Researching | Entanglement-free determination of pretilt angles of twisted nematic liquid-crystal cells by phase measurement

Journals >Chinese Optics Letters >Volume 15 >Issue 8 >Page 081203 > Article

Chinese Optics Letters
Vol. 15, Issue 8, 081203 (2017)

Entanglement-free determination of pretilt angles of twisted nematic liquid-crystal cells by phase measurement

Che-Wen Chiang^1、*, Ping-Chun Lin², and Kei-Hsiung Yang²

Author Affiliations

¹Institute of Photonic System, National Chiao Tung University, Tainan City 71150, China

²Institute of Imaging and Biomedical Photonics, National Chiao Tung University, Tainan City 71105, China

show less

DOI: 10.3788/COL201715.081203 Cite this Article Set citation alerts

Che-Wen Chiang, Ping-Chun Lin, Kei-Hsiung Yang. Entanglement-free determination of pretilt angles of twisted nematic liquid-crystal cells by phase measurement[J]. Chinese Optics Letters, 2017, 15(8): 081203 Copy Citation Text

show less

Abstract

The pretilt angle of a twisted nematic (TN) liquid crystal display has a strong effect on viewing angles and response times of the display as well as shifting the light-leaking disclination lines into the black-matrix area within pixels of a thin-film-transistor driven TN panel for a high contrast ratio. In this Letter, we develop an optical method to determine the TN pretilt angle based on heterodyne measurements of the phase versus the incident angle of a thin TN cell subjected to out-of-plane rotations. We believe that our method of measuring phases has advantages of simpler setup and calculations, better stability, and less sensitive to ambient electromagnetic interference than the commonly used method of measuring intensities.

ε = [\begin{matrix} ε_{x x} & ε_{x y} & ε_{x z} \\ ε_{y x} & ε_{y y} & ε_{y z} \\ ε_{z x} & ε_{z y} & ε_{z z} \end{matrix}],

(1)

View in Article

ε_{x x} = n_{o}^{2} + (n_{e}^{2} - n_{o}^{2}) \cos^{2} θ \cos^{2} Φ, ε_{x y} = ε_{y x} = (n_{e}^{2} - n_{o}^{2}) \cos^{2} θ \sin Φ \cos Φ, ε_{x z} = ε_{z x} = (n_{e}^{2} - n_{o}^{2}) \sin θ \cos θ \cos Φ, ε_{y y} = n_{o}^{2} + (n_{e}^{2} - n_{o}^{2}) \cos^{2} θ \sin^{2} Φ, ε_{y z} = ε_{z y} = (n_{e}^{2} - n_{o}^{2}) \sin θ \cos θ \sin Φ, ε_{z z} = n_{o}^{2} + (n_{e}^{2} - n_{o}^{2}) \sin^{2} θ .

(2)

View in Article

\overset{⇀}{k} = k_{0} (\sin θ_{k}, 0, \cos θ_{k}),

(3)

View in Article

k_{0} = \frac{2 π}{λ},

(4)

View in Article

{[\begin{matrix} E_{x} \\ E_{y} \end{matrix}]}_{out} = J_{m} J_{m - 1} \dots J_{2} J_{1} {[\begin{matrix} E_{x} \\ E_{y} \end{matrix}]}_{in},

(5)

View in Article

J_{m} = {(S G S^{- 1})}_{m},

(6)

View in Article

S = [\begin{matrix} 1 & c_{2} \\ c_{1} & 1 \end{matrix}]; G = [\begin{matrix} e^{i k_{z 1} \frac{d}{m}} & 0 \\ 0 & e^{i k_{z 2} \frac{d}{m}} \end{matrix}],

(7)

View in Article

\frac{k_{z 1}}{k_{0}} = \sqrt{[n_{o}^{2} - {(k_{x} / k_{0})}^{2}]},

(8)

View in Article

\frac{k_{z 2}}{k_{0}} = - \frac{ε_{x z}}{ε_{z z}} \frac{k_{x}}{k_{0}} + \frac{n_{o} n_{e}}{ε_{z z}} {[ε_{z z} - (1 - \frac{n_{e}^{2} - n_{o}^{2}}{n_{e}^{2}} \cos^{2} θ \sin^{2} Φ) {(\frac{k_{x}}{k_{o}})}^{2}]}^{1 / 2},

(9)

View in Article

c_{1} = \frac{[{(k_{x} / k_{0})}^{2} - ε_{z z}] ε_{y x} + [(k_{x} / k_{0}) (k_{z 1} / k_{0}) + ε_{z x}] ε_{y z}}{[{(k_{z 1} / k_{0})}^{2} + {(k_{x} / k_{0})}^{2} - ε_{y y}] [{(k_{x} / k_{0})}^{2} - ε_{z z}] - ε_{y z} ε_{z y}},

(10)

View in Article

c_{2} = {[{(k_{x} / k_{0})}^{2} - ε_{z z}] ε_{x y} + [(k_{x} / k_{0}) (k_{z 2} / k_{0}) + ε_{x z}] ε_{x z}} / {[{(k_{z 2} / k_{0})}^{2} - ε_{x x}] [{(k_{x} / k_{0})}^{2} - ε_{z z}] - [(k_{x} / k_{0}) (k_{z 2} / k_{0}) + ε_{z x}] [(k_{x} / k_{0}) (k_{z 2} / k_{0}) + ε_{x z}]} .

(11)

View in Article

n_{i} = A_{i} + B_{i} λ^{- 2} + C_{i} λ^{- 4},

(12)

View in Article

Figures&Tables (8)

References (13)

Copy Citation Text

Che-Wen Chiang, Ping-Chun Lin, Kei-Hsiung Yang. Entanglement-free determination of pretilt angles of twisted nematic liquid-crystal cells by phase measurement[J]. Chinese Optics Letters, 2017, 15(8): 081203

Download Citation

Set citation alerts for the article

Set citation alerts for the article

Save the article for my favorites

Paper Information

Recommended Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology

Set citation alerts for the article

Please enter your email address