Abstract

Matrix multiplication has been performed by optical analog methods using the scheme of Heinz et al. The most critical element was (a), the spatial filter corresponding to the two-dimensional Fourier transform of a. In the operation c = b × a, errors in the c elements were 1–2% when the a elements were all approximately the same. Very large errors occurred when the a elements differed significantly, and these were used directly [instead of the (a) derived values] in the numerical comparisons. These errors were attributed to the limited linear range of the amplitude transmittance characteristic of the film used. Suggestions for future work are made.

© 1972 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) (referenced in this present paper as HAL).
    [CrossRef] [PubMed]
  2. D. P. Jablonowski, R. A. Heinz, J. O. Artman, Appl. Opt. 10, 1988 (1971).
    [CrossRef] [PubMed]

1971

1970

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 (8)

Fig. 1
Fig. 1

Coherent optical correlation system.

Fig. 2
Fig. 2

Optical configuration of a matrix.

Fig. 3
Fig. 3

Optical configuration of b matrix.

Fig. 4
Fig. 4

Theoretical output for multiplication of two 2 × 2 matrices.

Fig. 5
Fig. 5

Amplitude transmittance vs exposure curve of Agfa-Gevaert 8E75 plate. Development time of 5 min in Kodak D-19.

Fig. 6
Fig. 6

Experimental impulse response of an (a) filter.

Fig. 7
Fig. 7

Experimental output for multiplication of two 2 × 2 matrices; compare with Fig. 4.

Fig. 8
Fig. 8

Theoretical impulse response of an (a) filter made by the multiple exposure technique.

Tables (3)

Tables Icon

Table I Comparison of the Theoretical and Experimental Impulse Responses of (a)

Tables Icon

Table II Comparison of the Theoretical and Experimental Values for the Multiplication of Various 2 × 2 Matrices

Tables Icon

Table III Comparison of the Theoretical and Experimental Impulse Responses of (a) When the alm Differ Significantly

Metrics