Abstract

We introduce a new filter for an optical correlator that produces a Bessel function correlation output. The advantage of this type of output is that the width of the central dark spot at the center of the correlator output is narrower than the width of the usual correlation spot. In addition, the dark spot is insensitive to changes in illumination intensity. We present experimental results with which we write the new filter onto a programmable magneto-optic spatial light modulator.

© 1997 Optical Society of America

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References

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  1. S. B. Vinas, Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, “Zone plates with black focal spots,” Appl. Opt. 31, 192–198 (1992).
    [CrossRef] [PubMed]
  2. J. Ojeda-Castaneda, P. Andres, M. Martinez-Corral, “Zero axial intensity by annular screens with angular variation,” Appl. Opt. 31, 4600–4602 (1992).
    [CrossRef]
  3. J. Ojeda-Castaneda, G. Ramirez, “Zone plates for zero axial irradiance,” Opt. Lett 18, 87–89 (1993).
    [CrossRef] [PubMed]
  4. Z. Jaroszewicz, A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
    [CrossRef]
  5. J. A. Davis, J. J. Kane, D. M. Cottrell, “Horner efficiency of phase-only and binary phase-only filters,” Appl. Opt. 32, 5095–5099 (1993).
    [CrossRef] [PubMed]
  6. 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]
  7. J. L. Horner, “Clarification of Horner efficiency,” Appl. Opt. 31, 4629 (1992).
    [CrossRef] [PubMed]
  8. D. C. O’Shea, J. W. Beletic, M. Poutous, “Binary-mask generation for diffractive optical elements using microcomputers,” Appl. Opt. 32, 2566–2572 (1992).
    [CrossRef]
  9. J. A. Davis, R. P. Tiangco, D. M. Cottrell, D. M. O’Shea, M. Poutous, “Four-plane space-variant Fresnel-transform optical processor with a random phase encoder,” Appl. Opt. 35, 3819–3828 (1996).
    [CrossRef] [PubMed]
  10. M. Giles, B. Bock, T. Crow, “Design considerations for miniature optical correlation systems that use pixelated input filter condensers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 297–309 (1990).
    [CrossRef]
  11. W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).
    [CrossRef]
  12. E. Carcole, J. A. Davis, D. M. Cottrell, “Astigmatic phase correction for the magneto-optic spatial light modulator,” Appl. Opt. 34, 5118–5120 (1995).
    [CrossRef] [PubMed]
  13. R. R. Kalman, D. H. Goldstein, “Phase-encoding input images for optical pattern recognition,” Opt. Eng. 33, 1806–1812 (1994).
    [CrossRef]

1996

1995

1994

R. R. Kalman, D. H. Goldstein, “Phase-encoding input images for optical pattern recognition,” Opt. Eng. 33, 1806–1812 (1994).
[CrossRef]

1993

J. Ojeda-Castaneda, G. Ramirez, “Zone plates for zero axial irradiance,” Opt. Lett 18, 87–89 (1993).
[CrossRef] [PubMed]

Z. Jaroszewicz, A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

J. A. Davis, J. J. Kane, D. M. Cottrell, “Horner efficiency of phase-only and binary phase-only filters,” Appl. Opt. 32, 5095–5099 (1993).
[CrossRef] [PubMed]

1992

1983

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).
[CrossRef]

Anderson, R. H.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).
[CrossRef]

Andres, P.

Beletic, J. W.

Bock, B.

M. Giles, B. Bock, T. Crow, “Design considerations for miniature optical correlation systems that use pixelated input filter condensers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 297–309 (1990).
[CrossRef]

Carcole, E.

Cottrell, D. M.

Crow, T.

M. Giles, B. Bock, T. Crow, “Design considerations for miniature optical correlation systems that use pixelated input filter condensers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 297–309 (1990).
[CrossRef]

Davis, J. A.

Giles, M.

M. Giles, B. Bock, T. Crow, “Design considerations for miniature optical correlation systems that use pixelated input filter condensers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 297–309 (1990).
[CrossRef]

Goldstein, D. H.

R. R. Kalman, D. H. Goldstein, “Phase-encoding input images for optical pattern recognition,” Opt. Eng. 33, 1806–1812 (1994).
[CrossRef]

Horner, J. L.

Jaroszewicz, Z.

Z. Jaroszewicz, A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

S. B. Vinas, Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, “Zone plates with black focal spots,” Appl. Opt. 31, 192–198 (1992).
[CrossRef] [PubMed]

Kalman, R. R.

R. R. Kalman, D. H. Goldstein, “Phase-encoding input images for optical pattern recognition,” Opt. Eng. 33, 1806–1812 (1994).
[CrossRef]

Kane, J. J.

Kolodziejczyk, A.

Z. Jaroszewicz, A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

S. B. Vinas, Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, “Zone plates with black focal spots,” Appl. Opt. 31, 192–198 (1992).
[CrossRef] [PubMed]

Martinez-Corral, M.

O’Shea, D. C.

O’Shea, D. M.

Ojeda-Castaneda, J.

Poutous, M.

Psaltis, D.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).
[CrossRef]

Ramirez, G.

J. Ojeda-Castaneda, G. Ramirez, “Zone plates for zero axial irradiance,” Opt. Lett 18, 87–89 (1993).
[CrossRef] [PubMed]

Ross, W. E.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).
[CrossRef]

Sypek, M.

Tiangco, R. P.

J. A. Davis, R. P. Tiangco, D. M. Cottrell, D. M. O’Shea, M. Poutous, “Four-plane space-variant Fresnel-transform optical processor with a random phase encoder,” Appl. Opt. 35, 3819–3828 (1996).
[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]

Vinas, S. B.

Appl. Opt.

Opt. Commun.

Z. Jaroszewicz, A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

Opt. Eng.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).
[CrossRef]

R. R. Kalman, D. H. Goldstein, “Phase-encoding input images for optical pattern recognition,” Opt. Eng. 33, 1806–1812 (1994).
[CrossRef]

Opt. Lett

J. Ojeda-Castaneda, G. Ramirez, “Zone plates for zero axial irradiance,” Opt. Lett 18, 87–89 (1993).
[CrossRef] [PubMed]

Other

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]

M. Giles, B. Bock, T. Crow, “Design considerations for miniature optical correlation systems that use pixelated input filter condensers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 297–309 (1990).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Binary patterns showing (a) the input letter R pattern and (b) the RPA pattern.

Fig. 2
Fig. 2

Filter patterns showing (a) a binary phase-only filter for the offset letter R, (b) a gray-scale phase pattern for the circular-harmonic angular function for n = 1, and (c) a binary phase-only filter for the offset letter R multiplied by the angular phase function for n = 1.

Fig. 3
Fig. 3

Experimental correlator output obtained by use of (a) the input letter R with the appropriate filter and (b) the RPA input pattern and appropriate filter.

Fig. 4
Fig. 4

Experimental correlator output obtained by use of (a) the RPA input pattern and a conventional filter, (b) the RPA input pattern and the filter corresponding to the n = 1 Bessel function, and (c) the RPA input pattern and the filter corresponding to the n = 2 Bessel function.

Fig. 5
Fig. 5

Experimental correlator output obtained by use of (a) the letter R input pattern and a conventional filter, (b) the letter R input pattern and a filter corresponding to the n = 1 Bessel function, and (c) the letter R input pattern and the filter corresponding to the n = 2 Bessel function.

Equations (3)

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cx=gxhx.
Bu=Huexpinθ,
cx=cx*Jnx,

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