The Integrated Study of Phase Unwrapping Technology and Its Application(I)

本計畫旨在整合近年來以自有設備能量電子斑點干涉術 (ESPI) 系統及其衍生無論硬體或軟體等相關題材，作一深入的分析與比對以發展相關技術並擴大應用的研究。本二年期計畫第一年將先以電子斑點干涉術取得各種不同型式(包括不同雜訊程度、不同形狀不連續等)的相位圖，以進行各種相位展開技術之特性分析與交叉比較，包括如強健性 (Robustness) 、耗費總時間、法則難易度、適用普遍性等，以建立完整之資料庫，並進而提出最佳化之相位展開法則，供學術及相關產業之用。分析結果更將於計畫第二年應用至動態振動模態振幅重建、合成孔徑雷達 (Synthetic Aperture Radar, SAR) 及MRI (Magnetic Resonance Imaging) 等領域之相位圖展開應用上，個人所知此兩領域的相位圖展開研究與應用，在歐美極受到重視且發展也相當快速，雖說其影像的來源與電子斑點干涉術不同，但無論就其影像的雜訊程度或形貌不連續的情形而言，都將於本計畫第一年時給予測試，因此所發展的相位展開技術，只需稍作調整就可逕行應用到SAR (Synthetic Aperture Radar) 及MRI (Magnetic Resonance Imaging) 等領域之相位圖展開應用上

結合區域型相位展開法及影像處理技術於具形貌不連續相位圖之創新式相位展開法研究

本計畫旨在針對具形貌不連續相位圖的相位展開技術作分析，並擬結合區域型相位展開法及分支切割技術之優點，進而發展出創新式的相位展開法則，以彌補現行唯一可解具形貌不連續相位圖之相位展開技術minimum Lp norm方法所不足之處。區域型相位展開法具有快速處理及全域考量之特性，本計畫擬以其為相位展開核心技術之一，此外，更假以新發展出之相位跳躍偵測技術，並藉由影像處理技術以取得完整乾淨可用的相位跳躍線 (高雜訊所造成的相關問題本研究計畫中將一併克服) ，藉由相位跳躍線不連續點偵測及剪切總量的最小化的最高指導原則下，形貌不連續所在位置可被正確決定，藉此進而進行區域的分割，最後再藉由區域間之搬移判斷與執行，可完成具形貌不連續高雜訊相位圖的相位展開。本計畫所發展之相位展開法擬將應用於解決實驗力學方法中之電子斑點干涉術 (Electronic Speckle Pattern Interferometry, ESPI) 進行具有瑕疵或有裂縫試件實驗時，所取得之具形貌不連續的高雜訊相位圖的相位展開技術需求上作實際的驗證，以確認所發展相位展開法的強健性

具形貌不連續之電子斑點干涉圖的相位展開研究

本計畫旨在針對具形貌不連續 (Physical Discontinuity) 電子斑點干涉術 (ESPI)相關之斑點影像特性參數、斑點相移技術、相位圖之建立機制、斑點條紋影像相關性分析比對、相位展開準則、區塊接合技術及相關之影像後處理等，作深入之比較、探討與研究，並整合目前已發展之技術與系統，以建立電子斑點干涉術相關技術之系統統合技術與分析能量。光電技術之快速發展，促使電子斑點影像干涉術 (ESPI) 展露頭角，然而相關技術之再提昇及斑點條紋圖後處理等問題之克服，尤其是具形貌不連續且高雜訊相位圖之相位還原，更是該領域目前當務之急。本計畫將就其相移、相關條紋分析、相位展開、相位圖濾波至結果呈現，作系統之探討研究以提出解決方法，藉以提昇電子斑點干涉術相關係統之後處理效能。計畫中將以壓電致動器 (PZT) 進行相移，並結合本實驗室所提出之相位自動標定技術及雷射光強調整技術，研究探討如何克服、降低電子斑點干涉系統所遭受環境之干擾，並建立較低相位不一致點相位圖之取得技術。對電子斑點干涉術之相位圖 (wrapped phase map) 而言，因載有極高之斑點雜訊，是故，需要相當強健之相位展開技術 (Phase Unwrapping) 以完成連續相位之重建，本計畫將以2002 年所提出之四篇相位展開論文為基礎，搭配現正發展中之局域可適應相位展開技術，擬建立及提出可逕行對具形貌不連續之電子斑點干涉相位圖相位還原之相位展開技術，以解決目前相關問題所面臨之瓶頸。另外，也擬搭配區域相位展開與接合技術，及結合統計分析，進行形貌不連續相位圖之相位還原工作。此外，本計劃亦將分析與發展以 Discrete Cosine Transform 及 Minimum Norm Method 之相位還原圖進行Rewrap ，再與原相位圖比對，進而修正其錯誤的結果，同時進行與前述發展方法之效能比較

具形貌不連續相位圖之時間域及空間域相位展開法比較研究

The project is aimed at the development of temporal and spatial phase unwrapping technique for phase map with real physical discontinuity. And, specially, it will be aimed at the tunings and adjustments of the two phase-shifted images simultaneously grabbed from two different CCD to overcome the related image distortion and image intensity difference problems.It is known that temporal phase unwrapping is much faster than the more usual spatial phase unwrapping methods, and can be implemented in real-time system. In addition, this method offers an increasing range, handles discontinuities in the object. However, since this method should combine images from different CCD into one single formulation, images distortion and image intensity adjustment problems arise then. In this project, the optical setup is going to be calibrated before the phase-shifted images are grabbed and the image intensity normalization technique is also going to be further applied to minimize the intensity differences between the two grabbed images from different CCD.In this project, spatial phase unwrapping technique is also used for the phase determination of the spatial phase map with physical discontinuity. Since regional phase unwrapping is with the merits of fast processing and global treatment consideration, it is chosen as one of the core techniques herein. In addition, our newly developed phase contours detecting technique and the minimization objective of total phase discontinuity will yield the locations of the real physical discontinuity. Based on the data, the wrapped map can be accordingly segmented and the segments are followed by correct movements between one another to stitch into an unwrapped phase map.Finally, the developed techniques are going to be verified by ESPI experiments on samples with surface defects or cracks. The results from temporal and spatial phase unwrapping technique will be compared to analyze the merits and drawbacks of them.本計畫旨在針對具形貌不連續相位圖的時間域及空間域二種不同方式的相位展開技術作比較分析與研究，並擬針對時間域光學系統中二CCD所取影像於結合時相關之校正與調整等問題進行研究，進而發展出創新式的相位展開法則。時間域相位展開法乃利用單一時刻取得二場以上之干涉條紋圖，藉由三角函數之運算計算出相位資訊，可逕克服空間域相位展開中形貌不連續判斷及處理等問題，唯其分別利用二台CCD同時進行取像，因此必須克服影像對位及光強調整等問題，始得取得正確之相位分佈資訊，計畫中擬以影像校正法及光強正歸化等方法克服相關的問題。本計畫中也擬針對文獻所提最小Lp-Norm方法及本實驗室先前已發展成功之具形貌不連續相位圖之空間域相位展開法，探討它們在形貌不連續相位圖上作一綜合表現比較外，更擬整合這些空間域相位展開法之優點，創新開發以子區塊為單元進行獨立相位展開後，藉由不連續點偵測及剪切總量最小化，形貌不連續所在位置可正確決定，最後再進行整場相位圖縫合之空間域相位展開法。本計畫所發展之相位展開法擬將應用於解決實驗力學方法中之電子斑點干涉術進行具有瑕疵或有裂縫試件實驗時，所取得之具形貌不連續的高雜訊相位圖的相位展開技術需求上作實際的驗證，以確認所發展相位展開法的強健性

Phase Unwrapping Work in Digital Photoelasticity

本計畫旨在針對數位光彈相關技術作一整合性的分析與探討，擬結合時間域及空間域二種相位展開技術，進行光彈主應力角與主應力差等相位資訊的展開，所發展技術並擬應用於靜態與動態的光彈實驗判讀上。光彈乃一全場的量測技術，可同時提供受測體上每一點的主應力角與主應力差資訊，可結合多場相移影像的擷取的方式，再經由反正切函數計算出主應力角與主應力差相位圖，若更結合使用高記憶容量及高運算速度的電腦資料處理能量及彩色、高解析數位相機，數位光彈的應用技術變得極為多樣，處理的能力上也大大地提昇。然而，相位圖的相位展開上面臨了主應力角與主應力差間交互作用所造成相位模糊的問題，目前文獻已提出處理模糊區域的方法有負載步階法、多波長法、影像處理判斷方式等時間域及空間域相位展開方式，本計畫中擬針對這些方法進行比較研究與探討，以提出更簡單有效的方式，擬利用力學特性逕行主應力角的正確相位展開，再以此正確主應力角資訊結合具自我修正能力的主應力差反正切計算公式，求得無模糊區域的相位圖，來進行主應力差資料的還原。最後進行光彈實驗來驗證所提方法的正確性與有效性，並以可瞬時同時取得多場光彈條紋影像的光學架構來進行動態光彈相移影像的擷取，相關光學系統校正調整及多場影像間的相關性處理，計畫中一併探討。Photoelastic stress analysis is a full-field optical technique for experimental stress analysis whose automation has received considerable research attention over the last two decades. Use of phase shifting has revolutionized the acquisition of photoelastic data. In addition, the availability of powerful computers with large memory capacity and colour, high resolution, cameras has made the digital photoelasticity technique with wide variety. However, since digital photoelasticity provides information on principal stress difference (isochomatic) and the orientation of principal stress direction (isoclinic) at every pixel in the stressed domain, a peculiar problem - isoclinic-isochromatic interaction is induced and leads to the so-called ambiguous zone in phase map. Therefore, one critical aspect which still deserves attention in phase shifting photoelasticity is phase unwrapping. To obtain the phase distribution by phase unwrapping, the phase map should be free of ambiguous zones. Various methodologies have been proposed to solve the ambiguity problems of photoelastic phase maps including load stepping, image processing skills, and different wavelengths etc. For obtaining isoclinic and isochromatic parameters many techniques are available. Among these techniques, the six-step phase shifting technique based on a circular polariscope arrangement is widely accepted and used for its simplicity and accuracy. Plane polariscope, however, is the simplest setup for isoclinic and isochromatic parameters extraction. Elliptical polariscope is used for the minimization of the dispersion of the wave plate under illumination of different wavelengths. The intercomparison between them, including easiness of individual setup, factors that affect quality of map, and noise reduction of calculated phase map, will be analyzed in details in the work. The sequential collection of the phase stepping photoelasticity grams has limited the application to only static analysis. Thus, the work herein will capture in real-time all the information needed to produce full-field maps of isochomatic fringe order and isoclinic angle and deal with the optical alignment of four phase shifted beams and the calibration of simultaneous grabbed images for the correct determination of photoelasticity parameters