臺灣博碩士論文加值系統

本文主要之目的在克服傳統條紋輪廓幾何法(FPP)與傅立葉轉換輪廓量測法(FTP)在高相位梯度處無法準確提取相位之問題。藉由短時傅立葉轉換(STFT)的觀念在原本混雜的頻譜中找到局部的條紋頻率，接著利用反向映射將原本的變形條紋圖像依第一次濾波找到的相位平移至參考面之相對相位的位置上。反向映射後若出現沒有資料的區域則藉Papoulis-Gerchberg演算法(P-G演算法)予以填補。如此將有利於檢查我們在頻率域上濾波所求的相位是否完整，若不完整則再縮小短時傅立葉轉換時所使用的分析窗。反覆此步驟，直到被物體曲面調變的相位全部被消除為止。實驗結果顯示經過反覆的找尋該濾波的位置配合反向映射及P-G演算法的檢查，傳統的FTP法較高頻條紋變化處的相位將有效的被找出並成功還原出物體調變的相位。

The propose of this paper is solving the problem that we can’t extract the precise phase at the high phase gradient when using the traditional Fringe Pattern Profilometry (FPP) and Fourier Transform Profilometry (FTP).With the idea of the Short Time Fourier Transform (STFT), we can find the partial frequency of the fringe in the original, messy spectrum. Using the inverse mapping, the original, deform fringe-pattern could be translated to the relative phase of the reference plane according to the phase of the first filtering.
After the inverse mapping, we can use the Papoulis-Gerchberg algorithm to fill the areas which have no data, so it would help us to examine the precise which are found of the filtering in the frequency domain. If the data is not complete, we could reduce the analysis window which is used in the STFT. Keep repeating this step, until the precise which are modulated by the contour of the surface are eliminated.
The experimental results display the precise which are modulated by the contour of the surface of the high fringe-diversification in the traditional FTP could be find and restore successfully by using the inverse mapping and the P-G algorithm to search the position of the filtering repeatedly.

誌謝 i
摘要 ii
Abstract iii
目錄 iv
圖目錄 vi
表目錄 x
第一章 緒論 1
1-1 前言 1
1-2研究相關文獻 2
1-3 研究動機 4
1-4 研究方法與論文架構 5
第二章 量測系統的相關研究 7
2-1.1 干涉原理 7
2-1.2結構光-條紋結構光 10
2-2 FPP法理論(Fringe Pattern Profilometry) 11
2-3相移法 14
2-3.1 三步相移法 16
2-3.2 四步相移法 17
2-3.3 五步相移法 17
2-4 FTP法(Fourier Transform Profilometry) 18
2-4.1傅立葉轉換基礎 18
2-4.2FTM法(Fourier Transform Method) 21
2-4.3窗函數 24
2-4.4頻率域的濾波 27
2-4.5消除載波頻率 31
2-4.6提取相位 33
2-4.7相位展開 33
2-5 FTP法的限制 36
第三章 改進FTP法理論 38
3-1 短時傅立葉轉換(STFT) 38
3-2 影像幾何轉換 50
3-2.1 正向映射 50
3-2.2 反向映射 51
3-3 消除物體調變相位 53
3-4 P-G演算法 57
3-5 其他影響相位的因素討論 61
3-5.1鏡頭畸變 61
3-5.2過飽和問題 62
第四章 實驗架設與結果 64
4.1實驗設備 64
4.2實驗結果 67
4.2.1 拍攝圖像分析結果 67
4.2.2 模擬圖像分析結果 72
第五章 結論與未來展望 80
結論 80
未來展望 82
參考文獻 84

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