Abstract

A method of optical matrix–matrix multiplication is presented. The feasibility of the method is also experimentally demonstrated by the use of a dichromated-gelatin multifocus holographic lens (hololens). With the specific values of matrices chosen, the average percentage error between the theoretical and experimental data of the elements of the output matrix of the multiplication of some specific pairs of 3 × 3 matrices is 0.4%, which corresponds to an 8-bit accuracy.

© 1984 Optical Society of America

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References

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1983 (2)

1982 (4)

1978 (1)

1977 (1)

M. A. Monahan, K. Bromely, R. P. Boeker, Proc. IEEE 65, 121 (1977).
[CrossRef]

1976 (1)

P. N. Tamura, J. C. Wyant, Proc. Soc. Photo-Opt. Instrum. Eng. 83, 97 (1976).

1975 (1)

W. Schneider, W. Fink, Opt. Acta 22, 879 (1975).
[CrossRef]

1974 (1)

1972 (1)

1970 (1)

Artman, J. O.

Athale, R. A.

R. A. Athale, W. C. Collins, Appl. Opt. 21, 2089 (1982).
[CrossRef] [PubMed]

R. A. Athale, in Proceedings of the 10th International Optical Computing Conference, Catalog No. 83CH1880-4 (Institute of Electrical and Electronics Engineers, New York, 1983), p. 24.

Bocker, R. P.

Boeker, R. P.

R. P. Boeker, S. R. Clayton, K. Bromeley, Appl. Opt. 22, 2019 (1983).
[CrossRef]

M. A. Monahan, K. Bromely, R. P. Boeker, Proc. IEEE 65, 121 (1977).
[CrossRef]

Bromeley, K.

Bromely, K.

M. A. Monahan, K. Bromely, R. P. Boeker, Proc. IEEE 65, 121 (1977).
[CrossRef]

Carolotto, M.

Casasent, D.

Caulfiend, H. J.

H. J. Caulfiend, W. T. Rhodes, M. J. Foster, S. Horwitz, Opt. Gommun. 40, 86 (1982).
[CrossRef]

Clayton, S. R.

Collins, W. C.

Dias, A. R.

J. W. Goodman, A. R. Dias, L. M. Woody, Opt. Lett. 2, 1 (1978).
[CrossRef] [PubMed]

A. R. Dias, NASA Conference Proceedings CP2207, 71 (1981).

Fink, W.

W. Schneider, W. Fink, Opt. Acta 22, 879 (1975).
[CrossRef]

Foster, M. J.

H. J. Caulfiend, W. T. Rhodes, M. J. Foster, S. Horwitz, Opt. Gommun. 40, 86 (1982).
[CrossRef]

Goodman, J. W.

Heinz, P. A.

Heinz, R. A.

Horwitz, S.

H. J. Caulfiend, W. T. Rhodes, M. J. Foster, S. Horwitz, Opt. Gommun. 40, 86 (1982).
[CrossRef]

Jablonowski, D. P.

Lee, S. H.

Liang, Y. Z.

Liu, H. K.

Monahan, M. A.

M. A. Monahan, K. Bromely, R. P. Boeker, Proc. IEEE 65, 121 (1977).
[CrossRef]

Rhodes, W. T.

H. J. Caulfiend, W. T. Rhodes, M. J. Foster, S. Horwitz, Opt. Gommun. 40, 86 (1982).
[CrossRef]

Schneider, W.

W. Schneider, W. Fink, Opt. Acta 22, 879 (1975).
[CrossRef]

Tamura, P. N.

P. N. Tamura, J. C. Wyant, Proc. Soc. Photo-Opt. Instrum. Eng. 83, 97 (1976).

Woody, L. M.

Wyant, J. C.

P. N. Tamura, J. C. Wyant, Proc. Soc. Photo-Opt. Instrum. Eng. 83, 97 (1976).

Zhao, D.

Appl. Opt. (8)

Opt. Acta (1)

W. Schneider, W. Fink, Opt. Acta 22, 879 (1975).
[CrossRef]

Opt. Gommun. (1)

H. J. Caulfiend, W. T. Rhodes, M. J. Foster, S. Horwitz, Opt. Gommun. 40, 86 (1982).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

M. A. Monahan, K. Bromely, R. P. Boeker, Proc. IEEE 65, 121 (1977).
[CrossRef]

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

P. N. Tamura, J. C. Wyant, Proc. Soc. Photo-Opt. Instrum. Eng. 83, 97 (1976).

Other (2)

A. R. Dias, NASA Conference Proceedings CP2207, 71 (1981).

R. A. Athale, in Proceedings of the 10th International Optical Computing Conference, Catalog No. 83CH1880-4 (Institute of Electrical and Electronics Engineers, New York, 1983), p. 24.

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram of a fully parallel optical matrix–matrix multiplication system. (a) Pictorial view. (b) Details of planes P1–P3.

Fig. 2
Fig. 2

The architecture of an alternative optical system with a single coherent source for matrix–matrix multiplication.

Tables (1)

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Table 1 Comparison of Theoretical and Experimental Data of C = A × B of Matrix Multiplication of 3 × 3 Matricesa

Equations (5)

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AB = C
c ij = i = 1 n a ik b kj .
[ a 11 a 12 a 21 a 22 ] [ b 11 b 12 b 21 b 22 ] = [ c 11 c 12 c 21 c 22 ] ,
c 11 = a 11 b 11 + a 12 b 21 , c 12 = a 11 b 12 + a 12 b 22 , c 12 = a 21 b 11 + a 22 b 21 , c 22 = a 21 b 12 + a 22 b 22 .
B = [ 1.00 0.50 0.60 0.80 1.00 0.40 0.50 0.40 1.00 ] .

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