雙光束偏振干涉術應用於滾轉與俯仰角位移量測

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姓名

張書菡(Shu-Han Chang) 查詢紙本館藏

畢業系所

光機電工程研究所

論文名稱

雙光束偏振干涉術應用於滾轉與俯仰角位移量測
(Dual Beam Polarization Interferometry for Roll and Pitch Angular Displacement Measurement)

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至系統瀏覽論文 (2025-8-30以後開放)

摘要(中)

本研究開發一種「雙光束偏振干涉術應用於滾轉與俯仰角位移量測」技術，改善傳統的旋轉誤差量測技術缺乏滾轉角的量測，有效克服現有技術在量測範圍受限、易受環境變化影響、體積過大及系統結構過於複雜等問題。本技術使用雙折射晶體作為量測元件，以偏振相機解析由晶體角位移引起的相位變化。並模擬在固定滾轉與俯仰角下，雙光束入射晶體所產生的相位變化關係曲線，以此做為依據將相位差量測值轉換為精確的滾轉與俯仰角位移量。在一系列量測實驗中，利用電控旋轉平台的回傳值與量測值進行誤差分析，同時透過重複性實驗確認系統的穩定性。本研究通過實驗評估系統的解析度及非線性週期性誤差，並對系統架構可能引起的誤差進行分析與提出解決辦法。實驗證實，本系統在6°的量測範圍內能精確地同時量測滾轉與俯仰角位移，其量測解析度分別達到2.9 arcsec與21.6 arcsec。

摘要(英)

This research develops a technique of “Dual Beam Polarization Interferometry for Roll and Pitch Angular Displacement Measurement”, addressing the deficiencies of traditional rotational error measurement methods that lack the capability for roll angle measurement. This technique effectively overcomes the limitations of existing technologies, such as restricted measurement range, susceptibility to environmental changes, excessive size, and overly complex system structures. The method uses a birefringent crystal as the measurement component, with a polarization camera analyzing the phase differences variations caused by the crystal′s angular displacement. By simulating the incidence of dual beams on the crystal at fixed roll and pitch angles, the resulting phase differences variation relationship curves are analyzed. These curves serve as a basis for converting measured phase differences into precise roll and pitch angular displacements. In a series of measurement experiments, error analysis is conducted by comparing the feedback values from an electronically controlled rotary stage with the measured values, while repeatability experiments are used to confirm the system′s stability. This study evaluates the system′s resolution and nonlinear periodic errors through experiments and analyzes potential errors introduced by the system′s architecture, proposing solutions to these issues. The experiments demonstrate that within a 6° measurement range, the system can accurately measure roll and pitch angular displacements, achieving measurement resolutions of 2.9 arcseconds and 21.6 arcseconds, respectively.

關鍵字(中)

★ 滾轉角量測
★ 俯仰角量測
★ 雙折射晶體
★ 偏振干涉解相技術
★ 偏振相機

關鍵字(英)

★ Roll angular displacement measurement
★ Pitch angular displacement measurement
★ birefringent crystals
★ polarization interference
★ polarization camera

論文目次

目錄
摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 VI
表目錄 VIII
第一章緒論 1
1-1 研究背景 1
1-2 文獻回顧 3
1-2-1滾轉角位移量測 4
1-2-2 姿態角三軸量測 6
1-3 研究動機、目的與方法 8
1-4 論文架構 9
第二章實驗原理 10
2-1 雙折射原理 10
2-1-1 雙折射與相位延遲 11
2-1-2 雙折射晶體的滾轉與俯仰位移與相位延遲之關係 12
2-1-3 相位延遲與相位差之關係 15
2-2 偏振干涉解相法 17
2-3滾轉與俯仰角位移與相位差之關係 22
2-4 小結 26
第三章系統架構 27
3-1 系統設計及元件 27
3-2 實驗步驟與流程 32
3-3量測訊號處理 34
3-4小結 36
第四章實驗結果與討論 37
4-1滾轉與俯仰角定位量測 37
4-1-1滾轉角位移之定位量測實驗 37
4-1-2 俯仰角位移之定位量測實驗 42
4-1-3 滾轉與俯仰角同時位移之定位量測實驗 45
4-2 滾轉與俯仰角位移量測 50
4-2-1滾轉角與俯仰角順序位移之量測 50
4-2-2 滾轉角與俯仰角同時位移之量測 51
4-3 系統性能 52
4-3-1 系統解析度 52
4-3-2 非線性週期性誤差 54
4-3-3 系統靈敏度與量測範圍 54
4-4 小結 56
第五章誤差分析 57
5-1 系統誤差 57
5-1-1 偏振相機的非線性增益 57
5-1-2 四分之一波片的不完美特性與對位誤差 59
5-2 隨機誤差 73
5-3 小結 75
第六章結論與未來展望 76
6-1 結論 76
6-2 未來展望 77
參考文獻 78

參考文獻

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指導教授

李朱育(Ju-Yi Lee)

審核日期

2024-8-20

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