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研究生: 蘇省任
Su, Sheng Jeng
論文名稱: 具大曲率之反射性表面形貌量測
Measurement of Specular Surface Profile having Large Curvature
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: 2013
畢業學年度: 101
語文別: 中文
論文頁數: 113
中文關鍵詞: 法向量計算方法大曲率反射表面三維形貌幾何校正高解析度
外文關鍵詞: outer normal calculation method, large curvature, specular surface, 3D profile, geometric correction, high resolution
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  • 本文提出一種新的法向量計算方法,利用1.攝影機於兩個位置的鏡心座標,2. 攝影機透過反射面觀察到的螢幕點座標以及3.攝影機的像素在空間中的指向,計算具大曲率反射表面之法向量。並發展出一套量測系統,此量測系統可以計算試件表面之法向量,換算成斜率並積分出物體的三維形貌,文中並利用有限元素法之幾何校正,處理因透視投影導致的試件影像幾何形狀扭曲。
    經由電腦模擬之結果,可知對於拋物面而言,在斜率沒有誤差的情況之下,解析度愈高,則因積分所導致的誤差愈小。若曲線的斜率較小,則因積分所導致的誤差也較小。其中曲線的斜率與待測試件表面有關,因此在量測上應提高解析度以降低積分所導致的誤差。另外對角線的誤差為x方向積分與y方向積分誤差的總和。
    在實驗結果方面, x方向積分的結果比起y方向積分的結果與預期較接近。在y方向積分結果的x方向,發現上下振盪的情況。這些狀況在量測平面鏡與凸面鏡時都有出現。若不先做幾何校正,則可消除形貌上下振盪的情況,然而準確性仍不足。

    In this paper, A novel outer normal calculation method is carried out. Using 1.the positions of the optical center of one CCD camera at two locations, 2.the positions of the screen points observed by the CCD camera through the specular surface and 3.the pointing vectors of the pixels in the CCD camera to calculate the outer normal of a specular surface with large curvature. A measurement system is developed and the outer normal can be calculated. The outer normal then convert into slope and the 3D profile of the surface can be found by integration. In this paper, the geometric correction based on finite element method is also applied to modify distortion images due to projective projection.
    According to the result of computer simulation, for a parabola surface, high resolution would lower the error due to integration method. If the slope of the curve is small, then the error due to integration method is also small. Since the slope of the curve is related to the surface of specimen, the resolution should be enhanced to minimize the error due to integration. Also, the error at the diagonal cross sections is the sum of the error at the x-direction and y-direction.
    In the experiment, the integration at x-direction is closer to expectation than the integration at y-direction. Saw-tooth profile is found at the xz cross section. It happens when measuring the plane mirror and the concave mirror. If we don’t do geometric correction at the first place, the saw-tooth is eliminated, however the precision is still not enough.

    目錄 摘要 I Abstract II 圖目錄 VII 表目錄 XVII 第一章 緒論 1 1-1研究背景 1 1-2研究目的 2 1-3文獻回顧 3 1-4本文架構 3 第二章 法向量計算方法與形貌積分方法 5 2-1法向量計算方法 5 2-2形貌積分方法 11 2-3 法向量計算方法與形貌積分方法之模擬驗證 12 2-3-1 拋物面 12 2-3-2 馬鞍形曲面 22 第三章 實驗系統參數計算 29 3-1攝影機鏡心位置校正方法[11][12] 29 3-2影像平面幾何校正方法 34 3-2-1建立未變形影像與扭曲影像之座標轉換關係[7][13][14] 34 3-2-2應用雙線性內插計算校正後灰階值 43 3-3 液晶螢幕之定位方法 45 3-4 實驗系統架設與系統參數計算 50 3-4-1攝影機鏡心之校正治具 52 3-4-2 幾何校正板 53 3-4-3 計算鏡心位置 54 3-4-4 影像幾何校正參數計算 58 3-4-5 液晶螢幕之定位 62 第四章 量測結果 69 4-1 量測平面鏡 69 4-2 量測凸面鏡 81 4-3 將凸面鏡傾斜後量測 88 4-4 先計算平面鏡形貌再幾何校正 98 4-5 先計算凸面鏡形貌再幾何校正 103 第五章 結論與建議 109 5-1 結論 109 5-2 建議 109 參考文獻 111

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