基於雙折射偏振干涉術之滾轉角量測技術

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宋瑋益(Wei-Yi Sung) 查詢紙本館藏

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光機電工程研究所

論文名稱

基於雙折射偏振干涉術之滾轉角量測技術
(Roll Angle Measurement based on Birefringence Polarization Interferometry)

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摘要(中)

隨著科技的進步，精密機械的加工精度與準確的機台校正及定位有密切的關係，不論是位移或是角度皆需要依靠高準確度的量測系統，提供加工機校正及定位，而本研究將提出針對滾轉角的量測方法。近年來有許多學者提出對於滾轉角量測的方法與技術，其中部分利用外差干涉儀結合相位延遲片或稜鏡等，亦有利用雷測準直儀結合光柵，對於不同的量測元件都可以達到滾轉角量測的目的，而本研究開發的系統是使用雙折射晶體做為量測元件。外差干涉儀具備高解析度的優點，但其傳統的解相系統體積龐大、架構複雜對於空間受限的區域並無法正常使用，因此本研究引進新穎的偏振相機，取代傳統解相系統，建立一套共光程滾轉角量測系統，以降低環境的干擾，並同時具備高解析度的優點。
本研究提出「基於雙折射偏振干涉術之滾轉角量測技術」，為一種共光程的滾轉角量測系統，其透過偏振相機結合偏振干涉術，可快速獲得雙折射晶體引入的相位差訊號，並且透過相位差與滾轉角關係式的計算，取得滾轉角的變化量。本系統有效的改善傳統干涉儀體積龐大、架構複雜等問題。本文藉由大、中、小不同滾轉角行程的量測實驗，驗證本量測系統的可行性，而行程量測實驗的滾轉角行程分別為0.5º、0.1º及0.05º，由實驗結果可顯示本量測系統的穩定度與準確度。此外根據量測不確定度原理分析，本研究的滾轉角量測系統解析度可以達到0.0023º，並且具備10º的量測範圍。最後透過系統誤差與隨機誤差分析，提出有效改善與補償誤差的方法，進而提升量測系統的穩定度與準確度。

摘要(英)

As technology advances, the processing accuracy of precision machinery is closely related to the accurate calibration and positioning of the processing machine. Whether it is displacement or angle, it needs to rely on a high-accuracy measurement system to provide the basis for the calibration and positioning of the processing machine. And this research will propose a measurement method for the roll angle. In recent years, many scholars have also proposed methods and techniques for measuring the roll angle. Some of them use heterodyne interferometers combined with phase retarders or prisms, and also use laser collimator combined with gratings, which can be achieved for different measurement components. The purpose of roll angle measurement. The system developed in this research uses a birefringent crystal as the measuring element. The heterodyne interferometer has the advantage of high resolution, but its traditional phase-resolving system is bulky and complex, so it cannot be used in areas with limited space. Therefore, this research introduces a novel polarization camera to replace the traditional phase-resolving system and establish a common-path measurement system to reduce environmental interference, and at the same time has the advantage of high resolution. This research proposes a "Roll Angle Measurement based on Birefringence Polarization Interferometry", which is a common-path roll angle measurement system, which can quickly obtain the phase difference signal introduced by the birefringent crystal through a polarization camera combined with polarization interferometry. And through the calculation of the relationship between the phase difference and the roll angle, the change amount of the roll angle is obtained. The system effectively improves the problems of traditional interferometers such as bulkiness and complex structure. This paper verifies the feasibility of the measurement system through the measurement experiments of different roll angular strokes of large, medium and small. The roll angular strokes of the stroke measurement experiment are respectively 0.5º, 0.1º and 0.05º. The experimental results can be used to verify the feasibility of the measurement system. In addition, according to the analysis of the measurement uncertainty principle, the resolution of the roll angle measurement system in this study can reach 0.0023º, and it has a measurement range of 10º. Finally, through the analysis of system error and random error, an effective method for improving and compensating the error is proposed, thereby improving the stability and accuracy of the measurement system.

關鍵字(中)

★ 雙折射
★ 偏振干涉術
★ 滾轉角量測
★ 偏振相機

關鍵字(英)

★ birefringence
★ polarization interferometry
★ roll angle measurement
★ polarization camera

論文目次

摘要 I
Abstract II
致謝 IV
目錄 V
圖目錄 VIII
第一章緒論 1
1-1 研究背景與動機 1
1-2 文獻回顧 3
1-2-1 外差干涉儀 3
1-2-2 雷射準直儀 9
1-2-3 橢圓度分析 12
1-3 研究目的與方法 13
1-4 本文架構 14
第二章基礎理論 15
2-1 雙折射效應 15
2-1-1 雙折射晶體特性 15
2-1-2 晶體傾斜引入o光與e光之相位差 17
2-1-3 線性偏光-晶體引入之s偏光與p偏光相位差 19
2-1-4 圓偏光-晶體引入之s偏光p偏光相位差 23
2-2 偏振解相技術 26
2-2-1 偏振干涉術 26
2-2-2 相位展開技術 28
2-2-3 線性偏光架構之相位變化 29
2-2-4 圓偏振光架構之相位變化 30
2-3 小結 35
第三章系統架構 36
3-1 元件儀器介紹 36
3-1-1 基本光學元件 36
3-1-2 偏振相機 38
3-2 實驗架構與流程 40
3-3 偏振相機訊號處理 43
3-4 相位訊號調解 45
3-5 小結 46
第四章實驗結果與討論 47
4-1 量測系統 47
4-1-1 特性曲線量測 47
4-1-2 入射角與相位差關係 50
4-1-3 靈敏度 51
4-2 量測實驗 52
4-2-1 大範圍量測 52
4-2-2 不同入射角量測 54
4-2-3 行程量測 55
4-2-4 電控旋轉平台間隙量測 61
4-3 系統性能 62
4-3-1 解析度 62
4-3-2 量測範圍 64
4-4 小結 65
第五章誤差分析 66
5-1 系統誤差 66
5-1-1 架構誤差 66
5-1-2 相位訊號誤差 72
5-2 隨機誤差 73
5-2-1 電子雜訊與環境光源 73
5-3 小結 76
第六章結論與未來展望 77
6-1 結論 77
6-2 未來展望 78
參考文獻 79

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指導教授

李朱育(Ju-Yi Lee)

審核日期

2021-8-18

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