Abstract

We report on a technique for producing a Bessel function correlation output for an arbitrary input pattern. The central dark spot at the center of the Bessel function correlator output is narrower than the width of the normal correlation spot and can be extremely useful for locating the center of the correlation signal. The Bessel function is produced by convolution of the extremely sharp correlation produced by an inverse filter with the Bessel function and is encoded with a single phase-only liquid-crystal spatial light modulator. To encode amplitude information on the filter, we spatially modulate the phase encoded on the filter. Amplitude modulation is obtained by modulation of the diffraction efficiency of the phase grating. Experimental results are presented.

© 1999 Optical Society of America

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References

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  1. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  2. J. A. Davis, L. L. Haavig, D. M. Cottrell, “Bessel function output from an optical correlator,” Appl. Opt. 36, 2376–2379 (1997).
    [CrossRef] [PubMed]
  3. F. T. S. Yu, Optical Information Processing (Wiley-Interscience, New York, 1983), Chap. 7, pp. 198–202.
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    [CrossRef] [PubMed]
  5. J. A. Davis, D. M. Cottrell, J. Campos, M. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
    [CrossRef]
  6. A. W. Lohmann, C. Thum, “Increased light efficiency of coherent-optical matched filters,” Appl. Opt. 23, 1503–1508 (1984).
    [CrossRef] [PubMed]
  7. J. A. Davis, D. M. Cottrell, R. P. Tiangco, “Analysis of the phase-only filter,” in Optical Pattern Recognition VI, D. P. Casasent, T. H. Chao, eds., Proc. SPIE2490, 77–87 (1994).
    [CrossRef]
  8. W. J. Dallas, Computer Generated Holograms, B. R. Frieden, ed., Vol. 41 of Topics in Applied Physics Series (Springer-Verlag, Berlin, 1980), Chap. 6.
  9. 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]
  10. 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]
  11. 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]
  12. 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]
  13. C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
    [CrossRef]
  14. I. Moreno, J. A. Davis, K. D’Nelly, D. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal light modulators,” Opt. Eng. 37, 3048–3052 (1998).
    [CrossRef]

1999

1998

I. Moreno, J. A. Davis, K. D’Nelly, D. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[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]

1997

1995

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

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

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]

1989

1988

1984

Allison, D.

I. Moreno, J. A. Davis, K. D’Nelly, D. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

Campos, J.

J. A. Davis, D. M. Cottrell, J. Campos, M. 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]

Cottrell, D. M.

D’Nelly, K.

I. Moreno, J. A. Davis, K. D’Nelly, D. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

Dallas, W. J.

W. J. Dallas, Computer Generated Holograms, B. R. Frieden, ed., Vol. 41 of Topics in Applied Physics Series (Springer-Verlag, Berlin, 1980), Chap. 6.

Davis, J. A.

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

I. Moreno, J. A. Davis, K. D’Nelly, D. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

J. A. Davis, L. L. Haavig, D. M. Cottrell, “Bessel function output from an optical correlator,” Appl. Opt. 36, 2376–2379 (1997).
[CrossRef] [PubMed]

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]

J. A. Davis, D. M. Cottrell, R. P. Tiangco, “Analysis of the phase-only filter,” in Optical Pattern Recognition VI, D. P. Casasent, T. H. Chao, eds., Proc. SPIE2490, 77–87 (1994).
[CrossRef]

Davis, J. E.

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]

Haavig, L. L.

Horner, J. L.

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]

Lilly, R. A.

Lohmann, A. W.

Lu, K.

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

Moreno, I.

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

I. Moreno, J. A. Davis, K. D’Nelly, D. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[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.

Soutar, C.

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

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]

Thum, C.

Tiangco, R. P.

J. A. Davis, D. M. Cottrell, R. P. Tiangco, “Analysis of the phase-only filter,” in Optical Pattern Recognition VI, D. P. Casasent, T. H. Chao, eds., Proc. SPIE2490, 77–87 (1994).
[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]

Wang, X. M.

Wang, Z. Q.

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]

F. T. S. Yu, Optical Information Processing (Wiley-Interscience, New York, 1983), Chap. 7, pp. 198–202.

Yzuel, M.

Yzuel, M. J.

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.

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.

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]

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]

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

I. Moreno, J. A. Davis, K. D’Nelly, D. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

Opt. Lett.

Other

F. T. S. Yu, Optical Information Processing (Wiley-Interscience, New York, 1983), Chap. 7, pp. 198–202.

J. A. Davis, D. M. Cottrell, R. P. Tiangco, “Analysis of the phase-only filter,” in Optical Pattern Recognition VI, D. P. Casasent, T. H. Chao, eds., Proc. SPIE2490, 77–87 (1994).
[CrossRef]

W. J. Dallas, Computer Generated Holograms, B. R. Frieden, ed., Vol. 41 of Topics in Applied Physics Series (Springer-Verlag, Berlin, 1980), Chap. 6.

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Figures (4)

Fig. 1
Fig. 1

Centered input object and offset reference object used in our experiments.

Fig. 2
Fig. 2

Experimental correlation plane images (a) for the phase-only filter (b) for the Bessel-function-coded phase-only filter.

Fig. 3
Fig. 3

Experimental correlation plane images (a) for the inverse phase-only filter (b) for the Bessel-function-coded inverse phase-only filter.

Fig. 4
Fig. 4

One-dimensional scans through the correlation peak (a) for the inverse phase-only filter (b) for the Bessel-function-coded inverse phase-only filter.

Equations (18)

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Gu, v=|Gu, v|expiΦGu, v,
Hu, v=|Hu, v|expiΦHu, v.
cx, y=gx, yhx, y.
H˜u, v=Hu, v|Hu, v|=expiΦHu, v.
c˜x, y=gx, yh˜x, y.
H˜u, v=1|Hu, v|expiΦHu, v.
c¯x, y=h˜x, yh˜x, y.
Bρ, θ=Hρ, θexpinθ.
gr, θhr, θ * Jnr, θ=cr, θ * Jnr, θ.
B¯ρ, θ=1|Hρ, θ|expiΦHρ, θexpinθ.
cr, θ=c˜r, θ * Jnr, θ=h˜r, θh˜r, θ * Jnr, θ.
Fu, v=Mu, vexpiϕu, v.
Tu, v=expiMu, vϕu, v.
Tu, v=n=- Tnu, vexpinϕu, v.
Tnu, v=expin-Mu, vπsinπn-Mu, vπn-Mu, v.
Mu, v=T1u, v=sinπ1-Mu, vπ1-Mu, v.
Tu, v=expiMu, vΦHu, v+2πuAexpinθ,
Mu, v=1if |Hu, v|<H0H0/|Hu, v|if |Hu, v|>H0.

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