Abstract

An associative-memory model and its optical implementation with grating structures are presented. The transmission function of each pixel of the content-addressable memory is calculated by use of scalar diffraction theory. The filter of the calculated transmission function can be fabricated with computer-generated holography and a multiexposure holographic technique. The proposed approach is found useful in terms of storage and the simple thresholding at the number of on-state pixels in the input.

© 1994 Optical Society of America

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References

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  1. T. Kohonen, Self-Organization and Associative Memory (Springer-Verlag, New York, 1984).
  2. J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Nat. Acad. Sci. USA 79, 2554–2558 (1982).
    [CrossRef] [PubMed]
  3. D. Psaltis, N. E. Farhat, “Optical information processing based on an associative-memory of neural nets with thresholding and feedback,” Opt. Lett. 10, 98–103 (1985).
    [CrossRef] [PubMed]
  4. E. G. Paek, D. Psaltis, “Optical associative memories using Fourier transform holograms,” Opt. Eng. 26, 428–433 (1987).
  5. B. Soffer, G. J. Dunning, Y. Owechko, E. Marom, “Associative holographic memory with feedback using phase-conjugating mirrors,” Opt. Lett. 11, 118–120 (1986).
    [CrossRef] [PubMed]
  6. H. J. White, W. A. Wright, “Holographic implementation of a Hopfield model with discrete weightings,” Appl. Opt. 27, 331–338 91987).
    [CrossRef]
  7. S. H. Song, S. S. Lee, “Properties of holographic associative memory prepared by polarization encoded process,” Appl. Opt. 25, 3149–3154 (1988).
    [CrossRef]
  8. T. Lu, X. Xu, S. Wu, F. T. S. Yu, “Neural network model using interpattern association,” Appl. Opt. 29, 284–288 (1990).
    [CrossRef] [PubMed]
  9. F. T. S. Yu, T. Lu, X. Yang, D. A. Gregory, “Optical neural network with pocket-sized liquid-crystal television,” Opt. Lett. 15, 863–865 (1990).
    [CrossRef] [PubMed]
  10. See, for example, J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  11. M. Kuato, K. Sakada, “Computer generated holograms: an application to intensity variable and demultiplexing hologram,” Appl. Opt. 31, 630–635 (1992).
    [CrossRef]
  12. T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical digital truth table look-up processing,” Optical Eng. 24, 48–58 (1985).

1992 (1)

1990 (2)

1988 (1)

S. H. Song, S. S. Lee, “Properties of holographic associative memory prepared by polarization encoded process,” Appl. Opt. 25, 3149–3154 (1988).
[CrossRef]

1987 (2)

H. J. White, W. A. Wright, “Holographic implementation of a Hopfield model with discrete weightings,” Appl. Opt. 27, 331–338 91987).
[CrossRef]

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

1986 (1)

1985 (2)

D. Psaltis, N. E. Farhat, “Optical information processing based on an associative-memory of neural nets with thresholding and feedback,” Opt. Lett. 10, 98–103 (1985).
[CrossRef] [PubMed]

T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical digital truth table look-up processing,” Optical Eng. 24, 48–58 (1985).

1982 (1)

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

Dunning, G. J.

Farhat, N. E.

Gaylord, T. K.

T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical digital truth table look-up processing,” Optical Eng. 24, 48–58 (1985).

Gregory, D. A.

Guest, C. C.

T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical digital truth table look-up processing,” Optical Eng. 24, 48–58 (1985).

Hopfield, J. J.

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

Kohonen, T.

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

Kuato, M.

Lee, S. S.

S. H. Song, S. S. Lee, “Properties of holographic associative memory prepared by polarization encoded process,” Appl. Opt. 25, 3149–3154 (1988).
[CrossRef]

Lu, T.

Marom, E.

Mirsalehi, M. M.

T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical digital truth table look-up processing,” Optical Eng. 24, 48–58 (1985).

Owechko, Y.

Paek, E. G.

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

Psaltis, D.

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

D. Psaltis, N. E. Farhat, “Optical information processing based on an associative-memory of neural nets with thresholding and feedback,” Opt. Lett. 10, 98–103 (1985).
[CrossRef] [PubMed]

Sakada, K.

Soffer, B.

Song, S. H.

S. H. Song, S. S. Lee, “Properties of holographic associative memory prepared by polarization encoded process,” Appl. Opt. 25, 3149–3154 (1988).
[CrossRef]

White, H. J.

Wright, W. A.

Wu, S.

Xu, X.

Yang, X.

Yu, F. T. S.

Appl. Opt. (4)

Opt. Eng. (1)

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

Opt. Lett. (3)

Optical Eng. (1)

T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical digital truth table look-up processing,” Optical Eng. 24, 48–58 (1985).

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

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

Other (2)

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

See, for example, J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (5)

Fig. 1
Fig. 1

(a) Three input patterns (T, +, and X) stored in the memory, (b) partial input given to the memory, (c) pattern generated at the output, (d) stored pattern obtained at the output after thresholding.

Fig. 2
Fig. 2

Schematic diagram of the proposed optical-implementation scheme.

Fig. 3
Fig. 3

Schematic diagram of the proposed holographic associative-memory fabrication scheme.

Fig. 4
Fig. 4

Input transparency used for obtaining the required transmission function at pixel (1, 1).

Fig. 5
Fig. 5

Schematic diagram of the holographic associative-memory fabrication scheme that uses multiple shots.

Equations (7)

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V i out = p V i p j V j p V j in .
V i p 0 = 1 for V i out n = 0 for V i out < n .
t ( x , y ) = 1 + m cos [ ( 2 π / λ z ) L y ] ,
U ( x 0 , y 0 ) = exp ( j 2 π z / λ ) exp [ j ( π / λ z ) ( x 0 2 + y 0 2 ) ] j λ z × t ( x , y ) x exp [ - j ( 2 π / λ z ) ( x 0 x + y 0 y ) ] d x d y .
I ( x 0 , y 0 ) = ( 1 / 4 π 2 ) δ ( x 0 , y 0 ) + ( m / 8 π 2 ) × [ δ ( x 0 , y 0 + L ) + δ ( x 0 , y 0 - L ) ] .
T i j ( x , y ) = 1 + 1 k p = 1 p n = 1 N m = 1 M S n m p S i j p × ( cos 2 π λ D { ( m - j ) a x + [ L - ( n + N - i ) a ] y } ) ,
k = p = 1 p n = 1 N m = 1 M S n m p .

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