Abstract

An optical realization of a single layer pattern classifier is described in which Perceptron learning is implemented to train the system weights. Novel use of the Stokes’s principle of reversability for light is made to realize both additive and subtractive weight modifications necessary for true Perceptron learning. This is achieved by using a double Mach-Zehnder interferometer in conjunction with photorefractive hologram recording. Experimental results are given which show the high quality subtractive changes that can be made.

© 1990 Optical Society of America

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References

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  1. D. Z. Anderson, D. M. Lininger, “Dynamic Optical Interconnects: Volume Holograms as Optical Two-Port Operators,” Appl. Opt. 26, 5031–5038 (1987).
    [CrossRef] [PubMed]
  2. D. Psaltis, D. Brady, K. Wagner, “Adaptive Optical Networks Using Photorefractive Crystals,” Appl. Opt. 27, 1752–1759 (1988).
    [CrossRef]
  3. A. Yariv, S. Kwong, “Associative Memories Based on Message-Bearing Optical Modes in Phase Conjugate Resonators,” Opt. Lett. 11, 186–188 (1986).
    [CrossRef] [PubMed]
  4. R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York1973).
  5. D. Psaltis, C. H. Park, J. Hong, “Higher Order Associative Memories and Their Optical Implementations,” Neural Networks 1, 149–163 (1988).
    [CrossRef]
  6. H. J. Caulfield, “Parallel N4 Weighted Optical Interconnections,” Appl. Opt. 26, 4039–4040 (1987).
    [CrossRef] [PubMed]
  7. P. Yeh, T. Y. Chang, P. H. Beckwith, “Real-time optical image subtraction using dynamic holographic interference in photorefractive media,” Opt. Lett. 13, 586–588 (1988).
    [CrossRef] [PubMed]
  8. J. H. Hong, P. Yeh, S. Campbell, “Trainable Optical Network for Pattern Recognition,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), p. 307.
  9. See, for example, P. Yeh, “Two-Wave Mixing in Nonlinear Media,” IEEE J. Quantum Electron. QE-25, 484–519 (1989).
    [CrossRef]

1989 (1)

See, for example, P. Yeh, “Two-Wave Mixing in Nonlinear Media,” IEEE J. Quantum Electron. QE-25, 484–519 (1989).
[CrossRef]

1988 (3)

1987 (2)

1986 (1)

Anderson, D. Z.

Beckwith, P. H.

Brady, D.

Campbell, S.

J. H. Hong, P. Yeh, S. Campbell, “Trainable Optical Network for Pattern Recognition,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), p. 307.

Caulfield, H. J.

Chang, T. Y.

Duda, R. O.

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York1973).

Hart, P. E.

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York1973).

Hong, J.

D. Psaltis, C. H. Park, J. Hong, “Higher Order Associative Memories and Their Optical Implementations,” Neural Networks 1, 149–163 (1988).
[CrossRef]

Hong, J. H.

J. H. Hong, P. Yeh, S. Campbell, “Trainable Optical Network for Pattern Recognition,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), p. 307.

Kwong, S.

Lininger, D. M.

Park, C. H.

D. Psaltis, C. H. Park, J. Hong, “Higher Order Associative Memories and Their Optical Implementations,” Neural Networks 1, 149–163 (1988).
[CrossRef]

Psaltis, D.

D. Psaltis, C. H. Park, J. Hong, “Higher Order Associative Memories and Their Optical Implementations,” Neural Networks 1, 149–163 (1988).
[CrossRef]

D. Psaltis, D. Brady, K. Wagner, “Adaptive Optical Networks Using Photorefractive Crystals,” Appl. Opt. 27, 1752–1759 (1988).
[CrossRef]

Wagner, K.

Yariv, A.

Yeh, P.

See, for example, P. Yeh, “Two-Wave Mixing in Nonlinear Media,” IEEE J. Quantum Electron. QE-25, 484–519 (1989).
[CrossRef]

P. Yeh, T. Y. Chang, P. H. Beckwith, “Real-time optical image subtraction using dynamic holographic interference in photorefractive media,” Opt. Lett. 13, 586–588 (1988).
[CrossRef] [PubMed]

J. H. Hong, P. Yeh, S. Campbell, “Trainable Optical Network for Pattern Recognition,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), p. 307.

Appl. Opt. (3)

IEEE J. Quantum Electron. (1)

See, for example, P. Yeh, “Two-Wave Mixing in Nonlinear Media,” IEEE J. Quantum Electron. QE-25, 484–519 (1989).
[CrossRef]

Neural Networks (1)

D. Psaltis, C. H. Park, J. Hong, “Higher Order Associative Memories and Their Optical Implementations,” Neural Networks 1, 149–163 (1988).
[CrossRef]

Opt. Lett. (2)

Other (2)

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York1973).

J. H. Hong, P. Yeh, S. Campbell, “Trainable Optical Network for Pattern Recognition,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), p. 307.

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Figures (12)

Fig. 1
Fig. 1

One layer neural network.

Fig. 2
Fig. 2

Inner product computation using volume hologram.

Fig. 3
Fig. 3

Multiple output holographic system: (a) recording (point source 1 is activated when w1(x,y) is in SLM and point source 2 is activated when w2(x,y) is in SLM); (b) read-out (y1 = <w1,f> and y2 = <w2,f>).

Fig. 4
Fig. 4

Grating phase control using phase shifting device.

Fig. 5
Fig. 5

Holographic phase control using Stokes’ principle of reversibility.

Fig. 6
Fig. 6

Experiment to view holographic fringes.

Fig. 7
Fig. 7

Scanned image of intensity grating: (a) shutter 1 on; (b) shutter 2 on; and (c) both shutters on.

Fig. 8
Fig. 8

Experiment to view subtraction of holograms using a BaTiO3 crystal.

Fig. 9
Fig. 9

Monitored diffraction efficiency (see text).

Fig. 10
Fig. 10

Optical pattern classifier.

Fig. 11
Fig. 11

Computer simulation learning curves (classification error shown as function of number of iterations): (a) photorefractive system with τ/10 exposure time; and (b) ideal Perceptron system.

Fig. 12
Fig. 12

Multiple category pattern classifier.

Equations (8)

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y = g ( i = 1 N w i x i ) ,             g ( z ) = { 1 if z > 0 0 otherwise
w i ( p + 1 ) = w i ( p ) + α ( p ) x i ( p ) ,
α ( p ) = { 0 if output y ( p ) was correct 1 if y ( p ) = 0 but should have been 1 - 1 if y ( p ) = 1 but should have been 0.
t = t and r t * + r t * = 0.
Γ 1 ( x , y ) = K ( 1 - exp ( - t 1 / τ ) ) A ( x , y ) I 0 + A ( x , y ) 2 ,
Γ ( x , y ) = K { ( 1 - exp ( - t 1 / τ ) ) exp ( - t 2 / τ ) - ( 1 - exp ( - t 2 / τ ) ) } A ( x , y ) I 0 + A ( x , y ) 2 .
w i ( p + 1 ) = exp ( - t e / τ ) w i ( p ) + [ 1 - exp ( - t e / τ ) ] α ( p ) x i ( p ) ,
y ( p ) = < w i ( p ) , x i ( p ) > 2 .

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