Abstract

General characteristics and advantages of 2-D optical cellular processors are listed and discussed, with reference to the concepts of cellular automata, symbolic substitution, and neural nets. The role of optical interconnections and of quasilinear processing combining linear array operations and pointwise nonlinearities is highlighted. An architecture for optical implementation of cellular automata is introduced; it features high density 3-D optical shift-invariant interconnections and programmability of the interconnection pattern through adequate use of holographic connectors.

© 1988 Optical Society of America

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References

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  1. J. Taboury, J. M. Wang, Pierre Chavel, F. Devos, Patrick Garda, “Optical Cellular Processor Architecture. 2: Experiments,” to be submitted to Applied Optics.
  2. S. Wolfram, Theory and Application of Cellular Automata, (World Scientific, Singapore, 1986).
  3. N. H. Packard, S. Wolfram, “Two-Dimensional Cellular Automata,” J. Stat. Phys. 38, 901 (1985).
    [CrossRef]
  4. R. A. Athale, BDM Corp., McLean, VA; private communication.
  5. A. Huang, “Parallel Algorithms for Optical Digital Computers,” in Technical Digest, IEEE Tenth International Optical Computing Conference (1983), pp. 13–17.
  6. K. H. Brenner, A. Huang, N. Streibl, “Digital Optical Computing with Symbolic Substitution,” Appl. Opt. 25, 3054 (1986).
    [CrossRef] [PubMed]
  7. J. N. Mait, K. H. Brenner, “Optical Systems for Symbolic Substitution,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), pp. 12–15.
  8. Y. Ichioka, J. Tanida, “Optical Parallel Logic Gaes Using a Shadowcasting System for Optical Digital Computing,” Proc. IEEE 72, 787 (1984).
    [CrossRef]
  9. H. O. Bartelt, A. W. Lohmann, E. E. Sicre, “Optical Logical Processing in Parallel with Theta Modulation,” J. Opt. Soc. Am. A 1, 944 (1984).
    [CrossRef]
  10. A. W. Lohmann, J. W. Weigelt, “Spatial Filtering Logic Based on Polarization,” Appl. Opt. 26, 131 (1987).
    [CrossRef] [PubMed]
  11. G. Eichmann, Y. Li, P. P. Ho, R. R. Alfano, “Digital Optical Isochronous Assay Processing,” Appl. Opt. 26, 2726 (1987).
    [CrossRef] [PubMed]
  12. D. Psaltis, N. Farhat, “Optical Information Processing Based on an Associative-Memory Model of Neural Nets with Thresholding and Feedback,” Opt. Lett. 10, 98 (1985).
    [CrossRef] [PubMed]
  13. J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. U.S.A. 79, 2554 (1982).
    [CrossRef] [PubMed]
  14. K. S. Huang, B. K. Jenkins, A. A. Sawchuk, “Binary Image Algebra and Digital Optical Cellular Image Processors,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), pp. 20–23.
  15. J. R. Fienup, C. D. Leonard, “Holographic Optics for a Method-Filter Optical Processor,” Appl. Opt. 18, 631 (1979).
    [CrossRef] [PubMed]
  16. M. J. Murdocca, “Techniques for Parallel Numeric and Non-Numeric Algorithm Design in Digital Optics,” M.Sc. Thesis, Rutgers U. (1985).
  17. S. Levialdi, “On Shrinking of Binary Patterns,” Commun. ACM 15, 7 (1972).
    [CrossRef]
  18. A 6 × 6-ferroelectric liquid crystal shutter array, for example, is commercially available (Displaytech, Boulder, CO).
  19. B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuk, T. C. Strand, “Architectural Implications of a Digital Optical Processor,” Appl. Opt. 23, 3465 (1984).
    [CrossRef] [PubMed]
  20. A. Huang, “Architectural Considerations Involved in the Design of an Optical Digital Computer,” Proc. IEEE 72, 780 (1984).
    [CrossRef]
  21. K. H. Brenner, “New Implementation of Symbolic Substitution Logic,” Appl. Opt. 25, 3061 (1986).
    [CrossRef] [PubMed]
  22. B. K. Jenkins, A. A. Sawchuk, T. C. Strand, R. Forchheimer, B. H. Soffer, “Sequential Optical Logic Implementation,” Appl. Opt. 23, 3455 (1984).
    [CrossRef] [PubMed]

1987 (2)

1986 (2)

1985 (2)

1984 (5)

1983 (1)

A. Huang, “Parallel Algorithms for Optical Digital Computers,” in Technical Digest, IEEE Tenth International Optical Computing Conference (1983), pp. 13–17.

1982 (1)

J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. U.S.A. 79, 2554 (1982).
[CrossRef] [PubMed]

1979 (1)

1972 (1)

S. Levialdi, “On Shrinking of Binary Patterns,” Commun. ACM 15, 7 (1972).
[CrossRef]

Alfano, R. R.

Athale, R. A.

R. A. Athale, BDM Corp., McLean, VA; private communication.

Bartelt, H. O.

Brenner, K. H.

K. H. Brenner, A. Huang, N. Streibl, “Digital Optical Computing with Symbolic Substitution,” Appl. Opt. 25, 3054 (1986).
[CrossRef] [PubMed]

K. H. Brenner, “New Implementation of Symbolic Substitution Logic,” Appl. Opt. 25, 3061 (1986).
[CrossRef] [PubMed]

J. N. Mait, K. H. Brenner, “Optical Systems for Symbolic Substitution,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), pp. 12–15.

Chavel, P.

Chavel, Pierre

J. Taboury, J. M. Wang, Pierre Chavel, F. Devos, Patrick Garda, “Optical Cellular Processor Architecture. 2: Experiments,” to be submitted to Applied Optics.

Devos, F.

J. Taboury, J. M. Wang, Pierre Chavel, F. Devos, Patrick Garda, “Optical Cellular Processor Architecture. 2: Experiments,” to be submitted to Applied Optics.

Eichmann, G.

Farhat, N.

Fienup, J. R.

Forchheimer, R.

Garda, Patrick

J. Taboury, J. M. Wang, Pierre Chavel, F. Devos, Patrick Garda, “Optical Cellular Processor Architecture. 2: Experiments,” to be submitted to Applied Optics.

Ho, P. P.

Hopfield, J. J.

J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. U.S.A. 79, 2554 (1982).
[CrossRef] [PubMed]

Huang, A.

K. H. Brenner, A. Huang, N. Streibl, “Digital Optical Computing with Symbolic Substitution,” Appl. Opt. 25, 3054 (1986).
[CrossRef] [PubMed]

A. Huang, “Architectural Considerations Involved in the Design of an Optical Digital Computer,” Proc. IEEE 72, 780 (1984).
[CrossRef]

A. Huang, “Parallel Algorithms for Optical Digital Computers,” in Technical Digest, IEEE Tenth International Optical Computing Conference (1983), pp. 13–17.

Huang, K. S.

K. S. Huang, B. K. Jenkins, A. A. Sawchuk, “Binary Image Algebra and Digital Optical Cellular Image Processors,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), pp. 20–23.

Ichioka, Y.

Y. Ichioka, J. Tanida, “Optical Parallel Logic Gaes Using a Shadowcasting System for Optical Digital Computing,” Proc. IEEE 72, 787 (1984).
[CrossRef]

Jenkins, B. K.

B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuk, T. C. Strand, “Architectural Implications of a Digital Optical Processor,” Appl. Opt. 23, 3465 (1984).
[CrossRef] [PubMed]

B. K. Jenkins, A. A. Sawchuk, T. C. Strand, R. Forchheimer, B. H. Soffer, “Sequential Optical Logic Implementation,” Appl. Opt. 23, 3455 (1984).
[CrossRef] [PubMed]

K. S. Huang, B. K. Jenkins, A. A. Sawchuk, “Binary Image Algebra and Digital Optical Cellular Image Processors,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), pp. 20–23.

Leonard, C. D.

Levialdi, S.

S. Levialdi, “On Shrinking of Binary Patterns,” Commun. ACM 15, 7 (1972).
[CrossRef]

Li, Y.

Lohmann, A. W.

Mait, J. N.

J. N. Mait, K. H. Brenner, “Optical Systems for Symbolic Substitution,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), pp. 12–15.

Murdocca, M. J.

M. J. Murdocca, “Techniques for Parallel Numeric and Non-Numeric Algorithm Design in Digital Optics,” M.Sc. Thesis, Rutgers U. (1985).

Packard, N. H.

N. H. Packard, S. Wolfram, “Two-Dimensional Cellular Automata,” J. Stat. Phys. 38, 901 (1985).
[CrossRef]

Psaltis, D.

Sawchuk, A. A.

B. K. Jenkins, A. A. Sawchuk, T. C. Strand, R. Forchheimer, B. H. Soffer, “Sequential Optical Logic Implementation,” Appl. Opt. 23, 3455 (1984).
[CrossRef] [PubMed]

B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuk, T. C. Strand, “Architectural Implications of a Digital Optical Processor,” Appl. Opt. 23, 3465 (1984).
[CrossRef] [PubMed]

K. S. Huang, B. K. Jenkins, A. A. Sawchuk, “Binary Image Algebra and Digital Optical Cellular Image Processors,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), pp. 20–23.

Sicre, E. E.

Soffer, B. H.

Strand, T. C.

Streibl, N.

Taboury, J.

J. Taboury, J. M. Wang, Pierre Chavel, F. Devos, Patrick Garda, “Optical Cellular Processor Architecture. 2: Experiments,” to be submitted to Applied Optics.

Tanida, J.

Y. Ichioka, J. Tanida, “Optical Parallel Logic Gaes Using a Shadowcasting System for Optical Digital Computing,” Proc. IEEE 72, 787 (1984).
[CrossRef]

Wang, J. M.

J. Taboury, J. M. Wang, Pierre Chavel, F. Devos, Patrick Garda, “Optical Cellular Processor Architecture. 2: Experiments,” to be submitted to Applied Optics.

Weigelt, J. W.

Wolfram, S.

N. H. Packard, S. Wolfram, “Two-Dimensional Cellular Automata,” J. Stat. Phys. 38, 901 (1985).
[CrossRef]

S. Wolfram, Theory and Application of Cellular Automata, (World Scientific, Singapore, 1986).

Appl. Opt. (7)

Commun. ACM (1)

S. Levialdi, “On Shrinking of Binary Patterns,” Commun. ACM 15, 7 (1972).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Stat. Phys. (1)

N. H. Packard, S. Wolfram, “Two-Dimensional Cellular Automata,” J. Stat. Phys. 38, 901 (1985).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (2)

Y. Ichioka, J. Tanida, “Optical Parallel Logic Gaes Using a Shadowcasting System for Optical Digital Computing,” Proc. IEEE 72, 787 (1984).
[CrossRef]

A. Huang, “Architectural Considerations Involved in the Design of an Optical Digital Computer,” Proc. IEEE 72, 780 (1984).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. U.S.A. 79, 2554 (1982).
[CrossRef] [PubMed]

Technical Digest, IEEE Tenth International Optical Computing Conference (1)

A. Huang, “Parallel Algorithms for Optical Digital Computers,” in Technical Digest, IEEE Tenth International Optical Computing Conference (1983), pp. 13–17.

Other (7)

J. N. Mait, K. H. Brenner, “Optical Systems for Symbolic Substitution,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), pp. 12–15.

R. A. Athale, BDM Corp., McLean, VA; private communication.

J. Taboury, J. M. Wang, Pierre Chavel, F. Devos, Patrick Garda, “Optical Cellular Processor Architecture. 2: Experiments,” to be submitted to Applied Optics.

S. Wolfram, Theory and Application of Cellular Automata, (World Scientific, Singapore, 1986).

K. S. Huang, B. K. Jenkins, A. A. Sawchuk, “Binary Image Algebra and Digital Optical Cellular Image Processors,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), pp. 20–23.

A 6 × 6-ferroelectric liquid crystal shutter array, for example, is commercially available (Displaytech, Boulder, CO).

M. J. Murdocca, “Techniques for Parallel Numeric and Non-Numeric Algorithm Design in Digital Optics,” M.Sc. Thesis, Rutgers U. (1985).

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Figures (9)

Fig. 1
Fig. 1

One cell of an optical cellular processor (OCP). Dotted lines outline the neighborhood of cell Cij; arrows indicate connections.

Fig. 2
Fig. 2

Thresholding function H(x).

Fig. 3
Fig. 3

Example of operation of the elementary cellular automaton recognizing pattern Pn.

Fig. 4
Fig. 4

Symbolic substitution of substitution pattern X for match pattern u.

Fig. 5
Fig. 5

(a) Impulse response of a holographic lens connector; (b) connection by the holographic lens in a double diffraction setup (feedback loop of the cellular processor not figured).

Fig. 6
Fig. 6

Two-hologram setup for programmable interconnect patterns. Only the first diffracted order of each hologram is shown.

Fig. 7
Fig. 7

Two-hologram interconnection architecture as proposed by Jenkins et al.18 Only first diffracted orders are shown.

Fig. 8
Fig. 8

Block diagram of the complete optical binary cellular automaton (OBCA).

Fig. 9
Fig. 9

Boolean description of memory behavior. Each cell of the memory array is equivalent to this circuit and is independent of all others.

Equations (7)

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

c i j = F i j ( c k l | C k l V i j ) ,
F ( c k l | C k l V i j ) = n = 1 n 0 F n ( c k l | C k l V i j ) ,
c = H [ c * P ¯ n + c ¯ * P n ] ,
H ( x ) = | 1 if x t 0 if x > t
pixel i , j of ( c * P ¯ n ) = ( k , l ) V 00 [ P ¯ n ] k l c i + k j + l .
c = H [ c * P ¯ n ] .
pixel i , j of ( c * P ¯ n ) = ( k , l ) V 00 P ¯ n k l · c i + k j + l .

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