自電子斑點干涉術(ESPI)發展以來，已經在精密量測技術中嶄露頭角，但其影像後處理技術仍待提昇。本論文參照學長賀子能先生所提之正規化處理技巧(normalization skill)，利用三角函數和差化積之運算，消除因雷射光強照射不均所導致斑點相關條紋對比不佳的情況。學生更進一步利用和差化積消除相關條紋高頻項雜訊，使對比更加清晰，如此可省去一般對相關條紋圖濾波所帶來之誤差，經由實驗結果印證，相關條紋對比確實明顯提昇許多。文中也論及過去幾位研究者所提之條紋對比提昇方法，進而與本文所提之方法做比較，驗證本文所提之方法其效果較佳且適應性較傳統濾波方法來得良好。
相位展開技術在後處理過程中更是重要的一環。尤其當處理對象為具有高雜訊，如電子斑點干涉術所得之結果，則相位展開技術必須要更為強健才能展開正確。經過本實驗室多年來的研究，對於高雜訊所造成的不連續現象(inconsistency)已有能力克服之；但對於原始相位本身就存在的不連續現象（例如：剪切平面），基本上比雜訊所造成的不連續現象更加不容易執行相位展開之程序。本論文以Dennis C. Ghiglia和Louis A. Romero在1996年所發表的Minimum LP-Norm Phase Unwrapping為基礎，針對原始相位本身就存在的不連續現象加以克服，並對此相位展開法之缺點，提出『區塊接合』理論，進而改善運算效率且提昇對雜訊之免疫能力。

Electronic speckle pattern interferometry (ESPI) has been used to elucidate the in-plane and out-of-plane displacements of an object. It is a method for measuring the deformation or displacement of the surface of an object by recording at least two speckle patterns, one before and one after the object is deformed. By adding, subtracting or multiplying the speckle patterns, correlation fringe patterns with poor signal to noise ratios are obtained. In general, the contrast of the correlation fringe patterns is enhanced using digital filter methods. However, digital filter methods cannot remove the speckle noise efficiently and sometimes leads to inaccurate digital filtering when the noise is intense. This thesis is based on Zi-Neng He’s thesis (in 2001) and further cooperated with several fringe and image analysis methods to enable the achievement of correlation fringes with excellent contrast. He’s thesis is based on a trigonometric operation to adjust and unify the intensities of all pixels of an interferogram (and is termed as normalization by him.) His method differed from most digital filter methods. An intercomparison of them shows that normalization method outperforms digital filtering method.
In addition, this thesis studies the phase unwrapping technology for ESPI maps with physical shear. In 1996, Dennis C. Ghiglia and Louis A. Romero published the minimum LP-norm 2-D phase unwrapping algorithm to restore the phase surface with real shear. It is unfortunate that the solution could fall if the solution has many local minima. Some of the local minima could be close to an actual global minimum and could thereby yield a solution that is useful for the application at hand. This unfortunate circumstance stems, in part, from the fact that there is no unique global minimum for L0-norm problem. This differs from the uniquely solvable L2-norm problem. Convergence to a local minimum is guaranteed; convergence to a global minimum is not. This disadvantage makes it difficult to analysis the wrapped phase map in ESPI and to obtain the phase distribution correctly. Hence, I propose an innovative method based on the submap-stitching rule and the branch-cut algorithm to circumvent the aforementioned main drawbacks. The computational simulations and experimental implementations of the thesis show the effectiveness of the proposed method.

中文摘要 Ⅰ
Abstract III
致謝 V
目錄 VI
圖目錄 VIII
第一章 緒論 01
1-1 研究動機與研究方向 01
1-2 論文大綱 04
第二章 電子斑點干涉術理論及其相關條紋圖對比提昇技術 05
2-1 實驗架設與原理 05
2-2 相移干涉術之簡介 12
2-3 條紋對比提昇技術之文獻回顧 13
2-4 正規化處理 18
2-5 影像消高頻 22
2-6 濾波與二值化 24
第三章 Minimum LP-Norm相位展開技術及其性能探討 27
3-1 相位展開技術之回顧 27
3-1.1 相位展開技術之基本分類 31
3-1.2 路徑相依型相位展開技術 32
3-1.3 路徑獨立型相位展開技術 34
3-1.4 相位展開過程所遭遇之問題 41
3-2 Minimum LP-Norm相位展開法基本原理 44
3-2.1 連續相位分布之數學式推導 46
3-2.2 不連續相位分布之數學式推導 48
3-3 最小平方相位展開法 51
3-4 加權最小平方相位展開法 53
3-4.1 數學表示式 53
3-4.2 Gauss-Seidel Relaxation Method 56
3-4.3 Picard Iteration Method 56
3-4.4 Preconditioned Conjugate Gradient Method 57
3-5 Minimum L0-Norm相位展開法 60
3-6 Minimum L0-Norm相位展開法性能測試 62
第四章 Minimum L0-Norm結合分支切割及接合技術
之相位展開法及其性能探討 67
第五章 結論與未來展望 88
參考文獻 90

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