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姓名	林慶煌(Ching-Huang Lin)  查詢紙本館藏	畢業系所	光電科學與工程學系
論文名稱	疊紋與小波技術於光學系統分析之研究 (Study of Moire Technology and WaveletTransform on Optical Systems Analysis)
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摘要(中)	中文摘要 本論文主要討論結合小波理論與moiré 疊紋技術來評估光學系統。疊紋技術 是用來放大微小量測的一個有效工具。例如應用疊紋效應在光學尺中來取得較佳 精度。另外近年疊紋效應也已廣泛應用在實驗力學中，包括量測表面形變量、分 析應變，求取應力等；而如何從充滿雜訊的影像中擷取有用訊號一直是研究的主 題。小波理論是近年快速發展且已經迅速應用領域的新興學科，應用其同時具有 時間（空間）平移與多尺度分辨率的概念，是一種更有效的訊號分析、處理工具； 首先我們將利用小波優越的濾波能力應用在鏡片聚焦長度量測分析上，實驗 選用長直條紋黑白相間的線條為物，透過待測透鏡後這些條紋將成像在CCD 感 測器矩陣像素上，兩組平行條紋疊加時、因條紋間距有些微差距時會時將形成另 一組平行的moire 條紋(此moire 條紋可視為兩組有稍微節距差距但平行的條紋 構成)。本實驗適當選取條紋寬度與物距來取得moiré 影像，再選用Mexican hat 小波函數來進行去除背景雜訊的工作；與其他方法比較：本方法結合疊紋與小波 技術具有裝置簡單，分析準確，容易操作等優點實驗經證明可提高測量精度，具 有工業實用之價值。 一般的鏡片像差量測乃是利用相干光源之干涉儀取得干涉條紋圖，再以多項 式函數來擬合干涉圖數據以取得像差係數；本論文提出以小波為基底來分析干涉 圖數據並取得像差係數，經數值模擬證明可運用在疊紋偏折術中並對雜訊抵抗能 力優於多項式擬合法，是一個分析準確，容易操作的方法。 其次我們應用另一類moire 條紋(因兩組平行條紋相對旋轉角度而產生的疊 紋)來解決＂如何精確判別三片LCD panels 與x-cube 晶體未對準良好的角 度” ；這是LCD 投影機組裝自動化的關鍵過程也是決定投影機畫質的主要因素。 已知將兩組平行條紋傾斜一角度交會時、會形成另一組新的條紋，利用此moiré 條紋可推算兩組平行條紋的交角。我們設定不同色光的直條紋線條由兩個不同 LCD panel 投射到參考螢幕上，另一組新的moiré 條紋將形成，條紋交角大小對 應到LCD panel 是否校正完全；只要能精確估算moiré 條紋間距則交角大小推算 越精確。本實驗對校正良好的panel 以旋轉0.3 度到10 度6 個不同角度來模擬 組裝不良時情形，以CCD 攝影機拍攝形成的moiré 影像，再利用小波之多分辨率 分析技術將疊紋影像按不同頻區進而分析所擷取疊紋的間距，實驗結果顯示在 iii 度以上皆能準確估算(誤差低於1.7%)，而在0.3 度時亦只有6.7%之誤差。顯然 本實驗決定傾斜角度的方法具有裝置簡單、分析準確、容易操作，數據將可進一 步提供工業自動化時採用。 本論文分別運用小波理論中之小波轉換、多分辨分析、小波級數，在不同形 態的moiré 條紋分析上，包括平行條紋的拍頻（beat）、及疊紋偏折術、斜向交 會等不同形態的疊紋分析上。在拍頻疊紋上：Mexican hat 小波轉換成功的降低 透鏡影像的雜訊，成功提出新的聚焦長度量測方法；用數值的方式來模擬疊紋偏 折儀所量測包含譟訊的透鏡干涉條紋，再以Morlet 小波為基底進行像差係數擬 合。結果顯示回復之係數皆能可接受之誤差範圍；其次小波多分辨解析簡化了 分析斜向交會的moiré 條紋的過程。且準確估算出LCD 投影器偏差角度，可作為 建立自動化量測暨調教的基準；最後。綜合上述可知配合小波與疊紋技術是非常 合適於光學系統的評估上，進一步研究發展是可期待的
摘要(英)	Moiré technology has been proven to be an excellent non-destructive method of experimental mechanics for contour mapping or surface topography in recent years. Wavelet transformation has been known as a novel tool for signal processing (or the image data analysis) since the late of 1980s. Appling wavelet analysis on moiré fringes analysis in modern optical system to measure the optical parameters was explored in this dissertation. In this study, different wavelets (i.e. the Mexican hat wavelet, the Daubaches’ wavelet, the Harr wavelet, and the Morlet wavelet) are chosen under the requirement for analyzing different types of moiré patterns. The Mexican hat wavelet is the one used to filter out the noise in moiré fringes for focal length measurement of lens. The image of a Ronchi ruling (i.e. a grating) arranged in front of the lens under test is superimposed with pixel arrays of the CCD camera, a moiré pattern on CCD camera formed and captured into computer for further processing. Since the pitch of the grating image depending on the power of the testing lens, the power of testing lens can be determined by the moiré fringe changes without or with testing lens. The experimental data show that this new method is simple and reliable for focal length measurement. Moiré deflectometry provides the lateral gradients of the optical path difference and is suitable for analysis of phase objects. The Morlet and Harr wavelets are respectively proposed to act as bases to reconstruct the phase functions form the fringes which are superposition of wave front of lens under test and it’s shearing. In moiré deflectometry, two matched transmitting gratings placed apart from each other are used, and the lens under test is placed before the gratings in the path of collimated beam. Numerical simulations are conducted in the wave front determination of optical lens with Seidel aberrations. Thirdly, wavelet analysis is used to improve the accuracy of the alignment angle between LCD panels and x-cubes in the of LCD projector arrangement processes which is the bottle neck for automatic alignment. Two straight parallel gratings are projected from different panels, and moiré patterns would be observed when panels are aligned properly. We find that Daubaches’ wavelet transformation with muti-resolution analysis is a lucid and reliable methodology to analyze the pitches of moiré patterns on the screen for estimating the angle of misalignment. From the study for the focal length measurement using moiré technology with wavelet, the setup is simpler than other methods based on interferometry, and the accuracy is compatible with theirs. The technology developed in finding the misaligned angle of LCD panels is adaptable for automatic control system in the assembly line. The Seidel aberration determination by wavelet bases is proved more stable than other polynomials. Hence, the combination of wavelet and moiré techniques in optical system metrology is promising and shows fully potential in the application of modern optical system
關鍵字(中)	★ 疊紋 ★ 小波	關鍵字(英)	★ moire ★ wavelet
論文目次	TABLE OF CONTENTS 中文摘要 ACKNOWLEDGMENTS……………………………………………….i ABSTRACT……………………………………………………………iv TABLE OF CONTENTS…………………………………………….…vi LIST OF FIGURES……………………………………………………viii LIST OF TABLES………………………………………………………ix NOTATIONS AND ABBREVIATIONS…………………………………x Chapter 1. Introduction ………………………………………………….1 1.1 Introduction………………………………...………………………...1 1.2 Research objective…………………………….…………………………2 1.3 Thesis organization………………………………..………………………3 Chapter 2. Moire Technology……………………………………………4 2.1 Moiré phenomena………………………………...………………………...4 2.2 Moire theory…………………………….…………………………………..5 Chapter 3. Wavelet Analysis……………………………………………9 3.1 Wavelet theory………………………………………………………………9 3.2 Discrete wavelet transform………………………………………………12 3.3 Wavelet series……………………………………………………………13 3.4 Mutiresolution analysis……………………………………………………14 3.5 Two dimensional wavelet decomposition algorithm……………………18 Chapter 4. Focal Length Measurement with Wavelet Transform………22 4.1 Introducton………………………………………………………………22 4.2 Theory……………………….……………………………………………22 4.3 Experimental setups and results…………………………………………27 4.4 Discussion and Conclusions………………………………………………28 Chapter 5. Wavefront Reconstruction on Moire Deflectometry………35 5.1 Introduction……………….……………………………………………….34 5.2 Moiré deflectometry….……………………………………………………37 5.3 Shearing interferometry…………….……………………………………42 5.4 Aberration coefficients by the least squares method………………………45 5.5 Aberration coefficients by continuous wavelet transform…………….…47 5.6 Computational simulation and results………………….…………………50 5.7 Discussion and conclusions………………………………………………51 Chapter 6 LCD Projector Alignment with Wavelet Analysis…………..64 6.1 Introduction………………………………………………………………64 6.2 Theory……………………………………………………………………64 6.3 Experimental Setups…….…………………………………………………67 6.4 Results and Conclusions….………………………………………………68 Chapter 7. Conclusions and Future Research Directions………………83 References………………………………………………………………84 Appendix………………………………………………………………95 Publication List…………………………………………………………101
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指導教授	張榮森(Rong-Seng Chang)	審核日期	2005-7-22
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