Abstract

Compared with conventional photometric methods of measuring cell parameters, including the cell gap and the pretilt angle of a nematic parallel-aligned liquid crystal (PALC) using multiple wavelengths at normal incidence, this research proposes the use of a phase-sensitive interferometric ellipsometer to determine cell parameters precisely based on a single wavelength at large oblique incidence angles. The advantage of this method is that it detects the phase difference using an optical heterodyne interferometer in which a common phase noise rejection mode is provided. Thus, there is a high signal-to-noise ratio (SNR) on the phase measurement. In addition, a range of large oblique incidence angles on the PALC is used so that a high sensitivity measurement of the cell parameters is obtained experimentally. During the measurements, the multiple reflections and spatial shifting effect of the emerging extraordinary ray (E-ray) and ordinary ray (O-ray) from the PALC at large oblique incidence angles are able to be reduced effectively by the use of retro-reflected geometry in the interferometer. The experimental results verify that the sensitivities for the cell gap and pretilt angle measurements are 0.3 nm and 0.01°, respectively.

© 2007 Optical Society of America

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References

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  1. S. V. Yablonskiĭ, K. Nakayama, S. Okazaki, M. Ozaki, K. Yoshino, S. P. Palto, M. Y. Baranovich, and A. S. Michailov, "Control of the bias tilt angles in nematic liquid crystals," J. Appl. Phys. 85, 2556-2561 (1999).
    [CrossRef]
  2. A. Baba, F. Kaneko, K. Shinbo, K. Kato, S. Kobayashi, and T. Wakamatsu, "Evaluation of tilt angles of nematic liquid crystal molecules on polyimide Langmuir-Blodgett films using the attenuated total reflection measurement method," Jpn. J. Appl. Phys. 37, 2581-2586 (1998).
    [CrossRef]
  3. Q. Lin, H. Zhu, Y. Tang, F. Yang, and H. Gao, "Accurate optical determination of liquid crystal tilt angle by the half-leaky guided mode technique," Displays 21, 111-119 (2000).
    [CrossRef]
  4. S. H. Lee, W. S. Park, G. D. Lee, K. Y. Han, T. H. Yoon, and J. C. Kin, "Low-cell-gap measurement by rotation of a wave retarder," Jpn. J. Appl. Phys. 41, 379-383 (2002).
    [CrossRef]
  5. R. Simon and D. M. Nicholas, "An interferometric method of measuring tilt angles in aligned thin films of nematic liquid crystals," J. Phys. D: Appl. Phys. 18, 1423-1430 (1985).
    [CrossRef]
  6. M. Kawamura and S. Sato, "Measurements of cell thickness distributions in reflective liquid crystal cells using a two-dimensional stokes parameter method," Jpn. J. Appl. Phys. 40, L621-624 (2001).
    [CrossRef]
  7. 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, 709-714 (2004).
    [CrossRef]
  8. S. T. Tang and H. S. Kwok, "Transmissive liquid crystal cell parameters measurement by spectroscopic ellipsometry," J. Appl. Phys. 89, 80-85 (2001).
    [CrossRef]
  9. H. L. Ong, "Cell thickness and surface pretilt angle measurements of a planar liquid-crystal cell with obliquely incidence light," J. Appl. Phys. 71, 140-144 (1992).
    [CrossRef]
  10. C. H. Hsieh, "Linear birefringence parameters of an uncoated multiple-order wave plate with a phase-sensitive optical heterodyne ellipsometry," M.S. thesis (Institute of Biophotonics, National Yang-Ming University, Taiwan 2006).
  11. Y. C. Huang, C. Chou, L. Y. Chou, J. C. Shyu, and M. Chang, "Polarized optical heterodyne profilometer," Jpn. J. Appl. Phys. 37, 351-354 (1998).
    [CrossRef]
  12. 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, 7509-7514 (2005).
    [CrossRef] [PubMed]
  13. L. C. Peng, C. Chou, C. W. Lyu, and J. C. Hsieh, "Zeeman laser-scanning confocal microscopy in turbid media," Opt. Lett. 26, 349-351 (2001).
    [CrossRef]
  14. M. Akiba, K. P. Chan and N. Tanno, "Real-time, micrometer depth-resolved imaging by low-coherence reflectometry and a two-dimensional heterodyne detection technique," Jpn. J. Appl. Phys. 39, L1194-L1196 (2000).
    [CrossRef]

2005 (1)

2004 (1)

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, 709-714 (2004).
[CrossRef]

2002 (1)

S. H. Lee, W. S. Park, G. D. Lee, K. Y. Han, T. H. Yoon, and J. C. Kin, "Low-cell-gap measurement by rotation of a wave retarder," Jpn. J. Appl. Phys. 41, 379-383 (2002).
[CrossRef]

2001 (3)

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

M. Kawamura and S. Sato, "Measurements of cell thickness distributions in reflective liquid crystal cells using a two-dimensional stokes parameter method," Jpn. J. Appl. Phys. 40, L621-624 (2001).
[CrossRef]

L. C. Peng, C. Chou, C. W. Lyu, and J. C. Hsieh, "Zeeman laser-scanning confocal microscopy in turbid media," Opt. Lett. 26, 349-351 (2001).
[CrossRef]

2000 (2)

M. Akiba, K. P. Chan and N. Tanno, "Real-time, micrometer depth-resolved imaging by low-coherence reflectometry and a two-dimensional heterodyne detection technique," Jpn. J. Appl. Phys. 39, L1194-L1196 (2000).
[CrossRef]

Q. Lin, H. Zhu, Y. Tang, F. Yang, and H. Gao, "Accurate optical determination of liquid crystal tilt angle by the half-leaky guided mode technique," Displays 21, 111-119 (2000).
[CrossRef]

1999 (1)

S. V. Yablonskiĭ, K. Nakayama, S. Okazaki, M. Ozaki, K. Yoshino, S. P. Palto, M. Y. Baranovich, and A. S. Michailov, "Control of the bias tilt angles in nematic liquid crystals," J. Appl. Phys. 85, 2556-2561 (1999).
[CrossRef]

1998 (2)

A. Baba, F. Kaneko, K. Shinbo, K. Kato, S. Kobayashi, and T. Wakamatsu, "Evaluation of tilt angles of nematic liquid crystal molecules on polyimide Langmuir-Blodgett films using the attenuated total reflection measurement method," Jpn. J. Appl. Phys. 37, 2581-2586 (1998).
[CrossRef]

Y. C. Huang, C. Chou, L. Y. Chou, J. C. Shyu, and M. Chang, "Polarized optical heterodyne profilometer," Jpn. J. Appl. Phys. 37, 351-354 (1998).
[CrossRef]

1992 (1)

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

1985 (1)

R. Simon and D. M. Nicholas, "An interferometric method of measuring tilt angles in aligned thin films of nematic liquid crystals," J. Phys. D: Appl. Phys. 18, 1423-1430 (1985).
[CrossRef]

Appl. Opt. (1)

Displays (1)

Q. Lin, H. Zhu, Y. Tang, F. Yang, and H. Gao, "Accurate optical determination of liquid crystal tilt angle by the half-leaky guided mode technique," Displays 21, 111-119 (2000).
[CrossRef]

J. Appl. Phys. (3)

S. V. Yablonskiĭ, K. Nakayama, S. Okazaki, M. Ozaki, K. Yoshino, S. P. Palto, M. Y. Baranovich, and A. S. Michailov, "Control of the bias tilt angles in nematic liquid crystals," J. Appl. Phys. 85, 2556-2561 (1999).
[CrossRef]

S. T. Tang and H. S. Kwok, "Transmissive liquid crystal cell parameters measurement by spectroscopic ellipsometry," J. Appl. Phys. 89, 80-85 (2001).
[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, 140-144 (1992).
[CrossRef]

J. Phys. D: Appl. Phys. (1)

R. Simon and D. M. Nicholas, "An interferometric method of measuring tilt angles in aligned thin films of nematic liquid crystals," J. Phys. D: Appl. Phys. 18, 1423-1430 (1985).
[CrossRef]

Jpn. J. Appl. Phys. (6)

M. Kawamura and S. Sato, "Measurements of cell thickness distributions in reflective liquid crystal cells using a two-dimensional stokes parameter method," Jpn. J. Appl. Phys. 40, L621-624 (2001).
[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, 709-714 (2004).
[CrossRef]

A. Baba, F. Kaneko, K. Shinbo, K. Kato, S. Kobayashi, and T. Wakamatsu, "Evaluation of tilt angles of nematic liquid crystal molecules on polyimide Langmuir-Blodgett films using the attenuated total reflection measurement method," Jpn. J. Appl. Phys. 37, 2581-2586 (1998).
[CrossRef]

S. H. Lee, W. S. Park, G. D. Lee, K. Y. Han, T. H. Yoon, and J. C. Kin, "Low-cell-gap measurement by rotation of a wave retarder," Jpn. J. Appl. Phys. 41, 379-383 (2002).
[CrossRef]

Y. C. Huang, C. Chou, L. Y. Chou, J. C. Shyu, and M. Chang, "Polarized optical heterodyne profilometer," Jpn. J. Appl. Phys. 37, 351-354 (1998).
[CrossRef]

M. Akiba, K. P. Chan and N. Tanno, "Real-time, micrometer depth-resolved imaging by low-coherence reflectometry and a two-dimensional heterodyne detection technique," Jpn. J. Appl. Phys. 39, L1194-L1196 (2000).
[CrossRef]

Opt. Lett. (1)

Other (1)

C. H. Hsieh, "Linear birefringence parameters of an uncoated multiple-order wave plate with a phase-sensitive optical heterodyne ellipsometry," M.S. thesis (Institute of Biophotonics, National Yang-Ming University, Taiwan 2006).

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Figures (7)

Fig. 1.
Fig. 1.

Experimental setup: BS, beam splitter; AOM, acousto-optic modulator; M, mirror; A, polarizer; S, test sample on three-dimensional rotation stage; PBS, polarization beam splitter; Dp, Ds, photo detectors; BPF, band-pass filter; LIA, lock-in amplifier; DSC, digital stepping controller; PC, personal computer; PALC, parallel-aligned liquid crystal.

Fig. 2.
Fig. 2.

Retro-reflected geometry of the PALC at a large oblique incidence angle. A thick BK7 glass plate is attached to the PA-LC in order to reduce multiple reflections of the laser beam.

Fig. 3.
Fig. 3.

Nematic PALC device is equivalent to the phase retardation wave plate where the optical axis is pretilted at θpre to the surface.

Fig. 4.
Fig. 4.

Schematic diagram of the nematic PALC at oblique incidence: (a) in y-z plane (tilted along x-axis), (b) in x-z plane (tilted along y-axis).

Fig. 5.
Fig. 5.

Phase retardation vs. oblique incidence angle: (a) without attaching the thick BK-7 glass plate, (b) after attaching the thick BK-7 glass plate.

Fig. 6.
Fig. 6.

Phase retardation vs. oblique incidence angle: (a) in y-z plane (tilted along x-axis), (b) in x-z plane (tilted along y-axis). The error bar of the measurement is smaller than the line width of red and blue lines.

Fig. 7.
Fig. 7.

Comparison of the experimental (-50°≤ϕty ≤-30°, 30°≤ϕty ≤50°) and theoretical (-50°≤ϕty ≤50°) curves scanned in the x-z plane (y-axial tilt) where theoretical curve is calculated by (ne,no)=(1.588,1.489), d=4.156µm, and θpre=2.59° at 632.8nm wavelength. The error bar is smaller than the line width of the measurements (red line).

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

I p ( Δ ω t ) = 2 I p 1 I p 2 cos ( Δ ω t + δ p ) .
I s ( Δ ω t ) = 2 I s 1 I s 2 cos ( Δ ω t + δ s ) ,
2 m π + Γ = 2 π λ ( Δ n ) d = 2 π λ [ n o n e ( θ pre ) ] d ,
n e ( θ pre ) = n e n o n e 2 sin 2 θ pre + n o 2 cos 2 θ pre .
δ tx ( ϕ tx ) = 2 2 π λ ( n o 2 sin 2 ϕ tx n e 2 ( θ pre ) sin 2 ϕ tx ) d .
δ ty ( ϕ ty ) = 2 2 π λ [ n o sin 2 ϕ ty n o 1 ( sin ϕ ty n o ) 2 n e sin 2 ϕ ty n e 1 ( sin ϕ ty n e ) 2 ] d
= 2 2 π λ [ n o 2 sin 2 ϕ ty n e 2 sin 2 ϕ ty ] d ,
n e = n e n o { n e 2 sin 2 [ θ pre sin 1 ( sin ϕ ty n e ) ] + n o 2 cos 2 [ θ pre sin 1 ( sin ϕ ty n e ) ] } 1 2 .

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