Abstract

A binary phase only filter is encoded using a simulated annealing algorithm to distinguish two similar characters. Characters that cannot be distinguished with conventional filter encoding methods are clearly distinguished with the annealed binary phase only filter in a computer simulation. Two binary phase only filters have been fabricated by use of electron beam lithography and chemical etching. One is an annealed binary phase only filter, and the other is a binary phase only filter encoded with a conventional method. Optical pattern recognition experiments using the filters agree well with computer simulation results.

© 1990 Optical Society of America

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References

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    [CrossRef] [PubMed]
  5. M. A. Flavin, J. L. Horner, “Correlation Experiments with a Binary Phase-Only Filter Implemented on a Quartz Plate,” Opt. Eng. 28, 470–473 (1989).
    [CrossRef]
  6. D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
    [CrossRef]
  7. D. M. Cottrell, R. A. Lilly, J. A. Davis, T. Day, “Optical Correlator Performance of Binary Phase-Only Filters Using Fourier and Hartley Transforms,” Appl. Opt. 26, 3755–3761 (1987).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–679 (1983).
    [CrossRef]
  10. H. Haneishi, T. Masuda, N. Ohyama, T. Honda, “Three-Dimensional Blood Vessel Reconstruction by Simulated Annealing,” Opt. Lett. 15, 1095–1097 (1989).
    [CrossRef]
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    [CrossRef] [PubMed]
  12. H. Szu, “Three Layers of Vector Outer Product Neural Networks for Optical Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 312–330 (1986).
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  14. S. Geman, D. Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 721–741 (1984).
    [CrossRef]
  15. P. Carnevali, L. Coletti, S. Patarnello, “Image Processing by Simulated Annealing,” IBM J. Res. Dev. 29, 569 (1985).
    [CrossRef]
  16. H. Farhoosh, M. R. Feldman, S. H. Lee, C. C. Guest, Y. Fainman, R. Eschbach, “Comparison of Binary Encoding Schemes for Electron-Beam Fabrication of Computer Generated Holograms,” Appl. Opt. 26, 4361–4372 (1987).
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    [CrossRef] [PubMed]

1990 (1)

1989 (5)

J. A. Davis, D. M. Cottrell, R. A. Lilly, S. W. Connely, “Multiplexed Phase-Encoded Lenses Written on Spatial Light Modulators,” Opt. Lett. 14, 420–422 (1989).
[CrossRef] [PubMed]

M. S. Kim, C. C. Guest, “Block Quantization of an Annealed Binary Phase Hologram for Optical Interconnects,” Proc. Soc. Photo-Opt. Instrum. Eng. 1151, 231–236 (1989).

M. A. Flavin, J. L. Horner, “Correlation Experiments with a Binary Phase-Only Filter Implemented on a Quartz Plate,” Opt. Eng. 28, 470–473 (1989).
[CrossRef]

H. Haneishi, T. Masuda, N. Ohyama, T. Honda, “Three-Dimensional Blood Vessel Reconstruction by Simulated Annealing,” Opt. Lett. 15, 1095–1097 (1989).
[CrossRef]

M. S. Kim, M. R. Feldman, C. C. Guest, “Optimum Encoding of Binary Phase-Only Filters with a Simulated Annealing Algorithm,” Opt. Lett. 14, 545–547 (1989).
[CrossRef] [PubMed]

1988 (1)

1987 (3)

1986 (1)

H. Szu, “Three Layers of Vector Outer Product Neural Networks for Optical Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 312–330 (1986).

1985 (2)

S. M. Arnold, “Electron Beam Fabrication of Computer Generated Holograms,” Opt. Eng. 24, 803–807 (1985).
[CrossRef]

P. Carnevali, L. Coletti, S. Patarnello, “Image Processing by Simulated Annealing,” IBM J. Res. Dev. 29, 569 (1985).
[CrossRef]

1984 (3)

S. Geman, D. Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 721–741 (1984).
[CrossRef]

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812–816 (1984).
[CrossRef] [PubMed]

1983 (1)

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–679 (1983).
[CrossRef]

1970 (1)

1967 (1)

1964 (1)

A. B. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Allebach, J. P.

Arnold, S. M.

S. M. Arnold, “Electron Beam Fabrication of Computer Generated Holograms,” Opt. Eng. 24, 803–807 (1985).
[CrossRef]

Carnevali, P.

P. Carnevali, L. Coletti, S. Patarnello, “Image Processing by Simulated Annealing,” IBM J. Res. Dev. 29, 569 (1985).
[CrossRef]

Coletti, L.

P. Carnevali, L. Coletti, S. Patarnello, “Image Processing by Simulated Annealing,” IBM J. Res. Dev. 29, 569 (1985).
[CrossRef]

Connely, S. W.

Cottrell, D. M.

Davis, J. A.

Day, T.

Eschbach, R.

Fainman, Y.

Farhoosh, H.

Farn, M. W.

Feldman, M. R.

Flavin, M. A.

M. A. Flavin, J. L. Horner, “Correlation Experiments with a Binary Phase-Only Filter Implemented on a Quartz Plate,” Opt. Eng. 28, 470–473 (1989).
[CrossRef]

Gelatt, C. D.

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–679 (1983).
[CrossRef]

Geman, D.

S. Geman, D. Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 721–741 (1984).
[CrossRef]

Geman, S.

S. Geman, D. Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 721–741 (1984).
[CrossRef]

Gianino, P. D.

Goodman, J. W.

Guest, C. C.

Haneishi, H.

H. Haneishi, T. Masuda, N. Ohyama, T. Honda, “Three-Dimensional Blood Vessel Reconstruction by Simulated Annealing,” Opt. Lett. 15, 1095–1097 (1989).
[CrossRef]

Honda, T.

H. Haneishi, T. Masuda, N. Ohyama, T. Honda, “Three-Dimensional Blood Vessel Reconstruction by Simulated Annealing,” Opt. Lett. 15, 1095–1097 (1989).
[CrossRef]

Horner, J. L.

M. A. Flavin, J. L. Horner, “Correlation Experiments with a Binary Phase-Only Filter Implemented on a Quartz Plate,” Opt. Eng. 28, 470–473 (1989).
[CrossRef]

J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812–816 (1984).
[CrossRef] [PubMed]

Kim, M. S.

Kirpatrick, S.

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–679 (1983).
[CrossRef]

Lee, S. H.

Lee, W. H.

Lilly, R. A.

Lohmann, A. W.

Masuda, T.

H. Haneishi, T. Masuda, N. Ohyama, T. Honda, “Three-Dimensional Blood Vessel Reconstruction by Simulated Annealing,” Opt. Lett. 15, 1095–1097 (1989).
[CrossRef]

Ohyama, N.

H. Haneishi, T. Masuda, N. Ohyama, T. Honda, “Three-Dimensional Blood Vessel Reconstruction by Simulated Annealing,” Opt. Lett. 15, 1095–1097 (1989).
[CrossRef]

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Paris, D. P.

Patarnello, S.

P. Carnevali, L. Coletti, S. Patarnello, “Image Processing by Simulated Annealing,” IBM J. Res. Dev. 29, 569 (1985).
[CrossRef]

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Seldowitz, M. S.

Sweeney, D. W.

Szu, H.

H. Szu, “Three Layers of Vector Outer Product Neural Networks for Optical Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 312–330 (1986).

VanderLugt, A. B.

A. B. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Vecchi, M. P.

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–679 (1983).
[CrossRef]

Venkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Appl. Opt. (8)

IBM J. Res. Dev. (1)

P. Carnevali, L. Coletti, S. Patarnello, “Image Processing by Simulated Annealing,” IBM J. Res. Dev. 29, 569 (1985).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. B. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

IEEE Trans. Pattern Anal. Machine Intell. (1)

S. Geman, D. Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 721–741 (1984).
[CrossRef]

Opt. Eng. (3)

S. M. Arnold, “Electron Beam Fabrication of Computer Generated Holograms,” Opt. Eng. 24, 803–807 (1985).
[CrossRef]

M. A. Flavin, J. L. Horner, “Correlation Experiments with a Binary Phase-Only Filter Implemented on a Quartz Plate,” Opt. Eng. 28, 470–473 (1989).
[CrossRef]

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Opt. Lett. (3)

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

M. S. Kim, C. C. Guest, “Block Quantization of an Annealed Binary Phase Hologram for Optical Interconnects,” Proc. Soc. Photo-Opt. Instrum. Eng. 1151, 231–236 (1989).

H. Szu, “Three Layers of Vector Outer Product Neural Networks for Optical Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 312–330 (1986).

Science (1)

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220, 671–679 (1983).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Optical system used for simulation of pattern recognition using the BPOF: I is the input pattern, L1 and L2 are Fourier transform lenses, O is the output plane, and f is the focal length of the lenses.

Fig. 2
Fig. 2

Input patterns P and R used for the computer simulation. These patterns are also used as inputs for the optical system in Fig. 6.

Fig. 3
Fig. 3

Flow diagram of the BPOF annealing algorithm.

Fig. 4
Fig. 4

Phase ϕ vs temperature as the temperature decreases.

Fig. 5
Fig. 5

Optical experiment setup for pattern recognition with the BPOFs: LA is a He–Ne laser, AT is an attenuator, CO is collimating optics, I is an input pattern, L1 and L2 are Fourier transform lenses, TVC is a TV camera, M is a TV monitor, OS is an oscilloscope, and f is the focal length of the lenses.

Fig. 6
Fig. 6

Computer simulations of the correlation performance of the conventional BPOF with (a) the input P and (b) the input R.

Fig. 7
Fig. 7

Computer simulations of the correlation performance of the annealed BPOF: (a) correlation of the input P with the annealed BPOF; (b) cross section through the correlation peaks of (a); (c) correlation of the input R with the annealed BPOF; (d) cross section through the correlation peaks of (c).

Fig. 8
Fig. 8

Impulse response of the conventional BPOF.

Fig. 9
Fig. 9

Oscilloscope trace through the correlation peaks given by the conventional BPOF with (a) the input P and (b) the input R.

Fig. 10
Fig. 10

Impulse response of the annealed BPOF.

Fig. 11
Fig. 11

Oscilloscope trace through the correlation peaks given by the annealed BPOF with (a) the input P and (b) the input R.

Tables (1)

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Table I Results from Computer Simulations and Experiments

Equations (17)

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F ^ ( u , v ) = [ 1 - exp ( j ϕ ) ] B ( u , v ) + exp ( j ϕ ) ,
F ^ ( u , v ) = 1 for B ( u , v ) = 1 , exp ( j ϕ ) for B ( u , v ) = 0.
G ( u , v ) = [ 1 - exp ( j ϕ ) ] B ( u , v ) A ( u , v ) + exp ( j ϕ ) A ( u , v ) ,
G ( u , v ) = [ 1 - exp ( j ϕ ) ] k = K / 2 K / 2 l = L / 2 L / 2 B k l A k l rect ( u - k Δ u Δ u , v - l Δ v Δ v ) + exp ( j ϕ ) k = K / 2 K / 2 l = L / 2 L / 2 A k l rect ( u - k Δ u Δ u , v - l Δ v Δ v ) ,
g ( x , y ) = [ 1 - exp ( j ϕ ) ] C g ˜ ( x , y ) + exp ( j ϕ ) C a ˜ ( x , y ) ,
C = Δ u Δ v sin c ( x Δ u , y Δ v ) , g ˜ ( x , y ) = k l B k l A k l exp [ - 2 π j ( k x Δ u + l y Δ v ) ] , a ˜ ( x , y ) = k l A k l exp [ - 2 π j ( k x Δ u + l y Δ v ) ] .
g ( m Δ x , n Δ y ) = [ 1 - exp ( j ϕ ) ] C g ˜ m n + exp ( j ϕ ) C a ˜ m n ,
g ˜ m n = k l B k l A k l exp [ - 2 π j ( k m / K + l n / L ) ] , a ˜ m n = k l A k l exp [ - 2 π j ( k m / K + ln / L ) ] .
g m n = [ 1 - exp ( j ϕ ) ] g ˜ m n + exp ( j ϕ ) a ˜ m n ,
Δ E = E new - E old ,
P ( Δ E ) = 1 1 + exp ( Δ E / T ) .
E = ( T A - A C [ P , P ] ) 2 + ( T A - A C [ R , R ] ) 2 + ( T C - C C [ P , R ] ) 2 + ( T C - C C [ R , P ] ) 2 ,
T = ( D T ) r T initial and D T = ( T final / T initial ) 1 / q ,
g ˜ m n new = g ˜ m n old - A k l exp [ - 2 π j ( m k / K + n l / L ) ] .
g ˜ m n new = g ˜ m n old + A k l exp [ - 2 π j ( m k / K + n l / L ) ] .
F ^ C ( u , v ) = 1 for Re [ A ( u , v ) ] > 0 - 1 otherwise .
L = λ ϕ 2 π ( n - 1 ) ,

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