基於全反射共光程偏振干涉術之折射率量測技術

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研究生：	江家宇 Chia-Yu Chiang
論文名稱：	基於全反射共光程偏振干涉術之折射率量測技術 Refractive index measurement based on total internal reflection with common-path polarization interferometry
指導教授：	李朱育 Ju-Yi Lee
口試委員:
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：	2021
畢業學年度：	109
語文別：	中文
論文頁數：	92
中文關鍵詞：	折射率量測、相位差極大值、偏振干涉解相技術、偏振相機
外文關鍵詞：	refractive index measurement, the maximum phase difference, polarization interference, polarization camera
相關次數：	點閱：11 下載：0
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本研究開發一種「基於全反射共光程偏振干涉術之折射率量測技術」，能夠精準的量測不規則形狀物體折射率，且改善現階段量測固體折射率所遇到的問題。本技術是基於待測物與空氣之間的全反射現象進行折射率量測，不需額外的混和匹配液體做輔助即可完成。在全反射現象發生時，反射光的偏振態(垂直偏振與水平偏振)會引進不同的相位延遲。透過本研究提出的偏振干涉解相法可計算出反射光的相位差，並運用相位差極大值與折射率的量測方程式，即可推算不規則形狀物體的折射率。
本技術架構結合位移平台與偏振相機形成一共光程系統，不僅能快速調整待測物的全反射現象，也能夠降低架構的複雜性且達到快速擷取不同偏振態的光強度訊號。在共光程系統中，藉由光束聚焦與偏振干涉解相法，能在特定角度範圍的反射光中快速找到相位差極大值。另一方面，本技術的折射率量測方程式僅與單一參數(相位差極大值)有關。相較於其它量測方程式，不受焦距、曲率及精確入射角度等多參數的影響，適合用於量測不規則形狀物體的折射率。
本研究宗旨為開發折射率量測技術應用於不規則形狀的物體。本研究技術透過提出的偏振干涉解相技術與偏振相機做結合，分析出垂直與水平偏振的相位差極大值，再利用量測方程式計算不規則形狀物體的折射率。在量測實驗中，不規則形狀物體分別是不同材料的稜鏡、非球面透鏡及柱狀透鏡。運用這三種不規則形狀物體的量測，驗證本技術的性能及系統的解析度可達 1.6e-3 RIU (Refractive Index Unit)。

This study develops a refractive index measurement based on total internal reflection with common-path polarization interferometry. The measurement can accurately obtain the refractive index of irregularly shaped samples and improve problems encountered in the measurement of solids currently. Based on the total internal reflection between samples and the air, this measurement can be used for the refractive index of samples without any additional matching liquids. When the total internal reflection occurs, the polarization states of the reflected light (vertical polarization and horizontal polarization) will introduce different phase shifts. The phase difference of the reflected light can be found by the polarization interference method proposed in this study. Then, the refractive index of samples can be obtained by the measurement equation which is the relationship between the maximum phase difference and the refractive index.
The system of this measurement combines the displacement platform and the polarization camera to form a common optical path system, which can not only quickly adjust the total internal reflection, but also reduce the complication of the architecture and rapidly capture different polarization light intensity. In the common-path, by means of focused beam and polarization interference, the maximum phase difference can be quickly found in the reflected light with a range of incident angle. On the other hand, the refractive index measurement equation of this study is only related to the single parameter (the maximum phase difference). Compared with other measurement equations, it is not affected by multiple parameters such as focal length, curvature and precise incident angle, and is suitable for measuring the refractive index of irregularly shaped samples.
The purpose of this study is to develop the refractive index measurement applied to irregularly shaped samples. By the proposed polarization interference with a polarization camera to analyze the maximum value of the phase difference between vertical and horizontal polarization, the system can use the measurement equation to obtain the refractive index of samples. In this study, the irregularly shaped samples include different materials of prisms, aspherical lens and cylindrical lens. By means of the measurement of these irregularly shaped samples, we demonstrate the feasibility of the proposed measurement and its system resolution of refractive index can be achieved to 1.6e-3 RIU (Refractive Index Unit).

摘要 ............................................................................................................................................. I
Abstract ...................................................................................................................................... II
致謝 .......................................................................................................................................... IV
圖目錄 .................................................................................................................................... VII
表目錄 ...................................................................................................................................... XI
第一章 緒論 .............................................................................................................................. 1
1-1 研究背景 ..................................................................................................................... 1
1-2 文獻回顧 ..................................................................................................................... 2
1-2-1 幾何式量測 ..................................................................................................... 2
1-2-2 液體浸沒法 ..................................................................................................... 3
1-2-3 干涉儀 ............................................................................................................. 6
1-3 研究動機、目的與方法 ........................................................................................... 11
1-4 論文架構 ................................................................................................................... 12
第二章 實驗原理 .................................................................................................................... 13
2-1 全反射原理 ............................................................................................................... 13
2-1-1 全反射現象 ................................................................................................... 13
2-1-2 全反射引入相位差 ....................................................................................... 17
2-1-3 相位差極大值與折射率關係 ....................................................................... 20
2-2 偏振干涉解相法 ....................................................................................................... 22
2-3 相位差分布 ............................................................................................................... 24
2-4 小結 ........................................................................................................................... 29
第三章 系統架構 .................................................................................................................... 30
3-1 系統設計 ................................................................................................................... 30
3-1-1 光學系統設計 ............................................................................................... 30
3-1-2 偏振相機 ....................................................................................................... 34
3-2 量測訊號處理 ........................................................................................................... 37
3-3 小結 ........................................................................................................................... 41
第四章 實驗結果與討論 ........................................................................................................ 42
4-1 全場相位差分布量測 ............................................................................................... 42
4-2 不規則形狀物體的量測 ........................................................................................... 45
4-2-1 重複性量測 ................................................................................................... 45
4-2-2 折射率分佈量測 ........................................................................................... 53
4-3 系統解析度 ............................................................................................................... 56
4-4 小結 ........................................................................................................................... 58
第五章 誤差分析 .................................................................................................................... 59
5-1 系統誤差 ................................................................................................................... 59
5-1-1偏振角度與消光比的影響 ............................................................................ 59
5-1-2 四分之一波片角度與延遲量的影響 ........................................................... 63
5-2 隨機誤差 ................................................................................................................... 67
5-2-1 環境光源 ....................................................................................................... 68
5-2-2 表面污點 ....................................................................................................... 69
5-3 小結 ........................................................................................................................... 70
第六章 結論與未來展望 ........................................................................................................ 71
6-1 結論 ........................................................................................................................... 71
6-2 未來展望 ................................................................................................................... 71
參考文獻 .................................................................................................................................. 72
                                

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