Abstract

Synthetic discriminant functions (SDF’s) are an effective tool for pattern-recognition applications. However, their experimental implementation is difficult because of the difficulty in writing full complex modulation functions onto spatial light modulators (SLM’s) with restricted coding domains. Iterative methods are required for the implementation of SDF filters in real SLM’s. A great deal of experimental research has been done with phase-only filters because they can be successfully implemented with liquid-crystal SLM’s. We have recently introduced a technique for encoding arbitrary amplitude information onto the phase-only filter, thus allowing us to encode an arbitrary complex function onto a phase-only SLM. We apply this technique to the generation of arbitrary complex SDF filters, thus avoiding the necessity of iterative algorithms. We examine the discrimination capabilities of fully complex SDF filters designed with different parameters and constraints. Experimental results obtained with liquid-crystal SLM’s are included.

© 2000 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Minimum average correlation energy filters,” Appl. Opt. 31, 1823–1833 (1987).
  4. Ph. Réfrégier, “Filter design for optical pattern recognition: multicriteria optimization approach,” Opt. Lett. 15, 854–856 (1990).
    [CrossRef] [PubMed]
  5. V. Laude, P. Chavel, Ph. Réfrégier, “Implementation of arbitrary real-valued correlation filters for the shadow-casting incoherent correlator,” Appl. Opt. 35, 5267–5274 (1996).
    [CrossRef] [PubMed]
  6. L. Figue, P. Ambs, “Implementation of optimal trade-off correlation filters with an optimized resolution technique,” J. Opt. A 1, 280–282 (1999).
    [CrossRef]
  7. J. L. Horner, P. D. Gianino, “Applying the phase-only filter concept to the synthetic discriminant function correlation filter,” Appl. Opt. 24, 851–855 (1985).
    [CrossRef] [PubMed]
  8. R. R. Kallman, “Optimal low noise phase-only and binary phase-only optical correlation filters for threshold detectors,” Appl. Opt. 25, 4216–4217 (1986).
    [CrossRef] [PubMed]
  9. D. A. Jared, D. J. Ennis, “Inclusion of filter modulation in synthetic-discriminant-function construction,” Appl. Opt. 28, 232–239 (1989).
    [CrossRef] [PubMed]
  10. U. Mahlab, J. Shamir, “Phase-only entropy-optimized filter generated by simulated annealing,” Opt. Lett. 14, 1168–1170 (1989).
    [CrossRef] [PubMed]
  11. M. Bernhardt, F. Wyrowski, O. Bryngdahl, “Encoding of SDF filters with methods of digital holography,” J. Mod. Opt. 40, 663–673 (1993).
    [CrossRef]
  12. R. D. Juday, “Optimal realizable filters and the minimum Euclidean distance principle,” Appl. Opt. 32, 5100–5111 (1993).
    [CrossRef] [PubMed]
  13. V. Laude, Ph. Réfrégier, “Multicriteria characterization of coding domains with optimal Fourier spatial light modulators filters,” Appl. Opt. 33, 4465–4471 (1994).
    [CrossRef] [PubMed]
  14. M. Montes-Usategui, J. Campos, I. Juvells, “Computation of arbitrarily constrained synthetic discriminant functions,” Appl. Opt. 34, 3904–3914 (1995).
    [CrossRef] [PubMed]
  15. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
    [CrossRef]
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    [CrossRef]
  17. J. A. Davis, D. M. Cottrell, J. E. Davis, R. A. Lilly, “Fresnel lens-encoded binary phase-only filters for optical pattern recognition,” Opt. Lett. 14, 659–661 (1989).
    [CrossRef] [PubMed]
  18. A. Tanone, Z. Zhang, C.-M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
    [CrossRef]
  19. Q. Tang, B. Javidi, “Multiple-object detection with a chirp-encoded joint transform correlator,” Appl. Opt. 32, 5079–5088 (1993).
    [CrossRef] [PubMed]
  20. I. Moreno, J. Campos, C. Gorecki, M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34, 6423–6432 (1995).
    [CrossRef]
  21. I. Moreno, J. Campos, M. J. Yzuel, V. Kober, “Implementation of bipolar real-valued input scenes in a real-time optical correlator. Application to color pattern recognition,” Opt. Eng. 37, 144–150 (1998).
    [CrossRef]
  22. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  23. G. G. Mu, X. M. Wang, Z. Q. Wang, “Amplitude-compensated matched filtering,” Appl. Opt. 27, 3461–3463 (1988).
    [CrossRef] [PubMed]

1999

L. Figue, P. Ambs, “Implementation of optimal trade-off correlation filters with an optimized resolution technique,” J. Opt. A 1, 280–282 (1999).
[CrossRef]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
[CrossRef]

1998

I. Moreno, J. Campos, M. J. Yzuel, V. Kober, “Implementation of bipolar real-valued input scenes in a real-time optical correlator. Application to color pattern recognition,” Opt. Eng. 37, 144–150 (1998).
[CrossRef]

1996

1995

M. Montes-Usategui, J. Campos, I. Juvells, “Computation of arbitrarily constrained synthetic discriminant functions,” Appl. Opt. 34, 3904–3914 (1995).
[CrossRef] [PubMed]

I. Moreno, J. Campos, C. Gorecki, M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34, 6423–6432 (1995).
[CrossRef]

1994

1993

A. Tanone, Z. Zhang, C.-M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
[CrossRef]

M. Bernhardt, F. Wyrowski, O. Bryngdahl, “Encoding of SDF filters with methods of digital holography,” J. Mod. Opt. 40, 663–673 (1993).
[CrossRef]

Q. Tang, B. Javidi, “Multiple-object detection with a chirp-encoded joint transform correlator,” Appl. Opt. 32, 5079–5088 (1993).
[CrossRef] [PubMed]

R. D. Juday, “Optimal realizable filters and the minimum Euclidean distance principle,” Appl. Opt. 32, 5100–5111 (1993).
[CrossRef] [PubMed]

1990

1989

1988

1987

1986

1985

1984

1980

Ambs, P.

L. Figue, P. Ambs, “Implementation of optimal trade-off correlation filters with an optimized resolution technique,” J. Opt. A 1, 280–282 (1999).
[CrossRef]

Bernhardt, M.

M. Bernhardt, F. Wyrowski, O. Bryngdahl, “Encoding of SDF filters with methods of digital holography,” J. Mod. Opt. 40, 663–673 (1993).
[CrossRef]

Bryngdahl, O.

M. Bernhardt, F. Wyrowski, O. Bryngdahl, “Encoding of SDF filters with methods of digital holography,” J. Mod. Opt. 40, 663–673 (1993).
[CrossRef]

Campos, J.

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
[CrossRef]

I. Moreno, J. Campos, M. J. Yzuel, V. Kober, “Implementation of bipolar real-valued input scenes in a real-time optical correlator. Application to color pattern recognition,” Opt. Eng. 37, 144–150 (1998).
[CrossRef]

M. Montes-Usategui, J. Campos, I. Juvells, “Computation of arbitrarily constrained synthetic discriminant functions,” Appl. Opt. 34, 3904–3914 (1995).
[CrossRef] [PubMed]

I. Moreno, J. Campos, C. Gorecki, M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34, 6423–6432 (1995).
[CrossRef]

Casasent, D.

Chavel, P.

Cottrell, D. M.

Davis, J. A.

Davis, J. E.

Ennis, D. J.

Figue, L.

L. Figue, P. Ambs, “Implementation of optimal trade-off correlation filters with an optimized resolution technique,” J. Opt. A 1, 280–282 (1999).
[CrossRef]

Gianino, P. D.

Gorecki, C.

I. Moreno, J. Campos, C. Gorecki, M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34, 6423–6432 (1995).
[CrossRef]

Gregory, D. A.

A. Tanone, Z. Zhang, C.-M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
[CrossRef]

Hester, C. F.

Horner, J. L.

Jared, D. A.

Javidi, B.

Juday, R. D.

Juvells, I.

Kallman, R. R.

Kober, V.

I. Moreno, J. Campos, M. J. Yzuel, V. Kober, “Implementation of bipolar real-valued input scenes in a real-time optical correlator. Application to color pattern recognition,” Opt. Eng. 37, 144–150 (1998).
[CrossRef]

Laude, V.

Lilly, R. A.

Mahalanobis, A.

Mahlab, U.

Montes-Usategui, M.

Moreno, I.

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
[CrossRef]

I. Moreno, J. Campos, M. J. Yzuel, V. Kober, “Implementation of bipolar real-valued input scenes in a real-time optical correlator. Application to color pattern recognition,” Opt. Eng. 37, 144–150 (1998).
[CrossRef]

I. Moreno, J. Campos, C. Gorecki, M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34, 6423–6432 (1995).
[CrossRef]

Mu, G. G.

Réfrégier, Ph.

Shamir, J.

Tang, Q.

Tanone, A.

A. Tanone, Z. Zhang, C.-M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
[CrossRef]

Uang, C.-M.

A. Tanone, Z. Zhang, C.-M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
[CrossRef]

Vijaya Kumar, B. V. K.

Vijaya Kumar and L. Hassebrook, B. V. K.

Wang, X. M.

Wang, Z. Q.

Wyrowski, F.

M. Bernhardt, F. Wyrowski, O. Bryngdahl, “Encoding of SDF filters with methods of digital holography,” J. Mod. Opt. 40, 663–673 (1993).
[CrossRef]

Yu, F. T. S.

A. Tanone, Z. Zhang, C.-M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
[CrossRef]

Yzuel, M. J.

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
[CrossRef]

I. Moreno, J. Campos, M. J. Yzuel, V. Kober, “Implementation of bipolar real-valued input scenes in a real-time optical correlator. Application to color pattern recognition,” Opt. Eng. 37, 144–150 (1998).
[CrossRef]

I. Moreno, J. Campos, C. Gorecki, M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34, 6423–6432 (1995).
[CrossRef]

Zhang, Z.

A. Tanone, Z. Zhang, C.-M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
[CrossRef]

Appl. Opt.

C. F. Hester, D. Casasent, “Multivariant technique for multiclass pattern recognition,” Appl. Opt. 19, 1758–1761 (1980).
[CrossRef] [PubMed]

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

J. L. Horner, P. D. Gianino, “Applying the phase-only filter concept to the synthetic discriminant function correlation filter,” Appl. Opt. 24, 851–855 (1985).
[CrossRef] [PubMed]

R. R. Kallman, “Optimal low noise phase-only and binary phase-only optical correlation filters for threshold detectors,” Appl. Opt. 25, 4216–4217 (1986).
[CrossRef] [PubMed]

G. G. Mu, X. M. Wang, Z. Q. Wang, “Amplitude-compensated matched filtering,” Appl. Opt. 27, 3461–3463 (1988).
[CrossRef] [PubMed]

D. A. Jared, D. J. Ennis, “Inclusion of filter modulation in synthetic-discriminant-function construction,” Appl. Opt. 28, 232–239 (1989).
[CrossRef] [PubMed]

B. V. K. Vijaya Kumar and L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
[CrossRef]

A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Minimum average correlation energy filters,” Appl. Opt. 31, 1823–1833 (1987).

Q. Tang, B. Javidi, “Multiple-object detection with a chirp-encoded joint transform correlator,” Appl. Opt. 32, 5079–5088 (1993).
[CrossRef] [PubMed]

R. D. Juday, “Optimal realizable filters and the minimum Euclidean distance principle,” Appl. Opt. 32, 5100–5111 (1993).
[CrossRef] [PubMed]

V. Laude, Ph. Réfrégier, “Multicriteria characterization of coding domains with optimal Fourier spatial light modulators filters,” Appl. Opt. 33, 4465–4471 (1994).
[CrossRef] [PubMed]

M. Montes-Usategui, J. Campos, I. Juvells, “Computation of arbitrarily constrained synthetic discriminant functions,” Appl. Opt. 34, 3904–3914 (1995).
[CrossRef] [PubMed]

V. Laude, P. Chavel, Ph. Réfrégier, “Implementation of arbitrary real-valued correlation filters for the shadow-casting incoherent correlator,” Appl. Opt. 35, 5267–5274 (1996).
[CrossRef] [PubMed]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
[CrossRef]

J. Mod. Opt.

M. Bernhardt, F. Wyrowski, O. Bryngdahl, “Encoding of SDF filters with methods of digital holography,” J. Mod. Opt. 40, 663–673 (1993).
[CrossRef]

J. Opt. A

L. Figue, P. Ambs, “Implementation of optimal trade-off correlation filters with an optimized resolution technique,” J. Opt. A 1, 280–282 (1999).
[CrossRef]

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

I. Moreno, J. Campos, C. Gorecki, M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34, 6423–6432 (1995).
[CrossRef]

Opt. Eng.

I. Moreno, J. Campos, M. J. Yzuel, V. Kober, “Implementation of bipolar real-valued input scenes in a real-time optical correlator. Application to color pattern recognition,” Opt. Eng. 37, 144–150 (1998).
[CrossRef]

A. Tanone, Z. Zhang, C.-M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
[CrossRef]

Opt. Lett.

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Figures (5)

Fig. 1
Fig. 1

Real-time optical convergent correlator: L1 and L2, convergent lenses; P, linear polarizers; HWP, half-wave plates; SLM1, input scene; and SLM2, Fourier filter.

Fig. 2
Fig. 2

Input scene.

Fig. 3
Fig. 3

Experimental correlation results with encoded filters. (a) Phase-only filter, (b) inverse filter. Correlation peaks are shifted with respect to the optical axis to be separated from the reconstruction of the input scene. (c) Sections through the correlation peaks. Dashed curve, phase-only filter; solid curve, inverse filter.

Fig. 4
Fig. 4

Three-dimensional plots of the experimental correlation results with encoded filters. (a) Phase-only filter, (b) inverse filter.

Fig. 5
Fig. 5

Experimental correlation results with encoded filters. (a) SDF filter with parameter μ = 0.9, c G = 1, c O = 0; (b) SDF filter with parameter μ = 0.9, c G = 1, c O = 1; (c) SDF filter with parameter μ = 0.999, c G = 1, c O = 0; and (d) SDF filter with parameter μ = 0.999, c G = 1, c O = 1.

Equations (9)

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

h+X=ct.
MSE=E1=h˜+S˜h˜.
CPE=E2=h˜+D˜h˜.
Eμ=μE1+1-μE2.
Fu=Muexpiϕu
sinπ1-Muπ1-Mu=Mu.
Tu=expiMuϕu.
Tu=n=-+ Tnuexpinϕu.
Tnu=sinπn-Muπn-Mu.

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