臺灣博碩士論文加值系統

本研究提出一套創新的弦波調制雙繞射光柵干涉儀，用以進行精密位移及旋轉角量測。此套干涉儀是以弦波訊號來針對WP雙折射晶體進行訊號調制，達到外差訊號調制的目的，進而降低環境低頻擾動對量測結果所造成的影響，而後透過獨特的雙繞射式光路設計來引入加倍的相位變化，有效提升系統的靈敏度及解析度。
此套量測技術主要是藉由WP元件及光柵元件的配合，成功地建構出「弦波調制雙繞射光柵干涉儀」架構，當雷射光束通過WP元件後形成偏振態相互垂直（p偏振光與s偏振光），我們藉著控制WP元件沿著面內方向進行高頻的弦波移動，即可將此高頻訊號引入相位中，形成外差光源。當外差光源的p偏振光與s偏振光各自通過光柵後形成繞射，光柵於面內位移時會引入相位變化，而後再藉由反射鏡將繞射光沿原路徑再次通過光柵及WP，進而引入加倍的待測相位變化量，而後利用弦波鎖相放大器先鎖定調制的頻率，並解出包覆於調制頻率中的待測相位，進而回推光柵的面內位移量，利用該技術可減少其他頻率所引入的雜訊，如此即可有效提升干涉儀系統的量測靈敏度及穩定度。
於研究中我們透過使用一橫向位移分光鏡(Lateral Displacement Beamsplitters,LDB)來形成兩道平行光束，使系統可於單一偵測架構下建立兩個偵測區域，用以進行四個自由度(x、z、θy、θz)的量測，且在以往的多自由度量測架構中，當系統量測面內位移量時，會使面外位移之量測光分離造成干涉訊號消失，因此，於本研究導入共面量測架構，可使整體系統不會在量測面內位移時造成面外位移之干涉訊號消失。此套系統只需使用一個一維穿透式光柵及反射鏡，即可達成多自由度的量測能力，不僅大幅縮短系統架設時間，更降低系統開發成本。
為了驗證此套弦波調制雙繞射光柵干涉儀量測技術的可行性，本研究進行了一系列的實驗，包括四自由度位移及旋轉角、解析度、重複性、穩定度、速度極限及靈敏度測試等實驗，並將此研究的量測結果與商用感測器的量測結果相比較，用以驗證WP弦波調制雙繞射光柵干涉儀的量測性能。由實驗結果證明，本研究所開發的雙繞射光柵干涉儀可同時提供四自由度位移及旋轉角度量測訊息，其位移與旋轉角之實際解析度分別可達5 nm與100 nrad，重複性可達0.8 nm與14 nrad，穩定度於5分鐘內之條件下優於50 nm與1200 nrad，由上述實驗結果驗證此套系統具備精準的位移及旋轉角度量測能力。

Laser interferometers have come to be broadly utilized in the fields of semiconductor industry, precision machinery industry, microscopic techniques, optical alignment systems, and medical research. According to the signal detection scheme, interferometers can be categorized into the types of homodyne and heterodyne. In comparison to homodyne detection interferometer, heterodyne detection interferometer proves a superior anti-noise ability. If high frequency noise signal is considered, nanometer resolution is easily being achieved by using heterodyne detection interferometer. Several heterodyne interferometers have been developed to provide exact displacement information with high resolution. However, the problem of poor measurement stability caused by the unstable wavelength of the light source is still difficult to avoid. Grating interferometry, one of the well-known interferometries, is proposed to overcome the problems resulting from the unstable wavelength of the light source. Many methods based on the measurement principle of grating interferometry have been carried out to measure displacement with high system stability.
In this study, a laser interferometer based on the techniques of heterodyne sinusoidal modulation and double-diffraction is proposed for displacement measurement. This interferometer has the advantages of grating interferometry, heterodyne interferometry, and double-diffraction technique. According to the optical configuration of our proposed interferometer, a novel heterodyne light source is obtained by using a sinusoidal modulation method to modulate a Wollaston prism. The heterodyne light source is then passed through a beam splitter, and the resulting transmission beam moves to the diffraction grating, and is diffracted. The diffracted beams are reflected back into the diffraction grating along the original optical path so that the grating phase is introduced into the diffracted beams two times, forming a double-diffraction optical configuration. System sensitivity and resolution can be effectively enhanced by using this method. The second diffraction also causes the two beams to overlap to form interference, and after passing through an analyzer, the interference signal can be received by a photodetector. The in-plane displacement of the grating can be obtained by calculating the phase variation of the interference signal.
In order to verify the measurement performance of the proposed measurement technique, several experiments are conducted and compared the results obtained from our double-diffraction interferometer with a commercial measuring instrument. The experiment results show that this double-diffraction interferometer is able to measure displacement with the resolution of 10 nm. This double-diffraction interferometer can be widely used in the fields of precision positioning systems, laser interference lithography, near-field optical microscopy, and automated optical detection.

摘要 I
Abstract III
致謝 V
符號說明 VI
目錄 XI
圖目錄 XIV
表目錄 XVII
第一章 緒論 1
1.1 研究背景 1
1.2 文獻回顧 2
1.2.1 同調干涉術(homodyne Interferometry)之文獻回顧 2
1.2.2 外差干涉術(heterodyne Interferometry)之文獻回顧 5
1.2.3 雙(多)繞射量測技術之文獻回顧 11
1.2.4 共面雙(多)自由度量測技術之文獻回顧 13
1.3 研究目的 18
1.4 論文架構 19
第二章 基礎理論 21
2.1 外差調制技術 21
2.1.1移動(旋轉)光柵法 22
2.1.2 賽曼雷射 23
2.1.3 聲光調制器 24
2.1.4 電光調制器 26
2.1.5 雷射二極體波長調制法 28
2.1.6 弦波調制技術 29
2.2 光柵干涉術 29
2.2.1 光柵相位測量法之原理 30
2.2.2 雙繞射架構 31
2.2.3 外差式光柵干涉儀 32
2.2.4 外差式雙繞射光柵干涉儀 33
2.3 共面雙(多)自由度光柵干涉儀量測技術 35
2.4 外差訊號相位解調 37
2.5 小結 38
第三章 弦波調制雙繞射光柵干涉儀 40
3.1 弦波調制雙繞射光柵干涉儀架構 40
3.1.1 Wollaston prism弦波調制技術 40
3.2 單自由度弦波調制雙繞射光柵干涉儀 41
3.3 雙自由度弦波調制雙繞射光柵干涉儀 44
3.4 四自由度弦波調制雙繞射光柵干涉儀 46
3.5 相位解調系統 50
3.5.1 容錯演算法(fault tolerance algorithm) 52
3.6 本研究所用到之光學元件及實驗儀器 54
3.7 小結 55
第四章 實驗結果與討論 57
4.1調制頻率選用 57
4.2 單自由度位移(x)量測實驗 58
4.3 雙自由度位移(z)量測實驗 61
4.4 四自由度位移(x, z, θx, θz)量測實驗 63
4.4.1 大行程位移與旋轉角度量測實驗(x, z, θx, θz) 63
4.4.2 中行程位移與旋轉角度量測實驗(x, z, θx, θz) 65
4.4.3 小行程位移與旋轉角度量測實驗(x, z, θx, θz) 66
4.5 量測系統性能測試與討論 68
4.5.1 解析度量測 68
4.5.2 重複性量測 70
4.5.3 穩定度量測 71
4.5.4 隨機波實驗 73
4.5.5 量測速度極限 74
4.6 小結 76
第五章 誤差分析 77
5.1 系統誤差 77
5.1.1 檢偏器消光比所產生之非線性誤差 78
5.1.2 Wollaston prism消光比所產生之非線性誤差 79
5.1.3 光柵架設誤差對於位移量測所產生之影響 81
5.1.4 光柵架設誤差之繞射光偏移對於面外量測所產生之影響 82
5.1.5 檢偏器方位角錯誤所造成之影響 83
5.1.6 Wollaston prism形貌變化對於調制訊號影響 84
5.2 隨機誤差 85
5.2.1 環境振動 85
5.2.2 電子雜訊 86
5.3 小結 86
第六章 結論與未來展望 87
6.1 結論 87
6.2 未來展望 88
參考文獻 90

[1] A. A. Michelson and E. W. Morley, "On the Relative Motion of the Earth and of the Luminiferous Ether," Sidereal Messenger, vol. 6, pp. 306-310, vol. 6, pp. 306-310, 1887.
[2] T. Suzuki and R. Hioki, "Translation of light frequency by a moving grating," JOSA, vol. 57, no. 12, pp. 1551-1551, 1967.
[3] Y. Xie and Y.-z. Wu, "Zeeman laser interferometer errors for high-precision measurements," Applied optics, vol. 31, no. 7, pp. 881-884, 1992.
[4] M. Ikram and G. Hussain, "Michelson interferometer for precision angle measurement," Applied optics, vol. 38, no. 1, pp. 113-120, 1999.
[5] H. Choi, J. La, and K. Park, "Electronic frequency modulation for the increase of maximum measurable velocity in a heterodyne laser interferometer," Review of scientific instruments, vol. 77, no. 10, p. 106102, 2006.
[6] W. Hou, "A new design of high precision differential plane mirror interferometer," in Sixth International Symposium on Precision Engineering Measurements and Instrumentation, 2010, vol. 7544: International Society for Optics and Photonics, p. 75446V.
[7] J. Cui, Z. He, Y. Jiu, J. Tan, and T. Sun, "Homodyne laser interferometer involving minimal quadrature phase error to obtain subnanometer nonlinearity," Applied optics, vol. 55, no. 25, pp. 7086-7092, 2016.
[8] V. C. P. Kumar, C. Joenathan, A. Ganesan, and U. Somasundram, "Increasing the sensitivity for tilt measurement using a cyclic interferometer with multiple reflections," Optical Engineering, vol. 55, no. 8, p. 084103, 2016.
[9] E. Higurashi and R. Sawada, "High-accuracy micro-encoder based on the higher-order diffracted light interference," in 2000 IEEE/LEOS International Conference on Optical MEMS (Cat. No.00EX399), 21-24 Aug. 2000 2000, pp. 143-144, doi: 10.1109/OMEMS.2000.879666.
[10] H. Hsieh, J. Lee, W. Wu, J. Chen, R. Deturche, and G. Lerondel, "Quasi-common-optical-path heterodyne grating interferometer for displacement measurement," Measurement science and technology, vol. 21, no. 11, p. 115304, 2010.
[11] Z.-H. He and X.-J. Liu, "A high precision displacement sensor based on dual-gratings interference," in 2011 International Conference on Electric Information and Control Engineering, 2011: IEEE, pp. 997-1000.
[12] C.-P. Chang, P.-C. Tung, L.-H. Shyu, Y.-C. Wang, and E. Manske, "Multi-interferometric displacement measurement system with variable measurement mirrors," Applied optics, vol. 52, no. 17, pp. 3902-3909, 2013.
[13] J.-Y. Lee, H.-L. Hsieh, and Z. Y. Lin, "Heterodyne grating interferometry based on sinusoidal phase modulation for displacement measurement," in Optical Measurement Systems for Industrial Inspection X, 2017, vol. 10329: International Society for Optics and Photonics, p. 103293S.
[14] R. Corey, A. Schmidt, and P. Saulnier, "Using a moving diffraction grating to simulate the function of an acousto‐optic modulator," American Journal of Physics, vol. 64, no. 5, pp. 614-617, 1996.
[15] S. Casillas-de la Torre, G. Martinez, G. Garcia-Torales, C. Solano, and J. Flores, "Optical heterodyne interferometer using an LCD grating as a spatial modulator," in Novel Optical Systems Design and Optimization VIII, 2005, vol. 5875: International Society for Optics and Photonics, p. 58750Q.
[16] J. Chen, Y. Ishii, and K. Murata, "Heterodyne interferometry with a frequency-modulated laser diode," Applied optics, vol. 27, no. 1, pp. 124-128, 1988.
[17] Y. Park and K. Cho, "Heterodyne interferometer scheme using a double pass in an acousto-optic modulator," Optics letters, vol. 36, no. 3, pp. 331-333, 2011.
[18] J.-Y. Lee, H.-Y. Chen, C.-C. Hsu, and C.-C. Wu, "Heterodyne interferometer for measurement of in-plane displacement with subnanometer resolution," in Third International Symposium on Precision Mechanical Measurements, 2006, vol. 6280: International Society for Optics and Photonics, p. 62800J.
[19] C.-C. Wu, C.-C. Hsu, J.-Y. Lee, and Y.-Z. Chen, "Heterodyne common-path grating interferometer with Littrow configuration," Optics express, vol. 21, no. 11, pp. 13322-13332, 2013.
[20] Y. Zhong, G. Zhang, C. Leng, and T. Zhang, "A differential laser Doppler system for one-dimensional in-plane motion measurement of MEMS," Measurement, vol. 40, no. 6, pp. 623-627, 2007.
[21] S. Lin and W. Syu, "Heterodyne angular interferometer using a square prism," Optics and Lasers in Engineering, vol. 47, no. 1, pp. 80-83, 2009.
[22] C.-C. Hsu, H. Chen, C.-W. Chiang, and Y.-W. Chang, "Dual displacement resolution encoder by integrating single holographic grating sensor and heterodyne interferometry," Optics express, vol. 25, no. 24, pp. 30189-30202, 2017.
[23] J. Deng et al., "Eightfold optical encoder with high-density grating," Applied optics, vol. 57, no. 10, pp. 2366-2375, 2018.
[24] J.-Y. Lee and G.-A. Jiang, "Displacement measurement using a wavelength-phase-shifting grating interferometer," Optics express, vol. 21, no. 21, pp. 25553-25564, 2013.
[25] Q. Lv et al., "Simple and compact grating-based heterodyne interferometer with the Littrow configuration for high-accuracy and long-range measurement of two-dimensional displacement," Applied optics, vol. 57, no. 31, pp. 9455-9463, 2018.
[26] C. Lin, S. Yan, D. Ding, and G. Wang, "Two-dimensional diagonal-based heterodyne grating interferometer with enhanced signal-to-noise ratio and optical subdivision," Optical Engineering, vol. 57, no. 6, p. 064102, 2018.
[27] 郭柏均, "雙自由度外差式雷射散斑干涉儀," 2016.
[28] C.-F. Kao, S.-H. Lu, H.-M. Shen, and K.-C. Fan, "Diffractive laser encoder with a grating in Littrow configuration," Japanese Journal of Applied Physics, vol. 47, no. 3R, p. 1833, 2008.
[29] E. Zhang, Q. Hao, B. Chen, L. Yan, and Y. Liu, "Laser heterodyne interferometer for simultaneous measuring displacement and angle based on the Faraday effect," Optics express, vol. 22, no. 21, pp. 25587-25598, 2014.
[30] "SIOS Meßtechnik GmbH." http://www.sios-de.com/ (accessed.
[31] W. H. Stevenson, "Optical frequency shifting by means of a rotating diffraction grating," Applied Optics, vol. 9, no. 3, pp. 649-652, 1970.
[32] C.-C. Wu, Y.-Z. Chen, and C.-H. Liao, "Common-path laser planar encoder," Optics express, vol. 21, no. 16, pp. 18872-18883, 2013.
[33] 王威程, "六自由度波長調制外差光柵干涉儀之開發," 2014.
[34] 吳乾埼, "繞射式雷射光學尺系統之硏製," National Taiwan University Department of Mechanical Engineering, 2001.
[35] C.-K. Lee et al., "Design and construction of linear laser encoders that possess high tolerance of mechanical runout," Applied optics, vol. 43, no. 31, pp. 5754-5762, 2004.
[36] 王雅馨, "鎖相放大器研究及其去除光雜訊之應用," 碩士, 光電科技研究所, 國立彰化師範大學, 彰化縣. [Online]. Available: https://hdl.handle.net/11296/t5jz7t
[37] 陳應誠, "電光晶體調制外差式干涉儀與其非線性誤差之消減," 碩士, 物理研究所, 國立清華大學, 新竹市, 1995. [Online]. Available: https://hdl.handle.net/11296/k894b3