000 holograms in LiNbO3:Fe,” Appl. Opt. 38, 386–393 (1999).
    [CrossRef]
  18. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949–964 (1979).
    [CrossRef]
  19. H. Lee, X. G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal crosstalk,” J. Appl. Phys. 65, 2191–2194 (1989).
    [CrossRef]
  20. T. Kohonen, Self-organizing Maps (Springer-Verlag, Berlin, 1997).
    [CrossRef]
  21. T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Adaptive photorefractive neurons for self-organizing networks,” Opt. Commun. 109, 35–42 (1994).
    [CrossRef]
  22. Y. Frauel, G. Pauliat, G. Roosen, “Improvement of holographic neural networks by reducing the deleterious influence of the limited contrast of spatial light modulators,” Opt. Commun. 182, 311–319 (2000).
    [CrossRef]
  23. H.-Y. S. Li, D. Psaltis, “Three dimensional holographic disks,” Appl. Opt. 33, 3764–3774 (1994).
    [CrossRef] [PubMed]

2000 (1)

Y. Frauel, G. Pauliat, G. Roosen, “Improvement of holographic neural networks by reducing the deleterious influence of the limited contrast of spatial light modulators,” Opt. Commun. 182, 311–319 (2000).
[CrossRef]

1999 (3)

1997 (4)

C. Berger, N. Collings, R. Völke, M. T. Gale, T. Hessler, “A microlens-array-based optical neural network application,” Pure Appl. Opt. 6, 683–689 (1997).
[CrossRef]

P. Aing, G. Pauliat, G. Roosen, “Noise issues in holographic photorefractive interconnections: application to neural networks,” Opt. Commun. 143, 87–94 (1997).
[CrossRef]

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
[CrossRef]

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network (Erratum),” Opt. Commun. 135, 335 (1997).
[CrossRef]

1996 (1)

1994 (3)

1993 (2)

1991 (1)

Y. Owechko, “Optical implementation of back-propagation neural networks using cascaded-grating holography,” Int. J. Opt. Comput. 2, 201–231 (1991).

1990 (1)

1989 (1)

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

1987 (1)

1985 (1)

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949–964 (1979).
[CrossRef]

Aing, P.

P. Aing, G. Pauliat, G. Roosen, “Noise issues in holographic photorefractive interconnections: application to neural networks,” Opt. Commun. 143, 87–94 (1997).
[CrossRef]

An, X.

Anderson, D. Z.

M. Saffman, D. Montgomery, A. A. Zozulya, D. Z. Anderson, “Topology-preserving mappings in a self-imaging photorefractively pumped ring resonator,” Chaos, Solitons Fractals4, 2077–2092 (1994).
[CrossRef]

Barge, M.

Berger, C.

C. Berger, N. Collings, R. Völke, M. T. Gale, T. Hessler, “A microlens-array-based optical neural network application,” Pure Appl. Opt. 6, 683–689 (1997).
[CrossRef]

Betzos, G. A.

G. A. Betzos, A. Lainé, P. A. Mitkas, “Improved associative recall of binary data in volume holographic memories,” Opt. Commun. 171, 37–44 (1999).
[CrossRef]

Burr, G. W.

Campbell, S.

Chevallier, R.

Collings, N.

C. Berger, N. Collings, R. Völke, M. T. Gale, T. Hessler, “A microlens-array-based optical neural network application,” Pure Appl. Opt. 6, 683–689 (1997).
[CrossRef]

Coufal, H.

de Bougrenet de la Tocnaye, J. L.

Duvillier, J.

Farhat, N. H.

Frauel, Y.

Y. Frauel, G. Pauliat, G. Roosen, “Improvement of holographic neural networks by reducing the deleterious influence of the limited contrast of spatial light modulators,” Opt. Commun. 182, 311–319 (2000).
[CrossRef]

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
[CrossRef]

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network (Erratum),” Opt. Commun. 135, 335 (1997).
[CrossRef]

Gale, M. T.

C. Berger, N. Collings, R. Völke, M. T. Gale, T. Hessler, “A microlens-array-based optical neural network application,” Pure Appl. Opt. 6, 683–689 (1997).
[CrossRef]

Galstyan, T.

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network (Erratum),” Opt. Commun. 135, 335 (1997).
[CrossRef]

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
[CrossRef]

T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Adaptive photorefractive neurons for self-organizing networks,” Opt. Commun. 109, 35–42 (1994).
[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]

Hanssen, H.

Heggarty, K.

Hessler, T.

C. Berger, N. Collings, R. Völke, M. T. Gale, T. Hessler, “A microlens-array-based optical neural network application,” Pure Appl. Opt. 6, 683–689 (1997).
[CrossRef]

Hong, J. H.

Idan, Y.

Killinger, M.

Kobras, S.

Kohonen, T.

T. Kohonen, Self-organizing Maps (Springer-Verlag, Berlin, 1997).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949–964 (1979).
[CrossRef]

Lainé, A.

G. A. Betzos, A. Lainé, P. A. Mitkas, “Improved associative recall of binary data in volume holographic memories,” Opt. Commun. 171, 37–44 (1999).
[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]

Li, H.-Y. S.

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949–964 (1979).
[CrossRef]

Mitkas, P. A.

G. A. Betzos, A. Lainé, P. A. Mitkas, “Improved associative recall of binary data in volume holographic memories,” Opt. Commun. 171, 37–44 (1999).
[CrossRef]

Mok, F. H.

F. H. Mok, H. M. Stoll, “Holographic inner-product processor for pattern recognition,” in Optical Pattern Recognition IV, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE1701, 312–322 (1992).

Montgomery, D.

M. Saffman, D. Montgomery, A. A. Zozulya, D. Z. Anderson, “Topology-preserving mappings in a self-imaging photorefractively pumped ring resonator,” Chaos, Solitons Fractals4, 2077–2092 (1994).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949–964 (1979).
[CrossRef]

Owechko, Y.

Y. Owechko, “Optical implementation of back-propagation neural networks using cascaded-grating holography,” Int. J. Opt. Comput. 2, 201–231 (1991).

Paek, E.

Pauliat, G.

Y. Frauel, G. Pauliat, G. Roosen, “Improvement of holographic neural networks by reducing the deleterious influence of the limited contrast of spatial light modulators,” Opt. Commun. 182, 311–319 (2000).
[CrossRef]

P. Aing, G. Pauliat, G. Roosen, “Noise issues in holographic photorefractive interconnections: application to neural networks,” Opt. Commun. 143, 87–94 (1997).
[CrossRef]

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
[CrossRef]

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network (Erratum),” Opt. Commun. 135, 335 (1997).
[CrossRef]

T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Adaptive photorefractive neurons for self-organizing networks,” Opt. Commun. 109, 35–42 (1994).
[CrossRef]

Prata, A.

Psaltis, D.

Qiao, Y.

Roosen, G.

Y. Frauel, G. Pauliat, G. Roosen, “Improvement of holographic neural networks by reducing the deleterious influence of the limited contrast of spatial light modulators,” Opt. Commun. 182, 311–319 (2000).
[CrossRef]

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
[CrossRef]

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network (Erratum),” Opt. Commun. 135, 335 (1997).
[CrossRef]

P. Aing, G. Pauliat, G. Roosen, “Noise issues in holographic photorefractive interconnections: application to neural networks,” Opt. Commun. 143, 87–94 (1997).
[CrossRef]

T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Adaptive photorefractive neurons for self-organizing networks,” Opt. Commun. 109, 35–42 (1994).
[CrossRef]

Saffman, M.

M. Saffman, D. Montgomery, A. A. Zozulya, D. Z. Anderson, “Topology-preserving mappings in a self-imaging photorefractively pumped ring resonator,” Chaos, Solitons Fractals4, 2077–2092 (1994).
[CrossRef]

Slagle, T. M.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949–964 (1979).
[CrossRef]

Stoll, H. M.

F. H. Mok, H. M. Stoll, “Holographic inner-product processor for pattern recognition,” in Optical Pattern Recognition IV, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE1701, 312–322 (1992).

Villing, A.

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network (Erratum),” Opt. Commun. 135, 335 (1997).
[CrossRef]

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
[CrossRef]

T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Adaptive photorefractive neurons for self-organizing networks,” Opt. Commun. 109, 35–42 (1994).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949–964 (1979).
[CrossRef]

Völke, R.

C. Berger, N. Collings, R. Völke, M. T. Gale, T. Hessler, “A microlens-array-based optical neural network application,” Pure Appl. Opt. 6, 683–689 (1997).
[CrossRef]

Wagner, K.

Yao, K.

Yeh, P.

Zozulya, A. A.

M. Saffman, D. Montgomery, A. A. Zozulya, D. Z. Anderson, “Topology-preserving mappings in a self-imaging photorefractively pumped ring resonator,” Chaos, Solitons Fractals4, 2077–2092 (1994).
[CrossRef]

Appl. Opt. (10)

J. Duvillier, M. Killinger, K. Heggarty, K. Yao, J. L. de Bougrenet de la Tocnaye, “All-optical implementation of a self-organizing map: a preliminary approach,” Appl. Opt. 33, 258–266 (1994).
[CrossRef] [PubMed]

M. Barge, K. Heggarty, Y. Idan, R. Chevallier, “64-channel correlator implementing a Kohonen-like neural network for handwritten-digit recognition,” Appl. Opt. 35, 4655–4665 (1996).
[CrossRef] [PubMed]

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

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

G. W. Burr, S. Kobras, H. Hanssen, H. Coufal, “Content-addressable data storage by use of volume holograms,” Appl. Opt. 38, 6779–6784 (1999).
[CrossRef]

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

H.-Y. S. Li, Y. Qiao, D. Psaltis, “Optical network for real-time face recognition,” Appl. Opt. 32, 5026–5035 (1993).
[CrossRef] [PubMed]

K. Wagner, T. M. Slagle, “Optical competitive learning with VLSI/liquid-crystal winner-take-all modulators,” Appl. Opt. 32, 1408–1435 (1993).
[CrossRef] [PubMed]

X. An, D. Psaltis, G. W. Burr, “Thermal fixing of 10,000 holograms in LiNbO3:Fe,” Appl. Opt. 38, 386–393 (1999).
[CrossRef]

H.-Y. S. Li, D. Psaltis, “Three dimensional holographic disks,” Appl. Opt. 33, 3764–3774 (1994).
[CrossRef] [PubMed]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949–964 (1979).
[CrossRef]

Int. J. Opt. Comput. (1)

Y. Owechko, “Optical implementation of back-propagation neural networks using cascaded-grating holography,” Int. J. Opt. Comput. 2, 201–231 (1991).

J. Appl. Phys. (1)

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

Opt. Commun. (6)

G. A. Betzos, A. Lainé, P. A. Mitkas, “Improved associative recall of binary data in volume holographic memories,” Opt. Commun. 171, 37–44 (1999).
[CrossRef]

P. Aing, G. Pauliat, G. Roosen, “Noise issues in holographic photorefractive interconnections: application to neural networks,” Opt. Commun. 143, 87–94 (1997).
[CrossRef]

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
[CrossRef]

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network (Erratum),” Opt. Commun. 135, 335 (1997).
[CrossRef]

T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Adaptive photorefractive neurons for self-organizing networks,” Opt. Commun. 109, 35–42 (1994).
[CrossRef]

Y. Frauel, G. Pauliat, G. Roosen, “Improvement of holographic neural networks by reducing the deleterious influence of the limited contrast of spatial light modulators,” Opt. Commun. 182, 311–319 (2000).
[CrossRef]

Pure Appl. Opt. (1)

C. Berger, N. Collings, R. Völke, M. T. Gale, T. Hessler, “A microlens-array-based optical neural network application,” Pure Appl. Opt. 6, 683–689 (1997).
[CrossRef]

Other (3)

M. Saffman, D. Montgomery, A. A. Zozulya, D. Z. Anderson, “Topology-preserving mappings in a self-imaging photorefractively pumped ring resonator,” Chaos, Solitons Fractals4, 2077–2092 (1994).
[CrossRef]

F. H. Mok, H. M. Stoll, “Holographic inner-product processor for pattern recognition,” in Optical Pattern Recognition IV, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE1701, 312–322 (1992).

T. Kohonen, Self-organizing Maps (Springer-Verlag, Berlin, 1997).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Volume holographic interconnections.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

Thirty-six grid-correlated vectors (bidimensional topology). Bright parts, 0s; dark parts, 1s.

Fig. 4
Fig. 4

Computer simulation: classification of a grid of vectors with metric discrepancy between readout and writing. (a) Kohonen’s algorithm, (b) modified algorithm.

Fig. 5
Fig. 5

Topological organization with 45 chain-correlated vectors. Circles, the winning neurons. They are linked by the straight lines in order of vector number.

Fig. 6
Fig. 6

Topological organization with 100 chain-correlated vectors. Circles, the winning neurons. They are linked by the straight lines in order of vector number.

Fig. 7
Fig. 7

Topological organization with 36 grid-correlated vectors. Straight lines link the winning neurons (circles) that respond to neighboring vectors in the initial correlation grid.

Fig. 8
Fig. 8

Topological organization with 16 vectors that code characteristics of animals.

Tables (1)

Tables Icon

Table 1 Vector Coding of Characteristics of Animals

Equations (4)

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

Dk  i=1N δnikRi, 1kM,
Dk  Wk·I.
ΔWk  ΔtI-Wk.
IN=N-1×0, 1, 1, 1, 1, 1, 1, 45-N×0),

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