Abstract

We report a new, to our knowledge, technique for encoding amplitude information onto a phase-only filter with a single liquid-crystal spatial light modulator. In our approach we spatially modulate the phase that is encoded onto the filter and, consequently, spatially modify the diffraction efficiency of the filter. Light that is not diffracted into the first order is sent into the zero order, effectively allowing for amplitude modulation of either the first-order or the zero-order diffracted light. This technique has several applications in both optical pattern recognition and image processing, including amplitude modulation and inverse filters. Experimental results are included for the new technique.

© 1999 Optical Society of America

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  1. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  2. H. K. Liu, J. A. Davis, R. A. Lilly, “Optical-data-processing properties of a liquid-crystal television spatial light modulator,” Opt. Lett. 10, 635–637 (1985).
    [CrossRef] [PubMed]
  3. D. A. Gregory, “Real-time pattern recognition using a modified liquid crystal television in a coherent optical correlator,” Appl. Opt. 25, 467–469 (1986).
    [CrossRef] [PubMed]
  4. F. T. S. Yu, S. Jutamulia, X. L. Huang, “Experimental application of low-cost liquid crystal TV to white-light optical signal processing,” Appl. Opt. 25, 3324–3326 (1986).
    [CrossRef] [PubMed]
  5. J. Amako, T. Sonehara, “Computer generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
    [CrossRef]
  6. N. Clark, C. M. Crancall, M. K. Giles, “Using liquid crystal TV’s in VanderLugt optical correlators,” in Optical Information Processing Systems and Architectures III, B. Javidi, ed., Proc. SPIE1564, 439–451 (1991).
    [CrossRef]
  7. C. Soutar, S. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
    [CrossRef]
  8. C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
    [CrossRef]
  9. L. G. Neto, D. Roberge, Y. Sheng, “Programmable optical phase-mostly holograms with coupled-mode modulation liquid-crystal television,” Appl. Opt. 34, 1944–1950 (1995).
    [CrossRef] [PubMed]
  10. L. G. Neto, D. Roberge, Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35, 4567–4576 (1996).
    [CrossRef] [PubMed]
  11. J. L. Pezzaniti, R. A. Chipman, “Phase-only modulation of a twisted nematic liquid-crystal TV by use of the eigenpolarization states,” Opt. Lett. 18, 1567–1569 (1993).
    [CrossRef] [PubMed]
  12. J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
    [CrossRef]
  13. I. Moreno, J. A. Davis, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal light modulators,” Opt. Eng. 37, 3048–3052 (1998).
    [CrossRef]
  14. R. D. Juday, “Optimal realizable filters and the minimum Euclidean distance principle,” Appl. Opt. 32, 5100–5111 (1993).
    [CrossRef] [PubMed]
  15. S. E. Monroe, C. Soutar, R. D. Juday, “Laboratory implementation of optimal filter algorithms for coupled spatial light modulators,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 278–283 (1993).
    [CrossRef]
  16. G. G. Mu, X. M. Wang, Z. Q. Wang, “Amplitude-compensated matched filtering,” Appl. Opt. 27, 3461–3463 (1988).
    [CrossRef] [PubMed]
  17. D. L. Flannery, J. S. Loomis, M. E. Milkovich, “Transform-ratio ternary phase-amplitude filter formulation for improved correlation discrimination,” Appl. Opt. 27, 4079–4083 (1988).
    [CrossRef] [PubMed]
  18. I. Moreno, E. Ahouzi, J. Campos, M. J. Yzuel, “Real-time binary-amplitude phase-only filters,” Appl. Opt. 36, 7428–7432 (1997).
    [CrossRef]
  19. R. W. Cohn, M. Liang, “Approximating fully complex spatial modulation with pseudo-random phase-only modulation,” Appl. Opt. 33, 4406–4415 (1994).
    [CrossRef] [PubMed]
  20. J. P. Kirk, A. L. Jones, “Phase-only complex-valued spatial filter,” J. Opt. Soc. Am. 61, 1023–1028 (1971).
    [CrossRef]
  21. D. C. Chu, J. W. Goodman, “Spectrum shaping with parity sequences,” Appl. Opt. 11, 1716–1724 (1972).
    [CrossRef] [PubMed]
  22. C. K. Hsush, A. A. Sawchuk, “Computer-generated double phase holograms,” Appl. Opt. 17, 3874–3884 (1978).
    [CrossRef]
  23. J. N. Mait, K. H. Brenner, “Dual-phase holograms: improved design,” Appl. Opt. 26, 4883–4892 (1987).
    [CrossRef] [PubMed]
  24. J. N. Mait, G. S. Himes, “Computer generated holograms by means of a magnetooptic spatial light modulator,” Appl. Opt. 28, 4879–4887 (1989).
    [CrossRef] [PubMed]
  25. O. Bryngdahl, F. Wyrowski, “Digital holography: computer-generated holograms,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1990), Vol. XXVIII.
    [CrossRef]
  26. F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
    [CrossRef]
  27. E. Noponen, J. Turunen, “Complex-amplitude modulation by high-carrier-frequency diffractive elements,” J. Opt. Soc. Am. A 13, 1422–1428 (1996).
    [CrossRef]
  28. E. Noponen, J. Turunen, “Binary high-frequency-carrier diffractive optical elements: electromagnetic theory,” J. Opt. Soc. Am. A 11, 1097–1109 (1994).
    [CrossRef]
  29. J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, E. Noponen, “Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements,” J. Mod. Opt. 43, 1389–1398 (1996).
  30. V. Kettunen, P. Vahimaa, J. Turunen, E. Noponen, “Zeroth-order coding of complex amplitude in two dimensions,” J. Opt. Soc. Am. A 14, 808–815 (1997).
    [CrossRef]
  31. W. J. Dallas, Computer Generated Holograms, B. R. Frieden, ed., Vol. 41 of Topics in Applied Physics Series (Springer-Verlag, Berlin, 1980), Chap. 6.
  32. 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]
  33. 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]
  34. 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]
  35. F. T. S. Yu, Optical Information Processing (Wiley-Interscience, New York, 1983), Chap. 7, pp. 198–202.
  36. 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]
  37. A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992), Chap. 3, pp. 123–128.

1998 (3)

I. Moreno, J. A. Davis, “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]

J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

1997 (2)

1996 (3)

1995 (2)

L. G. Neto, D. Roberge, Y. Sheng, “Programmable optical phase-mostly holograms with coupled-mode modulation liquid-crystal television,” Appl. Opt. 34, 1944–1950 (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 (4)

E. Noponen, J. Turunen, “Binary high-frequency-carrier diffractive optical elements: electromagnetic theory,” J. Opt. Soc. Am. A 11, 1097–1109 (1994).
[CrossRef]

C. Soutar, S. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[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]

R. W. Cohn, M. Liang, “Approximating fully complex spatial modulation with pseudo-random phase-only modulation,” Appl. Opt. 33, 4406–4415 (1994).
[CrossRef] [PubMed]

1993 (2)

1991 (1)

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

1990 (1)

J. Amako, T. Sonehara, “Computer generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
[CrossRef]

1989 (2)

1988 (2)

1987 (1)

1986 (2)

1985 (1)

1984 (1)

1978 (1)

1972 (1)

1971 (1)

Ahouzi, E.

Amako, J.

J. Amako, T. Sonehara, “Computer generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
[CrossRef]

Brenner, K. H.

Bryngdahl, O.

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

O. Bryngdahl, F. Wyrowski, “Digital holography: computer-generated holograms,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1990), Vol. XXVIII.
[CrossRef]

Campos, 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, E. Ahouzi, J. Campos, M. J. Yzuel, “Real-time binary-amplitude phase-only filters,” Appl. Opt. 36, 7428–7432 (1997).
[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]

Chipman, R. A.

Chu, D. C.

Clark, N.

N. Clark, C. M. Crancall, M. K. Giles, “Using liquid crystal TV’s in VanderLugt optical correlators,” in Optical Information Processing Systems and Architectures III, B. Javidi, ed., Proc. SPIE1564, 439–451 (1991).
[CrossRef]

Cohn, R. W.

Cottrell, D. M.

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]

Crancall, C. M.

N. Clark, C. M. Crancall, M. K. Giles, “Using liquid crystal TV’s in VanderLugt optical correlators,” in Optical Information Processing Systems and Architectures III, B. Javidi, ed., Proc. SPIE1564, 439–451 (1991).
[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, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

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

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]

H. K. Liu, J. A. Davis, R. A. Lilly, “Optical-data-processing properties of a liquid-crystal television spatial light modulator,” Opt. Lett. 10, 635–637 (1985).
[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.

Flannery, D. L.

Gianino, P. D.

Giles, M. K.

N. Clark, C. M. Crancall, M. K. Giles, “Using liquid crystal TV’s in VanderLugt optical correlators,” in Optical Information Processing Systems and Architectures III, B. Javidi, ed., Proc. SPIE1564, 439–451 (1991).
[CrossRef]

Goodman, J. W.

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.

Himes, G. S.

Honkanen, M.

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, E. Noponen, “Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements,” J. Mod. Opt. 43, 1389–1398 (1996).

Horner, J. L.

Hsush, C. K.

Huang, X. L.

Jones, A. L.

Juday, R. D.

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

S. E. Monroe, C. Soutar, R. D. Juday, “Laboratory implementation of optimal filter algorithms for coupled spatial light modulators,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 278–283 (1993).
[CrossRef]

Jutamulia, S.

Kettunen, V.

Kirk, J. P.

Knopp, J.

C. Soutar, S. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

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]

Liang, M.

Lilly, R. A.

Liu, H. K.

Loomis, J. S.

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]

Mait, J. N.

Milkovich, M. E.

Monroe, S.

C. Soutar, S. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

Monroe, S. E.

S. E. Monroe, C. Soutar, R. D. Juday, “Laboratory implementation of optimal filter algorithms for coupled spatial light modulators,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 278–283 (1993).
[CrossRef]

Moreno, I.

J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

I. Moreno, J. A. Davis, “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, E. Ahouzi, J. Campos, M. J. Yzuel, “Real-time binary-amplitude phase-only filters,” Appl. Opt. 36, 7428–7432 (1997).
[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.

Neto, L. G.

Noponen, E.

Pezzaniti, J. L.

Roberge, D.

Salminen, O.

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, E. Noponen, “Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements,” J. Mod. Opt. 43, 1389–1398 (1996).

Sawchuk, A. A.

Sheng, Y.

Sonehara, T.

J. Amako, T. Sonehara, “Computer generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
[CrossRef]

Soutar, C.

C. Soutar, S. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[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]

S. E. Monroe, C. Soutar, R. D. Juday, “Laboratory implementation of optimal filter algorithms for coupled spatial light modulators,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 278–283 (1993).
[CrossRef]

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]

Tsai, P.

Turunen, J.

Vahimaa, P.

V. Kettunen, P. Vahimaa, J. Turunen, E. Noponen, “Zeroth-order coding of complex amplitude in two dimensions,” J. Opt. Soc. Am. A 14, 808–815 (1997).
[CrossRef]

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, E. Noponen, “Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements,” J. Mod. Opt. 43, 1389–1398 (1996).

VanderLugt, A.

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992), Chap. 3, pp. 123–128.

Wang, X. M.

Wang, Z. Q.

Wyrowski, F.

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

O. Bryngdahl, F. Wyrowski, “Digital holography: computer-generated holograms,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1990), Vol. XXVIII.
[CrossRef]

Yu, F. T. S.

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, E. Ahouzi, J. Campos, M. J. Yzuel, “Real-time binary-amplitude phase-only filters,” Appl. Opt. 36, 7428–7432 (1997).
[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]

Appl. Opt. (15)

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

F. T. S. Yu, S. Jutamulia, X. L. Huang, “Experimental application of low-cost liquid crystal TV to white-light optical signal processing,” Appl. Opt. 25, 3324–3326 (1986).
[CrossRef] [PubMed]

J. N. Mait, K. H. Brenner, “Dual-phase holograms: improved design,” Appl. Opt. 26, 4883–4892 (1987).
[CrossRef] [PubMed]

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

D. L. Flannery, J. S. Loomis, M. E. Milkovich, “Transform-ratio ternary phase-amplitude filter formulation for improved correlation discrimination,” Appl. Opt. 27, 4079–4083 (1988).
[CrossRef] [PubMed]

J. N. Mait, G. S. Himes, “Computer generated holograms by means of a magnetooptic spatial light modulator,” Appl. Opt. 28, 4879–4887 (1989).
[CrossRef] [PubMed]

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

R. W. Cohn, M. Liang, “Approximating fully complex spatial modulation with pseudo-random phase-only modulation,” Appl. Opt. 33, 4406–4415 (1994).
[CrossRef] [PubMed]

I. Moreno, E. Ahouzi, J. Campos, M. J. Yzuel, “Real-time binary-amplitude phase-only filters,” Appl. Opt. 36, 7428–7432 (1997).
[CrossRef]

L. G. Neto, D. Roberge, Y. Sheng, “Programmable optical phase-mostly holograms with coupled-mode modulation liquid-crystal television,” Appl. Opt. 34, 1944–1950 (1995).
[CrossRef] [PubMed]

L. G. Neto, D. Roberge, Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35, 4567–4576 (1996).
[CrossRef] [PubMed]

J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

C. K. Hsush, A. A. Sawchuk, “Computer-generated double phase holograms,” Appl. Opt. 17, 3874–3884 (1978).
[CrossRef]

D. A. Gregory, “Real-time pattern recognition using a modified liquid crystal television in a coherent optical correlator,” Appl. Opt. 25, 467–469 (1986).
[CrossRef] [PubMed]

D. C. Chu, J. W. Goodman, “Spectrum shaping with parity sequences,” Appl. Opt. 11, 1716–1724 (1972).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, E. Noponen, “Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements,” J. Mod. Opt. 43, 1389–1398 (1996).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Jpn. J. Appl. Phys. (2)

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]

J. Amako, T. Sonehara, “Computer generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
[CrossRef]

Opt. Eng. (4)

C. Soutar, S. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[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, “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]

Opt. Lett. (3)

Rep. Prog. Phys. (1)

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

Other (7)

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992), Chap. 3, pp. 123–128.

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]

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

S. E. Monroe, C. Soutar, R. D. Juday, “Laboratory implementation of optimal filter algorithms for coupled spatial light modulators,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 278–283 (1993).
[CrossRef]

O. Bryngdahl, F. Wyrowski, “Digital holography: computer-generated holograms,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1990), Vol. XXVIII.
[CrossRef]

N. Clark, C. M. Crancall, M. K. Giles, “Using liquid crystal TV’s in VanderLugt optical correlators,” in Optical Information Processing Systems and Architectures III, B. Javidi, ed., Proc. SPIE1564, 439–451 (1991).
[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 (7)

Fig. 1
Fig. 1

Schematic drawing showing diffraction of light by a phase grating with (a) phase depth of 2π rad over each period, (b) phase depth of less than 2π rad over each period.

Fig. 2
Fig. 2

Schematic drawing showing diffraction of light by a phase grating where the phase depth varies spatially: (a) low-pass filter—first-order diffracted light is low-pass filtered, and zero-order light is high-pass filtered; (b) high-pass filter—first-order diffracted light is high-pass filtered, and zero-order light is low-pass filtered.

Fig. 3
Fig. 3

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

Fig. 4
Fig. 4

Experimental correlation plane images (a) for the phase-only filter (POF), (b) for the amplitude-encoded POF acting as a classic filter, (c) for the amplitude-encoded POF acting as an inverse filter.

Fig. 5
Fig. 5

Three-dimensional plots of experimental correlation peaks (a) for the POF, (b) for the amplitude-encoded POF acting as a classic filter, (c) for the amplitude-encoded POF acting as an inverse filter, (d) for the amplitude-encoded POF acting as an inverse filter with a lower threshold.

Fig. 6
Fig. 6

Distortion caused by the filter-encoding algorithm. Solid curve, original cosine-squared modulation curve; dashed curve, modified function T 1(u).

Fig. 7
Fig. 7

Three-dimensional plots of experimental correlation peaks (a) without a corrected modulation function [identical to Fig. 5(d)], (b) with a corrected modulation function.

Equations (40)

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Tu=expi2πMuA.
Tu=n=- Tn expi2πnuA,
Tn=expin-Mπsinπn-Mπn-M.
tx=n=- Tnδx-nA.
Tu=expi2πMuuA.
Fu=MuexpiΦu.
Tu=expiMuΦu.
Tu=n=- TnuexpinΦu,
Tnu=expin-Muπsinπn-Muπn-Mu.
tx=n=- F Tnu * F expinΦ(u,
tx=n=- tnx * δx-nA,
TLu=expiMuΦu+ΦLu.
TLu=n=- TnuexpinΦu+ΦLu.
Tqu=expiMuΦu+Φqu.
Gu=|Gu|expiΦGu,
Hu=|Hu|expiΦHu+2πuA.
cx=gx  hx * δx-A.
H˜u=Hu|Hu|=expiΦHu+2πuA.
c˜x=gx  h˜x * δx-A,
H¯u=1|Hu|expiΦHu+2πuA.
c¯x=h˜x  h˜x * δx-A.
Tu=expiMuΦHu+2πuA.
Tu=n=- TnuexpinΦHu+2πuA.
c¯x=n=- gx  tnx * h˜nx * δx-nA.
Mu=|Hu|/H0if |Hu|<H01if |Hu|>H0.
Mu=1if |Hu|<H0H0/|Hu|if |Hu|>H0.
T1u=sinπ1-Muπ1-Mu.
T1u=sinπ1-Muπ1-Mu=Mu.
Tu=expiMuΦu,
Tu=expiMuΦu=n=-p=0 BnpMup expinΦu,
Bnpu=12πp!02πpTuMupM=0 exp-inΦudΦu.
Tu=expiMuΦu=n=- TnuexpinΦu,
Tnu=p=0 BnpuMup.
pTuMupM=0=iΦup.
Bnpu=12πp!02πiΦup exp-inΦudΦu.
Tnu=p=012πp!02πiΦuMup×exp-inΦudΦu.
p=012πp!iMuΦup=expiMuΦu.
Tnu=02π exp-inΦuexpiMuΦudΦu.
Tnu=expin-Muπsinπn-Muπn-Mu.
Tu=n=-TnuexpinΦu,

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