Abstract

Several new higher-order spatial symbol recognition methods for optical symbolic substitution-based calculations are presented. In the case of logic processing, higher-order symbolic substitution (SS) rules can implement multivariable logic functions. For binary arithmetic calculations requiring carry propagation by simultaneously processing a number of bits, the computational speed increases. Finally, in image processing, the higher-order SS rules allow the use of larger local windows. For a higher-order spatial symbol recognition, both multiplicative and additive logic techniques are discussed. Four different higher-order SS recognition optical architectures are suggested: a multireflecting technique using an optical cavity, a lenslet array, an optical phase conjugation, and a content-addressable memory. Either dual-rail or triple-rail optical spatial intensity encoding is employed. Some preliminary experimental results are also presented.

© 1990 Optical Society of America

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    [CrossRef]
  2. S. P. Kozaitis, “Higher-Ordered Rules for Symbolic Substitution,” Opt. Commun. 65, 339–342 (1988).
    [CrossRef]
  3. F. T. S. Yu, C. Zhang, S. Jutamula, “Applications of One-Step Holographic Associative Memory to Symbolic Substitution,” Opt. Eng. 27, 399–402 (1988).
    [CrossRef]
  4. G. Eichmann, A. Kostrzewski, D. H. Kim, Y. Li, “Optical Parallel Register Transfer Microoperations Using Holographic Symbolic Substitution,” Appl. Opt. 28, 3860–3863 (1989).
    [CrossRef] [PubMed]
  5. M. J. Murdocca, “Digital Optical Computing with One-Rule Cellular Automata,” Appl. Opt. 26, 682–688 (1987).
    [CrossRef] [PubMed]
  6. J. N. Mait, K.-H. Brenner, “Optical Symbolic Substitution: System Design using Phase-Only Holograms,” Appl. Opt. 27, 1692–1700 (1988).
    [CrossRef] [PubMed]
  7. D. P. Casasent, E. C. Botha, “Multifunctional Optical Processor Based on Symbolic Substitution,” Opt. Eng. 28, 425–433 (1989).
    [CrossRef]
  8. K. H. Hwang, A. Louri, “Optical Multiplication and Division Using Modified-Signed-Digit Symbolic Substitution,” Opt. Eng. 28, 364–372 (1989).
    [CrossRef]
  9. K.-H. Brenner, “Programmable Optical Processor Based on Symbolic Substitution,” Appl. Opt. 27, 1687–1691 (1988).
    [CrossRef] [PubMed]
  10. R. Thalmann, G. Pedrini, B. Acklin, R. Dandliker, “Optical Symbolic Substitution Using Diffraction Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 635–641 (1988).
  11. J. N. Mait, “Design of Dammann Gratings for Optical Symbolic Substitution,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 646–652 (1988).
  12. M. T. Tsao et al., “Symbolic Substitution Using ZnS Interference Filters,” Opt. Eng. 26, 41–44 (1987).
    [CrossRef]
  13. K.-H. Brenner, A. W. Lohmann, T. M. Merklein, “Symbolic Substitution Implemented by Spatial Filtering Logic,” Opt. Eng. 28, 390–395 (1989).
    [CrossRef]
  14. Y. Li, G. Eichmann, R. Dorsinville, R. R. Alfano, “An and Operation-Based Optical Symbolic Recognizer,” Opt. Commun. 63, 375–379 (1987).
    [CrossRef]
  15. Y. Li, G. Eichmann, R. Dorsinville, R. R. Alfano, “Parallel Digital and Symbolic Optical Computation via Optical Phase Conjugation,” Appl. Opt. 27, 2025–2032 (1988).
    [CrossRef] [PubMed]
  16. C. D. Capps, R. A. Falk, T. L. Hook, “Optical Arithmetic/Logic Unit Based on Residue Arithmetic and Symbolic Substitution,” Appl. Opt. 27, 1682–1686 (1988).
    [CrossRef] [PubMed]
  17. R. P. Bocker, B. L. Drake, M. E. Lasher, T. B. Henderson, “Modified-Signed Digit Addition and Subtraction using Symbolic Substitution,” Appl. Opt. 25, 2456–2457 (1986).
    [CrossRef] [PubMed]
  18. D. Casasent, E. Botha, “Optical Symbolic Substitution for Morphological Transformations,” Appl. Opt. 27, 3806–3810 (1988).
    [CrossRef] [PubMed]
  19. G. Eichmann, J. Zhu, Y. Li, “Optical Parallel Image Skeletonization Using Content-Addressable Memory-Based Symbolic Substitution,” Appl. Opt. 27, 2905–2911 (1988).
    [CrossRef] [PubMed]
  20. P. A. Ramamoorthy, S. Antony, T. A. Grogan, “Symbolic-Substitution-Based Median Filters,” Opt. Eng. 27, 409–412 (1988).
    [CrossRef]
  21. S. D. Goodman, W. T. Rhodes, “Symbolic Substitution Applications to Image Processing,” Appl. Opt. 27, 1708–1714 (1988).
    [CrossRef] [PubMed]
  22. G. Eichmann, S. Basu, “Parallel Optical Syntactic Pattern Recognizer,” Appl. Opt. 26, 1859–1865 (1987).
    [CrossRef] [PubMed]
  23. M. M. Mirsalehi, T. K. Gaylord, “Truth-Table Look-Up Parallel Data Processing Using on Optical Content-Addressable Memory,” Appl. Opt. 25, 2277–2283 (1986).
    [CrossRef] [PubMed]
  24. Y. Li, D. H. Kim, A. Kostrzewski, G. Eichmann, “Content-Addressable-Memory-Based Single-Stage Optical Modified-Signed-Digit Arithmetic,” Opt. Lett. 14, 1254–1256(1989).
    [CrossRef] [PubMed]
  25. R. A. Fisher, Optical Phase Conjugation, (Academic, New York, 1983).
  26. J. O. White, A. Yariv, “Real-Time Image Processing via Four-Wave Mixing in a Photorefractive Medium,” Appl. Phys. Lett. 37, 5–7 (1980).
    [CrossRef]
  27. J. Jahns, A. Huang, “Planar Integration of Free-Space Optical Components,” Appl. Opt. 28, 1602–1605 (1989).
    [CrossRef] [PubMed]
  28. K.-H. Brenner, F. Sauer, “Diffractive–Reflective Optical Interconnects,” Appl. Opt. 27, 4251–4254 (1988).
    [CrossRef] [PubMed]
  29. J. B. McManus, R. S. Putnam, H. J. Caulfield, “Switched Holograms for Reconfigurable Optical Interconnection: Demonstration of a Prototype Device,” Appl. Opt. 27, 4244–4250 (1988).
    [CrossRef] [PubMed]
  30. A. Wuthrich, W. Lukosz, “Holographic with Guided Optical Waves,” Appl. Phys. Lett. 21, 55–58 (1980).
  31. R. K. Kostuk, M. Kato, Y-T. Huang, “Substrate Mode Holograms for Optical Interconnect,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 168–171.
  32. Y. Li, A. Kostrzewski, D. H. Kim, G. Eichmann, “A Compact Real-Time Programmable Optical Morphological Image Processor,” Opt. Lett. 14, 981–983 (1989).
    [CrossRef] [PubMed]
  33. J. S. Jang, S. Y. Shin, S. Y. Lee, “Adaptive Two-Dimensional Quadratic Associative Memory Using Holographic Lenslet Arrays,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 40–43.
  34. J. Tanida, Y. Ichioka, “Programming of Optical Array Logic. 1: Image Data Processing,” Appl. Opt. 27, 2926–2930 (1988).
    [CrossRef] [PubMed]
  35. M. M. Mirsalehi, T. K. Gaylord, D. C. Fielder, C. C. Guest, “Number Representation Effects in Truth-Table Look-Up Processing: 8-bit Addition Example,” Appl. Opt. 28, 1931–1939 (1989).
    [CrossRef] [PubMed]
  36. F. Kiamilev, S. C. Esener, Y. Fainman, C. C. Guest, S. H. Lee, “Programmable Optoelectronic Multiprocessor and Their Comparison with Symbolic Substitution for Digital Optical Computing,” Opt. Eng. 28, 396–409 (1989).
    [CrossRef]

1989

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

K. H. Hwang, A. Louri, “Optical Multiplication and Division Using Modified-Signed-Digit Symbolic Substitution,” Opt. Eng. 28, 364–372 (1989).
[CrossRef]

F. Kiamilev, S. C. Esener, Y. Fainman, C. C. Guest, S. H. Lee, “Programmable Optoelectronic Multiprocessor and Their Comparison with Symbolic Substitution for Digital Optical Computing,” Opt. Eng. 28, 396–409 (1989).
[CrossRef]

Y. Li, A. Kostrzewski, D. H. Kim, G. Eichmann, “A Compact Real-Time Programmable Optical Morphological Image Processor,” Opt. Lett. 14, 981–983 (1989).
[CrossRef] [PubMed]

Y. Li, D. H. Kim, A. Kostrzewski, G. Eichmann, “Content-Addressable-Memory-Based Single-Stage Optical Modified-Signed-Digit Arithmetic,” Opt. Lett. 14, 1254–1256(1989).
[CrossRef] [PubMed]

K.-H. Brenner, A. W. Lohmann, T. M. Merklein, “Symbolic Substitution Implemented by Spatial Filtering Logic,” Opt. Eng. 28, 390–395 (1989).
[CrossRef]

M. M. Mirsalehi, T. K. Gaylord, D. C. Fielder, C. C. Guest, “Number Representation Effects in Truth-Table Look-Up Processing: 8-bit Addition Example,” Appl. Opt. 28, 1931–1939 (1989).
[CrossRef] [PubMed]

G. Eichmann, A. Kostrzewski, D. H. Kim, Y. Li, “Optical Parallel Register Transfer Microoperations Using Holographic Symbolic Substitution,” Appl. Opt. 28, 3860–3863 (1989).
[CrossRef] [PubMed]

J. Jahns, A. Huang, “Planar Integration of Free-Space Optical Components,” Appl. Opt. 28, 1602–1605 (1989).
[CrossRef] [PubMed]

1988

C. D. Capps, R. A. Falk, T. L. Hook, “Optical Arithmetic/Logic Unit Based on Residue Arithmetic and Symbolic Substitution,” Appl. Opt. 27, 1682–1686 (1988).
[CrossRef] [PubMed]

K.-H. Brenner, “Programmable Optical Processor Based on Symbolic Substitution,” Appl. Opt. 27, 1687–1691 (1988).
[CrossRef] [PubMed]

J. N. Mait, K.-H. Brenner, “Optical Symbolic Substitution: System Design using Phase-Only Holograms,” Appl. Opt. 27, 1692–1700 (1988).
[CrossRef] [PubMed]

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

Y. Li, G. Eichmann, R. Dorsinville, R. R. Alfano, “Parallel Digital and Symbolic Optical Computation via Optical Phase Conjugation,” Appl. Opt. 27, 2025–2032 (1988).
[CrossRef] [PubMed]

G. Eichmann, J. Zhu, Y. Li, “Optical Parallel Image Skeletonization Using Content-Addressable Memory-Based Symbolic Substitution,” Appl. Opt. 27, 2905–2911 (1988).
[CrossRef] [PubMed]

J. Tanida, Y. Ichioka, “Programming of Optical Array Logic. 1: Image Data Processing,” Appl. Opt. 27, 2926–2930 (1988).
[CrossRef] [PubMed]

D. Casasent, E. Botha, “Optical Symbolic Substitution for Morphological Transformations,” Appl. Opt. 27, 3806–3810 (1988).
[CrossRef] [PubMed]

J. B. McManus, R. S. Putnam, H. J. Caulfield, “Switched Holograms for Reconfigurable Optical Interconnection: Demonstration of a Prototype Device,” Appl. Opt. 27, 4244–4250 (1988).
[CrossRef] [PubMed]

K.-H. Brenner, F. Sauer, “Diffractive–Reflective Optical Interconnects,” Appl. Opt. 27, 4251–4254 (1988).
[CrossRef] [PubMed]

P. A. Ramamoorthy, S. Antony, T. A. Grogan, “Symbolic-Substitution-Based Median Filters,” Opt. Eng. 27, 409–412 (1988).
[CrossRef]

S. P. Kozaitis, “Higher-Ordered Rules for Symbolic Substitution,” Opt. Commun. 65, 339–342 (1988).
[CrossRef]

F. T. S. Yu, C. Zhang, S. Jutamula, “Applications of One-Step Holographic Associative Memory to Symbolic Substitution,” Opt. Eng. 27, 399–402 (1988).
[CrossRef]

R. Thalmann, G. Pedrini, B. Acklin, R. Dandliker, “Optical Symbolic Substitution Using Diffraction Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 635–641 (1988).

J. N. Mait, “Design of Dammann Gratings for Optical Symbolic Substitution,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 646–652 (1988).

1987

M. T. Tsao et al., “Symbolic Substitution Using ZnS Interference Filters,” Opt. Eng. 26, 41–44 (1987).
[CrossRef]

Y. Li, G. Eichmann, R. Dorsinville, R. R. Alfano, “An and Operation-Based Optical Symbolic Recognizer,” Opt. Commun. 63, 375–379 (1987).
[CrossRef]

M. J. Murdocca, “Digital Optical Computing with One-Rule Cellular Automata,” Appl. Opt. 26, 682–688 (1987).
[CrossRef] [PubMed]

G. Eichmann, S. Basu, “Parallel Optical Syntactic Pattern Recognizer,” Appl. Opt. 26, 1859–1865 (1987).
[CrossRef] [PubMed]

1986

1980

J. O. White, A. Yariv, “Real-Time Image Processing via Four-Wave Mixing in a Photorefractive Medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

A. Wuthrich, W. Lukosz, “Holographic with Guided Optical Waves,” Appl. Phys. Lett. 21, 55–58 (1980).

Acklin, B.

R. Thalmann, G. Pedrini, B. Acklin, R. Dandliker, “Optical Symbolic Substitution Using Diffraction Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 635–641 (1988).

Alfano, R. R.

Y. Li, G. Eichmann, R. Dorsinville, R. R. Alfano, “Parallel Digital and Symbolic Optical Computation via Optical Phase Conjugation,” Appl. Opt. 27, 2025–2032 (1988).
[CrossRef] [PubMed]

Y. Li, G. Eichmann, R. Dorsinville, R. R. Alfano, “An and Operation-Based Optical Symbolic Recognizer,” Opt. Commun. 63, 375–379 (1987).
[CrossRef]

Antony, S.

P. A. Ramamoorthy, S. Antony, T. A. Grogan, “Symbolic-Substitution-Based Median Filters,” Opt. Eng. 27, 409–412 (1988).
[CrossRef]

Basu, S.

Bocker, R. P.

Botha, E.

Botha, E. C.

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

Brenner, K.-H.

Capps, C. D.

Casasent, D.

Casasent, D. P.

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

Caulfield, H. J.

Dandliker, R.

R. Thalmann, G. Pedrini, B. Acklin, R. Dandliker, “Optical Symbolic Substitution Using Diffraction Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 635–641 (1988).

Dorsinville, R.

Y. Li, G. Eichmann, R. Dorsinville, R. R. Alfano, “Parallel Digital and Symbolic Optical Computation via Optical Phase Conjugation,” Appl. Opt. 27, 2025–2032 (1988).
[CrossRef] [PubMed]

Y. Li, G. Eichmann, R. Dorsinville, R. R. Alfano, “An and Operation-Based Optical Symbolic Recognizer,” Opt. Commun. 63, 375–379 (1987).
[CrossRef]

Drake, B. L.

Eichmann, G.

Esener, S. C.

F. Kiamilev, S. C. Esener, Y. Fainman, C. C. Guest, S. H. Lee, “Programmable Optoelectronic Multiprocessor and Their Comparison with Symbolic Substitution for Digital Optical Computing,” Opt. Eng. 28, 396–409 (1989).
[CrossRef]

Fainman, Y.

F. Kiamilev, S. C. Esener, Y. Fainman, C. C. Guest, S. H. Lee, “Programmable Optoelectronic Multiprocessor and Their Comparison with Symbolic Substitution for Digital Optical Computing,” Opt. Eng. 28, 396–409 (1989).
[CrossRef]

Falk, R. A.

Fielder, D. C.

Fisher, R. A.

R. A. Fisher, Optical Phase Conjugation, (Academic, New York, 1983).

Gaylord, T. K.

Goodman, S. D.

Grogan, T. A.

P. A. Ramamoorthy, S. Antony, T. A. Grogan, “Symbolic-Substitution-Based Median Filters,” Opt. Eng. 27, 409–412 (1988).
[CrossRef]

Guest, C. C.

M. M. Mirsalehi, T. K. Gaylord, D. C. Fielder, C. C. Guest, “Number Representation Effects in Truth-Table Look-Up Processing: 8-bit Addition Example,” Appl. Opt. 28, 1931–1939 (1989).
[CrossRef] [PubMed]

F. Kiamilev, S. C. Esener, Y. Fainman, C. C. Guest, S. H. Lee, “Programmable Optoelectronic Multiprocessor and Their Comparison with Symbolic Substitution for Digital Optical Computing,” Opt. Eng. 28, 396–409 (1989).
[CrossRef]

Henderson, T. B.

Hook, T. L.

Huang, A.

J. Jahns, A. Huang, “Planar Integration of Free-Space Optical Components,” Appl. Opt. 28, 1602–1605 (1989).
[CrossRef] [PubMed]

A. Huang, “Parallel Algorithms for Optical Digital Computers,” in Proceedings, Tenth International Optical Computing Conference (IEEE Computer Society, Los Angeles, 1983), pp 13–17.
[CrossRef]

Huang, Y-T.

R. K. Kostuk, M. Kato, Y-T. Huang, “Substrate Mode Holograms for Optical Interconnect,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 168–171.

Hwang, K. H.

K. H. Hwang, A. Louri, “Optical Multiplication and Division Using Modified-Signed-Digit Symbolic Substitution,” Opt. Eng. 28, 364–372 (1989).
[CrossRef]

Ichioka, Y.

Jahns, J.

Jang, J. S.

J. S. Jang, S. Y. Shin, S. Y. Lee, “Adaptive Two-Dimensional Quadratic Associative Memory Using Holographic Lenslet Arrays,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 40–43.

Jutamula, S.

F. T. S. Yu, C. Zhang, S. Jutamula, “Applications of One-Step Holographic Associative Memory to Symbolic Substitution,” Opt. Eng. 27, 399–402 (1988).
[CrossRef]

Kato, M.

R. K. Kostuk, M. Kato, Y-T. Huang, “Substrate Mode Holograms for Optical Interconnect,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 168–171.

Kiamilev, F.

F. Kiamilev, S. C. Esener, Y. Fainman, C. C. Guest, S. H. Lee, “Programmable Optoelectronic Multiprocessor and Their Comparison with Symbolic Substitution for Digital Optical Computing,” Opt. Eng. 28, 396–409 (1989).
[CrossRef]

Kim, D. H.

Kostrzewski, A.

Kostuk, R. K.

R. K. Kostuk, M. Kato, Y-T. Huang, “Substrate Mode Holograms for Optical Interconnect,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 168–171.

Kozaitis, S. P.

S. P. Kozaitis, “Higher-Ordered Rules for Symbolic Substitution,” Opt. Commun. 65, 339–342 (1988).
[CrossRef]

Lasher, M. E.

Lee, S. H.

F. Kiamilev, S. C. Esener, Y. Fainman, C. C. Guest, S. H. Lee, “Programmable Optoelectronic Multiprocessor and Their Comparison with Symbolic Substitution for Digital Optical Computing,” Opt. Eng. 28, 396–409 (1989).
[CrossRef]

Lee, S. Y.

J. S. Jang, S. Y. Shin, S. Y. Lee, “Adaptive Two-Dimensional Quadratic Associative Memory Using Holographic Lenslet Arrays,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 40–43.

Li, Y.

Lohmann, A. W.

K.-H. Brenner, A. W. Lohmann, T. M. Merklein, “Symbolic Substitution Implemented by Spatial Filtering Logic,” Opt. Eng. 28, 390–395 (1989).
[CrossRef]

Louri, A.

K. H. Hwang, A. Louri, “Optical Multiplication and Division Using Modified-Signed-Digit Symbolic Substitution,” Opt. Eng. 28, 364–372 (1989).
[CrossRef]

Lukosz, W.

A. Wuthrich, W. Lukosz, “Holographic with Guided Optical Waves,” Appl. Phys. Lett. 21, 55–58 (1980).

Mait, J. N.

J. N. Mait, “Design of Dammann Gratings for Optical Symbolic Substitution,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 646–652 (1988).

J. N. Mait, K.-H. Brenner, “Optical Symbolic Substitution: System Design using Phase-Only Holograms,” Appl. Opt. 27, 1692–1700 (1988).
[CrossRef] [PubMed]

McManus, J. B.

Merklein, T. M.

K.-H. Brenner, A. W. Lohmann, T. M. Merklein, “Symbolic Substitution Implemented by Spatial Filtering Logic,” Opt. Eng. 28, 390–395 (1989).
[CrossRef]

Mirsalehi, M. M.

Murdocca, M. J.

Pedrini, G.

R. Thalmann, G. Pedrini, B. Acklin, R. Dandliker, “Optical Symbolic Substitution Using Diffraction Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 635–641 (1988).

Putnam, R. S.

Ramamoorthy, P. A.

P. A. Ramamoorthy, S. Antony, T. A. Grogan, “Symbolic-Substitution-Based Median Filters,” Opt. Eng. 27, 409–412 (1988).
[CrossRef]

Rhodes, W. T.

Sauer, F.

Shin, S. Y.

J. S. Jang, S. Y. Shin, S. Y. Lee, “Adaptive Two-Dimensional Quadratic Associative Memory Using Holographic Lenslet Arrays,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 40–43.

Tanida, J.

Thalmann, R.

R. Thalmann, G. Pedrini, B. Acklin, R. Dandliker, “Optical Symbolic Substitution Using Diffraction Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 635–641 (1988).

Tsao, M. T.

M. T. Tsao et al., “Symbolic Substitution Using ZnS Interference Filters,” Opt. Eng. 26, 41–44 (1987).
[CrossRef]

White, J. O.

J. O. White, A. Yariv, “Real-Time Image Processing via Four-Wave Mixing in a Photorefractive Medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Wuthrich, A.

A. Wuthrich, W. Lukosz, “Holographic with Guided Optical Waves,” Appl. Phys. Lett. 21, 55–58 (1980).

Yariv, A.

J. O. White, A. Yariv, “Real-Time Image Processing via Four-Wave Mixing in a Photorefractive Medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Yu, F. T. S.

F. T. S. Yu, C. Zhang, S. Jutamula, “Applications of One-Step Holographic Associative Memory to Symbolic Substitution,” Opt. Eng. 27, 399–402 (1988).
[CrossRef]

Zhang, C.

F. T. S. Yu, C. Zhang, S. Jutamula, “Applications of One-Step Holographic Associative Memory to Symbolic Substitution,” Opt. Eng. 27, 399–402 (1988).
[CrossRef]

Zhu, J.

Appl. Opt.

M. M. Mirsalehi, T. K. Gaylord, “Truth-Table Look-Up Parallel Data Processing Using on Optical Content-Addressable Memory,” Appl. Opt. 25, 2277–2283 (1986).
[CrossRef] [PubMed]

R. P. Bocker, B. L. Drake, M. E. Lasher, T. B. Henderson, “Modified-Signed Digit Addition and Subtraction using Symbolic Substitution,” Appl. Opt. 25, 2456–2457 (1986).
[CrossRef] [PubMed]

M. J. Murdocca, “Digital Optical Computing with One-Rule Cellular Automata,” Appl. Opt. 26, 682–688 (1987).
[CrossRef] [PubMed]

G. Eichmann, S. Basu, “Parallel Optical Syntactic Pattern Recognizer,” Appl. Opt. 26, 1859–1865 (1987).
[CrossRef] [PubMed]

C. D. Capps, R. A. Falk, T. L. Hook, “Optical Arithmetic/Logic Unit Based on Residue Arithmetic and Symbolic Substitution,” Appl. Opt. 27, 1682–1686 (1988).
[CrossRef] [PubMed]

K.-H. Brenner, “Programmable Optical Processor Based on Symbolic Substitution,” Appl. Opt. 27, 1687–1691 (1988).
[CrossRef] [PubMed]

J. N. Mait, K.-H. Brenner, “Optical Symbolic Substitution: System Design using Phase-Only Holograms,” Appl. Opt. 27, 1692–1700 (1988).
[CrossRef] [PubMed]

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

Y. Li, G. Eichmann, R. Dorsinville, R. R. Alfano, “Parallel Digital and Symbolic Optical Computation via Optical Phase Conjugation,” Appl. Opt. 27, 2025–2032 (1988).
[CrossRef] [PubMed]

G. Eichmann, J. Zhu, Y. Li, “Optical Parallel Image Skeletonization Using Content-Addressable Memory-Based Symbolic Substitution,” Appl. Opt. 27, 2905–2911 (1988).
[CrossRef] [PubMed]

J. Tanida, Y. Ichioka, “Programming of Optical Array Logic. 1: Image Data Processing,” Appl. Opt. 27, 2926–2930 (1988).
[CrossRef] [PubMed]

D. Casasent, E. Botha, “Optical Symbolic Substitution for Morphological Transformations,” Appl. Opt. 27, 3806–3810 (1988).
[CrossRef] [PubMed]

J. B. McManus, R. S. Putnam, H. J. Caulfield, “Switched Holograms for Reconfigurable Optical Interconnection: Demonstration of a Prototype Device,” Appl. Opt. 27, 4244–4250 (1988).
[CrossRef] [PubMed]

K.-H. Brenner, F. Sauer, “Diffractive–Reflective Optical Interconnects,” Appl. Opt. 27, 4251–4254 (1988).
[CrossRef] [PubMed]

M. M. Mirsalehi, T. K. Gaylord, D. C. Fielder, C. C. Guest, “Number Representation Effects in Truth-Table Look-Up Processing: 8-bit Addition Example,” Appl. Opt. 28, 1931–1939 (1989).
[CrossRef] [PubMed]

G. Eichmann, A. Kostrzewski, D. H. Kim, Y. Li, “Optical Parallel Register Transfer Microoperations Using Holographic Symbolic Substitution,” Appl. Opt. 28, 3860–3863 (1989).
[CrossRef] [PubMed]

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Figures (12)

Fig. 1
Fig. 1

(a) Spatially DR encoded primitive elements 0 and 1. (b) Higher-order SS rules for the addition of two 2-bit binary numbers. (c) Using the addition rules in (b) we obtain a two-step addition example for binary numbers 0011 and 1010.

Fig. 2
Fig. 2

(a) Triple-rail (TR) encoding rule for the primitive elements 0 and 1. (b) Murdocca’s encoding rule5 for the primitive elements 0 and 1. (c) The spatially encoded binary number 001 using a matrix TR encoding rule. (d) The spatially encoded binary number 001 using a vector TR encoding rule.

Fig. 3
Fig. 3

(a) Spatially TR encoded input data for a CAM based symbol recognition. (b) The corresponding CAM mask for search symbol 001. It consists of a periodically replicated spatially encoded complemented symbol 100. (c) The result for a CAM recognizer. The location of the search symbol is indicated by a completely blocked 3 × 3 pixel area. Search symbol 001 is located at positions (1,3) and (3,3).

Fig. 4
Fig. 4

A CAM-based system for a three-channel symbol recognition. L1L3 are the lenses of a lenslet array. Lenses L1L3 together with a projection lens L4 generate three angularly multiplexed beams, where each channel is used to recognize a different search symbol. The input data are displayed on an SLM. The spacing d between two adjacent light sources is equal to the linear SLM dimension. To recognize three search symbols at the mask plane, three masks (M1, M2, and M3) are placed. Lenslet array L5 performs the light intensity integration over each symbol’s aperture.

Fig. 5
Fig. 5

Optical system architecture for an OPC symbol recognizer. To input the encoded symbols, SLMs and three identical lenses L1L3, all placed at a focal length f distance away from a nonlinear optical material (NOM), are utilized. The generated OPC beam, directed via a beam splitter (BS) to an output point, contains the recognition result.

Fig. 6
Fig. 6

Schematic of an optical cavity based multiplicative symbol recognizer: M1 and M2 are mirrors. The spatial symbols (input data) are displayed on the SLM in a vector format. The incident beam angle is θ and the SLM pixel dimension is a.

Fig. 7
Fig. 7

Optical architecture of an optical cavity-based symbol recognizer: MA1 and MA2 are binary masks with vertical openings; M1 and M2 are half-mirrors. The encoded input data are displayed on an SLM.

Fig. 8
Fig. 8

Diagram of a lenslet array based recognition system. The programmable lenslet array consists of SLM1 and lenslet array L1 with an elemental aperture equal to D1. The encoded data are displayed on SLM2 with a dimension of D2. The smallest shift at the output plane is δ. At the output plane, at distance d from lens L2, five shifted copies of the input image are shown.

Fig. 9
Fig. 9

Lenslet array based switch configuration corresponding to the input symbols: (a) 111 and (b) 110.

Fig. 10
Fig. 10

Experimental results for a lenslet array based higher-order symbol recognition: (a) binary input data; (b) TR spatially encoded input data; (c),(d) three (four) superimposed shifted copies of the input image used in the recognition of the search symbol 111 (110); (e) binary mask used to mask the images of (c) and (d); and (f),(g) results of the image operations. The locations of the high intensity pixels indicate the positions of the search symbol 111 (110) in the input data.

Fig. 11
Fig. 11

Experimental results for a CAM based higher-order symbol recognition: (a) binary input data; (b) TR spatially encoded input data; (c),(d) binary mask used to recognize the search symbols 011 (110); (e),(f) masked version of the input image used to recognize the search symbols 011 (110); and (g),(h) for symbols 011 (110), the integration for each of 3 × 3 pixel area result. The positions of the low intensity pixels indicate the position of the search symbol.

Fig. 12
Fig. 12

Experimental results for an optical cavity-based higher-order symbol recognition: (a) binary input data; (b) spatially DR encoded input data; and (c),(d) positions of the high intensity pixels indicating the locations of search symbols 000 (010) in the input data.

Tables (3)

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Table I Logical Functions Fk for a Dual-Rail (DR) Encoding for 3-Bit Binary Numbers as a Function of High Intensity Pixelsa

Tables Icon

Table II Logical Function Fk Representation for 3-Bit Binary Numbers for a Triple-Rall (TR) Encoding Schemea

Tables Icon

Table III Distances d1 (d2) from the Input Mask to Mirrors M1 (M2), Respectively, for Various 3-Bt Inputs

Equations (22)

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

F 0 i = x 1 i ,
F 1 i = x 2 i ,
x 1 i = 0 ,
x 2 i = 1 ,
x 1 i = 1 ,
x 2 i = 0 ,
x 1 i = x 2 i ¯ ,
F k = F ( 110 ) = F 11 F 12 F 03 = x 21 x 22 x 13 ,
F 0 i = x 2 i ,
F 1 i = x 1 x 3 i ,
F 6 = F ( 110 ) = F 11 F 12 F 03 = x 11 x 31 x 12 x 32 x 23 .
F 6 = F 6 ¯ ¯ = x 21 x 22 x 13 ¯ ¯ .
F 6 = x 11 + x 12 + x 23 ¯ .
x 2 i ¯ = x 1 i + x 3 i ,
x 1 i x 3 i ¯ = x 2 i .
F 6 = x 21 + x 22 + x 13 + x 33 ¯ .
B = 0011 0110 0111 .
B e = 01011010 01101001 01101010 , P e = 10010110 10010110 10010110 , A e = 00010010 , 00000000 , 00000010.
d = a 2 tan θ ,
δ = d D 1 f 2 .
O ( x , y ) = A ( x - i δ , y - j δ ) ,
d = a f 2 D 1 .

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