Abstract

A novel orthogonal shadow-casting and imaging optical system is proposed for performing multiple matrix multiplication. An analysis is given for describing the construction of a matrix processor. Preliminary experiments of matrix multiplication are demonstrated.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. A. Heinz, J. O. Artman, S. H. Lee, Appl. Opt. 9, 2161 (1970).
    [CrossRef] [PubMed]
  2. P. N. Tamura, J. C. Wyant, Proc. Soc. Photo-Opt. Instrum. Eng. 83, 97 (1976).
  3. H. Nakano, K. Hotate, Appl. Opt. 24, 4238 (1985).
    [CrossRef] [PubMed]
  4. H. Nakano, K. Hotate, Appl. Opt. 26, 917 (1987).
    [CrossRef] [PubMed]
  5. W. Schneider, W. Fink, Opt. Acta 22, 879 (1975).
    [CrossRef]
  6. Y. Z. Liang, H. K. Liu, Opt. Lett. 9, 322 (1984).
    [CrossRef] [PubMed]
  7. R. A. Athale, J. N. Lee, Opt. Lett. 8, 590 (1983).
    [CrossRef] [PubMed]
  8. R. A. Athale, Proc. Soc. Photo-Opt. Instrum. Eng. 634, 96 (1986).
  9. A. A. Sawchuk, B. K. Jenkins, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143 (1986).
  10. R. P. Bocker, Opt. Eng. 23, 26 (1984).
  11. F. T. S. Yu, T. Lu, Opt. Commun. 71, 39 (1989).
    [CrossRef]
  12. W. Brouwer, Matrix Methods in Optical Instrument Design (Benjamin, New York, 1964).
  13. H. Huang, L. Liu, Acta Opt. Sinica 9, 537 (1989).

1989

F. T. S. Yu, T. Lu, Opt. Commun. 71, 39 (1989).
[CrossRef]

H. Huang, L. Liu, Acta Opt. Sinica 9, 537 (1989).

1987

1986

R. A. Athale, Proc. Soc. Photo-Opt. Instrum. Eng. 634, 96 (1986).

A. A. Sawchuk, B. K. Jenkins, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143 (1986).

1985

1984

1983

1976

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

1975

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

1970

Artman, J. O.

Athale, R. A.

R. A. Athale, Proc. Soc. Photo-Opt. Instrum. Eng. 634, 96 (1986).

R. A. Athale, J. N. Lee, Opt. Lett. 8, 590 (1983).
[CrossRef] [PubMed]

Bocker, R. P.

R. P. Bocker, Opt. Eng. 23, 26 (1984).

Brouwer, W.

W. Brouwer, Matrix Methods in Optical Instrument Design (Benjamin, New York, 1964).

Fink, W.

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

Heinz, R. A.

Hotate, K.

Huang, H.

H. Huang, L. Liu, Acta Opt. Sinica 9, 537 (1989).

Jenkins, B. K.

A. A. Sawchuk, B. K. Jenkins, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143 (1986).

Lee, J. N.

Lee, S. H.

Liang, Y. Z.

Liu, H. K.

Liu, L.

H. Huang, L. Liu, Acta Opt. Sinica 9, 537 (1989).

Lu, T.

F. T. S. Yu, T. Lu, Opt. Commun. 71, 39 (1989).
[CrossRef]

Nakano, H.

Sawchuk, A. A.

A. A. Sawchuk, B. K. Jenkins, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143 (1986).

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).

Wyant, J. C.

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

Yu, F. T. S.

F. T. S. Yu, T. Lu, Opt. Commun. 71, 39 (1989).
[CrossRef]

Acta Opt. Sinica

H. Huang, L. Liu, Acta Opt. Sinica 9, 537 (1989).

Appl. Opt.

Opt. Acta

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

Opt. Commun.

F. T. S. Yu, T. Lu, Opt. Commun. 71, 39 (1989).
[CrossRef]

Opt. Eng.

R. P. Bocker, Opt. Eng. 23, 26 (1984).

Opt. Lett.

Proc. Soc. Photo-Opt. Instrum. Eng.

R. A. Athale, Proc. Soc. Photo-Opt. Instrum. Eng. 634, 96 (1986).

A. A. Sawchuk, B. K. Jenkins, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143 (1986).

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

Other

W. Brouwer, Matrix Methods in Optical Instrument Design (Benjamin, New York, 1964).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Typical configuration of the OSIS for triple matrix multiplication. (a) Pictorial view, (b) side view, and (c) top view.

Fig. 2
Fig. 2

Diagram of the multiple matrix multiplier cascaded with the basic OSIS blocks.

Fig. 3
Fig. 3

Data of the input triplet matrices and the corresponding theoretical results.

Fig. 4
Fig. 4

Photographs of the experimental results.

Equations (8)

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

f 4 ( x 4 , y 4 , u 4 , υ 4 ) = f 1 ( x 1 , y 1 ) f 2 ( x 2 , y 2 ) f 3 ( x 3 , y 3 ) ,
x 2 = x 1 , y 2 = υ 1 f , x 3 = u 1 f + 2 x 1 , y 3 = y 1 , x 4 = x 3 , y 4 = y 2 , u 4 = ( 2 x 4 x 1 ) / f , υ 4 = y 1 / f .
I 0 ( x 4 , y 4 ) = f 1 ( x 1 , y 1 ) f 2 ( x 1 , y 4 ) f 3 ( x 4 , y 1 ) d u 4 d υ 4 .
I 0 ( x 4 , y 4 ) = f 1 ( x 1 , y 1 ) f 2 ( x 1 , y 4 ) f 3 ( x 4 , y 1 ) d x 1 d y 1 .
f 1 ( x 1 , y 1 ) = k l B lk rect [ ( x 1 kd ) / D ] rect [ ( y 1 ld ) / D ] , f 2 ( x 2 , y 2 ) = k n A nk rect [ ( x 2 kd ) / D ] rect [ ( y 2 nd ) / D ] , f 3 ( x 3 , y 3 ) = m l C lm rect [ ( x 3 md ) / D ] rect [ ( y 3 ld ) / D ] .
I 0 ( x 4 , y 4 ) = n m D n m rect [ ( x 4 m d ) / D ] rect [ ( y 4 n d ) / D ]
D n m = P k l A n k B l k C l m ,
[ A out ] = [ A n ] [ A n + 1 ] [ A 1 ] [ A 0 ] [ A 1 ] [ A n ] .

Metrics