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研究生: 李家成
Lee, Chia-Cheng
論文名稱: 單拍陰影疊紋法於表面形貌量測之研究
Surface Profile Measurement by One Shot Shadow Moiré
指導教授: 陳元方
Chen, Terry Yuan-Fang
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: 2017
畢業學年度: 105
語文別: 中文
論文頁數: 124
中文關鍵詞: 陰影疊紋法螺旋正交轉換光流法
外文關鍵詞: Shadow Moiré, spiral phase quadrature transform, optical flow
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  • 本文發展了一套能快速量測物體表面形貌的單拍陰影疊紋法,避免了傳統相位移法在拍攝過程中,試件或系統因加熱或震動產生的變異,所造成量測上的誤差。本文的相位解析法使用螺旋正交轉換與光流法,使用此法最少需兩張不同相位的疊紋圖,為了同時取得兩張疊紋圖,陰影疊紋法的設置可以稍做改變,即在設置中多加一顆LED燈,藉由兩顆不同顏色的LED燈(紅色與綠色)在不同位置同時照向光柵,經彩色CCD相機取像後,即可從相片中分離出兩張不同波長疊紋圖,達到單拍的效果,做完螺旋正交轉換並取得條紋相位後,經由相位展開法展開相位並將相位轉換為高度值,便可得到試件表面形貌。在模擬實驗方面,首先分析光流法在三種條紋(直紋、斜紋、圓形條紋),不同條紋相位變化下,計算條紋方向角的誤差,並由誤差結果分析出適合的光流平滑限制參數(α =1000 or EX 2 + Ey 2),接著以陰影疊紋法理論探討兩張疊紋圖的條紋相位差值,可知條紋相位差與表面高度呈線性關係,與光源入射角呈正切函數關係,由此關係可分析出合適的光源擺放位置 (ØR = tan-1(1- g/2W)),在程式參數與系統設置都確定後,最後模擬三種已知高度曲面(二斜面與一球面)並換算成條紋圖,經條紋相位解析、相位展開並換算高度後,成功重建曲面,模擬結果三種曲面最大高度誤差、高度平均誤差皆不超過1%,誤差標準差皆小於0.01%

    This paper presents a quick surface profile measurement method by means of one shot shadow moiré method. One shot shadow moiré method’s demodulation method uses spiral phase quadrature transform and optical flow, using this method at least needs two different phase moiré images, in order to get two moiré images at same time. Shadow moiré’s set up can be rearranged by adding another light source. Using two LEDs (with green and red peak wavelengths) in different position to illuminate the grating, a polychromatic shadow moiré fringe pattern is produced. Therefore, taking the image of this polychromatic fringe pattern with a RGB CCD camera, two moiré patterns can be capture at same time and attain one shot shadow moiré method’s requirement.

    摘要 I Abstract III 致謝 VI 目錄 VII 圖目錄 X 表目錄 XIII 符號說明 XV 第一章 緒論 1 1.1 研究背景及目的 1 1.2 文獻回顧 2 1.3 本文架構 3 第二章 陰影疊紋法之原理[15] 4 2.1 陰影疊紋法 4 2.2 條紋圖之影像處理 10 第三章 條紋圖之相位解析 14 3.1 里斯轉換(Riesz transform) 15 3.1.1 螺旋相位(Spiral phase) 16 3.2 條紋方向角(Fringe orientation angle) 18 3.3 螺旋正交轉換(Spiral phase quadrature transform) 20 3.4 光流法原理 25 3.4.1 亮度守恆方程式 25 3.4.2 光流平滑限制(Optical flow smoothness constraint) 28 3.5 Macy相位展開法[20] 33 3.6 條紋方向角(β)對相位的影響 34 第四章 干涉條紋模擬分析與討論 36 4.1 光流法於條紋圖之分析 36 4.1.1 斜紋分析 42 4.1.2 圓形條紋分析 47 4.2 光源入射角於條紋圖之分析 58 4.3 條紋方向角與螺旋正交轉換分析 63 4.4 表面形貌模擬分析 68 4.4.1 斜面模擬與分析 69 4.4.2 曲面模擬與分析 74 第五章 結論與未來展望 85 5.1 結論 85 5.2 未來展望與建議 87 參考文獻 88 附錄 90 附錄A 希爾伯特轉換(Hilbert transfom) 90 A.1 希爾伯特轉換之性質與應用[21] 90 A.2 正、餘弦函數之希爾伯特轉換 92 A.3 希爾伯特轉換的傅立葉轉換 96 附錄B 穩態相位法(Stationary Phase Method) 102 B.1 一維穩態相位法概述 102 B.2 二維穩態相位法[22] 105 附錄C 螺旋正交轉換完整推導 113 附錄D Laplacian遮罩[23] 123

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