Abstract

A grating-lens combination unit is developed to form a scaling self-transform function that can self-image on scale. Then an array of many such grating-lens units is used for the optical interconnection of a two-dimensional neural network, and experiments are carried out. We find that our idea is feasible, the optical interconnection system is simple, and optical adjustment is easy.

© 1998 Optical Society of America

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1997 (1)

J. Hua, L. Liu, G. Li, “Dual self-transform function,” J. Phys. A 30, 1–4 (1997).
[CrossRef]

1996 (2)

1995 (1)

A. Lakhlakia, “Physical fractals: self-similarity and square-integrability,” Speculat. Sci. Technol. 18, 153–156 (1995).

1994 (3)

L. Liu, “Periodic self-Fourier–Fresnel function,” J. Phys. A 27, L285–L289 (1994).
[CrossRef]

E. Bonet, P. Andrés, J. C. Barreiro, A. Pons, “Self-imaging properties of periodic microlens array: versatile array illuminator realization,” Opt. Commun. 106, 39–44 (1994).
[CrossRef]

V. Arrizon, J. Ojeda-Castaneda, “Multilevel phase gratings for array illuminators,” Appl. Opt. 33, 5925–5931 (1994).
[CrossRef] [PubMed]

1992 (2)

1991 (1)

M. J. Caola, “Self-Fourier function,” J. Phys. A 24, L1143–L1144 (1991).
[CrossRef]

1990 (6)

1989 (2)

F. Ito, K. Kitayama, “Optical implementation of the Hopfield neural network using multiple fiber nets,” Appl. Opt. 28, 4176–4181 (1989).
[CrossRef] [PubMed]

S. Lin, L. Liu, Z. Wang, “Optical implementation of the 2-D Hopfield model for a 1-D associative memory,” Opt. Commun. 76, 87–91 (1989).
[CrossRef]

1988 (1)

1987 (1)

1986 (1)

1985 (1)

1983 (1)

1982 (1)

J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

Andrés, P.

E. Bonet, P. Andrés, J. C. Barreiro, A. Pons, “Self-imaging properties of periodic microlens array: versatile array illuminator realization,” Opt. Commun. 106, 39–44 (1994).
[CrossRef]

Arrizon, V.

Athale, R. A.

Barreiro, J. C.

E. Bonet, P. Andrés, J. C. Barreiro, A. Pons, “Self-imaging properties of periodic microlens array: versatile array illuminator realization,” Opt. Commun. 106, 39–44 (1994).
[CrossRef]

Bonet, E.

E. Bonet, P. Andrés, J. C. Barreiro, A. Pons, “Self-imaging properties of periodic microlens array: versatile array illuminator realization,” Opt. Commun. 106, 39–44 (1994).
[CrossRef]

Brady, D.

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

Caola, M. J.

M. J. Caola, “Self-Fourier function,” J. Phys. A 24, L1143–L1144 (1991).
[CrossRef]

Choen-Sabban, Y.

Dunning, G. J.

Farhat, N. H.

Friedlander, C. B.

Gregory, D. A.

Gu, X-G.

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

Hopfield, J. J.

J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

Hua, J.

J. Hua, L. Liu, G. Li, “Dual self-transform function,” J. Phys. A 30, 1–4 (1997).
[CrossRef]

J. Hua, L. Liu, “Exact periodic self-Fourier–Fresnel function,” Optik 103, 75–76 (1996).

Ito, F.

Joyeux, D.

Kitayama, K.

Lakhlakia, A.

A. Lakhlakia, “Physical fractals: self-similarity and square-integrability,” Speculat. Sci. Technol. 18, 153–156 (1995).

Leger, J. R.

Li, G.

J. Hua, L. Liu, G. Li, “Dual self-transform function,” J. Phys. A 30, 1–4 (1997).
[CrossRef]

Lin, S.

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

S. Lin, L. Liu, Z. Wang, “Optical implementation of the 2-D Hopfield model for a 1-D associative memory,” Opt. Commun. 76, 87–91 (1989).
[CrossRef]

Liu, L.

J. Hua, L. Liu, G. Li, “Dual self-transform function,” J. Phys. A 30, 1–4 (1997).
[CrossRef]

J. Hua, L. Liu, “Exact periodic self-Fourier–Fresnel function,” Optik 103, 75–76 (1996).

L. Liu, “Periodic self-Fourier–Fresnel function,” J. Phys. A 27, L285–L289 (1994).
[CrossRef]

L. Liu, X. Liu, L. Ye, “Joint Talbot effect and logic-operated moiré patterns,” J. Opt. Soc. Am. A 7, 970–976 (1990).
[CrossRef]

C. Pan, L. Liu, “Study of fill factor in self-imaging aperture filling of phase-locked arrays,” Opt. Commun. 77, 210–214 (1990).
[CrossRef]

S. Lin, L. Liu, Z. Wang, “Optical implementation of the 2-D Hopfield model for a 1-D associative memory,” Opt. Commun. 76, 87–91 (1989).
[CrossRef]

Liu, T.

Liu, X.

Lohmann, A. W.

Lopez-Olazagasti, E.

Lu, T.

Marom, E.

Mendlovic, D.

Ojeda-Castaneda, J.

Owechko, Y.

Pan, C.

C. Pan, L. Liu, “Study of fill factor in self-imaging aperture filling of phase-locked arrays,” Opt. Commun. 77, 210–214 (1990).
[CrossRef]

Peak, E.

Pons, A.

E. Bonet, P. Andrés, J. C. Barreiro, A. Pons, “Self-imaging properties of periodic microlens array: versatile array illuminator realization,” Opt. Commun. 106, 39–44 (1994).
[CrossRef]

Prata, A.

Psaltis, D.

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

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

Serrano-Heredia, A.

Soffer, B. H.

Swanson, G. J.

Szu, H. H.

Wang, Z.

S. Lin, L. Liu, Z. Wang, “Optical implementation of the 2-D Hopfield model for a 1-D associative memory,” Opt. Commun. 76, 87–91 (1989).
[CrossRef]

White, H. J.

Wright, W. A.

Yang, X.

Ye, L.

Yu, F. T. S.

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Phys. A (3)

M. J. Caola, “Self-Fourier function,” J. Phys. A 24, L1143–L1144 (1991).
[CrossRef]

J. Hua, L. Liu, G. Li, “Dual self-transform function,” J. Phys. A 30, 1–4 (1997).
[CrossRef]

L. Liu, “Periodic self-Fourier–Fresnel function,” J. Phys. A 27, L285–L289 (1994).
[CrossRef]

Nature (1)

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

Opt. Commun. (4)

E. Bonet, P. Andrés, J. C. Barreiro, A. Pons, “Self-imaging properties of periodic microlens array: versatile array illuminator realization,” Opt. Commun. 106, 39–44 (1994).
[CrossRef]

A. W. Lohmann, “Array illuminators and complexity theory,” Opt. Commun. 89, 167–172 (1992).
[CrossRef]

C. Pan, L. Liu, “Study of fill factor in self-imaging aperture filling of phase-locked arrays,” Opt. Commun. 77, 210–214 (1990).
[CrossRef]

S. Lin, L. Liu, Z. Wang, “Optical implementation of the 2-D Hopfield model for a 1-D associative memory,” Opt. Commun. 76, 87–91 (1989).
[CrossRef]

Opt. Lett. (4)

Optik (1)

J. Hua, L. Liu, “Exact periodic self-Fourier–Fresnel function,” Optik 103, 75–76 (1996).

Proc. Natl. Acad. Sci. USA (1)

J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

Speculat. Sci. Technol. (1)

A. Lakhlakia, “Physical fractals: self-similarity and square-integrability,” Speculat. Sci. Technol. 18, 153–156 (1995).

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