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研究生:楊桓
研究生(外文):HuanYang
論文名稱:以史托克參數法量測垂直向列型液晶之參數
論文名稱(外文):A Stokes-parameter-based Method for Determining the Properties of Vertical-alignment Liquid Crystal Device
指導教授:羅裕龍
指導教授(外文):Yu-Lung Lo
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:80
中文關鍵詞:垂直向列型液晶預傾角主軸角史托克參數瓊斯矩陣繆勒矩陣疊代法
外文關鍵詞:vertical alignmentliquid crystalStokes parameterJones matrixMueller matrixiterative method
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本研究基於史托克參數法及繆勒矩陣量測垂直向列型液晶盒之偏極光學特性,並藉以推算液晶盒的物理參數,包含厚度、預傾角、以及主軸方向。因液晶本身依其排列模式會產生不同的光學異相性及旋光性,利用瓊斯矩陣建立光學模型,再轉換為繆勒矩陣後即可模擬特定偏極光經液晶盒樣本後的偏極態改變。本研究分析其物理參數與光學參數的關聯性後,可以設計並建立一套反推液晶盒物理參數的實驗架構及演算法。相較於基因演算法,此方法具有較高的可靠性以及簡便的演算流程,且可以得到唯一解。
經模擬及實驗驗證,本研究所開發的演算法可以反推垂直向列型液晶之厚度、預傾角、以及主軸方向。而誤差及環境造成的影響也以程式模擬分析,可作為實際設計專用機台時的參考。
In this study, a method is proposed for determining the cell gap, pretilt angle and azimuth angle of vertical alignment liquid crystal devices (VA-LCDs), which is base on Jones matrix and Stokes parameters method. Because VA-LCD is both a linear birefringence and circular birefringence material, we can measure the output Stokes parameters with specific polarization state incidence and determine the physical parameters of VA-LCD samples. This study also analysis the relation between the physical parameters and the Stokes vectors, and design an effective algorithm by using iterative method. Compare with the genetic algorithm, iterative method can solve the variables faster.
The accuracy of algorithm has been confirmed by simulations, and the errors are also determined in this study. These achievements can help us to design similar systems.
Abstract I
中文摘要 II
Acknowledgements III
Table of Contents IV
List of Figures VI
List of Tables X
Chapter 1 Introduction 1
1.1 Preface 1
1.2 Review of VA-LCD Measurement 1
Chapter 2 Basic Mathematical Models 7
2.1 Jones Matrix of Retardation Model [Huang et al., 2009] 7
2.2 Jones Matrix of VA-LCD Cells [Yeh et al., 1999]. 11
2.2.1 Jones Matrix of VA-LCD Cells 12
2.2.2 Definition of Coordinate Axis 14
2.3 Transmittance of Interfaces [Yeh et al., 1999] 14
2.4 Mueller Matrix Transformation from Jones matrix [Huang et al., 2009] 17
2.5 Stokes Parameter Method [Huang et al., 2009] 18
Chapter 3 Design of Algorithm 20
3.1 Simulate the Stokes Parameters of ECB/ITN Type VA-LCD 20
3.2 Objective Functions of ECB/ITN Type VA-LCD 31
3.3 Extracting Parameters of VA-LCD with Iterative Method 43
3.4 Simulation of VA-LCD 51
Chapter 4 Error Analysis 54
4.1 Geometric Error of System 54
4.2 Error Cause by Temperature Difference 56
4.3 Random Error 58
Chapter 5 Experimental Setup and Result of VA-LCD cells 64
5.1 Experimental Setup 64
5.2 Experimental Result of ECB-LCD 66
5.3 Experimental Result of ITN-LCD 68
Chapter 6 Conclusion and Future Works 71
Reference 77
Autobiography 80

S.-C. Hsiao, J.-S. Hsu, B.-J. Liang, and S.-H. Chen, “Cell-gap
and pretilt-angle determination of a vertically aligned reflective
liquid-crystal display, J. SID, vol. 11, no. 4, p. 629, 2003.

J.S. Hsu, B.J. Liang, and S.H. Chen, “A Simple Method for Determining the Pretilt Angle of a Vertically Aligned Reflective LCD, IEEE Trans Electron. Dev., Vol.52(5), pp.918-921, 2005.

Hong, Q., Wu, T.X., Zhu, X., Lu, R., and Wu, S. T., “Extraordinarily high-contrast and wide-view liquid-crystal displays, Appl. Phys. Lett., Vol. 86, pp. 121107, Mar, (2005).

Huang, R. R. and Lo, Y. L., Novel method for determination of the azimuthal angle, twist angle, cell thickness and distribution of pretilt angle in twisted nematic liquid crystal cell, 2010

Lien, A. and Takano, H., Cell gap measurement of filled twisted nematic liquid crystal displays by a phase compensation method, J. Appl. Phys. 69, 1304-1309, 1991.

Lin, Q., Zhu, H.N., Tang, Y.X., Yang, F.Z., and Gao, H.J., Accurate optical determination of liquid crystal tilt angle by the half-leaky guided mode technique, Displays 21, 111-119, 2000.

C.H. Lin, “Extraordinarily wide-view and high-transmittance vertically aligned liquid crystal displays, Appl. Phys. Lett. Vol.90, pp.151112-1 , 2007.

Y.W. Li, J.Y.L. Ho, F.S.Y. Yeung, and H. S. Kwok, “Simultaneous determination of large pretilt angles and cell gap in liquid crystal displays, J. Disp. Technol., Vol. 4(1), pp. 13–17, 2008.

Lin, W. L., Yu, T. C., Lo, Y. L., and Lin, J. F., A hybrid approach for measuring the parameters of twisted-nematic liquid crystal cells utilizing the Stokes parameter method and a genetic algorithm, J. Lightwave Technol. 27, 4136-4144, 2009.

Moreno, I., Bennis, N., Davis, J.A., and Ferreira, C., Twist angle determination in liquid crystal displays by location of local adiabatic points, Opt. Commun. 158, 213-238, 1998.

Ma´rquez, A., Yamauchi, M., Davis, J.A., and Franich, D.J., Phase measurement of a twist nematic liquid crystal spatial light modulator with a common-path interferometer, Opt. Commun. 190, 129-133, 2001.

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

Tsai, C.C., Chou, C., Han, C.Y., Hsieh, C.H., Liao, K.Y., and Chao, Y.F., Determination of optical parameters of a twisted-nematic liquid crystal by phase-sensitive optical heterodyne interferometric ellipsometry, Appl. Opt. 44, 7509-7514, 2005.

Yeh, P. and Gu, C., Optics of liquid crystal displays, Wiley, New York, 121, 2000.

Yu, T. C. and Lo, Y. L., A novel heterodyne polarimeter for the multiple-parameter measurements of twisted nematic liquid crystal cell using a genetic algorithm approach, J. Lightwave Technology 25, 946-951, 2007.

Zhou, Y., He, Z., and Sato, S., 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.

Zhou, Y., He, Z., and Sato, S., An improved Stokes parameter method for determination of cell thickness and twist angle distributions in twisted nematic liquid crystal devices, Jpn. J. Appl. Phys. 37, 2567-2571, 1998.

池弘偉,全場式光學外差干涉儀應用於量測雙折射晶體光學參數之設計與研究,國立成功大學機械工程研究所碩士論文,2005.

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