國立清華大學光測力學實驗室所發展之穿透率極值光彈理論(Transmissivity Extremities Theory of Photoelasticity, TEToP)，係結合光譜儀(Spectrometer)與白光光彈法(White Light Photoelasticity, WLP)建立一穿透率對應應力與波長之三維系統化關係，進而推導出應力量化公式(Stress Quantifying Formula, SQF)，應用於物體內之應力量測。由於光譜儀與WLP具有高靈敏度及高解析度等特色，TEToP較一般光彈法能更準確地量測物體內之應力。

為進一步提升TEToP量測之精度，本研究針對材料校正程序及實驗架設進行改善，並比較由SQF直接量測與理論求得結果之差異，探討差異值與各穿透率極值線性關係(Transmissivity Extremities Linear Equation, TELE)間之相關性，驗證SQF之正確性。

此外，本研究藉各TELE間之相關性，發展時間域相位展開法(Temporal Phase Unwrapping Theory, TPUT)，並帶入模擬與實驗結果驗證TEToP運用於高階應力量測之可行性。

關鍵字：穿透率極值光彈理論、光譜儀、白光光彈法、應力量測、時間域相位展開法

By integrating the spectrometer and white light photoelasticity, the transmissivity extremities theory of photoelasticity (TEToP) was developed by the Photomechanics Laboratory, National Tsing Hua University, Taiwan, Republic of China. The TEToP was used to establish the three-dimensional systematic relationship between the transmissivity and the corresponding stress and wavelength.
Furthermore, the stress quantifying formula (SQF) was derived and applied on the stress measurement of the structural components. In contrast to the traditional photoelasticity, with the high sensitivity and high resolution of both the spectrometer and white light photoelasticity, the stress measurement of the structural components can be measured more accurately by using the TEToP.

To further upgrade the measurement accuracy of the TEToP, material calibration procedure and experimental setup were ameliorated. By comparing the calculated stress obtained by SQF and the theoretical stress, the correlation between stress differences and transmissivity extremities linear equations (TELEs) was investigated and the feasibility of SQF can be confirmed.
Based on the correlation between TELES found in this thesis, the temporal phase unwrapping theory (TPUT) was derived and used in the simulation and experimental work to verify the feasibility of employing the TEToP for the higher level stress measurement.

Keywords: Transmissivity extremities theory of photoelasticity; Spectrometer; White light photoelasticity; Stress measurement; Temporal phase unwrapping theory.

目錄
一、 簡介 1
二、 文獻回顧 3
三、 實驗原理 7
3.1 應力與穿透率光譜間之特殊關係 7
3.2 平面偏光儀下之等色線條紋穿透率光譜方程式 9
3.3 穿透率極值光彈理論之應力量化公式[4, 29] 12
3.4 迴歸分析取得應力量化公式參數[5] 15
3.5 不同穿透率極值線性相關關係[5] 19
3.6 應力量化公式與試片厚度間之關係[5] 20
3.7 應力展開理論[5] 21
四、 實驗試片與裝置 33
4.1 實驗試片規劃 33
4.2 實驗裝置 33
五、 實驗分析程序 38
5.1 系統校正 38
5.1.1 光路校準 38
5.1.2 穿透率校正 39
5.2 材料校正 39
六、 實驗結果與討論 42
6.1 系統校正 42
6.1.1 試片表面傾斜造成穿透率量測誤差之量化分析 42
6.1.2 試片表面特性造成穿透率差異之修正 44
6.2 材料校正 44
6.2.1 各厚度玻璃試片sine函數擬合情形及TELE 44
6.2.2 不同厚度玻璃試片TELE之比例關係 46
6.3 計算應力與理論應力之比較結果 50
6.3.1 同厚度SQF所求得之應力值比較 51
6.3.2 不同厚度SQF所求得之應力值比較 51
6.4 應用TETOP於高階應力量測結果 52
七、 結論與未來展望 55
7.1 結論 55
7.2 未來展望 58
八、 參考文獻 60
 
表目錄
表3.1平偏兩步相位移之TS方程式 64
表6.1各厚度玻璃試片入射與反射之綠光雷射偏差量 64
表6.2厚度3.97mm玻璃試片於各波長下使用sine函數擬合曲線之RMS差異值 65
表6.3以厚度3.97mm玻璃試片為基準，比較各厚度下 之 及 與厚度比值差異 65
表6.4以厚度3.97mm玻璃試片為基準，比較保留不同應力範圍區間數據以進行sine函數擬合於各厚度下 之 及 與厚度比值差異 66
表6.5以厚度3.97mm玻璃試片為基準，比較移除前面15筆低應力值數據後於各波長下sine函數擬合曲線之RMS差異值 67
表6.6以厚度3.97mm玻璃試片為基準，比較其他厚度玻璃試片 與 之平均差異量 67
表6.7各厚度玻璃試片下 之平均值 67
表6.8各厚度玻璃試片下量測所得與由TELE所推得 值之
平均差異 67
表6.9相同厚度玻璃試片之計算應力與理論應力之平均差異量 68
表6.10不同厚度玻璃試片之計算應力與理論應力之平均差異量 68
表6.11厚度5.80mm PSM-1試片各TELE之 與 數值[6] 68
 
圖目錄
圖3.1 TEToP架構圖 69
圖3.2 PSM-1試片受不同單軸向拉伸負載之TS圖[4] 70
(a)負載0~4Kg
(b)負載5~9Kg
(c)負載10~14Kg
(d)負載14~18Kg
圖3.3 PSM-1試片穿透率對應應力與波長之三維色階圖[4] 72
(a)立體圖
(b)俯視圖
圖3.4玻璃試片 對應應力與波長之三維色階圖[4] 73
(a)立體圖
(b)俯視圖
圖3.5玻璃試片 對應應力與波長之三維色階圖[4] 74
(a)立體圖
(b)俯視圖
圖3.6利用式(14)重建 對應應力與波長之三維色階圖[4] 75
(a)立體圖
(b)俯視圖
圖3.7 TEToP之實驗程序架構圖 76
圖3.8各TELE間之關係示意圖[6] 76
圖3.9模擬TEToP計算應力之示意圖 77
圖3.10應力展開極限範圍內轉換後 、 與 間之規律性 77
圖3.11 模數相位之TPUT演算法之區域歸類流程圖 78
圖3.12 模數相位之TPUT演算法第一步驟中之區域歸類 83
圖3.13 模數相位之TPUT演算法第二步驟中之區域歸類 83
圖3.14 模數相位之TPUT演算法第三步驟中之區域歸類 84
圖4.1玻璃圓盤試片 84
圖4.2實驗架設實景圖 85
圖4.3鹵素光源之光譜分布圖 85
圖4.4綠光雷射模組 86
圖4.5光譜儀實景圖 86
圖4.6徑向負載試驗施載架實景圖 87
圖4.7壓縮夾具實景圖 88
圖5.1光路校準架設示意圖 88
圖6.1使用綠光雷射進行光路校準之實景架構圖 89
圖6.2入射與反射之綠光雷射偏差量測實景圖 89
圖6.3僅放置各厚度玻璃試片之光譜分布圖 90
圖6.4以厚度3.97mm玻璃試片穿透率為比較基準之穿透率
比例因子 90
圖6.5厚度3.97mm玻璃試片TS對應應力與波長之三維色階圖 91
圖6.6厚度3.97mm玻璃試片TS對應應力與波長之二維圖 91
圖6.7厚度2.02mm玻璃試片於各波長下之sine函數擬合曲線 92
(a) 400nm
(b) 450nm
(c) 550nm
(d) 650nm
(e) 750nm
圖6.8厚度2.97mm玻璃試片於各波長下之sine函數擬合曲線 93
(a) 400nm
(b) 450nm
(c) 550nm
(d) 650nm
(e) 750nm
圖6.9厚度3.97mm玻璃試片於各波長下之sine函數擬合曲線 94
(a) 400nm
(b) 450nm
(c) 550nm
(d) 650nm
(e) 750nm
圖6.10厚度6.02mm玻璃試片於各波長下之sine函數擬合曲線 95
(a) 400nm
(b) 450nm
(c) 550nm
(d) 650nm
(e) 750nm
圖6.11各厚度玻璃試片於波長450nm至750nm之TELE 96
(a) 2.02mm
(b) 2.97mm
(c) 3.97mm
(d) 6.02mm
圖6.12各厚度玻璃試片之 及 值 98
(a)
(b)
圖6.13各厚度玻璃試片之 及 值 99
(a)
(b)
圖6.14各厚度玻璃試片實驗結果所得與由TELE所推得之 值 100
圖6.15厚度2.02mm玻璃試片所求得之計算應力與理論應力
比較圖 100
圖6.16厚度2.97mm玻璃試片所求得之計算應力與理論應力
比較圖 101
圖6.17厚度3.97mm玻璃試片所求得之計算應力與理論應力
比較圖 101
圖6.18厚度6.02mm玻璃試片所求得之計算應力與理論應力
比較圖 102
圖6.19厚度5.80mm PSM-1試片於各波長下之sine函數
擬合曲線[6] 103
(a) 400nm
(b) 450nm
(c) 550nm
(d) 650nm
(e) 750nm
圖6.20厚度5.80mm PSM-1試片於波長450nm至750nm
之TELE[6] 104
圖6.21模擬厚度5.80mm PSM-1試片受力時，施加應力對應
應力與波長之三維色階圖 105
(a)立體圖
(b)俯視圖
圖6.22模擬厚度5.80mm PSM-1試片受力時，TEToP計算應力對應應力與波長之三維色階圖 106
(a)立體圖
(b)俯視圖
圖6.23於波長670nm、650nm與630nm下之 、 及 與施加應力關係圖 107
圖6.24以發展之TPUT演算法還原應力值之結果 107
圖6.25於波長690nm、650nm與610nm下之 、 及 與實驗結果經TPUT演算法還原之應力值關係圖 108
圖6.26加入 作為展開依據，於波長690nm、650nm與
610nm下之 、 及 與實驗結果經TPUT演算法還原之應力值關係圖 109

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