Abstract

It is shown that by taking advantage of the superposition property of optical signals, one can further improve the performance of optical symbolic substitution processors.

© 1990 Optical Society of America

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References

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  1. A. A. Sawchuk, T. C. Stand, “Digital Optical Computing,” Proc. IEEE 72, 758–779 (1984).
    [CrossRef]
  2. A. Huang, “Parallel Algorithms for Optical Digital Computers,” in Proceedings, IEEE Tenth International Optical Computing Conference (1983), pp. 13–17.
  3. K.-H. Brenner, A. Huang, N. Streibl, “Digital Optical Computing with Symbolic Substitution,” Appl. Opt. 25, 3054–3060 (1986).
    [CrossRef] [PubMed]
  4. Y. Li, G. Eichmann, “Conditional Symbolic Modified Signed-Digit Arithmetic Using Optical Content-Addressable Memory Logic Elements,” Appl. Opt. 26, 2328 (1987).
    [CrossRef] [PubMed]
  5. K. Hwang, A. Louri, “Optical Multiplication and Division Using Modified Signed-Digit Symbolic Substitution,” Opt. Eng. 28, 364–373 (1989).
    [CrossRef]
  6. S. D. Goodman, W. T. Rhodes, “Symbolic Substitution Applications to Image Processing,” Appl. Opt. 27, 1708–1714 (1988).
    [CrossRef] [PubMed]
  7. A. K. Cherri, M. A. Karim, “Uses of Optical Symbolic Substitution in Image Proessing: Median Filters,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), vol. 9, pp. 100–103.
  8. R. A. Schmidt, W. T. Cathey, “Optical Implementations of Mathematical Resolution,” Appl. Opt. 26, 1852–1858 (1987).
    [CrossRef] [PubMed]
  9. D. P. Casasent, E. C. Botha, “Mulifunctional Optical Processor Based on Symbolic Substitution,” Opt. Eng. 28, 425–433 (1989).
    [CrossRef]
  10. A. Louri, “A Parallel Architecture and Algorithms for Optical Computing,” Opt. Commun. 72, 27–37 (1989).
    [CrossRef]
  11. A. D. McAulay, “Optical Prolog Computer Using Symbolic Substitution,” Proc. Soc. Photo-Opt. Instrum. Eng. 881, 223–229 (1988).
  12. M. J. Murdocca, “Design of a Symbolic Substitution-Based Optical Random Access Memory,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989) Vol. 9, pp. 92–95.

1989 (3)

K. Hwang, A. Louri, “Optical Multiplication and Division Using Modified Signed-Digit Symbolic Substitution,” Opt. Eng. 28, 364–373 (1989).
[CrossRef]

D. P. Casasent, E. C. Botha, “Mulifunctional Optical Processor Based on Symbolic Substitution,” Opt. Eng. 28, 425–433 (1989).
[CrossRef]

A. Louri, “A Parallel Architecture and Algorithms for Optical Computing,” Opt. Commun. 72, 27–37 (1989).
[CrossRef]

1988 (2)

A. D. McAulay, “Optical Prolog Computer Using Symbolic Substitution,” Proc. Soc. Photo-Opt. Instrum. Eng. 881, 223–229 (1988).

S. D. Goodman, W. T. Rhodes, “Symbolic Substitution Applications to Image Processing,” Appl. Opt. 27, 1708–1714 (1988).
[CrossRef] [PubMed]

1987 (2)

1986 (1)

1984 (1)

A. A. Sawchuk, T. C. Stand, “Digital Optical Computing,” Proc. IEEE 72, 758–779 (1984).
[CrossRef]

Botha, E. C.

D. P. Casasent, E. C. Botha, “Mulifunctional Optical Processor Based on Symbolic Substitution,” Opt. Eng. 28, 425–433 (1989).
[CrossRef]

Brenner, K.-H.

Casasent, D. P.

D. P. Casasent, E. C. Botha, “Mulifunctional Optical Processor Based on Symbolic Substitution,” Opt. Eng. 28, 425–433 (1989).
[CrossRef]

Cathey, W. T.

Cherri, A. K.

A. K. Cherri, M. A. Karim, “Uses of Optical Symbolic Substitution in Image Proessing: Median Filters,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), vol. 9, pp. 100–103.

Eichmann, G.

Goodman, S. D.

Huang, A.

K.-H. Brenner, A. Huang, N. Streibl, “Digital Optical Computing with Symbolic Substitution,” Appl. Opt. 25, 3054–3060 (1986).
[CrossRef] [PubMed]

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

Hwang, K.

K. Hwang, A. Louri, “Optical Multiplication and Division Using Modified Signed-Digit Symbolic Substitution,” Opt. Eng. 28, 364–373 (1989).
[CrossRef]

Karim, M. A.

A. K. Cherri, M. A. Karim, “Uses of Optical Symbolic Substitution in Image Proessing: Median Filters,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), vol. 9, pp. 100–103.

Li, Y.

Louri, A.

K. Hwang, A. Louri, “Optical Multiplication and Division Using Modified Signed-Digit Symbolic Substitution,” Opt. Eng. 28, 364–373 (1989).
[CrossRef]

A. Louri, “A Parallel Architecture and Algorithms for Optical Computing,” Opt. Commun. 72, 27–37 (1989).
[CrossRef]

McAulay, A. D.

A. D. McAulay, “Optical Prolog Computer Using Symbolic Substitution,” Proc. Soc. Photo-Opt. Instrum. Eng. 881, 223–229 (1988).

Murdocca, M. J.

M. J. Murdocca, “Design of a Symbolic Substitution-Based Optical Random Access Memory,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989) Vol. 9, pp. 92–95.

Rhodes, W. T.

Sawchuk, A. A.

A. A. Sawchuk, T. C. Stand, “Digital Optical Computing,” Proc. IEEE 72, 758–779 (1984).
[CrossRef]

Schmidt, R. A.

Stand, T. C.

A. A. Sawchuk, T. C. Stand, “Digital Optical Computing,” Proc. IEEE 72, 758–779 (1984).
[CrossRef]

Streibl, N.

Appl. Opt. (4)

Opt. Commun. (1)

A. Louri, “A Parallel Architecture and Algorithms for Optical Computing,” Opt. Commun. 72, 27–37 (1989).
[CrossRef]

Opt. Eng. (2)

D. P. Casasent, E. C. Botha, “Mulifunctional Optical Processor Based on Symbolic Substitution,” Opt. Eng. 28, 425–433 (1989).
[CrossRef]

K. Hwang, A. Louri, “Optical Multiplication and Division Using Modified Signed-Digit Symbolic Substitution,” Opt. Eng. 28, 364–373 (1989).
[CrossRef]

Proc. IEEE (1)

A. A. Sawchuk, T. C. Stand, “Digital Optical Computing,” Proc. IEEE 72, 758–779 (1984).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

A. D. McAulay, “Optical Prolog Computer Using Symbolic Substitution,” Proc. Soc. Photo-Opt. Instrum. Eng. 881, 223–229 (1988).

Other (3)

M. J. Murdocca, “Design of a Symbolic Substitution-Based Optical Random Access Memory,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989) Vol. 9, pp. 92–95.

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

A. K. Cherri, M. A. Karim, “Uses of Optical Symbolic Substitution in Image Proessing: Median Filters,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), vol. 9, pp. 100–103.

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Figures (3)

Fig. 1
Fig. 1

New symbolic substitution rules for optical binary addition.

Fig. 2
Fig. 2

Optical encoding of the binary values 0 and 1 and the new substitution rules for addition.

Fig. 3
Fig. 3

Example illustrating use of the new substitution rules for optical binary addition.

Equations (6)

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

w = N 2 m × d × T d - bit operations / s ,
w = N 4 × N d d × p = N 2 4 × d 2 × p d - bit additions / s .
w n = N 2 2 × d × ( d + 1 ) × p d - bit additions / s .
F = w n w = 2 × d d + 1
F = 2 × k with 0.9 < k < 1.
F = m × k with m 2 a n d 0.9 < k < 1.

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