Abstract

The optical disk is a computer-addressable binary storage medium with very high capacity. More than 1010 bits of information can be recorded on a 12-cm-diameter optical disk. The natural two-dimensional format of the data recorded on an optical disk makes this medium particularly attractive for the storage of images and holograms, while parallel access provides a convenient mechanism through which such data may be retrieved. In this paper we discuss a closed-loop optical associative memory based on the optical disk. This system incorporates image correlation, using photorefractive media to compute the best association in a shift-invariant fashion. When presented with a partial or noisy version of one of the images stored on the optical disk, the optical system evolves to a stable state in which those stored images that best match the input are temporally locked in the loop.

© 1993 Optical Society of America

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References

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  1. D. Psaltis, M. A. Neifeld, A. Yamamura, S. Kobayashi, “Optical memory disks in optical information processing,” Appl. Opt. 29, 2038–2057 (1990).
    [CrossRef] [PubMed]
  2. D. Psaltis, M. A. Neifeld, A. Yamamura, “Image correlators using optical memory disks,” Opt. Lett. 14, 429–431 (1989).
    [CrossRef] [PubMed]
  3. A. A. Yamamura, M. A. Neifeld, S. Kobayashi, D. Psaltis, “Optical disk based artificial neural systems,” Opt. Comput. Process. 1, 3–12 (1991).
  4. D. Gabor, “Associative holographic memories,” IBM J. Res. Dev. 13, 156–159 (1969).
    [CrossRef]
  5. Y. Owechko, G. Dunning, E. Marom, B. Sofer, “Holographic associative memory with nonlinearities in the correlation domain,” Appl. Opt. 26, 1900–1910 (1987).
    [CrossRef] [PubMed]
  6. K. Hsu, H. Li, D. Psaltis, “Holographic implementation of a fully connected neural network,” Proc. IEEE 78, 1637–1645 (1990).
    [CrossRef]
  7. D. Anderson, “Coherent optical eigenstate memory,” Opt. Lett. 11, 56–58 (1986).
    [CrossRef] [PubMed]
  8. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
    [CrossRef]
  9. J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 114–120 (1987).
  10. C. Gu, J. Hong, S. Campbell, “2-D shift invariant volume holographic correlator,” Opt. Commun. 88, 4646–4648 (1992).
    [CrossRef]
  11. J. Lazzaro, S. Ryckebusch, M. A. Mahowald, C. A. Mead, “Winner-take-all networks of O(N) complexity,” in Advances in Neural Information Processing I, D. S. Touretzky, ed. (Kaufmann, San Mateo, Calif., 1989), pp. 703–711.
  12. C. Mead, Analog VLSI and Neural Systems (Addison-Wesley, Reading, Mass.1989), pp. 67–78.

1992 (1)

C. Gu, J. Hong, S. Campbell, “2-D shift invariant volume holographic correlator,” Opt. Commun. 88, 4646–4648 (1992).
[CrossRef]

1991 (1)

A. A. Yamamura, M. A. Neifeld, S. Kobayashi, D. Psaltis, “Optical disk based artificial neural systems,” Opt. Comput. Process. 1, 3–12 (1991).

1990 (2)

K. Hsu, H. Li, D. Psaltis, “Holographic implementation of a fully connected neural network,” Proc. IEEE 78, 1637–1645 (1990).
[CrossRef]

D. Psaltis, M. A. Neifeld, A. Yamamura, S. Kobayashi, “Optical memory disks in optical information processing,” Appl. Opt. 29, 2038–2057 (1990).
[CrossRef] [PubMed]

1989 (1)

1987 (1)

1986 (1)

1969 (1)

D. Gabor, “Associative holographic memories,” IBM J. Res. Dev. 13, 156–159 (1969).
[CrossRef]

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Anderson, D.

Campbell, S.

C. Gu, J. Hong, S. Campbell, “2-D shift invariant volume holographic correlator,” Opt. Commun. 88, 4646–4648 (1992).
[CrossRef]

Dunning, G.

Gabor, D.

D. Gabor, “Associative holographic memories,” IBM J. Res. Dev. 13, 156–159 (1969).
[CrossRef]

Gu, C.

C. Gu, J. Hong, S. Campbell, “2-D shift invariant volume holographic correlator,” Opt. Commun. 88, 4646–4648 (1992).
[CrossRef]

Hong, J.

C. Gu, J. Hong, S. Campbell, “2-D shift invariant volume holographic correlator,” Opt. Commun. 88, 4646–4648 (1992).
[CrossRef]

Hsu, K.

K. Hsu, H. Li, D. Psaltis, “Holographic implementation of a fully connected neural network,” Proc. IEEE 78, 1637–1645 (1990).
[CrossRef]

Kobayashi, S.

A. A. Yamamura, M. A. Neifeld, S. Kobayashi, D. Psaltis, “Optical disk based artificial neural systems,” Opt. Comput. Process. 1, 3–12 (1991).

D. Psaltis, M. A. Neifeld, A. Yamamura, S. Kobayashi, “Optical memory disks in optical information processing,” Appl. Opt. 29, 2038–2057 (1990).
[CrossRef] [PubMed]

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 I, D. S. Touretzky, ed. (Kaufmann, San Mateo, Calif., 1989), pp. 703–711.

Li, H.

K. Hsu, H. Li, D. Psaltis, “Holographic implementation of a fully connected neural network,” Proc. IEEE 78, 1637–1645 (1990).
[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 I, D. S. Touretzky, ed. (Kaufmann, San Mateo, Calif., 1989), pp. 703–711.

Marom, E.

Mead, C.

C. Mead, Analog VLSI and Neural Systems (Addison-Wesley, Reading, Mass.1989), pp. 67–78.

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 I, D. S. Touretzky, ed. (Kaufmann, San Mateo, Calif., 1989), pp. 703–711.

Mok, F.

J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 114–120 (1987).

Neifeld, M. A.

Owechko, Y.

Psaltis, D.

A. A. Yamamura, M. A. Neifeld, S. Kobayashi, D. Psaltis, “Optical disk based artificial neural systems,” Opt. Comput. Process. 1, 3–12 (1991).

K. Hsu, H. Li, D. Psaltis, “Holographic implementation of a fully connected neural network,” Proc. IEEE 78, 1637–1645 (1990).
[CrossRef]

D. Psaltis, M. A. Neifeld, A. Yamamura, S. Kobayashi, “Optical memory disks in optical information processing,” Appl. Opt. 29, 2038–2057 (1990).
[CrossRef] [PubMed]

D. Psaltis, M. A. Neifeld, A. Yamamura, “Image correlators using optical memory disks,” Opt. Lett. 14, 429–431 (1989).
[CrossRef] [PubMed]

J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 114–120 (1987).

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 I, D. S. Touretzky, ed. (Kaufmann, San Mateo, Calif., 1989), pp. 703–711.

Sofer, B.

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Yamamura, A.

Yamamura, A. A.

A. A. Yamamura, M. A. Neifeld, S. Kobayashi, D. Psaltis, “Optical disk based artificial neural systems,” Opt. Comput. Process. 1, 3–12 (1991).

Yu, J.

J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 114–120 (1987).

Appl. Opt. (2)

IBM J. Res. Dev. (1)

D. Gabor, “Associative holographic memories,” IBM J. Res. Dev. 13, 156–159 (1969).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Opt. Commun. (1)

C. Gu, J. Hong, S. Campbell, “2-D shift invariant volume holographic correlator,” Opt. Commun. 88, 4646–4648 (1992).
[CrossRef]

Opt. Comput. Process. (1)

A. A. Yamamura, M. A. Neifeld, S. Kobayashi, D. Psaltis, “Optical disk based artificial neural systems,” Opt. Comput. Process. 1, 3–12 (1991).

Opt. Lett. (2)

Proc. IEEE (1)

K. Hsu, H. Li, D. Psaltis, “Holographic implementation of a fully connected neural network,” Proc. IEEE 78, 1637–1645 (1990).
[CrossRef]

Other (3)

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

C. Mead, Analog VLSI and Neural Systems (Addison-Wesley, Reading, Mass.1989), pp. 67–78.

J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 114–120 (1987).

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Figures (15)

Fig. 1
Fig. 1

Schematic of the photorefractive optical-disk-based image correlator.

Fig. 2
Fig. 2

Geometry used for calculating horizontal shift invariance.

Fig. 3
Fig. 3

Geometry used for calculating vertical shift invariance.

Fig. 4
Fig. 4

Photorefractive correlator diffraction efficiency simulation for (a) bipolar and (b) unipolar images.

Fig. 5
Fig. 5

Image used for PR correlator experiments. The photograph was taken from the disk by using the diffractive readout scheme described in Ref. 1.

Fig. 6
Fig. 6

Correlation results for shift invariance in the horizontal direction: (a) 2-D correlation pattern, (b) slice through y = 0 showing a multilobed pattern.

Fig. 7
Fig. 7

Correlation results for shift invariance in the vertical direction: (a) 2-D correlation pattern, (b) slice through y = 0 showing a single-lobed pattern.

Fig. 8
Fig. 8

Correlation results for the input image from sector 1 and reference image from sector 2: (a) expanded correlation peak of Fig. 7(b) for comparison with (b) the reduced signal from sector 2.

Fig. 9
Fig. 9

Schematic of optical-disk-based image associative memory.

Fig. 10
Fig. 10

Winner-take-all detector array: (a) circuit diagram, (b) photograph of chip.

Fig. 11
Fig. 11

Reference image library used in the associative memory experiments.

Fig. 12
Fig. 12

Compare-phase data taken from AM: (a) memory 1 as input, (b) memory 2 as input.

Fig. 13
Fig. 13

Compare-phase data taken from AM with partial inputs: (a) first two lines of memory 1, (b) first line only of memory 1 as input.

Fig. 14
Fig. 14

Image completion with the disk-based AM: (a) partial input of memory 1, (b) completed image retrieved from the system; (c) partial input of memory 2, (d) completed image retrieved from the system.

Fig. 15
Fig. 15

Wobble-compensation scheme for the PR correlator: (a) no disk wobble, (b) disk wobble causing a shift in the reference image spectrum, (c) piezo mirror compensating for disk wobble.

Equations (21)

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

k x 1 = π Δ x / λ F ,
k x 2 = - π Δ x / λ F ,
E REF exp [ i ( k x sin θ + k z cos θ ) ] exp ( i k x sin θ ) exp ( i k z ) ,
E 0 exp ( i k z ) ,
E 1 exp ( i k y N Δ y / 2 F ) exp ( i k z ) ,
E 2 exp ( - i k y N Δ y / 2 F ) exp ( i k z ) ,
N Δ y 2 F y + x sin θ = 0.
L < 2 λ F 2 sin θ / π ( N Δ y ) 2 .
λ F / π Δ x < L < 2 λ F 2 sin θ / π Y 2 ,
p ( a i j = 1 ) = p ( a i j = - 1 ) = 1 / 2 , i , j ,
p ( a i j = k , a m n = k ) = p ( a i j = k ) p ( a m n = k ) , i m , j n ,
c m n = i = m + 1 N j = n + 1 N a i j a i - m , j - n ,
c 00 = i = 1 N j = 1 N ( a i j ) 2 ,
E { c m n 2 } = E { i = m + 1 N i = m + 1 N j = n + 1 N j = n + 1 N a i , j a i - m , j - n a i , j a i - m , j - n } = ( N - m ) ( N - n ) .
P Σ = 4 m = 1 N n = 1 N E { c m n 2 } ,
η P = c 00 2 / ( P Σ + c 00 2 )
= N 4 / ( 2 N 4 - 2 N 3 + N 2 ) ,
c k = i = 1 N j = k + 1 N a i j a i , j - k ,
P Σ = 2 k = 1 N E { c k 2 } .
η ( T c ) I c η ( 0 ) I c - T ( SNR ) ,
I c = T ( SNR ) η ( 0 ) [ 1 - exp ( - β T c I c ) ] .

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