本研究針對傳統反射式光彈法用於低應力光學係數之玻璃應力量測之準確性進行探討，並以傳統反射式光彈法所使用之四步相位移法為依據，導入菲涅耳方程式(Fresnel Equations)與司乃耳定律(Snell’s Law)於反射式光彈法之光強方程式中，提出修正型反射式光彈法理論以修正傳統反射式光彈法所忽略之前表面反射光強資訊。
本研究量測施加徑向負載之玻璃圓盤試片主應力差，並計算與理論值之方均根值及平均絕對差異量百分比以驗證所提出之修正理論與程序之正確性及準確度。利用反射式光彈法所得之方均根值及平均絕對差異量百分比於修正前分別為1.7889MPa及36.32%，修正後則降至0.0887MPa及1.51%，與穿透式光彈法所得之方均根值0.0869MPa及平均絕對差異量百分比1.23%比較下已相當接近，因而驗證了本研究所推導之修正型反射式光彈法理論。

By using the traditional reflective photoelasticity based on the four-step phase shifting technique, this research focuses on the accuracy of the stress measurement of glass plates of low stress-optic coefficient. Furthermore, this research combined the Fresnel equations and the Snell’s law into the light intensity of the traditional reflective photoelasticity to derive a correction theory of the light intensity of the traditional reflective photoelasticity. The correction theory includes the reflection light intensity of front surface of the material that the traditional reflective photoelasticity has ignored.
Principal stress differences of circular glass disks under the diametrical compression were measured. To verify the validity and accuracy of the correction theory and the correction procedure, the root mean square difference and average absolute difference percentage between the experimentally obtained and theoretical principal stress difference were calculated. By using the traditional reflective photoelasticity, the root mean square difference and average absolute difference percentage are 1.7889MPa and 36.32%, respectively. When the correction theory was used, the root mean square difference and average absolute difference percentage reduced to 0.0887MPa and 1.51%, respectively. The values are close to those of the root mean square difference and average absolute difference percentage obtained by using the transmission photoelasticity, i.e. 0.0869MPa and 1.23%. Therefore, the validity and accuracy of the correction theory of the reflective photoelasticity were confirmed.

一、 簡介 1
二、 文獻回顧 5
三、 實驗原理 9
3.1 光彈法 9
3.1.1 穿透式光彈法 9
3.1.2 反射式光彈法 12
3.2 相位移光彈理論[4] 13
3.3 四步相位移法對應反射式光彈法之修正 17
3.3.1 電場振幅之反射比及透射比[22] 17
3.3.2 菲涅耳方程式[23] 19
3.3.3 傳統反射式光彈法與修正式反射式光彈法之比較 22
3.3.4 反射式光彈法理論之修正(Correction Theory) 24
3.3.4.1 未受負載之情況 24
3.3.4.2 施加負載之情況 30
3.3.4.3 相位移法於反射式光彈之修正 32
3.3.4.4 相位移法於反射式光彈振幅光強項之計算 37
四、 實驗試片與裝置 40
4.1 實驗試片規劃 40
4.2 實驗裝置 40
五、 實驗量測與分析程序 44
5.1 實驗量測與分析程序 44
5.1.1 實驗量測程序 44
5.1.2 實驗分析程序 45
5.2 主應力差之理論解 48
六、 結果與討論 50
6.1 應力光學係數之量測與驗證 50
6.1.1 應力光學係數之量測 50
6.1.2 應力光學係數之驗證 52
6.2 修正式反射式光彈法理論驗證 53
6.3 穿透式光彈法及反射式光彈法之準確性探討 57
6.4 振幅光強項 59
七、 結論與未來展望 62
7.1 結論 62
7.2 未來展望 64
八、 參考文獻 65

[1] Website : http://www.auo.com/?sn=15&lang=zh-TW
[2] G. H. Kim, W. J. Kim, S. M. Kim, and J. G. Son, “Analysis of Thermo-Physical and Optical Properties of a Diffuser Using PET/PC/PBT Copolymer in LCD Backlight Units,” Display, vol. 26, pp. 37-43, 2005.
[3] 王偉中、宋泊錡、沈明興、洪德恆、朱駿逸，“顯示器玻璃基板殘餘應力與厚度不均與Mura現象間之光測力學探討”，行政院國家科學委員會專題研究計畫期末報告，計畫編號：NSC 102–2221–E007–041，執行期間：2013/08/01~2014/07/31。
[4] 宋泊錡，“檢測材料應力與厚度創新光測力學方法之研究”，國立清華大學動力機械工程學系博士論文，2014。
[5] R. D. Mindlin, “A Review of the Photoelastic Method of Stress Analysis. I,” Journal of Applied Physics, vol. 10, pp. 222-241, 1939.
[6] J. C. Maxwell, “On the Equilibrium of Elastic Solids,” Transactions of the Royal Society of Edinburgh, vol. 20, pp. 87-120, 1853.
[7] E. G. Coker and L. N. G. Filon, “A Treatise on Photoelasticity,” Cambridge University Press, Cambridge, U.S.A., 1931.
[8] M. Mesnager, “Sur la determination optique des tensions interieures dans les solides a trois dimensions,” Comptes Rendus, Paris, vol. 190, pp.1249, 1930.
[9] J. W. Dally and W. F. Riley, “Experimental Stress Analysis,” 3rd ed., McGraw-Hill, New York, U.S.A., 1991.
[10] LF/Z-2 Reflection Polariscope System, PhotoStress® Analysis, Micro-Measurements, Vishay Precision Group, North Carolina, U.S.A.
Website: http://www.vishaypg.com/docs/49913/photostr.pdf
[11] GFP1000-PSA, Stress Photonics Inc., Wisconsin, U.S.A.
Website: http://www.stressphotonics.com/PSA/PSA_Intro.html
[12] K. Ramesh and S. K. Mangal, “Automation of Data Acquisition in Reflection Photoelasticity by Phase Shifting Methodology,” Strain, vol. 33, pp. 95-100, 1997.
[13] K. Bhowmik, “Multiple-Reflection Effects in Photoelastic Stress Analysis”, Applied Optics, vol. 40, pp. 2687-2691, 2001.
[14] R. M. A. Azzam and F. F. Sudradjat, “Reflection Coefficients of P- And S-polarized Light by a Quarter-wave Layer: Explicit Expressions and Application to Beam Splitters”, Applied Optics, vol. 47, pp. 1103-1108, 2008.
[15] 宋泊錡，“光彈參數互相影響問題排除與修正”，國立中興大學機械工程學研究所碩士論文，2009。
[16] F. W. Hecker and B. Morche, “Computer-Aided Measurement of Relative Retardations in Plane Photoelasticity,” Proceedings of the VIIIth International Conference on Experimental Stress Analysis, Amsterdam, Netherlands, pp. 535-542, 1986.
[17] G. M. Brown and J. L. Sullivan, “The Computer-Aided Holophotoelastic Method,” Experimental Mechanics, vol. 30, pp. 135-144, 1990.
[18] S. K. Mangal and K. Ramesh, “Use of Multiple Loads to Extract Continuous Isoclinic Fringes by Phase-Shifting,” Strain, vol. 35, pp. 15-17, 1999.
[19] T. Kihara, “Automatic Whole-Field Measurement of Principal Stress Directions Using Three Wavelengths,” Proceedings of the 10th International Conference on Experimental Mechanics, Lisbon, Portugal, pp. 95-99, 1994.
[20] A. D. Nurse, “Full-Field Automated Photoelasticity by Use of a Three-Wavelength Approach to Phase Stepping,” Applied Optics, vol. 36, pp. 5781-5786, 1997.
[21] K. Ramesh, “Digital Photoelasticity: Advanced Techniques and Applications,” Springer, Berlin, Germany, 2000.
[22] F. L. Pedrotti, L. M. Pedrotti, and L. S. Pedrotti, “Introduction to Optics (3rd Edition),” Addison-Wesley, U.S.A., 2006.
[23] M. Born and E. Wolf, “Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light,” Cambridge University Press, New York, U.S.A., 1999.
[24] 葉玉堂、饒建珍、肖峻，“幾何光學”，台北，五南，2008。
[25] Website: http://www.schott.com/taiwan/chinese/
[26] Website: http://www.itrc.narl.org.tw/
[27] MATLAB Help Handbook, The MathWorks, Inc.
[28] Website: http://www.optimax.com.tw/
[29] Website: http://www.hamamatsu.com/us/en/index.html
[30] Website: http://www.futek.com/
[31] Website: http://www.accusystech.com/
[32] Website: http://www.sbig.com/
[33] Website: http://www.newport.com/
[34] M. M. Frocht, “Photoelasticity,” Wiley, New York, U.S.A., 1984.