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研究生： 翁精鋒
Weng, Jing-Feng
論文名稱： 雜訊偵測演算法應用於高度不連續物體之相位圖
New Noise Detection Scheme for Noisy Phase Map of Objects Containing Height Discontinuities
指導教授： 羅裕龍
Lo, Yu-Lung
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2009
畢業學年度： 97
語文別： 英文
論文頁數： 89
中文關鍵詞： 濾波法 、系統雜訊移除 、相位解纏繞 、相位重建
外文關鍵詞： Phase unwrapping, Noise, algorithms and filters, Image recognition
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    • CCD擷取影像應用於干涉量測已是相當常見的技術，量測範圍大至衛星量測，小至奈微米等級量測，特別是在奈微米等級，高度不連續的三維形貌物體，在相位解纏繞演算法(phase unwrapping algorithm)中是相當困難的問題。原因在於CCD鏡頭在高度不連續處拍攝結果容易模糊不清，模糊的原因除了儀器的好壞與CCD的解析度有影響外，最大原因是繞射極限的限制。根據五步相移演算法，使用CCD擷取五張干涉圖形後，經演算重建後可得相位圖(wrapped phase map)，此時，干涉圖中影像在高度不連續處會模糊，經演算重建後會轉換成雜訊。除此之外，光斑雜訊(speckle noise)、殘留雜訊(residual noise)也是相當常見的雜訊。為了解決這三種雜訊，本論文提出“雜訊偵測演算法”能夠有效且同時地偵測到這三種雜訊。一般來說，在相位圖(wrapped phase map)被執行相位展開演算法之前，會執行線性濾波演算法(linear filtering algorithm)，將干涉圖形中的雜訊移除，避免雜訊影響相位展開的結果。不幸的，除了雜訊因線性濾波法而平滑達到移除的目的外，相位遷躍處(phase jump)也會因線性濾波法而平滑。平滑的相位遷躍處代表誤差。本論文提出的雜訊偵測演算法可以準確分辨出雜訊與相位遷躍處的位置，這個優點易於應用在濾波演算法與相位展開法之中。應用於濾波演算法中，能濾除雜訊同時保留相位遷躍；應用於相位展開法之中，能避開雜訊而使相位展開演算法成功。

    In the wrapped phase map of the 3D object containing the height discontinuities, this paper develops an enhanced noise detection scheme to enable the three types of noise, the speckle noise, the residual noise, and the noise at the lateral surface of height discontinuities, to be efficiently and simultaneously detected with a greater degree of precision. Since any threshold of this scheme is related to the number of noise and does not influence the phase jumps, the application with filtering operations enables the edges of the phase jumps without smearing and the application with the phase unwrapping algorithms enables the unwrapping path to avoid the positions of the noise, especially, at the height discontinuities.

    Abstract I 中文摘要 II List of Table VI List of Figure VII Symbols X CHAPTER 1 Introduction 1 1.1 Preface 1 1.2 Reviewers and Key Subject of this Study 3 1.3 Overview of Chapters 6 1.4 Software for This Study 7 CHAPTER 2 Theories of Interference and Phase-shifting Algorithms 8 2.1 Theory of Interference 8 2.2 Common Phase-shifting Algorithms 13 2.2.1 Three-frame Phase-shifting Algorithm 14 2.2.2 Four-frame Phase-shifting Algorithm 15 2.2.3 Carre’ Algorithm 15 2.2.4 Five-frame Phase-shifting Algorithm 16 2.3 Phase Reconstruction Technique 19 2.4 Simulation Results 20 CHAPTER3 Basic Phase Unwrapping Algorithms 23 3.1. Two Typical Wrapped Phase Maps for this Chapter 24 3.2. MACY Algorithm, Path-dependent Algorithm 29 3.2.1 Theory of MACY Algorithm 29 3.2.2 Simulation Results of MACY Algorithm 31 3.3. CA Algorithm, Path-independent Algorithm 34 3.3.1 Theory of CA Algorithm 35 3.3.2 Two Dimensional Simulation Process 37 3.3.3 Simulation Results of CA Algorithm 40 3.4. Conclusions of Phase Unwrapping Algorithms 42 CHAPTER 4 Filtering Algorithms 44 4.1Noisy-Wrapped Phase Map for this Chapter 45 4.2 Theory of Linear Filter- Convolution 48 4.3 Smoothing Filtering Mask 50 4.3.1 Mean Filter 51 4.3.2 Lowpass Filter 52 4.3.3 Highpass Filter 53 4.3.4 Kernel Filter 53 4.4 Simulation Results for Linear Filters 54 4.5 Unwrapping Results for the Noise-reduced Wrapped Maps 64 CHAPTER 5 Proposed Theory of the Noise Detection Scheme 71 5.1 Theory of Proposed Noise Detection Scheme 72 5.2 Simulation Results 77 5.3 Conclusions 82 Future work 84 References 85 Autobiography 89

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