鏡片加工過程中所產生之殘餘應力可能使鏡片表面形貌發生變化，因此有必要於鏡片製作過程中，進行鏡片殘餘應力之量測。故本研究嘗試開發鏡片軸對稱殘餘應力量測之方法，以做為預先消除殘餘應力並再加工之依據。
積分光彈法(Integrated Photoelasticity)可應用於量測僅存在熱殘餘應力的軸對稱試片之應力分布，然而，中、大型玻璃鏡片均採用傳統加工方式進行鏡片製作，其殘餘應力狀態複雜，無法使用已知之積分光彈法進行量測。因此，本研究運用力平衡之概念開發改良式線性近似積分光彈法(Improved Linear Approximation Integrated Photoelasticity, ILAIP)以及改良式非線性演算之積分光彈法(Improved Nonlinear Algorithm Integrated Photoelasticity, INAIP)計算軸對稱物件之殘餘應力，以適用於殘餘應力狀態複雜之傳統加工鏡片。
本研究初步使用模擬方法探討ILAIP於應力計算上產生之誤差，並進而驗證理論之正確性。本研究進一步使用INAIP進行應力計算以降低ILAIP所產生之誤差，進而提升應力計算上之精度。

The residual stress generated from fabrication processing may cause the lens surface profile deform. Thus, measuring the residual stress of the lens during fabrication processing is needed. In this thesis, a method for measuring axisymmetric residual stress of the lens was proposed so that it is possible to optimize the fabrication parameters to reduce the residual stress of the lens in advance.
Integrated photoelasticity can be used to measure the axisymmetric thermal residual stress in an axisymmetric specimen. However, the axisymmetric residual stress distribution produced by the traditional fabrication methods for the large mirrors is complicated so that the existing integrated photoelastic methods cannot be used. In this thesis, by using the stress equilibrium, improved linear approximation integrated photoelasticity (ILAIP) and improved nonlinear algorithm integrated photoelasticity (INAIP) were presented to calculate the axisymmetric residual stress in general cases.
In this thesis, the calculation error of implementing ILAIP was first investigated by simulation and the applicability of ILAIP was then verified. Furthermore, the calculation error by using the ILAIP can be effectively reduced by using the INAIP.

一、 緒論 1
1.1 研究動機 1
1.2 文獻回顧 4
二、 原理 8
2.1 光彈法 8
2.1.1 應力光學定律[30] 8
2.1.2 瓊斯微積分[32] 9
2.1.3 延遲量與等傾角之計算 11
2.2 積分光彈法 13
2.2.1 線性近似積分光彈法 13
2.2.2 廣義洋蔥剝皮法 16
2.2.3 改良式線性近似積分光彈法 20
2.2.4 改良式非線性演算之積分光彈法 22
三、 模擬流程與規劃 26
3.1 試片之建立與規劃 26
3.2 模擬光彈效應與驗證 32
四、 結果與討論 34
4.1 驗證改良式積分光彈法理論 34
4.1.1 試片1至試片9之模擬結果 34
4.1.2 試片10之模擬結果 35
4.2 ILAIP與INAIP之比較 36
4.2.1 試片10之模擬結果 37
4.2.2 試片11之模擬結果 38
4.2.3 試片12之模擬結果 39
4.3 模擬結果再探討 39
4.4 應力凍結法試片之實驗驗證 41
五、 結論與未來展望 45
5.1 結論 45
5.2 未來展望 46
六、 參考文獻 47

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