Abstract

Procedures for planning and executing arbitrary parallel processing with optical array logic are generalized as a systematic programming technique of optical parallel processing. Optical array logic is a technique for achieving any parallel neighborhood operation with simple coding and optical correlation. An original symbolic notation facilitates programming of parallel processing with optical array logic, so that many problems can be optically solved using optical array logic. Two examples of image data processing are presented to illustrate the programming procedure of parallel processing with optical array logic.

© 1988 Optical Society of America

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References

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  1. A. A. Sawchuk, T. C. Strand, “Digital Optical Computing,” Proc. IEEE 72, 758 (1984).
    [CrossRef]
  2. T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical Digital Truth Table Look-Up Processing,” Opt. Eng. 24, 48 (1985).
    [CrossRef]
  3. K-H. Brenner, A. Huang, N. Steibl, “Digital Optical Computing with Symbolic Substitution,” Appl. Opt. 25, 3054 (1986).
    [CrossRef] [PubMed]
  4. Y. Fainman, C. C. Guest, S. H. Lee, “Optical Digital Logic Operations by Two-Beam Coupling in Photorefractive Material,” Appl. Opt. 25, 1598 (1986).
    [CrossRef] [PubMed]
  5. A. W. Lohmann, J. Weigelt, “Spatial Filtering Logic Based on Polarization,” Appl. Opt. 26, 131 (1987).
    [CrossRef] [PubMed]
  6. J. Tanida, Y. Ichioka, “Optical Logic Array Processor Using Shadowgrams,” J. Opt. Soc. Am. 73, 800 (1983).
    [CrossRef]
  7. J. Tanida, Y. Ichioka, “Optical-Logic-Array Processor Using Shadowgrams. III. Parallel Neighborhood Operations and an Architecture of an Optical Digital-Computing System,” J. Opt. Soc. Am. A 2, 1245 (1985).
    [CrossRef]
  8. J. Tanida, Y. Ichioka, “OPALS: Optical Parallel Array Logic System,” Appl. Opt. 25, 1565 (1986).
    [CrossRef] [PubMed]
  9. H. Fleisher, L. I. Maissel, “An Introduction to Array Logic,” IBM J. Res. Dev. 19, 98 (1975).
    [CrossRef]
  10. K. Preston, M. J. B. Duff, Modern Cellular Automata Theory and Applications (Plenum, New York, 1984).
  11. J. Tanida, M. Fukui, Y. Ichioka, “Programming of Optical Array Logic. 2: Numerical Data Processing Based on Pattern Logic,” Appl. Opt. 27 (1988), same issue.
    [CrossRef] [PubMed]
  12. Y. Tanida, Y. Ichioka, “Modular Components for an Optical Array Logic System,” Appl. Opt. 26, 3954 (1987).
    [CrossRef] [PubMed]

1988 (1)

J. Tanida, M. Fukui, Y. Ichioka, “Programming of Optical Array Logic. 2: Numerical Data Processing Based on Pattern Logic,” Appl. Opt. 27 (1988), same issue.
[CrossRef] [PubMed]

1987 (2)

1986 (3)

1985 (2)

1984 (1)

A. A. Sawchuk, T. C. Strand, “Digital Optical Computing,” Proc. IEEE 72, 758 (1984).
[CrossRef]

1983 (1)

1975 (1)

H. Fleisher, L. I. Maissel, “An Introduction to Array Logic,” IBM J. Res. Dev. 19, 98 (1975).
[CrossRef]

Brenner, K-H.

Duff, M. J. B.

K. Preston, M. J. B. Duff, Modern Cellular Automata Theory and Applications (Plenum, New York, 1984).

Fainman, Y.

Fleisher, H.

H. Fleisher, L. I. Maissel, “An Introduction to Array Logic,” IBM J. Res. Dev. 19, 98 (1975).
[CrossRef]

Fukui, M.

J. Tanida, M. Fukui, Y. Ichioka, “Programming of Optical Array Logic. 2: Numerical Data Processing Based on Pattern Logic,” Appl. Opt. 27 (1988), same issue.
[CrossRef] [PubMed]

Gaylord, T. K.

T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical Digital Truth Table Look-Up Processing,” Opt. Eng. 24, 48 (1985).
[CrossRef]

Guest, C. C.

Y. Fainman, C. C. Guest, S. H. Lee, “Optical Digital Logic Operations by Two-Beam Coupling in Photorefractive Material,” Appl. Opt. 25, 1598 (1986).
[CrossRef] [PubMed]

T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical Digital Truth Table Look-Up Processing,” Opt. Eng. 24, 48 (1985).
[CrossRef]

Huang, A.

Ichioka, Y.

Lee, S. H.

Lohmann, A. W.

Maissel, L. I.

H. Fleisher, L. I. Maissel, “An Introduction to Array Logic,” IBM J. Res. Dev. 19, 98 (1975).
[CrossRef]

Mirsalehi, M. M.

T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical Digital Truth Table Look-Up Processing,” Opt. Eng. 24, 48 (1985).
[CrossRef]

Preston, K.

K. Preston, M. J. B. Duff, Modern Cellular Automata Theory and Applications (Plenum, New York, 1984).

Sawchuk, A. A.

A. A. Sawchuk, T. C. Strand, “Digital Optical Computing,” Proc. IEEE 72, 758 (1984).
[CrossRef]

Steibl, N.

Strand, T. C.

A. A. Sawchuk, T. C. Strand, “Digital Optical Computing,” Proc. IEEE 72, 758 (1984).
[CrossRef]

Tanida, J.

Tanida, Y.

Weigelt, J.

Appl. Opt. (6)

IBM J. Res. Dev. (1)

H. Fleisher, L. I. Maissel, “An Introduction to Array Logic,” IBM J. Res. Dev. 19, 98 (1975).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Eng. (1)

T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical Digital Truth Table Look-Up Processing,” Opt. Eng. 24, 48 (1985).
[CrossRef]

Proc. IEEE (1)

A. A. Sawchuk, T. C. Strand, “Digital Optical Computing,” Proc. IEEE 72, 758 (1984).
[CrossRef]

Other (1)

K. Preston, M. J. B. Duff, Modern Cellular Automata Theory and Applications (Plenum, New York, 1984).

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Figures (8)

Fig. 1
Fig. 1

Neighborhood area.

Fig. 2
Fig. 2

Processing procedure of OAL.

Fig. 3
Fig. 3

Decomposition of an operation kernel into kernel units.

Fig. 4
Fig. 4

All patterns of a kernel unit corresponding to a two-variable binary logic function. Function symbols used for symbolic notation of OAL are also tabulated.

Fig. 5
Fig. 5

Location map of kernel units referenced by (m,n).

Fig. 6
Fig. 6

Modified shadow-casting system for OAL.

Fig. 7
Fig. 7

Experimental results of edge detection with OAL: (a) object to be processed, (b)–(e) results of product term operation, (f) resultant image of edge detection.

Fig. 8
Fig. 8

Simulation results of extracting connected area: (a) object to be processed, (b) core pixel pointing to extracted area, (c)–(f) output of first, second, fifth, and thirteenth iteration, respectively, (f) final result of extraction of connected area including the sign pixel.

Equations (9)

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c i , j = f ( a i , j , b i , j ) ,             ( i , j = 1 , , N ) ,
a i , j = { a i + m , j + n m , n = - L , , L } ,
b i , j = { b i + m , j + n m , n = - L , , L } .
c i , j = k = 1 K m = - L L n = - L L f m , n ; k ( a i + m , j + n , b i + m , j + n ) , ( i , j = 1 , , N ) ,
c i , j = a i , j ( a ¯ i - 1 , j + a ¯ i + 1 , j + a ¯ i , j - 1 + a ¯ i , j + 1 ) ,
c i , j = a i , j a ¯ i - 1 , j + a i , j a ¯ i + 1 , j + a i , j a ¯ i , j - 1 + a i , j a ¯ i , j + 1 .
[ .. 0. .. .. 1. _ .. .. .. .. ] + [ .. .. .. .. 1. _ .. .. 0. .. ] + [ .. .. .. 0. 1. _ .. .. .. .. ] + [ .. .. .. .. 1. _ 0. .. .. .. ] .
c i , j = a i , j b i , j + a i , j a i - 1 , j b i - 1 , j + a i , j a i + 1 , j b i + 1 j + a i , j a i , j - 1 b i , j - 1 + a i , j a i , j + 1 b i , j + 1 .
[ .. .. .. .. 11 _ .. .. .. .. ] + [ .. 11 .. .. 1. _ .. .. .. .. ] + [ .. .. .. .. 1. _ .. .. 11 .. ] + [ .. .. .. 11 1. _ .. .. .. .. ] + [ .. .. .. .. 1. _ 11 .. .. .. ]

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