在光學檢測領域中，對影像中干涉條紋進行相位的演算是還原物體形貌必要的一個程序，其相關的實驗包括了干涉儀、Moiré分析和投影輪廓儀。然而在使用雷射光為光源時，光斑是必然所產生的結果。在本論文中，我們研究了以經驗模態分解法消除雷射光斑的可行性，並發現經過我們發展出來的模式，相位將得以精確地展開，從而還原出更清晰的影像。

Phase-extraction from fringe patterns is an inevitable procedure in many applications, such as interferometry,Moiré analysis, and profilometry using structured light illumination. However, speckle noises could be introduced when a coherent light source is used. In this thesis, we use the empirical mode decomposition (EMD) to perform the speckle-reduction. It is found that phases can be extracted with high accuracy once speckle-reduction is performed with the EMD.

Contents
Page
Abstract………………………………………………………….. I
Contents………………………………………………………..... II
List of Figures…………………………………………………… III
Chapter 1
Introduction…………………………………………………….... 1
Chapter 2
Speckle Noise…………………………………………………… 3
Chapter 3
Signal extraction by the EMD
3.1 Principle of EMD……………………………………….. 5
3.2 Quantitative analysis to speckles in frequency domain… 9
3.3 Simulation of speckle-reduction using EMD…………… 12
3.4 Statistic simulation to speckle removal…………………. 16
Chapter 4
Phase-extraction
4.1 Five-step phase-shifting algorithm……………………... 18
4.2 Phase-extraction from noisy fringe patterns……………. 19
Chapter 5
Experiments: Noise reduction using the EMD
5.1 Experiment setup……………………………………….. 21
5.2 Phase-extraction………………………………………… 23
5.3 Comparison between the EMD and bandpass- filtering
algorithm……………………………………………....... 34
Chapter 6
Conclusion……………………………………………………..... 37
References……………………………………………………….. 38

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