Abstract

We present an algorithm for optical interconnection of two-dimensional arrays by transmitting the input through a phase-code mask then correlating it with a control image constructed from the interconnection weights. An arbitrary complex-weighted interconnection pattern can be encoded. We show how the output signal-to-noise ratio can be traded for control image size and complexity by adjusting the phase-code feature size. Theoretical calculations of the average output signal-to-noise ratio are compared with computer simulations of the algorithm.

© 1990 Optical Society of America

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References

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  1. J. Shamir, H. J. Caulfield, R. B. Johnson, Appl. Opt. 28, 311 (1988).
    [CrossRef]
  2. D. Psaltis, D. Brady, K. Wagner, Appl. Opt. 27, 1752 (1988).
    [CrossRef]
  3. R. A. Heinz, J. O. Artman, S. H. Lee, Appl. Opt. 9, 2161 (1970).
    [CrossRef] [PubMed]
  4. E. G. Paek, D. Psaltis, Opt. Eng. 26, 428 (1987).
  5. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Sec. 2.9.
  6. D. M. Pepper, J. Au Yeung, D. Fekete, A. Yariv, Opt. Lett. 3, 7 (1978).
    [CrossRef] [PubMed]
  7. J. E. Ford, Y. Fainman, S. H. Lee, in Conference Record of 1990 International Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, 1990), p. 414.

1988 (2)

1987 (1)

E. G. Paek, D. Psaltis, Opt. Eng. 26, 428 (1987).

1978 (1)

1970 (1)

Artman, J. O.

Au Yeung, J.

Brady, D.

Caulfield, H. J.

Fainman, Y.

J. E. Ford, Y. Fainman, S. H. Lee, in Conference Record of 1990 International Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, 1990), p. 414.

Fekete, D.

Ford, J. E.

J. E. Ford, Y. Fainman, S. H. Lee, in Conference Record of 1990 International Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, 1990), p. 414.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Sec. 2.9.

Heinz, R. A.

Johnson, R. B.

Lee, S. H.

R. A. Heinz, J. O. Artman, S. H. Lee, Appl. Opt. 9, 2161 (1970).
[CrossRef] [PubMed]

J. E. Ford, Y. Fainman, S. H. Lee, in Conference Record of 1990 International Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, 1990), p. 414.

Paek, E. G.

E. G. Paek, D. Psaltis, Opt. Eng. 26, 428 (1987).

Pepper, D. M.

Psaltis, D.

D. Psaltis, D. Brady, K. Wagner, Appl. Opt. 27, 1752 (1988).
[CrossRef]

E. G. Paek, D. Psaltis, Opt. Eng. 26, 428 (1987).

Shamir, J.

Wagner, K.

Yariv, A.

Appl. Opt. (3)

Opt. Eng. (1)

E. G. Paek, D. Psaltis, Opt. Eng. 26, 428 (1987).

Opt. Lett. (1)

Other (2)

J. E. Ford, Y. Fainman, S. H. Lee, in Conference Record of 1990 International Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, 1990), p. 414.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Sec. 2.9.

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Figures (2)

Fig. 1
Fig. 1

Conceptual construction of the correlation matrix–tensor multiplier algorithm in three steps. (a) Correlation of the input array with the control image produces the connected output at sites embedded in a field of noise. (b) Phase coding of the input and control images reduces background noise relative to the signal. (c) The final control image H(x, y) is produced by compressing (overlapping) W′(x, y), reducing the control SBP at the cost of superimposing noise onto the signal sites.

Fig. 2
Fig. 2

Output SNR for a computer-simulated 16-node hypercube connection. At least 200 runs were averaged for each k. The overall average (circles) and average minimum (asterisks) SNR both grow as k2, following the theoretical prediction (solid curve) of the average minimum SNR.

Equations (7)

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c p q = i , j = 1 N W ijpq g ij , p , q = 1 , 2 , N .
g ( x , y ) = i , j = 1 N g ij rect ( x Δ i , y Δ j ) .
W ( x , y ) = p , q = 1 N i , j = 1 N W ijpq rect ( x Δ p N + N i , y Δ q N + N j ) p , q = 1 N W pq ( x , y ) .
c ( x , y ) g ( x , y ) W * ( x , y ) = g ( α , β ) p , q = 1 N W p q ( α x , β y ) d α d β .
H ( x , y ) p , q = 1 N W pq ( x p Δ , y q Δ ) × exp [ j ϕ ( x p Δ , y q Δ ) ] .
c ( x , y ) = { g ( x , y ) exp [ j ϕ ( x , y ) ] } { p , q = 1 N W pq * × ( x p Δ , y q Δ ) exp [ j ϕ ( x p Δ , y q Δ ] } ,
SNR I = 1 + 64 G ( k / N ) 2 F π ( 9 12 / N 2 + 1 / N 4 ) ,

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