臺灣博碩士論文加值系統

液晶的排列指向在液晶應用是很重要的性質。在本篇論文中，我們利用加入混合垂直配向的延展態液晶盒做為例，以模擬計算與量測的光學結果相比較，得到靜態與動態液晶指向分佈資訊。我們模擬計算液晶的排列與光學反應使用液晶自由能張量表現型式。實驗量測使用高靈敏度攝影機搭配延遲時間產生器來擷取液晶盒的動態影像。我們針對取得液晶的排列指向逆問題做了理論分析與實驗示範。結果發現在加入混合垂直配向可消除延展態液晶的暖機時間，但也增加了液晶盒的反應時間。在利用逆問題的方法取得液晶的排列指向，我們提出了符合液晶特性的正則化矩陣，並驗證使用大範圍入射角的光學測量數據和系統量測誤差在百分之十下，在此逆問題求解是穩定而可靠的。從實際實驗示範成功展示在不同施加電壓下的液晶盒內之液晶排列指向可穩定而可靠取得。

The liquid crystal (LC) director profile is an important property for a variety of LC applications. In this study, we combine simulation and experimental measurement of the optical responses of hybrid alignment liquid crystal cells to demonstrate the functionality of LC director profile retrieval. Our simulation invokes the Q-tensor formalism of liquid crystal director calculation and Berreman matrix method for the optical response of LC. An electron-multiplying charge coupled device and a delay time generator were combined to capture the dynamic optical image of the liquid crystal cells. We discovered that by including a hybrid alignment region into an OCB cell, the warm up time of the LC cell can be effectively eliminated. The relaxation time was unfortunately also increased. We also study the inverse problem of LC to retrieve the director profile of liquid crystal cell directly from the measured optical transmittance data. To retrieve the director profile from the inverse problem technique, we proposed a regularization matrix based on a priori knowledge of LC. We found our method can yield LC director profile reliably from the measured optical data covering a wide range of incident angle and 10% noise level. We further demonstrated the functionality by retrieving the liquid crystal director profiles of LC cells with applied voltage from the experimentally measured data.

Chapter 1 Introduction to the Physical and Optical Properties of LC 1
1.1 Motivation.....................................................................................2
1.2 The Physics of Liquid Crystal......................................................3
1.3 The Optical Properties of Liquid Crystal......................................7
Chapter 2 Models of the LC Alignment Structure and the Optical Response
12
2.1 The Q-Tensor Formalism............................................................13
2.2 The Berreman Matrix Method....................................................21
2.3 The Application Examples..........................................................30
Chapter 3 Dynamic Optical Probing for Hybrid Alignment Liquid Crystal Cells 38
3.1 Introduction.................................................................................38
3.2 The Modification of The Existing OCB Cell…………………..39
3.3 Experimental Setup of the Dynamic Optical Probing
Apparatus....................................................................................41
3.4 Results and Discussion…………...............................................43
Chapter 4 Inverse Problem of Liquid Crystal Director Profile 56
4.1 Introduction to the Inverse Problem...........................................56
4.2 The Inverse Problem of Liquid Crystal Director Profile............62
4.3 Theoretical Details......................................................................65
4.4 Simulation Results and Discussion.............................................71
Chapter 5 Inverse Retrieval of Liquid Crystal Director Profile from
Measured Optical Transmittance Data 81
5.1 Experimental Apparatus for Inverse Problem Retrieval.............81
5.2 Experiment Results and Discussion............................................82
Chapter 6 Conclusions and Future Prospect of This Thesis Study 92
References 97

[1] Denis Andrienko, Introduction to Liquid Crystal, International Max Planck Research School,
http://www.mpip-mainz.mpg.de/~andrienk/teaching/IMPRS/slides.pdf
[2] B. Jerome, Rep. Prog. Phys., 54, 391, 1991
[3] E. Hecht, Optics, Addison-Wesley, 2002
[4] Hiroyuki Mori, Eugene C. Gartland Jr., Jack R. Kelly and Philip J. Bos, Jpn. J. Appl. Phys., 38, 135-146, 1999
[5] P.G. de Gennes and J. Prost, The Physics of Liquid Crystal, Oxford University Press, Oxford, 1993
[6] N. J. Mottram and C. J. Newton, “Introduction to Q-tensor theory”, Tech. Rep. 10/04, University of Strathclyde, 2004
[7] S. Dickman, J. Eschler, O. Cossalter and D. A. Mlynski, SID’93 Digest, 638, 1993
[8] Toralf Scharf, Polarized Light in Liquid Crystals and Polymers, John Wiley & Sons, 2002
[9] Gi-dong Lee, Philip J. Bos, Seon hong Ahn and Kyeong Hyeon Kim, Phys. Rev. E, 67, 041715, 2003
[10] S. Faetti and G. C. Mutinati, Phys. Rev. E, 68, 026601, 2003
[11] T. A. Davis and E. C. Gartland JR., SIAM J. Numer. Anal., 35, No. 1, pp. 336-362, 1998
[12] COMSOL Multiphysics, http://www.comsol.com/
[13] E. J. Acosta, M. J. Towler and H. G. Waltonm, Liquid Crystal, 27, No.7, pp. 977-984, 2000
[14] K. Kuboki, T. Miyashita, T. Ishinabe and T. Uchida, Mol. Cryst. Liq. Cryst., 410, pp. 391-400, 2004
[15] Philip J. Bos, P. A. Johnson Jr., Rickey Koehlen and K. Beran, SID’83 Digest, 30, 1983
[16] J. Chen, J. Appl. Phys., 52, 724, 1981
[17] W. R. B. Lionheart and C. J. P. Newton, New J. Phys, 9, 63, 2007
[18] Alex G. Ramm, Inverse Problems: Mathematical and Analytical Techniques with Applications to Engineering, Springer, 2005
[19] L. Rosasco, A. Caponnetto, E. De Vito and U. De Giovannini, Learning, Regularization and Ill-Posed Inverse Problems,
http://www6.cityu.edu.hk/ma/people/caponnetto/pub_files/lip_nips(CP1).pdf
[20] Fortran Linear Inverse Problem Solver (FLIPS),
http://kavaro.com/mediawiki/index.php/Flips
[21] Per Christian Hansen, Iterative Regularization Methods,
http://www2.imm.dtu.dk/~pch/Talks/iterative.ps
[22] A. Kirsche and C. Bockmann, Pade iteration method for regularization, ScienceDirect Applied Mathematics and Computation, 180, pp. 648-663, 2006
[23] K. Fukumizu and S. Watanabe, Probability Density Estimation by Regularization Method, International Joint Conference on Neural Networks, 2, pp. 1727-1730, 1993