The Application of Optical Phase Unwrapping on a Vibrating Plate

光學量測技術擁有高精密度和非接觸式的優點，並可應用於快速檢測的系統上，故本文利用此優點和延續本實驗室張淑華博士之研究，進行光學相位重建對於平板振動模態應用之研究，並確認光學相位重建之準確度。 本文使用共光路之橫向剪切干涉術，共光路架構可減低環境干擾之影響，在得到干涉條紋圖後，配合相移干涉術和平行性2π相位重建法還原平板振動模態的正確分佈，以期達到只須經由實驗而不需經由軟體模擬即可求出整場的模態趨勢。為了得到較佳的重建模態，故本文加入數位影像處理之技術，利用強度轉換得到光分佈較平均之干涉條紋圖，和使用傅立葉轉換濾波得到較平滑的模態重建圖，並針對平行性2π相位重建法之遮罩進行改良，比較其收斂型遮罩和發散型遮罩在不同雜訊下重建的狀況，其中又以收斂型遮罩對邊界雜訊的處理效果良好。 近年來台灣光學產業發展快速，本文之研究，期待可使本實驗室之光學量測系統，更加趨於完備，建立起快速且高準確度之光學量測系統。The optical measurement has the merits of high-resolution and non-contact, and can also be applied to the system of fast-inspection. Therefore, this study uses the above advantages to continue the research about the earlier study of Dr. Shu-Hua Chang in the acoustic laboratory. We make the study in progress on the application of optical phase unwrapping to the vibrational mode on plates, and further confirm its precision. To greatly reduce the influence by the interference from environment, the lateral shearing interferometry of common optical path is used for this study. After getting interferometric fringe patterns, phase shifting interferometry and parallel 2π phase unwrapping are used to reconstruct the correct shapes of vibrational mode on plate in order to obtain the full-field mode shapes without the simulation of software. In order to obtain a better reconstruction of mode, the technique of digital image processing is used in this paper. Using the transformation of intensity can obtain the interferometric fringe patterns with much uniform light distribut and using Fourier transform filter to obtain more smooth image of reconstructed mode. Furthemore, it is to improve the mask of parallel 2π phase unwrapping for the convergent mask and the divergent mask, and to make comparison between them for various noises. Recently, industry in optics grows fastly in Taiwan. It is to be expected that the study of this paper can make the system of optical measurement in the acoustic laboratory to become more complete with quickly picking up characteristics and high-accuracy.誌謝 Ⅰ文摘要 Ⅱ文摘要 Ⅲ錄 Ⅴ目錄 Ⅶ一章 緒論 1-1 研究動機與方向 1-2 文獻回顧 2-3 論文大綱 7二章 橫向剪切干涉術 9-1 光學干涉基本概念 9-2 橫向剪切干涉理論 12-3 剪切元件介紹 16 2-3-1 平行剪影板 16 2-3-2 楔形剪影板 18 2-3-3直角稜鏡剪影板 20三章 相移干涉術 23-1 相移的數學通式 23 3-1-1 三步相移法 24 3-1-2 四步相移法 25-2 相位展開 27四章 相位重建技術 31-1 相位重建之基本概念 31-2細胞自制演算法 33-3細胞自制演算法改良 35-4收斂型遮罩與發散型遮罩 40五章 平板模態理論與數位影像處理技術 43-1 平板的運動分析 43-2 影像強度轉換 48-3 傅立葉轉換濾波影像平滑化 51六章 實驗方法與實驗結果討論 56-1 實驗方法 56 6-1-1 實驗佈置 56 6-1-2 實驗步驟 62-2 實驗結果 67-3 實驗結果討論 75-4 遮罩模擬試驗與結果 76七章 結論與未來展望 81考文獻 8