摘要
疊紋法是一種技術發展成熟且常見的變形量測技術，本文將小波理論融入數位疊紋法創造一個新型、可量測在微奈米尺度下的平面內位移以及應變的測量技術。將經由原子力顯微鏡掃描後的試片光柵影像以及由影像處理技術製作的虛擬光柵影像疊合後就會產生疊紋，並可藉由疊紋分析變形的資訊。
但疊合後的疊紋是低對比且存在雜訊，並且會影響實驗分析。所以本文利用具有優良的特徵以及邊緣偵測的能力的小波來解決這個問題。利用二維小波分析，將疊合後的影像過濾就可以得到所須的疊紋並分析其變形，而小波同時具有雜訊過濾的能力，所以可以降低因為實驗過程所造的雜訊以增加實驗的準確性。相位移技法是一種提高疊紋法解析度的技術，本文利用改變虛擬光柵相位的方式達成四步相位移技術以增加本方法的解析度。本文量測BGA (ball grid array) 與高序石墨(HOPG, highly oriented pyrolytic graphite) 表面的熱變形並證明此方法的可行性，並且利用電子束製作高精密度的試片光柵提高疊紋法的解析度。
而疊紋法除了可以量測平面內位移也可以量測平面外的變形，本文將前面量測平面內位移的概念應用到投影疊紋法，將小波以及虛擬光柵應用到投影疊紋法並量測物體平面外變形以及表面輪廓分析，並將實驗值與有限元素法計算結果比較以證明實驗準確性。
本文將實驗所需的基本理論包括數位疊紋法、數位投影疊紋法、小波理論以及相位移法等相關理論都有詳細解說，並藉由實驗證明本文提出方法的可行性。而由實驗的結果可知，本實驗方法具有不錯的準確性且並且較以往的方法更方便且更有效率。

Abstract
Moiré method is a popular and well-developed technique for measuring the displacement fields. In the present study, a novel digital moiré method with wavelet theory is explored to measure the in-plane displacement and strain fields in the micro and nano scale. Moiré patterns are generated by overlapping the images of the specimen grating obtained from atomic force microscopy (AFM) scanning and the virtual reference grating produced by a digital image generating process. The displacement and strain filed can be obtained by analyzed the moiré patterns.
Nevertheless, the resultant moiré image suffers from having low contrast which, if left untreated, might distort the measurement result. Therefore, the wavelet transformation (WT), known for its sharpened abilities of characteristic and edge detection, is employed to capture the target moiré patterns and improve the measurement accuracy. The phase-shifting technique is one of the existing phase-evaluation methods explored to improve the resolution of the moiré method. The proposed method employs the four-step phase-shifting technique to obtain the continuous displacement fields from target moiré patterns. The four-steps phase-shifting method is realized by translating the phase of the virtual reference grating from 0 to 2 . In the present study, the BGA (Ball grid array) and HOPG (Highly oriented pyrolytic graphite) surface are used as the specimen in the in-plane deformation experiments. Also, the high sensitivity specimen grating is made by e-beam to increase the resolution of the digital moiré method.
In the other hand, the similar concept of the digital moiré method is applied in the projection moiré method. The digital projection moiré method with wavelet transformation and phase-shifting technique is applied to measure the out-of-plane deformation and surface topography. The experiment results are compared with these from the finite element method.
In the present study, the principle of the digital moiré method, digital projection moiré method, phase-shifting technology and wavelet theory are described in detail. The proposed method has been carried out in the laboratory. Experimental results have shown that the proposed method is convenient and efficient for the displacement measurement.

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