Abstract

Joint-transform correlation architecture is employed for digital matrix multiplication. Real-valued matrix–vector, complex-valued matrix–vector, real-valued matrix–matrix, and complex-valued matrix–matrix multiplication operations can all be realized simply by programming of the data arrangement in the input plane of a multiple-input joint-transform correlator. The proposed method benefits from the advantages of speed because of the real-time processing capability of the joint-transform correlator and of high accuracy because of the digital representation of the multiplied numbers. Computer-simulation results are provided in which the negative binary encoding method is used to encode matrix elements.

© 1999 Optical Society of America

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  1. C. S. Weaver, J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  2. F. T. S. Yu, X. J. Lu, “A programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
    [CrossRef]
  3. J. Wang, B. Javidi, “Multiobject detection using the binary joint transform correlator with different types of thresholding methods,” Opt. Eng. 33, 1793–1804 (1994).
    [CrossRef]
  4. M. Deutsch, J. Garcia, D. Mendlovic, “Multichannel single-output color pattern recognition by use of a joint-transform correlator,” Appl. Opt. 35, 6976–6982 (1996).
    [CrossRef] [PubMed]
  5. M. S. Alam, M. A. Karim, “Arithmetic processing with a joint-transform correlator,” Appl. Opt. 31, 4693–4699 (1992).
    [CrossRef] [PubMed]
  6. S. P. Kozaitis, M. A. Getbehead, “Multiple-input joint transform correlator for wavelet feature extraction,” Opt. Eng. 37, 1325–1331 (1998).
    [CrossRef]
  7. R. A. Hemz, J. O. Artman, S. H. Lee, “Matrix multiplication by optical methods,” Appl. Opt. 9, 2161–2168 (1970).
    [CrossRef]
  8. Q. W. Song, M. C. Lee, P. Talbot, L. Cheng, “Matrix–vector multiplication by using pinhole holograms,” Appl. Opt. 33, 800–805 (1994).
    [CrossRef]
  9. Y. Z. Liang, H.-K. Liu, “Optical matrix–matrix multiplication method demonstrated by the use of a multifocus hololens,” Opt. Lett. 9, 322–324 (1984).
    [CrossRef] [PubMed]
  10. W. T. Rhodes, P. S. Guilfoyle, “Acoustooptic algebraic processing architectures,” Proc. IEEE 72, 820–830 (1984).
    [CrossRef]
  11. H. Nakano, K. Hotate, “Optical system for real-time multiplication of the multiple matrix with a 2-D light source array,” Appl. Opt. 26, 917–923 (1987).
    [CrossRef] [PubMed]
  12. D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in International Optical Computing Conference II, W. T. Rhodes, ed., Proc. SPIE232, 151–156 (1980).
  13. M. A. Karim, A. A. S. Awwal, Optical Computing: An Introduction (Wiley, New York, 1992).
  14. R. P. Bocker, K. Bromley, S. R. Clayton, “Electro-optical matrix multiplication using 2’s complement arithmetic for improved accuracy,” Appl. Opt. 22, 2019–2021 (1983).
    [CrossRef]
  15. C. Perlee, D. P. Casasent, “Negative base encoding in optical linear algebra processors,” Appl. Opt. 25, 168–169 (1986).
    [CrossRef] [PubMed]
  16. L. Liu, G. Li, Y. Yin, “Optical complex matrix–vector multiplication with negative binary inner products,” Opt. Lett. 19, 1759–1761 (1994).
    [CrossRef] [PubMed]
  17. G. Li, L. Liu, L. Shao, Z. Wang, “Negative binary arithmetic algorithms for digital parallel optical computation,” Opt. Lett. 19, 1337–1339 (1994).
    [CrossRef] [PubMed]
  18. D. S. Kalivas, “Real-time optical multiplication with accuracy,” Opt. Eng. 33, 3427–3430 (1994).
    [CrossRef]
  19. G. Li, L. Liu, C. Zhou, “Simplified optical complex multiplication using quarter-imaginary number representation,” Opt. Commun. 122, 16–22 (1995).
    [CrossRef]
  20. F. Cheng, P. Andres, F. T. S. Yu, “Removal of the intra-class associations in a joint power transform spectrum,” Opt. Commun. 99, 7–12 (1993).
    [CrossRef]
  21. C. Li, S. Yin, F. T. S. Yu, “Nonzero-order joint transform correlators,” Opt. Eng. 37, 58–65 (1998).
    [CrossRef]
  22. G. Lu, Z. Zhang, S. Wu, F. T. S. Yu, “Implementation of dc spectra-free joint transform correlator using phase-shifting techniques,” Appl. Opt. 36, 470–483 (1997).
    [CrossRef] [PubMed]

1998

S. P. Kozaitis, M. A. Getbehead, “Multiple-input joint transform correlator for wavelet feature extraction,” Opt. Eng. 37, 1325–1331 (1998).
[CrossRef]

C. Li, S. Yin, F. T. S. Yu, “Nonzero-order joint transform correlators,” Opt. Eng. 37, 58–65 (1998).
[CrossRef]

1997

1996

1995

G. Li, L. Liu, C. Zhou, “Simplified optical complex multiplication using quarter-imaginary number representation,” Opt. Commun. 122, 16–22 (1995).
[CrossRef]

1994

1993

F. Cheng, P. Andres, F. T. S. Yu, “Removal of the intra-class associations in a joint power transform spectrum,” Opt. Commun. 99, 7–12 (1993).
[CrossRef]

1992

1987

1986

1984

Y. Z. Liang, H.-K. Liu, “Optical matrix–matrix multiplication method demonstrated by the use of a multifocus hololens,” Opt. Lett. 9, 322–324 (1984).
[CrossRef] [PubMed]

F. T. S. Yu, X. J. Lu, “A programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

W. T. Rhodes, P. S. Guilfoyle, “Acoustooptic algebraic processing architectures,” Proc. IEEE 72, 820–830 (1984).
[CrossRef]

1983

1970

1966

Alam, M. S.

Andres, P.

F. Cheng, P. Andres, F. T. S. Yu, “Removal of the intra-class associations in a joint power transform spectrum,” Opt. Commun. 99, 7–12 (1993).
[CrossRef]

Artman, J. O.

Awwal, A. A. S.

M. A. Karim, A. A. S. Awwal, Optical Computing: An Introduction (Wiley, New York, 1992).

Bocker, R. P.

Bromley, K.

Carlotto, M.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in International Optical Computing Conference II, W. T. Rhodes, ed., Proc. SPIE232, 151–156 (1980).

Casasent, D.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in International Optical Computing Conference II, W. T. Rhodes, ed., Proc. SPIE232, 151–156 (1980).

Casasent, D. P.

Cheng, F.

F. Cheng, P. Andres, F. T. S. Yu, “Removal of the intra-class associations in a joint power transform spectrum,” Opt. Commun. 99, 7–12 (1993).
[CrossRef]

Cheng, L.

Clayton, S. R.

Deutsch, M.

Garcia, J.

Getbehead, M. A.

S. P. Kozaitis, M. A. Getbehead, “Multiple-input joint transform correlator for wavelet feature extraction,” Opt. Eng. 37, 1325–1331 (1998).
[CrossRef]

Goodman, J. W.

Guilfoyle, P. S.

W. T. Rhodes, P. S. Guilfoyle, “Acoustooptic algebraic processing architectures,” Proc. IEEE 72, 820–830 (1984).
[CrossRef]

Hemz, R. A.

Hotate, K.

Javidi, B.

J. Wang, B. Javidi, “Multiobject detection using the binary joint transform correlator with different types of thresholding methods,” Opt. Eng. 33, 1793–1804 (1994).
[CrossRef]

Kalivas, D. S.

D. S. Kalivas, “Real-time optical multiplication with accuracy,” Opt. Eng. 33, 3427–3430 (1994).
[CrossRef]

Karim, M. A.

Kozaitis, S. P.

S. P. Kozaitis, M. A. Getbehead, “Multiple-input joint transform correlator for wavelet feature extraction,” Opt. Eng. 37, 1325–1331 (1998).
[CrossRef]

Lee, M. C.

Lee, S. H.

Li, C.

C. Li, S. Yin, F. T. S. Yu, “Nonzero-order joint transform correlators,” Opt. Eng. 37, 58–65 (1998).
[CrossRef]

Li, G.

Liang, Y. Z.

Liu, H.-K.

Liu, L.

Lu, G.

Lu, X. J.

F. T. S. Yu, X. J. Lu, “A programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Mendlovic, D.

Nakano, H.

Neft, D.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in International Optical Computing Conference II, W. T. Rhodes, ed., Proc. SPIE232, 151–156 (1980).

Perlee, C.

Psaltis, D.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in International Optical Computing Conference II, W. T. Rhodes, ed., Proc. SPIE232, 151–156 (1980).

Rhodes, W. T.

W. T. Rhodes, P. S. Guilfoyle, “Acoustooptic algebraic processing architectures,” Proc. IEEE 72, 820–830 (1984).
[CrossRef]

Shao, L.

Song, Q. W.

Talbot, P.

Wang, J.

J. Wang, B. Javidi, “Multiobject detection using the binary joint transform correlator with different types of thresholding methods,” Opt. Eng. 33, 1793–1804 (1994).
[CrossRef]

Wang, Z.

Weaver, C. S.

Wu, S.

Yin, S.

C. Li, S. Yin, F. T. S. Yu, “Nonzero-order joint transform correlators,” Opt. Eng. 37, 58–65 (1998).
[CrossRef]

Yin, Y.

Yu, F. T. S.

C. Li, S. Yin, F. T. S. Yu, “Nonzero-order joint transform correlators,” Opt. Eng. 37, 58–65 (1998).
[CrossRef]

G. Lu, Z. Zhang, S. Wu, F. T. S. Yu, “Implementation of dc spectra-free joint transform correlator using phase-shifting techniques,” Appl. Opt. 36, 470–483 (1997).
[CrossRef] [PubMed]

F. Cheng, P. Andres, F. T. S. Yu, “Removal of the intra-class associations in a joint power transform spectrum,” Opt. Commun. 99, 7–12 (1993).
[CrossRef]

F. T. S. Yu, X. J. Lu, “A programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Zhang, Z.

Zhou, C.

G. Li, L. Liu, C. Zhou, “Simplified optical complex multiplication using quarter-imaginary number representation,” Opt. Commun. 122, 16–22 (1995).
[CrossRef]

Appl. Opt.

Opt. Commun.

F. T. S. Yu, X. J. Lu, “A programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

G. Li, L. Liu, C. Zhou, “Simplified optical complex multiplication using quarter-imaginary number representation,” Opt. Commun. 122, 16–22 (1995).
[CrossRef]

F. Cheng, P. Andres, F. T. S. Yu, “Removal of the intra-class associations in a joint power transform spectrum,” Opt. Commun. 99, 7–12 (1993).
[CrossRef]

Opt. Eng.

C. Li, S. Yin, F. T. S. Yu, “Nonzero-order joint transform correlators,” Opt. Eng. 37, 58–65 (1998).
[CrossRef]

J. Wang, B. Javidi, “Multiobject detection using the binary joint transform correlator with different types of thresholding methods,” Opt. Eng. 33, 1793–1804 (1994).
[CrossRef]

S. P. Kozaitis, M. A. Getbehead, “Multiple-input joint transform correlator for wavelet feature extraction,” Opt. Eng. 37, 1325–1331 (1998).
[CrossRef]

D. S. Kalivas, “Real-time optical multiplication with accuracy,” Opt. Eng. 33, 3427–3430 (1994).
[CrossRef]

Opt. Lett.

Proc. IEEE

W. T. Rhodes, P. S. Guilfoyle, “Acoustooptic algebraic processing architectures,” Proc. IEEE 72, 820–830 (1984).
[CrossRef]

Other

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in International Optical Computing Conference II, W. T. Rhodes, ed., Proc. SPIE232, 151–156 (1980).

M. A. Karim, A. A. S. Awwal, Optical Computing: An Introduction (Wiley, New York, 1992).

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