Abstract

An optical system which performs the multiplication of binary numbers is described and proof-of-principle experiments are performed. The simultaneous generation of all partial products, optical regrouping of bit products, and optical carry look-ahead addition are novel features of the proposed scheme which takes advantage of the parallel operations capability of optical computers. The proposed processor uses liquid crystal light valves (LCLVs). By space-sharing the LCLVs one such system could function as an array of multipliers. Together with the optical carry look-ahead adders described, this would constitute an optical matrix–vector multiplier.

© 1986 Optical Society of America

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References

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  1. R. A. Athale, “Optical Matrix Algebraic Processors: A Survey,” in Proceedings, IEEE Tenth International Optical Computing Conference, IEEE Catalog No. CH1880-4/83 (IEEE, New York, 1983), pp. 24–31.
    [CrossRef]
  2. A. A. Sawchuk, T. C. Strand, “Digital Optical Computing,” Proc. IEEE 72, 758 (1984).
    [CrossRef]
  3. H. J. Caulfield, J. A. Neff, W. T. Rhodes, “Optical Computing: The Coming Revolution in Optical Signal Processing,” Laser Focus 19, 100 (Nov.1983).
  4. C. C. Guest, T. K. Gaylord, “Truth-Table Look-Up Optical Processing Utilizing Binary and Residue Arithmetic,” Appl. Opt. 19, 1201 (1980).
    [CrossRef] [PubMed]
  5. R. A. Athale, S. H. Lee, “Development of an Optical Parallel Logic Device and a Half-Adder Circuit for Digital Optical Processing,” Opt. Eng. 18, 513 (1979).
    [CrossRef]
  6. J. Tanida, Y. Ichioka, “Optical Logic Array Processor,” in Proceedings, IEEE Tenth International Optical Computing Conference, IEEE Catalog No. CH1880-4/83 (IEEE, New York, 1983), pp. 18–23.
    [CrossRef]
  7. N. Patkar, “Numerical Optical Processing,” M.S. Thesis, Department of Electrical Engineering/Computer Science, Texas Tech U. (1984).
  8. A. Huang, Y. Tsunoda, J. W. Goodman, S. Ishihara, “Optical Computation Using Residue Arithmetic,” Appl. Opt. 18, 149 (1979).
    [CrossRef] [PubMed]
  9. D. Psaltis, D. Casasent, “Optical Residue Arithmetic: A Correlation Approach,” Appl. Opt. 18, 163 (1979).
    [CrossRef] [PubMed]
  10. D. H. Schaefer, J. P. Strong, “Tse Computers,” Proc. IEEE 65, 129 (1977).
    [CrossRef]
  11. M. T. Fatehi, K. C. Wasmundt, S. A. Collins, “Optical Logic Gates Using a Liquid Crystal Light Valve: Implementation and Application Example,” Appl. Opt. 20, 2250 (1981).
    [CrossRef] [PubMed]
  12. B. Arazi, “An Electrooptical Adder,” Proc. IEEE 73, 162 (1985).
    [CrossRef]
  13. E. Marom, B. H. Soffer, U. Efron, “Pixel-by-Pixel Array Division by Optical Computing,” Opt. Lett. 10, 43 (1985).
    [CrossRef] [PubMed]
  14. A. D. Fisher, “Review of Spatial Light Modulators,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1985).
  15. V. Chandran, “Techniques for Optical Binary Multiplication,” M.S. Thesis, Department of Electrical Engineering/Computer Science, Texas Tech U. (1985).

1985

1984

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

1983

H. J. Caulfield, J. A. Neff, W. T. Rhodes, “Optical Computing: The Coming Revolution in Optical Signal Processing,” Laser Focus 19, 100 (Nov.1983).

1981

1980

1979

1977

D. H. Schaefer, J. P. Strong, “Tse Computers,” Proc. IEEE 65, 129 (1977).
[CrossRef]

Arazi, B.

B. Arazi, “An Electrooptical Adder,” Proc. IEEE 73, 162 (1985).
[CrossRef]

Athale, R. A.

R. A. Athale, S. H. Lee, “Development of an Optical Parallel Logic Device and a Half-Adder Circuit for Digital Optical Processing,” Opt. Eng. 18, 513 (1979).
[CrossRef]

R. A. Athale, “Optical Matrix Algebraic Processors: A Survey,” in Proceedings, IEEE Tenth International Optical Computing Conference, IEEE Catalog No. CH1880-4/83 (IEEE, New York, 1983), pp. 24–31.
[CrossRef]

Casasent, D.

Caulfield, H. J.

H. J. Caulfield, J. A. Neff, W. T. Rhodes, “Optical Computing: The Coming Revolution in Optical Signal Processing,” Laser Focus 19, 100 (Nov.1983).

Chandran, V.

V. Chandran, “Techniques for Optical Binary Multiplication,” M.S. Thesis, Department of Electrical Engineering/Computer Science, Texas Tech U. (1985).

Collins, S. A.

Efron, U.

Fatehi, M. T.

Fisher, A. D.

A. D. Fisher, “Review of Spatial Light Modulators,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1985).

Gaylord, T. K.

Goodman, J. W.

Guest, C. C.

Huang, A.

Ichioka, Y.

J. Tanida, Y. Ichioka, “Optical Logic Array Processor,” in Proceedings, IEEE Tenth International Optical Computing Conference, IEEE Catalog No. CH1880-4/83 (IEEE, New York, 1983), pp. 18–23.
[CrossRef]

Ishihara, S.

Lee, S. H.

R. A. Athale, S. H. Lee, “Development of an Optical Parallel Logic Device and a Half-Adder Circuit for Digital Optical Processing,” Opt. Eng. 18, 513 (1979).
[CrossRef]

Marom, E.

Neff, J. A.

H. J. Caulfield, J. A. Neff, W. T. Rhodes, “Optical Computing: The Coming Revolution in Optical Signal Processing,” Laser Focus 19, 100 (Nov.1983).

Patkar, N.

N. Patkar, “Numerical Optical Processing,” M.S. Thesis, Department of Electrical Engineering/Computer Science, Texas Tech U. (1984).

Psaltis, D.

Rhodes, W. T.

H. J. Caulfield, J. A. Neff, W. T. Rhodes, “Optical Computing: The Coming Revolution in Optical Signal Processing,” Laser Focus 19, 100 (Nov.1983).

Sawchuk, A. A.

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

Schaefer, D. H.

D. H. Schaefer, J. P. Strong, “Tse Computers,” Proc. IEEE 65, 129 (1977).
[CrossRef]

Soffer, B. H.

Strand, T. C.

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

Strong, J. P.

D. H. Schaefer, J. P. Strong, “Tse Computers,” Proc. IEEE 65, 129 (1977).
[CrossRef]

Tanida, J.

J. Tanida, Y. Ichioka, “Optical Logic Array Processor,” in Proceedings, IEEE Tenth International Optical Computing Conference, IEEE Catalog No. CH1880-4/83 (IEEE, New York, 1983), pp. 18–23.
[CrossRef]

Tsunoda, Y.

Wasmundt, K. C.

Appl. Opt.

Laser Focus

H. J. Caulfield, J. A. Neff, W. T. Rhodes, “Optical Computing: The Coming Revolution in Optical Signal Processing,” Laser Focus 19, 100 (Nov.1983).

Opt. Eng.

R. A. Athale, S. H. Lee, “Development of an Optical Parallel Logic Device and a Half-Adder Circuit for Digital Optical Processing,” Opt. Eng. 18, 513 (1979).
[CrossRef]

Opt. Lett.

Proc. IEEE

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

D. H. Schaefer, J. P. Strong, “Tse Computers,” Proc. IEEE 65, 129 (1977).
[CrossRef]

B. Arazi, “An Electrooptical Adder,” Proc. IEEE 73, 162 (1985).
[CrossRef]

Other

A. D. Fisher, “Review of Spatial Light Modulators,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1985).

V. Chandran, “Techniques for Optical Binary Multiplication,” M.S. Thesis, Department of Electrical Engineering/Computer Science, Texas Tech U. (1985).

J. Tanida, Y. Ichioka, “Optical Logic Array Processor,” in Proceedings, IEEE Tenth International Optical Computing Conference, IEEE Catalog No. CH1880-4/83 (IEEE, New York, 1983), pp. 18–23.
[CrossRef]

N. Patkar, “Numerical Optical Processing,” M.S. Thesis, Department of Electrical Engineering/Computer Science, Texas Tech U. (1984).

R. A. Athale, “Optical Matrix Algebraic Processors: A Survey,” in Proceedings, IEEE Tenth International Optical Computing Conference, IEEE Catalog No. CH1880-4/83 (IEEE, New York, 1983), pp. 24–31.
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Optical techniques for binary multiplication: (a) formation of the partial products of 1101 × 1011; (b) diagonal regrouping of the bit products and addition of the new binary words to obtain the final product.

Fig. 2
Fig. 2

Optical carry look-ahead adder.

Fig. 3
Fig. 3

Nonlinear characteristics of the three subsystems: (a) 0 system; (b) 1 system; (c) 2 system; solid line, actual curves; dashed line, ideal curves; x represents input intensity; and y represents output intensity.

Fig. 4
Fig. 4

Carry generator takes the 2 system and the 0 system outputs and generates the carries simultaneously as shown. It makes use of a partial reflector (STM) and a polarizer–analyzer (PA) besides the LCLV.

Fig. 5
Fig. 5

Algorithm for optical carry look-ahead addition of two binary numbers.

Fig. 6
Fig. 6

Experimental formation of the array of partial products.

Fig. 7
Fig. 7

Carries generated in three cases (a), (b), and (c). The mixed binary sum is shown above. The arrows indicate positions where carries should be generated.

Fig. 8
Fig. 8

Matrix–vector multiplication using the same configuration and space-sharing the LCLVs.

Equations (4)

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I w = r 2 N - 2 ( 1 - r ) 2 I in .
I max = ( 1 - r ) 2 I in .
I min = I w .
R = I max I min = 1 r 2 N - 2 .

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