Abstract

Five cell parameters of a twisted nematic liquid crystal device (TNLCD), namely, cell gap, pretilt angle, twisted angle, rubbing angle, and phase retardation are precisely measured by the developed amplitude-sensitive heterodyne polarimeter (ASHP) simultaneously integrated with Yeh and Gu’s transfer matrix and Lien’s transfer matrix. This proposed method can characterize the five cell parameters under the arrangement of a single wavelength at normal incidence. In contrast to the conventional methods on cell parameter detection either by adopting a multiple wavelength laser beam at normal incidence or by using a single wavelength laser beam under oblique incident to TNLCD, this method presents the advantage of not only having a simple setup but also the possibility to measure simultaneously five cell parameters on the characterization of TNLCD at high speed.

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  1. F. Nakano, M. Isogai, and M. Sato, “Simple method of determining liquid crystal tilt-bias angle,” Jpn. J. Appl. Phys. 19(10), 2013–2014 (1980).
    [CrossRef]
  2. H. L. Ong, “Cell thickness and surface pretilt angle measurements of a planar liquid-crystal cell with obliquely incidence light,” J. Appl. Phys. 71(1), 140–144 (1992).
    [CrossRef]
  3. Y. Zhou, Z. He, and S. Sato, “A novel method determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36(Part 1, No. 5A), 2760–2764 (1997).
    [CrossRef]
  4. M. Kawamura, Y. Goto, and S. Sato, “A two-dimensional pretilt angle distribution measurement of twisted nematic liquid crystal cells using Stokes parameters at plural wavelengths,” Jpn. J. Appl. Phys. 43(2), 709–714 (2004).
    [CrossRef]
  5. S. T. Tang and H. S. Kwok, “Transmissive liquid crystal cell parameters measurement by spectroscopic ellipsometry,” J. Appl. Phys. 89(1), 80–85 (2001).
    [CrossRef]
  6. T. C. Yu and Y. L. Lo, “A novel heterodyne polarimeter for the multiple-parameter measurements of twisted nematic liquid crystal cell using a genetic algorithm approach,” J. Lightwave Technol. 25(3), 946–951 (2007).
    [CrossRef]
  7. C. C. Tsai, C. Chou, C. Y. Han, C. H. Hsieh, K. Y. Liao, and Y. F. Chao, “Determination of optical parameters of a twisted-nematic liquid crystal by phase-sensitive optical heterodyne interferometric ellipsometry,” Appl. Opt. 44(35), 7509–7514 (2005).
    [CrossRef] [PubMed]
  8. P. Yeh, and C. Gu, Optics of Liquid Crystal Displays (Wiley Interscience, New York, 1999), pp. 119–136.
  9. H. C. Wei, C. C. Tsai, L. P. Yu, T. E. Lin, C. J. Yu, M. H. Liu, and C. Chou, “Two-dimensional cell parameters of twisted nematic liquid crystal with an amplitude-sensitive heterodyne ellipsometer,” Appl. Opt. 48(9), 1628–1634 (2009).
    [CrossRef] [PubMed]
  10. A. Lien, “The general and simplified Jones matrix representations for the high pretilt twisted nematic cell,” J. Appl. Phys. 67(6), 2853 (1990).
    [CrossRef]
  11. I. Scierski and F. Ratajczyk, “The Jones matrix of the real dichroic elliptic object,” Optik (Stuttg.) 68, 121–125 (1984).
  12. Y. C. Huang, M. Chang, and C. Chou, “Effect of elliptical birefringence on the measurement of the phase retardation of a quartz wave plate by an optical heterodyne polarimeter,” J. Opt. Soc. Am. A 14(6), 1367–1372 (1997).
    [CrossRef]
  13. C. Chou, Y. C. Huang, and M. Chang, “Polarized common path optical heterodyne interferometer for measuring the elliptical birefringence of a quartz wave plate,” Jpn. J. Appl. Phys. 35(Part 1, No. 10), 5526–5529 (1996).
    [CrossRef]
  14. The cell parameter of TNLCD was provided by Chi-Mei Optoelectronics Co., Tainan, Taiwan, where the refractive indices are ne = 1.7426, no = 1.5216; twisted angle is – 90°; rubbing angle is – 45°; cell gap is 4 μm; and pretilt angle is 3.2°.
  15. I. Moreno, J. A. Davis, K. G. D’Nelly, and D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37(11), 3048–3052 (1998).
    [CrossRef]

2009

2007

2005

2004

M. Kawamura, Y. Goto, and S. Sato, “A two-dimensional pretilt angle distribution measurement of twisted nematic liquid crystal cells using Stokes parameters at plural wavelengths,” Jpn. J. Appl. Phys. 43(2), 709–714 (2004).
[CrossRef]

2001

S. T. Tang and H. S. Kwok, “Transmissive liquid crystal cell parameters measurement by spectroscopic ellipsometry,” J. Appl. Phys. 89(1), 80–85 (2001).
[CrossRef]

1998

I. Moreno, J. A. Davis, K. G. D’Nelly, and D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37(11), 3048–3052 (1998).
[CrossRef]

1997

Y. Zhou, Z. He, and S. Sato, “A novel method determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36(Part 1, No. 5A), 2760–2764 (1997).
[CrossRef]

Y. C. Huang, M. Chang, and C. Chou, “Effect of elliptical birefringence on the measurement of the phase retardation of a quartz wave plate by an optical heterodyne polarimeter,” J. Opt. Soc. Am. A 14(6), 1367–1372 (1997).
[CrossRef]

1996

C. Chou, Y. C. Huang, and M. Chang, “Polarized common path optical heterodyne interferometer for measuring the elliptical birefringence of a quartz wave plate,” Jpn. J. Appl. Phys. 35(Part 1, No. 10), 5526–5529 (1996).
[CrossRef]

1992

H. L. Ong, “Cell thickness and surface pretilt angle measurements of a planar liquid-crystal cell with obliquely incidence light,” J. Appl. Phys. 71(1), 140–144 (1992).
[CrossRef]

1990

A. Lien, “The general and simplified Jones matrix representations for the high pretilt twisted nematic cell,” J. Appl. Phys. 67(6), 2853 (1990).
[CrossRef]

1984

I. Scierski and F. Ratajczyk, “The Jones matrix of the real dichroic elliptic object,” Optik (Stuttg.) 68, 121–125 (1984).

1980

F. Nakano, M. Isogai, and M. Sato, “Simple method of determining liquid crystal tilt-bias angle,” Jpn. J. Appl. Phys. 19(10), 2013–2014 (1980).
[CrossRef]

Allison, D. B.

I. Moreno, J. A. Davis, K. G. D’Nelly, and D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37(11), 3048–3052 (1998).
[CrossRef]

Chang, M.

Y. C. Huang, M. Chang, and C. Chou, “Effect of elliptical birefringence on the measurement of the phase retardation of a quartz wave plate by an optical heterodyne polarimeter,” J. Opt. Soc. Am. A 14(6), 1367–1372 (1997).
[CrossRef]

C. Chou, Y. C. Huang, and M. Chang, “Polarized common path optical heterodyne interferometer for measuring the elliptical birefringence of a quartz wave plate,” Jpn. J. Appl. Phys. 35(Part 1, No. 10), 5526–5529 (1996).
[CrossRef]

Chao, Y. F.

Chou, C.

D’Nelly, K. G.

I. Moreno, J. A. Davis, K. G. D’Nelly, and D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37(11), 3048–3052 (1998).
[CrossRef]

Davis, J. A.

I. Moreno, J. A. Davis, K. G. D’Nelly, and D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37(11), 3048–3052 (1998).
[CrossRef]

Goto, Y.

M. Kawamura, Y. Goto, and S. Sato, “A two-dimensional pretilt angle distribution measurement of twisted nematic liquid crystal cells using Stokes parameters at plural wavelengths,” Jpn. J. Appl. Phys. 43(2), 709–714 (2004).
[CrossRef]

Han, C. Y.

He, Z.

Y. Zhou, Z. He, and S. Sato, “A novel method determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36(Part 1, No. 5A), 2760–2764 (1997).
[CrossRef]

Hsieh, C. H.

Huang, Y. C.

Y. C. Huang, M. Chang, and C. Chou, “Effect of elliptical birefringence on the measurement of the phase retardation of a quartz wave plate by an optical heterodyne polarimeter,” J. Opt. Soc. Am. A 14(6), 1367–1372 (1997).
[CrossRef]

C. Chou, Y. C. Huang, and M. Chang, “Polarized common path optical heterodyne interferometer for measuring the elliptical birefringence of a quartz wave plate,” Jpn. J. Appl. Phys. 35(Part 1, No. 10), 5526–5529 (1996).
[CrossRef]

Isogai, M.

F. Nakano, M. Isogai, and M. Sato, “Simple method of determining liquid crystal tilt-bias angle,” Jpn. J. Appl. Phys. 19(10), 2013–2014 (1980).
[CrossRef]

Kawamura, M.

M. Kawamura, Y. Goto, and S. Sato, “A two-dimensional pretilt angle distribution measurement of twisted nematic liquid crystal cells using Stokes parameters at plural wavelengths,” Jpn. J. Appl. Phys. 43(2), 709–714 (2004).
[CrossRef]

Kwok, H. S.

S. T. Tang and H. S. Kwok, “Transmissive liquid crystal cell parameters measurement by spectroscopic ellipsometry,” J. Appl. Phys. 89(1), 80–85 (2001).
[CrossRef]

Liao, K. Y.

Lien, A.

A. Lien, “The general and simplified Jones matrix representations for the high pretilt twisted nematic cell,” J. Appl. Phys. 67(6), 2853 (1990).
[CrossRef]

Lin, T. E.

Liu, M. H.

Lo, Y. L.

Moreno, I.

I. Moreno, J. A. Davis, K. G. D’Nelly, and D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37(11), 3048–3052 (1998).
[CrossRef]

Nakano, F.

F. Nakano, M. Isogai, and M. Sato, “Simple method of determining liquid crystal tilt-bias angle,” Jpn. J. Appl. Phys. 19(10), 2013–2014 (1980).
[CrossRef]

Ong, H. L.

H. L. Ong, “Cell thickness and surface pretilt angle measurements of a planar liquid-crystal cell with obliquely incidence light,” J. Appl. Phys. 71(1), 140–144 (1992).
[CrossRef]

Ratajczyk, F.

I. Scierski and F. Ratajczyk, “The Jones matrix of the real dichroic elliptic object,” Optik (Stuttg.) 68, 121–125 (1984).

Sato, M.

F. Nakano, M. Isogai, and M. Sato, “Simple method of determining liquid crystal tilt-bias angle,” Jpn. J. Appl. Phys. 19(10), 2013–2014 (1980).
[CrossRef]

Sato, S.

M. Kawamura, Y. Goto, and S. Sato, “A two-dimensional pretilt angle distribution measurement of twisted nematic liquid crystal cells using Stokes parameters at plural wavelengths,” Jpn. J. Appl. Phys. 43(2), 709–714 (2004).
[CrossRef]

Y. Zhou, Z. He, and S. Sato, “A novel method determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36(Part 1, No. 5A), 2760–2764 (1997).
[CrossRef]

Scierski, I.

I. Scierski and F. Ratajczyk, “The Jones matrix of the real dichroic elliptic object,” Optik (Stuttg.) 68, 121–125 (1984).

Tang, S. T.

S. T. Tang and H. S. Kwok, “Transmissive liquid crystal cell parameters measurement by spectroscopic ellipsometry,” J. Appl. Phys. 89(1), 80–85 (2001).
[CrossRef]

Tsai, C. C.

Wei, H. C.

Yu, C. J.

Yu, L. P.

Yu, T. C.

Zhou, Y.

Y. Zhou, Z. He, and S. Sato, “A novel method determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36(Part 1, No. 5A), 2760–2764 (1997).
[CrossRef]

Appl. Opt.

J. Appl. Phys.

A. Lien, “The general and simplified Jones matrix representations for the high pretilt twisted nematic cell,” J. Appl. Phys. 67(6), 2853 (1990).
[CrossRef]

H. L. Ong, “Cell thickness and surface pretilt angle measurements of a planar liquid-crystal cell with obliquely incidence light,” J. Appl. Phys. 71(1), 140–144 (1992).
[CrossRef]

S. T. Tang and H. S. Kwok, “Transmissive liquid crystal cell parameters measurement by spectroscopic ellipsometry,” J. Appl. Phys. 89(1), 80–85 (2001).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

C. Chou, Y. C. Huang, and M. Chang, “Polarized common path optical heterodyne interferometer for measuring the elliptical birefringence of a quartz wave plate,” Jpn. J. Appl. Phys. 35(Part 1, No. 10), 5526–5529 (1996).
[CrossRef]

F. Nakano, M. Isogai, and M. Sato, “Simple method of determining liquid crystal tilt-bias angle,” Jpn. J. Appl. Phys. 19(10), 2013–2014 (1980).
[CrossRef]

Y. Zhou, Z. He, and S. Sato, “A novel method determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36(Part 1, No. 5A), 2760–2764 (1997).
[CrossRef]

M. Kawamura, Y. Goto, and S. Sato, “A two-dimensional pretilt angle distribution measurement of twisted nematic liquid crystal cells using Stokes parameters at plural wavelengths,” Jpn. J. Appl. Phys. 43(2), 709–714 (2004).
[CrossRef]

Opt. Eng.

I. Moreno, J. A. Davis, K. G. D’Nelly, and D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37(11), 3048–3052 (1998).
[CrossRef]

Optik (Stuttg.)

I. Scierski and F. Ratajczyk, “The Jones matrix of the real dichroic elliptic object,” Optik (Stuttg.) 68, 121–125 (1984).

Other

P. Yeh, and C. Gu, Optics of Liquid Crystal Displays (Wiley Interscience, New York, 1999), pp. 119–136.

The cell parameter of TNLCD was provided by Chi-Mei Optoelectronics Co., Tainan, Taiwan, where the refractive indices are ne = 1.7426, no = 1.5216; twisted angle is – 90°; rubbing angle is – 45°; cell gap is 4 μm; and pretilt angle is 3.2°.

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Figures (6)

Fig. 1
Fig. 1

The test TNLCD cell configuration. Φ: the twist angle; Γ: untwisted phase retardation; α: rubbing angle, where i is the director of rubbing in and o is the direction of rubbing out; d: cell gap of two glass substrates; θ: pretilt angle of TNLCD.

Fig. 2
Fig. 2

Experimental setup: BS, beam splitter; AOM, acousto-optic modulator; M, mirror; A, polarizer; QWP, quarter-wave plate; TN-LC, twisted nematic liquid crystal cell; PBS, polarization beam splitter; D, photodetector; DVM, digital voltmeter; DSM, digital stepping motor; PC, personal computer.

Fig. 3
Fig. 3

Plot of the stability in this experiment. The total measurement times were 1,200 s. The [ I s a c / I p a c ] ratio was maintained at 1 before either QWP or TNLCD could be inserted into the sample arm.

Fig. 4
Fig. 4

Least squares fitting between the experimental data (dotted curve) and theoretical calculation (solid curve), in which the QWP of ( γ , δ f ) = ( 89 .5438 ° ,   0 .4133 ° ) was measured.

Fig. 5
Fig. 5

Measurement of the least squares fitting among the experimental data (dot), theoretical calculation applying Lien’s theoretical model (circle), and theoretical calculation applying Yeh and Gu’s theoretical model (plus sign) for the tested TNLCD cell.

Fig. 6
Fig. 6

2-D distribution of the TNLCD cell: (a) twist angle Φ, (b) untwisted phase retardation Γ, (c) rubbing angle α, (d) cell gap d, (e) pretilt angle θ.

Tables (1)

Tables Icon

Table 1 The comparison of experimental data versus given values.

Equations (16)

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I p = | E p 1 exp ( i ω 1 t ) + E p 2 ( o ) exp [ i ( ω 2 t + δ p 2 ( o ) ) ] | 2
= E p 1 2 + ( E p 2 ( o ) ) 2 + 2 E p 1 E p 2 ( o ) cos ( Δ ω t + δ p 2 ( o ) ) ,
I s = | E s 1 exp ( i ω 1 t ) + E s 2 ( o ) exp [ i ( ω 2 t + δ s 2 ( o ) ) ] | 2
= E s 1 2 + ( E s 2 ( o ) ) 2 + 2 E s 1 E s 2 ( o ) cos ( Δ ω t + δ s 2 ( o ) ) ,
X E s E p exp [ i ( δ s δ p ) ] = | X | exp ( i δ ) ,
X ( o ) = | X ( o ) | exp ( i δ ( o ) ) = t 21 + t 22 | X ( i ) | exp ( i δ ( i ) ) t 11 + t 12 | X ( i ) | exp ( i δ ( i ) ) ,
[ I s a c I p a c ] = E s 1 E s 2 ( o ) E p 1 E p 2 ( o ) = | X 1 | | X 2 ( o ) | ,
M Q W P = [ cos 2 β + sin 2 β e i γ sin β cos β ( 1 e i γ ) e i δ f sin β cos β ( 1 e i γ ) e i δ f sin 2 β + cos 2 β e i γ ] ,
M T N L C = [ A B B * A * ] = [ a 1 + i a 2 b 1 + i b 2 ( b 1 i b 2 ) a 1 i a 2 ] .
M Y e h = [ a 1 + i a 2 b 1 + i b 2 ( b 1 i b 2 ) a 1 i a 2 ]
= [ p cos Φ + q r sin Φ i q s cos ( 2 α + Φ ) p sin Φ + q r cos Φ i q s sin ( 2 α + Φ ) p sin Φ q r cos Φ i q s sin ( 2 α + Φ ) p cos Φ + q r sin Φ + i q s cos ( 2 α + Φ ) ] ,
M L i e n = [ cos α sin α sin α cos α ] [ a 1 + i a 2 b 1 + i b 2 ( b 1 i b 2 ) a 1 i a 2 ] [ cos α sin α sin α cos α ] ,
a 1 = 1 1 + u 2 sin Φ sin ( 1 + u 2 Φ ) + cos Φ cos ( 1 + u 2 Φ ) ,
a 2 = u 1 + u 2 cos Φ sin ( 1 + u 2 Φ ) ,
b 1 = 1 1 + u 2 cos Φ sin ( 1 + u 2 Φ ) sin Φ cos ( 1 + u 2 Φ ) ,
b 2 = u 1 + u 2 sin Φ sin ( 1 + u 2 Φ ) ,

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