臺灣博碩士論文加值系統

本研究提出一套創新的雙外差式散斑干涉儀，用以進行精密的位移及旋轉角度量測。此套干涉儀主要是以散斑干涉術做為主要的量測基礎，同時我們依據分頻多工的概念設計了一組「雙電光調制光路」來形成雙外差光源，即干涉儀系統將同時操作於兩個相疊加的調制頻率模式下，而後透過散斑干涉的光路設計建構出對稱式及非對稱式的光路架設，使不同維度的待測位移與角度資訊載於相對應的調制頻率上，再利用自行開發的雙通道濾波鎖相放大器模組及相位解調模組將不同頻率的干涉訊號進行濾波及解調，而後回推各自由度的位移及角度訊息。
此套雙外差式散斑干涉儀的主要特色是透過雙電光調制技術來降低系統使用的感測器數量，同時賦予系統具備抵抗外界低頻擾動之能力，亦可有效提高訊號之雜訊比，使系統具備高靈敏度及高解析度；藉由散斑干涉術的運用克服傳統干涉儀面內位移量測範圍受平面鏡或光柵大小所限制之問題，使系統具備大行程的量測能力；透過光柵、Wollaston prism及透鏡元件的搭配，建立「對稱式」光路架構，使系統易於架設及調校，亦可有效降低裝置誤差；藉由偏光元件、分光鏡及稜鏡的使用來建構出「非對稱式」光路架構，使系統架構簡單且運用靈活，亦可在不改變光學系統架構下，同時提供五自由度的量測訊息。
為了驗證本研究所提出的雙外差式散斑干涉儀的可行性及其系統性能，我們進行了多項驗證實驗，並將干涉儀的量測結果與商用感測器的量測結果相相比較。由實驗結果證明，此套雙外差式散斑干涉儀可同時提供五自由度位移(x、y、z)及旋轉角(θx、θz)量測訊息，其面內(x、y)及面外(z)位移之實際解析度分別可達5 nm與15 nm，重複性可達2.3 nm及7.2 nm，旋轉角重複性約為41 nrad，靈敏度於三軸向位移(x、y、z)分別約為0.569 ˚/nm、0.198 ˚/nm及0.017 ˚/nm。由上述結果驗證此雙外差式散斑干涉儀具備精準的位移及旋轉角度量測能力，未來可廣泛應用於需大量測範圍及多自由度量測的場合中。

In this study, an innovative dual-heterodyne speckle interferometer for measuring precision displacement and rotation angle is proposed. By using the speckle interferometric as the main measuring technique, a “double electro-optic optical path” is developed through the design of frequency-division multiplexing to form the dual-heterodyne light source. In other words, the interferometer system operates in two superimposed modulation frequency modes simultaneously, then through the optical path design of speckle interference, symmetrical and asymmetric optical paths are constructed, so that the displacement and rotation angle information in different dimensions can be carried on the corresponding modulation frequency. Then, by using the self-designed dual-channel filter lock-in amplifier, the interference signal of different frequency is filtered and demodulated, so that the information of the displacement and rotation angle can be obtained.
The feature of the proposed dual-heterodyne speckle interferometer is to reduce the number of sensors used in the system through dual electro-optic modulation technique, while giving the system the ability to resist low-frequency external disturbances and effectively improving the signal-to-noise ratio, so that the system has high sensitivity and high resolution. By using speckle interferometry, the system is capable of long measurement range, solving the problem of in-plane displacement measurement range of traditional interferometer is limited by the size of mirror or grating. Through the combination of grating, Wollaston Prism and lens elements, a “symmetric” optical path configuration is established, making the system easy to set up and adjusted, and effectively reducing device errors. By using polarizer, beam splitter and prism, an “asymmetric” optical path configuration is constructed, which makes the system simple and flexible. It can also provide 5-DOF measurement information without changing the optical system architecture.
In order to verify the feasibility and performance of the proposed system, several experiments were conducted and the measurement results are compared with the commercial sensor. It can be known from the experimental results that the proposed system can provide the information of 5-DOF displacement (x, y, z) and rotation angle (θx, θz) simultaneously, where the actual resolution of in-plane (x, y) and out-of-plane (z) can reach 5 nm and 15 nm, repeatability can reach 2.3 nm and 7.2 nm for displacement, 41 nrad for rotation angle, sensitivities are 0.569 ˚/nm, 0.198 ˚/nm and 0.017 ˚/nm, respectively, proving that the proposed system has capabilities of precision displacement and rotation angle measurement and can be widely used in the situation of long measurement range and multi-DOF measurement in the future.

摘要 I
Abstract II
致謝 IV
符號說明 V
目錄 XI
圖目錄 XIII
表目錄 XVI
第一章 緒論 1
1.1 研究背景 1
1.2 文獻回顧 2
1.2.1 同調干涉儀(術)之文獻回顧 2
1.2.2 外差干涉儀(術)之文獻回顧 7
1.2.3 多自由度量測技術之文獻回顧 13
1.2.4 多頻率調制技術之文獻回顧 19
1.3 研究目的 23
1.4 論文架構 23
第二章 基礎理論 25
2.1 雷射干涉術 25
2.2 外差調制技術 26
2.2.1 賽曼雷射 27
2.2.2 聲光調變器 28
2.2.3 電光調變器 29
2.2.4 雷射二極體波長調制法 31
2.3 散斑干涉術 32
2.3.1 都卜勒移頻 32
2.3.2 散斑干涉術 33
2.3.3 對稱式散斑光路架構 35
2.3.4 非對稱式散斑光路架構 36
2.4 外差訊號解調技術 37
2.5 小結 39
第三章 多自由度雙外差式散斑干涉儀 40
3.1 雙電光調制光路 40
3.2 雙自由度雙外差式散斑干涉儀 41
3.3 三自由度雙外差式散斑干涉儀 44
3.4 五自由度雙外差式散斑干涉儀 48
3.5 雙通道濾波鎖相放大器模組及相位解調模組 50
3.6 本研究所使用之光學元件及實驗儀器 54
3.7 小結 54
第四章 實驗結果與討論 56
4.1 干涉光強訊號之頻譜分析 56
4.2 雙自由度位移(x、y)量測實驗 57
4.3 三自由度位移(z)量測實驗 60
4.4 五自由度位移及旋轉角(x、y、z、θx、θz)量測實驗 62
4.5 隨機波形運動量測實驗 70
4.6 量測系統性能測試與討論 72
4.6.1 重複性量測 72
4.6.2 解析度量測 73
4.6.3 靈敏度量測 74
4.7 小結 76
第五章 誤差分析 77
5.1 系統誤差 77
5.1.1 光源方位角偏差對於量測結果所造成之影響 77
5.1.2 電光調變器(EOM)對位誤差對於量測結果所造成之影響 80
5.1.3 檢偏器方位角誤差對於量測結果所造成之影響 82
5.1.4 檢偏器消光比誤差對於量測結果所造成之影響 83
5.1.5 Beam Displacer消光比誤差對於量測結果所造成之影響 84
5.2 隨機誤差 86
5.2.1 波長變化 86
5.2.2 環境振動 87
5.2.3 電子雜訊 87
5.3 小結 87
第六章 結論與未來展望 89
6.1 結論 89
6.2 未來展望 90
參考文獻 92

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