成功大學博碩士論文系統

簡易檢索 / 詳目顯示

回結果列表

研究生：	鄭諭燦 Jeng, Yu-Tsan
論文名稱：	共路徑外差干涉儀順序量測雙折射晶體光學參數之設計與研究 Sequential Measurements for the Optical Parameters of the Birefringent Materials by Using a New Common-Path Heterodyne Interferometer
指導教授：	羅裕龍 Lo, Yu-Lung
學位類別：	碩士 Master
系所名稱：	工學院 - 機械工程學系 Department of Mechanical Engineering
論文出版年：	2005
畢業學年度：	93
語文別：	英文
論文頁數：	99
中文關鍵詞：	共路徑外差干涉儀，主軸，相位延遲，階數
外文關鍵詞：	Order, Heterodyne Polariscope, Principal Axis, Birefringence
相關次數：	點閱：84 下載：4
分享至:	分享至facebook 分享至twitter

查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

　　由於科技不斷提升，因此對產品品質的要求也愈來愈嚴格，然而產品品質的監控則有賴於高精確度和多功能量測儀器的發展。在近代光學科技中雙折射晶體是一種最常見的光學元件之一諸如波片、雙折射稜鏡、液晶…等等。一般而言，其光學參數包含有主軸角度、相位遲延、折射率及厚度…性等參數，這些參數在光學工業上及生物醫學上均佔有相當程度上的地位，然而能精確地解析出其光學參數對於應用上是相當重要的。
　　因此本實驗將提出一共路徑外差干涉儀利用順序量測的方式搭配鎖相放大器，用其精密量測技術監控相位變化再配合簡易的光訊號處理，來進行光學元件的主軸角度、相位遲延、階數、厚度及尋常光與非尋常光折射率等參數的測量。因為此量測技術是運用共路徑外差干涉術(Common-Path Heterodyne Interferometer)，可避免週期性誤差且對於雜訊免疫力及靈敏度的提高也有很大的幫助，所以有高精密度的量測優勢。
　　此外本文分別利用多階四分之一波片和水平排列相列型液晶為待測物，均證實了此系統對於具雙折射性物質的可行性，且有直接容易的訊號處理、簡潔的光學架構及不受光強擾動影響…等特點。

　To measure the complete optical parameters of linear birefringence materials, a new heterodyne polariscope with sequential measurement method is proposed. In this study, a multiple-order crystalline quartz quarter-waveplate used as a test sample is measured by two sequential setups.
　The proposed method has average absolute errors of and 0.15 % with respect to the principal axis angle and the phase retardation. The order, thickness and refractive indices also have a good agreement with the known sample data. On the other hand, in order to validate the functions of the measuring system, a homogeneous alignment liquid crystal cell is utilized as a sample for the system, too.
　As compared to its conventional counterparts, the proposed heterodyne polariscope has a more compact setup, simpler in signal process and especially in multi-function measurements.

Abstract	I
中文摘要	III
誌謝	V
Table of Contents	VI
List of Tables	VIII
List of Figures	IX
Chapter 1 Introduction	1
1.1 Review of Measurements in the Birefringence Materials	1
1.2 Destinations and Motivations of the Research	3
1.3 Overview of Chapters	3
Chapter 2 Birefringence Materials	10
2.1 Preface	10
2.2 The Optical Properties of Birefringence	10
2.3 Phase Retardation	14
2.4 Optical Activity	17
Chapter 3 The Heterodyne Interferometer	25
3.1 Preface	25
3.2 Principle of Traditional Interference	25
3.3 Basic Theory of Heterodyne Interference	26
3.4 Common-Path Heterodyne Interferometry	28
3.5 The Modulating Technique of Electro-Optic Modulator	29
3.5.1 Electro-Optic Effect	30
3.5.2 Electro-Optic Modulation	31
3.5.2.1 Amplitude Modulation	31
3.5.2.2 Phase Modulation	35
3.6 Calibration the Axis Alignment of an EO modulator	36
3.7 Phase Locked Theorem	38
3.7.1 Phase-Sensitive Detection	39
3.7.2 Magnitudes and Phase	41
Chapter 4 The Sequential Measurement System with Phase-Locked Extraction	48
4.1 Preface	48
4.2 Phase-Locked Methodology for Extracting the Complete Optical Parameters	48
4.2.1 Two Basic Optical Arrangements	48
4.2.2 Principle	49
4.2.2.1 Method for Measuring the Principal Axis Angle of a Birefringent Material	49
4.2.2.2 Method for Measuring the Phase Retardation of a Birefringent Material	51
4.2.2.3 Method for Measuring the Order of a Birefringent Material	52
4.2.2.4 Method for Measuring the Thickness of a Birefringent Material	54
4.2.2.5 Method for Determining the Refractive Indices (ne and no)	56
4.3 Simulation	57
4.4 Conclusions	58
Chapter 5 Experimental Results and Error Analysis	68
5.1 Experimental Results	68
5.1.1 Experimental Setup	68
5.1.2 Calibration in the Measurement System	68
5.1.3 Results on Experiment	69
5.1.3.1 Experimental Results for a Multi-Order Quarter Waveplate	69
5.1.3.2 Experimental Results for a Homogeneous Alignment Nematic Liquid Crystal	72
5.2 Errors Analysis	74
5.2.1 The Sources of Experimental Errors	74
5.2.2 Discussion of Jones Matrix for a Tilted Birefringent Plate	75
5.3 Conclusions	82
Chapter 6 Conclusions and Future Works	92
6.1 Conclusions	92
6.2 Suggestions	93
Bibliography	94
Autobiography	99

Tabel 2.1 The refractive index of common uniaxial and biaxial crystals	24
Table 4.1 Simulated results of negative uniaxial calcite crystal.	66
Table 5.1 Experimental results of the principal axis angle and phase retardation. (Multi-Order Quarter Waveplate, CVI, Model QWPM-633-10-4-R15)	84
Table 5.2 Experimental results of the phase retardation. (Homogeneous Alignment Nematic Liquid Crystal, Meadowlark, Model B1020, Part #: 03.340)	88

Figure 1.1 The structure of Serreze and Goldner [Serreze et al., 1974].	5
Figure 1.2 The structure of Shindo and Hanabusa [Shindo et al., 1983].	5
Figure 1.3 The structure of Chiu, et al. [Chiu et al., 1996]	6
Figure 1.4 The structure of Cameron and Cóte [Cameron et al., 1997]	6
Figure 1.5 The structure of Ohkubo and Umeda [Ohkubo et al., 2001]	7
Figure 1.6 The structure of Lo et al. [Lo et al., 2004].	7
Figure 1.7 The structure of Huang et al. [Huang et al., 1997].	8
Figure 1.8 Wedge-shaped crystal. [Hsu and Su, 2002].	8
Figure 1.9 The structure of Hsu and Su [Hsu and Su, 2002].	9
Figure 2.1 Images in sodium chloride and calcite single crystals	20
Figure 2.2 The refractive index ellipsoid of isotropic materials.	20
Figure 2.3 The refractive index ellipsoid of uniaxial crystal.	21
Figure 2.4 (a) Positive uniaxial crystal ; (b) Negative uniaxial Crystal.	21
Figure 2.5 The refractive index ellipsoid of biaxial crystals.	22
Figure 2.6 Light traveling through a birefringent medium	22
Figure 2.7 The two axes of the birefringent material.	23
Figure 2.8 The phase retardation of the wave.	23
Figure 2.9 Rotation of the plane of polarization by an optically active medium. The case for levorotatory is shown	24
Figure 3.1 The traditional interference.	43
Figure 3.2 The structure of the amplitude modulation by an EO modulator.	43
Figure 3.3 The intensity of the amplitude modulation.	44
Figure 3.4 Saw-tooth wave voltage.	44
Figure 3.5 Circular heterodyne light source.	45
Figure 3.6 Calibration the axis alignment of an EO modulator.	45
Figure 3.7 Signal waveform in the lock-in amplifier.	46
Figure 3.8 Functional block diagram of the lock-in amplifier.	47
Figure 3.9 Front panel of the lock-in amplifier.	47
Figure 4.1 Setup for common-path circular polariscope.	59
Figure 4.2 Senarmont setup.	60
Figure 4.3 Schematic diagram for tilting a sample.	61
Figure 4.4 The relationship between   and  	62
Figure 4.5 Setup in the phase-locked methodology.	63
Figure 4.6 Effective Refractive Index.	64
Figure 4.7 Schematic diagram for tilting a sample.	65
Figure 4.8 Simulation of measurements in the principal angle and phase retardation of a quarter waveplates.	66
Figure 4.9 Flow Chart.	67
Figure 5.1 Experimental results of the principal axis angle and the phase retardation. (Multi-Order Quarter Waveplate, CVI, Model QWPM-633-10-4-R15)	83
Figure 5.2 Meadowlark, Model B1020, Part #: 03.340.	85
Figure 5.3 Liquid Crystal Cell construction showing molecular alignment without applied voltage.	85
Figure 5.4 Liquid Crystal Cell construction showing molecular alignment with applied voltage.	86
Figure 5.5 Typical Liquid Crystal Variable Retarder performance at 632.8 nm, 21 oC. (a) without compensator, and (b) with compensator	86
Figure 5.6 Experimental results of the phase retardation.	87
Figure 5.7 Geometrical structure of a birefringent plate. [Zhu, 1994].	89
Figure 5.8 Beam splitting inside a birefringent plate. [Zhu, 1994].	89
Figure 5.9 Variations in the three effective refractive-index differences  ,  ,   as functions of the rotation angle  . [Zhu, 1994].	90
Figure 5.10 The relationship between the simplified formula and approximate formula ( ).	91
Figure 5.11 The relationship between the simplified formula and approximate formula ( ).	91


                                    

Cameron, B. D. and C’ote, G. L., ”Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Transactions on Biomedical Engineering, Vol. 44, No. 12, pp.1221-1227, 1997.
Chiu, M. H., Chen, C. D. and Su, D. C., “Simple two frequency laser,” Prec. Eng., Vol. 18, pp. 161-163, 1996.
Chiu, M. H., Chen, C. D. and Su, D. C., “Method for determining the fast axis and phase retardation of a wave plate,” J. Opt. Soc. Am. A, Vol. 13, pp.1924-1929, 1996.
Fowles, G. R., Introduction to Modern Optics, 2nd ed., Holt, Rinehart and Winston, New York, Ch. 6, pp. 185-188, 1975.
Freitas, J. M. De and Player, M. A., “Importance of rotational beam alignment in the generation of second harmonic errors in laser heterodyne interferometry ”, Meas. Sci. Tech. Vol. 4, pp. 1173-1176, 1993.
Gazalet, M. G., Ravez, M., Haine, F., Bruneel, C., and Bridoux, E., “Acousto-optic low frequency shifter,” Appl. Opt., Vol. 33, pp. 1293-1298, 1994.
Gelmini, E., Minomi, U., and Docchio, F., “Tunable, double-wavelength heterodyne detection interferometer for absolute distance measurement,” Opt. Lett., Vol. 19, pp. 213-215, 1994.
Guenther, Modern optics, McGraw-Hill, Ch. 13, p. 530, 1995.
Hariharan, P., Optical interfeometry, Academic Press, 1983.
Haus, H. A., Waves and fields in optoelectronics, Prientice-Hall, Inc., Englewood Cliffs, New Jersey, Ch. 12, 1984.
Hecht, Optics, Addision-Wesley, 4th ed., Ch. 7, pp. 282-286, 1998.
Hecht, Optics, Addision-Wesley, 4th ed., Ch. 8, pp. 336-344, 1998.
Hou, W. and Wilkening, G., “Investigation and compensation of nonlinearity of heterodyne interferometers.”, Pre. Eng. Vol. 14 No. 2, pp. 91-98, 1992.
Hsu, C. C. and Su, D. C., “Method for determining the optical axis and (ne, no) of birefringent crystal,” Applied Optics, Vol. 41, pp. 3936-3940, 2002.
Huang, Y. C., Chou, C., and Chang, M., “Direct measurement of refractive indices of a linear birefringent retardation plate,” Opt. Commun., Vol.133, pp.11-16, 1997.
Kemp, J. C., “Piezo-optical birefringence modulators: new use for a long known effect,” J. Opt. Sci. Am., Vol. 59, pp. 950-954, 1969.
Kothiyal, M. P. and Delisle, C., “Optical frequency shifter for heterodyne interferometry using coumterrotating wave plates,” Opt. Lett., Vol. 9, pp. 319-321, 1984.
Kurzynowski, P. and Wozniak, W. A., “Phase retardation measurement in simple and reverse senarmont compensators without calibrated quarter wave plates,” Optik, Vol. 113, pp. 51-53, 2002.
Lo, Y. L., Lin, J. F., and Lee, S. Y., “Polariscope for the simultaneous measurements of the principal axis and phase retardation using two phase-locked extractions,” Applied Optics, Vol. 43, pp. 6248-6254, 2004.
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., Vol. 190, pp. 129-133, 2001.
Model SR530 Lock-in Amplifier Manual.
Ohkubo, S. and Umeda, N., “Near-field scanning optical microscope based on fast birefringence measurements,” Sens. and Mater., Vol. 13, pp.433-443, 2001.
Palik, E. D., Handbook of optical constants of solids III, Academic, New York, p. 729, 1998.
Rochford, K. B., Rose, A. H. and Wang, C. M., “NIST study investigates retardance uncertainty,” Laser Focus World, pp. 223-227, 1997.
Rosenbluth, A. E. and Bobroff, N., “Optical sources of nonlinearity in heterodyne interferometers.”, Pre. Eng. Vol. 12 No. 1, pp. 7-11, 1990.
Serreze, H. B. and Goldner, R. B., “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum., Vol. 45, pp.1613-1614, 1974.
Shindo, Y. and Hanabusa, H., “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun., Vol. 24, pp.240-244, 1983.
Suits, J. C., “Magneto-optical rotation and ellipticity measurements with a spinning analyzer,” Rev. Sci. Instrum., Vol. 42, pp. 19-22, 1971.
Suzuki, T. and Hioki, R., “Translation of light frequency by moving grating,” J. Opt. Soc. Am., Vol. 57, pp. 1551, 1967.
Takasaki, H., Umeda, N., and Tsukiji, M., “Stabilized transverse Zeeman laser as a new light source for optical measurement,” Appl. Opt., Vol. 19, pp. 435-441, 1980.
Wickramasingle, H. K., Laser heterodyne probes, Optical Metrology, NATO ASI series, 1987.
William, A. Shurcliff., Polarized Lignt., Cambridge, 1962.
Zhu, X., “Explicit Jones transformation matrix for a tilted birefringent plate with its optic axis parallel to the plate surface,” Applied Optics, Vol. 33, pp. 3502-3506, 1994.
http://www.meadowlark.com/catalog/LiquidCrystals/liqcrys4.htm.
許正治，使用外差干涉儀測量光學常數之研究，國立交通大學光電工程研究所碩士論文，2003.
郭彥珍，邱宗明，李信，激光偏振干涉光路的非線性分析計算，計量學報，Vol. 16, No. 4, Oct. 1995.
游展汶，以旋光外差干涉術測量雙折射晶體之尋常光及非尋常光折射率，國立交通大學光電工程研究所碩士論文，2000.

校內：2008-07-15公開
校外：2008-07-15公開

簡易檢索 / 詳目顯示

相關論文