Abstract

The parameters of a twisted-nematic liquid-crystal display (TN-LCD) are measured with no ambiguity when we measure the intensity transmittance of a system that simply consists of a TN-LCD, two polarizers, a quarter-wave plate, and a monochromatic beam. First we show analytically that the director angle can have a 90° ambiguity and the twist angle of the liquid-crystal molecules a 180° ambiguity. Then we uniquely measure the parameters by fitting the theoretical predictions to the intensity transmittance measured with and without the quarter-wave plate and by using the quasi local-adiabatic condition. The birefringence of the TN-LCD is measured next as a function of the applied voltage. We design a phase spatial light modulator by using the measured parameters and measure the phase delay of the output beam to excellent agreement with the theoretical prediction. © 2005 Optical Society of America

© 2005 Optical Society of America

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  1. 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]
  2. C. Stolz, L. Bigue, P. Ambs, “Implementation of high-resolution diffractive optical elements on coupled phase and amplitude spatial light modulators,” Appl. Opt. 40, 6415–6424 (2001).
    [CrossRef]
  3. N. Konforti, E. Marom, S.-T. Wu, “Phase-only modulation with twisted-nematic liquid-crystal spatial light modulators,” Opt. Lett. 13, 251–253 (1988).
    [CrossRef] [PubMed]
  4. T. H. Barnes, T. Eiju, K. Matusda, N. Ooyama, “Phase-only modulation using a twisted-nematic liquid-crystal television,” Appl. Opt. 28, 4845–4852 (1989).
    [CrossRef] [PubMed]
  5. K. Lu, B. E. A. Saleh, “Theory and design of the liquid-crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
    [CrossRef]
  6. M. Yamauchi, T. Eiju, “Optimization of twisted-nematic liquid-crystal panels for spatial light phase modulation,” Opt. Commun. 115, 19–25 (1995).
    [CrossRef]
  7. 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]
  8. J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
    [CrossRef]
  9. M. Yamauchi, A. Marquez, J. A. Davis, D. J. Franich, “Interferometric phase measurements for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Commun. 181, 1–6 (2000).
    [CrossRef]
  10. A. Marquez, C. Lemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
    [CrossRef]
  11. C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid-crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
    [CrossRef]
  12. J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
    [CrossRef]
  13. J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
    [CrossRef]
  14. I. Moreno, N. Bennis, J. A. Davis, C. Ferreira, “Twist angle determination in liquid-crystal displays by location of local adiabatic points,” Opt. Commun. 158, 231–238 (1998).
    [CrossRef]
  15. Y. Iimura, N. Kobayashi, S. Kobayashi, “A new method for measuring the azimuthal anchoring energy of a nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 434–436 (1994).
    [CrossRef]
  16. T. Akahane, H. Kaneko, M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35, 4434–4437 (1996).
    [CrossRef]
  17. Y. Zhou, Z. He, S. Sato, “A novel method for determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36, 2760–2764 (1997).
    [CrossRef]
  18. R. Guist, J. P. Goedgebuer, “Determination of the twist angle and the retardation properties of twisted-nematic liquid-crystal television by spectral measurements,” Opt. Eng. 37, 629–634 (1998).
    [CrossRef]
  19. M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, X. Huang, “Method of studying surface torsional anchoring of nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 1242–1244 (1994).
    [CrossRef]
  20. J. Coy, M. Zaldarriaga, D. F. Grosz, O. E. Martinez, “Characterization of a liquid-crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
    [CrossRef]
  21. A. Marquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Lemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted-nematic liquid-crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
    [CrossRef]

2001

A. Marquez, C. Lemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

C. Stolz, L. Bigue, P. Ambs, “Implementation of high-resolution diffractive optical elements on coupled phase and amplitude spatial light modulators,” Appl. Opt. 40, 6415–6424 (2001).
[CrossRef]

2000

M. Yamauchi, A. Marquez, J. A. Davis, D. J. Franich, “Interferometric phase measurements for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Commun. 181, 1–6 (2000).
[CrossRef]

A. Marquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Lemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted-nematic liquid-crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

1999

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

1998

I. Moreno, N. Bennis, J. A. Davis, C. Ferreira, “Twist angle determination in liquid-crystal displays by location of local adiabatic points,” Opt. Commun. 158, 231–238 (1998).
[CrossRef]

R. Guist, J. P. Goedgebuer, “Determination of the twist angle and the retardation properties of twisted-nematic liquid-crystal television by spectral measurements,” Opt. Eng. 37, 629–634 (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

Y. Zhou, Z. He, S. Sato, “A novel method for determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36, 2760–2764 (1997).
[CrossRef]

1996

J. Coy, M. Zaldarriaga, D. F. Grosz, O. E. Martinez, “Characterization of a liquid-crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

T. Akahane, H. Kaneko, M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35, 4434–4437 (1996).
[CrossRef]

1995

M. Yamauchi, T. Eiju, “Optimization of twisted-nematic liquid-crystal panels for spatial light phase modulation,” Opt. Commun. 115, 19–25 (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]

Y. Iimura, N. Kobayashi, S. Kobayashi, “A new method for measuring the azimuthal anchoring energy of a nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 434–436 (1994).
[CrossRef]

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, X. Huang, “Method of studying surface torsional anchoring of nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 1242–1244 (1994).
[CrossRef]

1993

1990

K. Lu, B. E. A. Saleh, “Theory and design of the liquid-crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

1989

1988

1985

Akahane, T.

T. Akahane, H. Kaneko, M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35, 4434–4437 (1996).
[CrossRef]

Allison, D. B.

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

Ambs, P.

Barnes, T. H.

Bennis, N.

I. Moreno, N. Bennis, J. A. Davis, C. Ferreira, “Twist angle determination in liquid-crystal displays by location of local adiabatic points,” Opt. Commun. 158, 231–238 (1998).
[CrossRef]

Bigue, L.

Campos, J.

A. Marquez, C. Lemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

A. Marquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Lemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted-nematic liquid-crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

Chipman, R. A.

Coy, J.

J. Coy, M. Zaldarriaga, D. F. Grosz, O. E. Martinez, “Characterization of a liquid-crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

D’Nelly, K. G.

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

Davis, J. A.

A. Marquez, C. Lemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

M. Yamauchi, A. Marquez, J. A. Davis, D. J. Franich, “Interferometric phase measurements for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Commun. 181, 1–6 (2000).
[CrossRef]

A. Marquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Lemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted-nematic liquid-crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

I. Moreno, N. Bennis, J. A. Davis, C. Ferreira, “Twist angle determination in liquid-crystal displays by location of local adiabatic points,” Opt. Commun. 158, 231–238 (1998).
[CrossRef]

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

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]

Eiju, T.

M. Yamauchi, T. Eiju, “Optimization of twisted-nematic liquid-crystal panels for spatial light phase modulation,” Opt. Commun. 115, 19–25 (1995).
[CrossRef]

T. H. Barnes, T. Eiju, K. Matusda, N. Ooyama, “Phase-only modulation using a twisted-nematic liquid-crystal television,” Appl. Opt. 28, 4845–4852 (1989).
[CrossRef] [PubMed]

Ferreira, C.

I. Moreno, N. Bennis, J. A. Davis, C. Ferreira, “Twist angle determination in liquid-crystal displays by location of local adiabatic points,” Opt. Commun. 158, 231–238 (1998).
[CrossRef]

Franich, D. J.

M. Yamauchi, A. Marquez, J. A. Davis, D. J. Franich, “Interferometric phase measurements for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Commun. 181, 1–6 (2000).
[CrossRef]

Goedgebuer, J. P.

R. Guist, J. P. Goedgebuer, “Determination of the twist angle and the retardation properties of twisted-nematic liquid-crystal television by spectral measurements,” Opt. Eng. 37, 629–634 (1998).
[CrossRef]

Grosz, D. F.

J. Coy, M. Zaldarriaga, D. F. Grosz, O. E. Martinez, “Characterization of a liquid-crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

Guist, R.

R. Guist, J. P. Goedgebuer, “Determination of the twist angle and the retardation properties of twisted-nematic liquid-crystal television by spectral measurements,” Opt. Eng. 37, 629–634 (1998).
[CrossRef]

He, Z.

Y. Zhou, Z. He, S. Sato, “A novel method for determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36, 2760–2764 (1997).
[CrossRef]

Huang, X.

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, X. Huang, “Method of studying surface torsional anchoring of nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 1242–1244 (1994).
[CrossRef]

Iimura, Y.

Y. Iimura, N. Kobayashi, S. Kobayashi, “A new method for measuring the azimuthal anchoring energy of a nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 434–436 (1994).
[CrossRef]

Jiang, M.

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, X. Huang, “Method of studying surface torsional anchoring of nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 1242–1244 (1994).
[CrossRef]

Kaneko, H.

T. Akahane, H. Kaneko, M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35, 4434–4437 (1996).
[CrossRef]

Kimura, M.

T. Akahane, H. Kaneko, M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35, 4434–4437 (1996).
[CrossRef]

Kobayashi, N.

Y. Iimura, N. Kobayashi, S. Kobayashi, “A new method for measuring the azimuthal anchoring energy of a nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 434–436 (1994).
[CrossRef]

Kobayashi, S.

Y. Iimura, N. Kobayashi, S. Kobayashi, “A new method for measuring the azimuthal anchoring energy of a nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 434–436 (1994).
[CrossRef]

Konforti, N.

Lemmi, C.

A. Marquez, C. Lemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

A. Marquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Lemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted-nematic liquid-crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

Lilly, R. A.

Liu, H.-K.

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]

K. Lu, B. E. A. Saleh, “Theory and design of the liquid-crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Ma, K.

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, X. Huang, “Method of studying surface torsional anchoring of nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 1242–1244 (1994).
[CrossRef]

Ma, R.

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, X. Huang, “Method of studying surface torsional anchoring of nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 1242–1244 (1994).
[CrossRef]

Marom, E.

Marquez, A.

A. Marquez, C. Lemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

M. Yamauchi, A. Marquez, J. A. Davis, D. J. Franich, “Interferometric phase measurements for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Commun. 181, 1–6 (2000).
[CrossRef]

A. Marquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Lemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted-nematic liquid-crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

Martinez, O. E.

J. Coy, M. Zaldarriaga, D. F. Grosz, O. E. Martinez, “Characterization of a liquid-crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

Matusda, K.

Moreno, A.

A. Marquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Lemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted-nematic liquid-crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

Moreno, I.

A. Marquez, C. Lemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

A. Marquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Lemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted-nematic liquid-crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

I. Moreno, N. Bennis, J. A. Davis, C. Ferreira, “Twist angle determination in liquid-crystal displays by location of local adiabatic points,” Opt. Commun. 158, 231–238 (1998).
[CrossRef]

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

Ooyama, N.

Pezzaniti, J. L.

Robert, A.

A. Marquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Lemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted-nematic liquid-crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

Saleh, B. E. A.

K. Lu, B. E. A. Saleh, “Theory and design of the liquid-crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Sato, S.

Y. Zhou, Z. He, S. Sato, “A novel method for determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36, 2760–2764 (1997).
[CrossRef]

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]

Stolz, C.

Sun, R.

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, X. Huang, “Method of studying surface torsional anchoring of nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 1242–1244 (1994).
[CrossRef]

Tsai, P.

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

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

Wang, Z.

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, X. Huang, “Method of studying surface torsional anchoring of nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 1242–1244 (1994).
[CrossRef]

Wilson, M. L.

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

Wu, S.-T.

Yamauchi, M.

M. Yamauchi, A. Marquez, J. A. Davis, D. J. Franich, “Interferometric phase measurements for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Commun. 181, 1–6 (2000).
[CrossRef]

M. Yamauchi, T. Eiju, “Optimization of twisted-nematic liquid-crystal panels for spatial light phase modulation,” Opt. Commun. 115, 19–25 (1995).
[CrossRef]

Yzuel, M. J.

A. Marquez, C. Lemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

A. Marquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Lemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted-nematic liquid-crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

Zaldarriaga, M.

J. Coy, M. Zaldarriaga, D. F. Grosz, O. E. Martinez, “Characterization of a liquid-crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

Zhou, Y.

Y. Zhou, Z. He, S. Sato, “A novel method for determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36, 2760–2764 (1997).
[CrossRef]

Appl. Opt.

Jpn. J. Appl. Phys.

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, X. Huang, “Method of studying surface torsional anchoring of nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 1242–1244 (1994).
[CrossRef]

Y. Iimura, N. Kobayashi, S. Kobayashi, “A new method for measuring the azimuthal anchoring energy of a nematic liquid crystal,” Jpn. J. Appl. Phys. 33, 434–436 (1994).
[CrossRef]

T. Akahane, H. Kaneko, M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35, 4434–4437 (1996).
[CrossRef]

Y. Zhou, Z. He, S. Sato, “A novel method for determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36, 2760–2764 (1997).
[CrossRef]

Opt. Commun.

M. Yamauchi, T. Eiju, “Optimization of twisted-nematic liquid-crystal panels for spatial light phase modulation,” Opt. Commun. 115, 19–25 (1995).
[CrossRef]

M. Yamauchi, A. Marquez, J. A. Davis, D. J. Franich, “Interferometric phase measurements for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Commun. 181, 1–6 (2000).
[CrossRef]

I. Moreno, N. Bennis, J. A. Davis, C. Ferreira, “Twist angle determination in liquid-crystal displays by location of local adiabatic points,” Opt. Commun. 158, 231–238 (1998).
[CrossRef]

Opt. Eng.

K. Lu, B. E. A. Saleh, “Theory and design of the liquid-crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

J. Coy, M. Zaldarriaga, D. F. Grosz, O. E. Martinez, “Characterization of a liquid-crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

A. Marquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Lemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted-nematic liquid-crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

A. Marquez, C. Lemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[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]

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

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[CrossRef]

Opt. Lett.

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Figures (8)

Fig. 1
Fig. 1

Twisted-nematic liquid-crystal molecules twisted from θS to θE along the z axis.

Fig. 2
Fig. 2

Twisted-nematic liquid-crystal display in System I: d, total thickness of the TN-LCD; dedge, thickness of the edge plate.

Fig. 3
Fig. 3

Twisted-nematic liquid-crystal display in System II.

Fig. 4
Fig. 4

Experimental setup for measuring the intensity transmittance: M, mirrors; B.E, beam expander.

Fig. 5
Fig. 5

Normalized intensity transmittance with no voltage applied to the TN-LCD in System I: solid and dotted curves, theory; circles and squares, experiment.

Fig. 6
Fig. 6

Relative rotation of the analyzer for the maximum intensity transmittance in System I. The ambiguity in the twist angle is solved from the rotation sense of the analyzer with increased birefringence: solid, dotted, and dashed curves, theory; circles, experiment.

Fig. 7
Fig. 7

Normalized intensity transmittance with a voltage applied to the TN-LCD in System I: (a) gray scale 255 (minimum voltage), (b) gray scale 128, (c) gray scale 0. The birefringence is measured by fitting curves, solid and dotted curves, to the experimental data, circles, and squares.

Fig. 8
Fig. 8

(a) Normalized intensity transmittance versus applied voltage in System II. The ambiguity in the director angle is solved by the quarter-wave plate: solid, dotted, and dashed curves, theory; circles, experiment. (b) Phase delay versus applied voltage in System II: solid curve, theory; circles, experiment.

Tables (1)

Tables Icon

Table 1 Measured Birefringence of the TN-LCD versus Gray Scale

Equations (22)

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J LCD = c exp [ - i ( β + ϕ 0 ) ] ( f - i g - h - i j h - i j f + i g ) ,
f = θ E - θ S γ sin γ sin ( θ E - θ S ) + cos γ cos ( θ E - θ S ) , g = β γ sin γ cos ( θ E + θ S ) , h = - θ E - θ S γ sin γ cos ( θ E - θ S ) + cos γ sin ( θ E - θ S ) , j = β γ sin γ sin ( θ E + θ S ) ,     f 2 + g 2 + h 2 + j 2 = 1 ,
[ E x LCD E y LCD ] = J LCD J ( ψ P ) [ E x E y ] ,
J ( ψ P ) = [ cos 2 ψ P sin ψ P cos ψ P sin ψ P cos ψ P sin 2 ψ P ] .
E x LCD = c exp ( - i β ) ( E x cos ψ P + E y sin ψ P ) [ ( f cos ψ P - h sin ψ P ) - i ( g cos ψ P + j sin ψ P ) ] , E y LCD = c exp ( - i β ) ( E x cos ψ P + E y sin ψ P ) [ ( f sin ψ P + h cos ψ P ) + i ( g sin ψ P - j cos ψ P ) ] .
[ - θ E - θ S γ sin γ cos ( 2 ψ P - 2 θ S ) + cos γ sin ( 2 ψ P - 2 θ S ) ] β γ sin γ = 0.
ψ P q = 1 2 arctan ( θ E - θ S γ tan γ ) + θ S .
[ E x out E y out ] = J ( ψ A ) J LCD J ( ψ P q ) [ E x E y ] = exp ( - i β ) ( E x cos ψ P q + E y sin ψ P q ) T [ cos ψ A sin ψ A ] ,
T = c [ θ E - θ S γ sin γ sin ( ψ P q - ψ A + θ E - θ S ) + cos γ cos ( ψ P q - ψ A + θ E - θ S ) ] - i c β γ sin γ cos ( ψ P q + ψ A - θ E - θ S ) .
ψ P q + ψ A q - θ E - θ S = n π ,
J edge in = exp ( - i β edge ) R ( - θ S ) × [ exp ( - i β edge ) 0 0 exp ( i β edge ) ] R ( θ S ) ,
R ( θ S ) = [ cos θ S sin θ S - sin θ S cos θ S ] .
J LCD = J edge out J center J edge in = c exp ( - i β ) [ f ¯ - i g ¯ - h ¯ - i j ¯ h ¯ - i j ¯ f ¯ + i g ¯ ] .
f ¯ = [ 1 - β center Θ - cot Θ - sin ( 2 β edge ) ] Θ - γ sin γ sin Θ - + [ cos ( 2 β edge ) ] cos γ cos Θ - , g ¯ = [ cos ( 2 β edge ) + γ β center cot γ sin ( 2 β edge ) ] × β center γ sin γ cos Θ + , h ¯ = - [ 1 + β center Θ - tan Θ - sin ( 2 β edge ) ] × Θ - γ sin γ cos Θ - + [ cos ( 2 β edge ) ] cos γ sin Θ - , j ¯ = [ cos ( 2 β edge ) + γ β center cot γ sin ( 2 β edge ) ] × β center γ sin γ sin Θ + , β = β center + 2 β edge ,     f ¯ 2 + g ¯ 2 + h ¯ 2 + j ¯ 2 = 1 ,
[ E x out E y out ] = J ( ψ A ) J LCD J ( ψ p ) [ E x E y ] = c exp ( - i β ) T ˜ ψ P , ψ A ( E x cos ψ P + E y sin ψ P ) [ cos ψ A sin ψ A ] .
T ˜ ψ P , ψ A = f ¯ cos ( ψ A - ψ P ) + h ¯ sin ( ψ A - ψ P ) - i g ¯ cos ( ψ A + ψ P ) - i j ¯ sin ( ψ A + ψ P ) ,
δ ψ p , ψ A = β - arg ( T ˜ ψ p , ψ A ) ,
[ E x out E y out ] = J ( ψ A ) W ( ψ Q ) J LCD J ( ψ P ) [ E x E y ] = c 2 exp ( - i β ) T ˜ ψ P , ψ A , ψ Q ( E x cos ψ P + E y sin ψ P ) [ cos ψ A sin ψ A ] ,
W ( ψ Q ) = R ( - ψ Q ) [ exp ( - i π / 4 ) 0 0 exp ( i π / 4 ) ] R ( ψ Q ) = 1 2 [ 1 - i cos 2 ψ Q - i sin 2 ψ Q - i sin 2 ψ Q 1 + i cos 2 ψ Q ] ,
T ˜ ψ P , ψ A , ψ Q = ( f ¯ - g ¯ cos 2 ψ Q - j ¯ sin 2 ψ Q ) cos ( ψ A - ψ P ) + ( h ¯ - g ¯ sin 2 ψ Q + j ¯ cos 2 ψ Q ) sin ( ψ A - ψ P ) - i [ ( g ¯ + f ¯ cos 2 ψ Q + h ¯ sin 2 ψ Q ) cos ( ψ A + ψ P ) + ( j ¯ + f ¯ sin 2 ψ Q - h ¯ cos 2 ψ Q ) sin ( ψ A + ψ P ) ] .
δ ψ P , ψ A , ψ Q = β - arg ( T ˜ ψ P , ψ A , ψ Q ) ,
| c 2 T ˜ ψ P , ψ A , ψ Q | 2 .

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