Abstract

An analog optical processor for evaluating weighted sums of outer products in parallel is described. It uses a linear array of light sources oriented along the diagonal, two-dimensional spatial light modulators to encode input vectors, a two-dimensional detector array to generate the output, and conventional spherical and cylindrical lenses. This system can be used to multiply two matrices as well as to evaluate a weighted rank-1 synthesis of images in a single clock cycle of the processor. Initial experimental results are presented, and factors limiting the performance are described. Implications of this architecture to optical signal- and image-processing systems are discussed.

© 1993 Optical Society of America

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Corrections

Ravindra A. Athale, Kannan Raj, and Vikram A. Savkar, "Fully parallel analog optical calculation of multiple outer products: erratum," Opt. Lett. 18, 1573-1573 (1993)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-18-18-1573

References

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    [CrossRef] [PubMed]
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    [CrossRef]
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1991 (1)

1990 (1)

1987 (1)

1986 (3)

D. Psaltis, R. A. Athale, Appl. Opt. 25, 3071 (1986).
[CrossRef] [PubMed]

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

A. D. Fisher, R. C. Fukuda, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

1985 (1)

1981 (1)

T. M. Turpin, Proc. IEEE 69, 79 (1981).
[CrossRef]

1976 (1)

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

1970 (1)

Artman, J. O.

Astor, M. E.

R. A. Athale, M. E. Astor, in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper ThAA7.

Athale, R. A.

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

D. Psaltis, R. A. Athale, Appl. Opt. 25, 3071 (1986).
[CrossRef] [PubMed]

R. A. Athale, M. E. Astor, in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper ThAA7.

Dias, A. R.

A. R. Dias, in Optical Information Processing for Aerospace Applications, NASA Conference Publ. 2207 (National Technical Information Service, Springfield, Va., 1981).

Fisher, A. D.

A. D. Fisher, R. C. Fukuda, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

Fukuda, R. C.

A. D. Fisher, R. C. Fukuda, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

Heinz, R. A.

Hong, J.

Hotate, K.

Huang, H.

Lee, J. N.

A. D. Fisher, R. C. Fukuda, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

Lee, S. H.

Liu, L.

Nakano, H.

Psaltis, D.

Tamura, P. N.

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

Turpin, T. M.

T. M. Turpin, Proc. IEEE 69, 79 (1981).
[CrossRef]

Wang, Z.

Wyant, J. C.

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

Yeh, P.

Appl. Opt. (4)

Opt. Lett. (2)

Proc. IEEE (1)

T. M. Turpin, Proc. IEEE 69, 79 (1981).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (3)

A. D. Fisher, R. C. Fukuda, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

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

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

Other (2)

R. A. Athale, M. E. Astor, in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper ThAA7.

A. R. Dias, in Optical Information Processing for Aerospace Applications, NASA Conference Publ. 2207 (National Technical Information Service, Springfield, Va., 1981).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the fully parallel optical processor for evaluating multiple outer products.

Fig. 2
Fig. 2

(a) Input matrix masks A and B (reverse contrast). (b) Individual outer products generated by the processor shown in Fig. 1 and with the input vectors shown in (a). (c) Simultaneous calculation of several outer product terms shown in (b).

Fig. 3
Fig. 3

Light distribution in (a) plane P2 and (b) plane P3 of the optical system.

Equations (5)

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

O ( i , j ) = k r ( k ) A k ( i ) B k ( j ) ,
a = 2 f tan Ψ 2 - ( M - 1 ) s .
s = 2 λ f δ ,
s = 2 λ f N 2 f tan Ψ 2 - ( M - 1 ) s .
η = [ 1 - ( M - 1 ) s 2 f tan Ψ 2 ] 2 .

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