在光學量測系統中，條紋投影輪廓儀(Projected Fringe Profilometry)在量測物體時具有不直接與待測物體接觸、快速擷取所需影像資訊、不易受環境干擾…等優點，常被運用在量測物體之表面形貌檢測。然而，在擷取並轉換不連續相位資訊為連續相位時，過程中常面臨對於待測物邊緣、顏色變化落差很大以及深度方向的斷層現象等因素，都容易產生誤判的問題。
本研究發現，在量測動態物體常使用傅立葉轉換法(FFT)擷取相位。雖然僅需拍攝一張影像即可獲取相位資訊，但為達到更高精準度的量測結果，常需要使用相位移轉技術。然而，該技術又需要拍攝多張照片，不適用於量測動態物體。因此，本研究提出了一種新的量測方法，利用彩色RGB條紋光柵圖結合條紋投影輪廓儀進行，可同時達到高精準度與量測動態物體的效果，並能還原出物體的三維形貌。
本研究中，設計了一種彩色RGB條紋圖進行條紋投影的方法，利用不同灰階值的區別，將其拆解成純紅色、純綠色和純藍色三張不同的影像，用於進行相位移轉技術的計算。該條紋投影技術將彩色條紋圖投影到待測物體上，並使用CCD Camera擷取彩色條紋影像數據。最後，利用MATLAB軟體進行條紋圖案的分析和計算，還原待測物體之表面形貌。儘管經過校正後，彩色條紋弦波圖會因不同顏色通道之間的Crosstalk干擾對相位測量造成誤差，但由於每個彩色條紋投影所產生的相位分布在校正系統範圍內都會有相似的影響程度，因此即使存在誤差，解析出來的相位值仍然能夠得到物體相對應的真實座標值，並可達到高達250 μm的精確值。

In optical measurement systems, Projected Fringe Profilometry, a technique that does not directly contact the test object, quickly captures the required image information, and is resistant to environmental interference, is commonly employed for surface topography inspection of objects. However, during the process of extracting and converting discontinuous phase information into continuous phase, challenges often arise due to factors such as significant variations in the edges of the test object, color changes, and depth-related discontinuities. These factors can potentially lead to misinterpretation issues.
This study has discovered that Fourier Transform (FFT) is commonly used for phase extraction in dynamic object measurements. While it only requires capturing a single image to obtain phase information, phase-shifting techniques are often employed to achieve higher measurement accuracy. However, these techniques typically involve capturing multiple images and are not suitable for measuring dynamic objects. Therefore, this study proposes a novel measurement method that combines color RGB fringe patterns with Projected Fringe Profilometry. This approach allows for high accuracy and measurement of dynamic objects while enabling the reconstruction of the object's three-dimensional surface morphology.
This study devised a method for projecting color RGB fringe patterns, utilizing distinct grayscale values to decompose the pattern into three separate images: pure red, pure green, and pure blue. These images are then used for phase-shifting calculations. The color fringe projection technique involves projecting the color fringe pattern onto the object under test and capturing the color fringe images using a CCD camera. Finally, MATLAB software is employed for analyzing and computing the fringe patterns, thus reconstructing the surface morphology of the object under test. Despite potential errors introduced by crosstalk interference between different color channels in the calibrated color fringe patterns, the phase values obtained can still correspond to the object's true coordinates with high precision, reaching up to 250 μm.

論文審定書 i
公開授權書 ii
致謝 iii
摘要 iv
Abstract v
目錄 vii
圖次 ix
表次 xiii
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 4
1.3 研究動機與目的 6
1.4 論文架構 8
第二章 條紋投影輪廓移 9
2.1 條紋投影技術 9
2.2 相位擷取技術 14
2.2.1 傅立葉轉換 16
2.2.2 相位轉移技術 (三步相位移) 18
2.3 相位展開技術及演算法 21
第三章 實驗方法與推導 25
3.1 彩色條紋圖案之設計 25
3.2 白紙之RGB灰階分佈 32
3.3 彩色條紋圖案之實驗 35
3.4 彩色條紋圖案之系統校正 40
3.5 待測物RGB顏色分佈之分析 44
第四章 研究與討論 47
4.1 實驗裝置與儀器設備 47
4.2 RGB顏色之間互相干擾Crosstalk 54
4.3 精確值分析 61
4.3.1 貼有白紙的平整鋼板之精確值分析 62
4.4 白色待測物體之三維形貌量測 69
4.4.1 幾何物體之三維形貌量測 70
4.4.2 紙盤子之三維形貌量測 76
4.4.3 花朵盤子之三維形貌量測 81
4.4.4 手模型之三維形貌量測 86
4.5 待測物表面顏色不為白色之分析 90
4.5.1 牛皮紙袋之RGB灰階分佈 90
4.5.2 牛皮紙袋之三維形貌還原 93
第五章 結論 97
參考文獻 99
附錄 104

[1] F. Chen, G. M. Brown, and M. M. Song, "Overview of three-dimensional shape measurement using optical methods," Optical Engineering, Review vol. 39, no. 1, pp. 10-22, Jan 2000.
[2] Z. H. Zhang, "Review of single-shot 3d shape measurement by phase calculation-based fringe projection techniques," Optics and Lasers in Engineering, Review vol. 50, no. 8, pp. 1097-1106, Aug 2012.
[3] CJ Peach and Richard John Lisle, "A fortran iv program for the analysis of tectonic strain using deformed elliptical markers," Computers & Geosciences, vol. 5, no. 3-4, pp. 325-334, 1979.
[4] 黃懷萱, "利用條紋投影技術進行旋轉物體之三維形貌與切線速度量測," 材料與光電科學學系研究所, 國立中山大學, 高雄市, 2021.
[5] SH Rowe and WT Welford, "Surface topography of non-optical surfaces by projected interference fringes," Nature, vol. 216, no. 5117, pp. 786-787, 1967.
[6] H. Takasaki, "Moiré topography," Applied Optics, vol. 9, no. 6, pp. 1467-1472, 1970/06/01 1970.
[7] S. H. Rowe, "Projected interference fringes in holographic interferometry," Journal of the Optical Society of America, Article vol. 61, no. 12, pp. 1599-&, 1971.
[8] Charles Dyer Martin DeGroot, Peter Kovesi, "Additional temporal projections by structured-light encoding," Optical Engineering, pp. 953-961, Dec 1981.
[9] M. Takeda, H. Ina, and S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," Journal of the Optical Society of America, Article vol. 72, no. 1, pp. 156-160, 1982.
[10] V. Srinivasan, H. C. Liu, and M. Halioua, "Automated phase-measuring profilometry of 3-d diffuse objects," Applied Optics, Article vol. 23, no. 18, pp. 3105-3108, 1984.
[11] V. Srinivasan, H. C. Liu, and M. Halioua, "Automated phase-measuring profilometry - a phase mapping approach," Applied Optics, Article vol. 24, no. 2, pp. 185-188, 1985.
[12] X. Y. Su, W. S. Zhou, G. Vonbally, and D. Vukicevic, "Automated phase-measuring profilometry using defocused projection of a ronchi grating," Optics Communications, Article vol. 94, no. 6, pp. 561-573, Dec 1992.
[13] Satoru Toyooka and Yuuji Iwaasa, "Automatic profilometry of 3-d diffuse objects by spatial phase detection," Applied Optics, vol. 25, no. 10, pp. 1630-1633, 1986.
[14] Katherine Creath, "V phase-measurement interferometry techniques," in Progress in optics, vol. 26: Elsevier, 1988, pp. 349-393.
[15] J. L. Li, H. J. Su, and X. Y. Su, "Two-frequency grating used in phase-measuring profilometry," Applied Optics, Article vol. 36, no. 1, pp. 277-280, Jan 1997.
[16] Joaquim Salvi, Jordi Pages, and Joan Batlle, "Pattern codification strategies in structured light systems," Pattern recognition, vol. 37, no. 4, pp. 827-849, 2004.
[17] Hui Jun Chen, Jue Zhang, and Jing Fang, "Surface height retrieval based on fringe shifting of color-encoded structured light pattern," Optics Letters, vol. 33, no. 16, pp. 1801-1803, 2008.
[18] 顏睿賢, "量測光滑物體三維形貌之光學系統," 材料與光電科學學系研究所, 國立中山大學, 高雄市, 2022.
[19] Hongyu Liu, Wei-Hung Su, Karl Reichard, and Shizhuo Yin, "Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3d surface profile measurement," Optics Communications, vol. 216, no. 1-3, pp. 65-80, 2003.
[20] 劉子翔, "條紋投影輪廓儀搭配二維弦狀圖案進行三維形貌量測," 材料與光電科學學系研究所, 國立中山大學, 高雄市, 2020.
[21] C. Zuo, S. J. Feng, L. Huang, T. Y. Tao, W. Yin, and Q. Chen, "Phase shifting algorithms for fringe projection profilometry: A review," Optics and Lasers in Engineering, Review vol. 109, pp. 23-59, Oct 2018.
[22] M. Takeda and K. Mutoh, "Fourier-transform profilometry for the automatic-measurement of 3-d object shapes," Applied Optics, Article vol. 22, no. 24, pp. 3977-3982, 1983.
[23] 郭崇銘, "利用條紋投影技術進行加熱物表溫度分佈之量測," 材料與光電科學學系研究所, 國立中山大學, 高雄市, 2022.
[24] Haitao Guo, G. A. Sitton, and C. Burrus, "The quick fourier transform: An fft based on symmetries," IEEE Trans. Signal Process., vol. 46, pp. 335-341, 1998.
[25] Yasuhiro Awatsuji, Atsushi Fujii, Toshihiro Kubota, and Osamu Matoba, "Parallel three-step phase-shifting digital holography," Applied Optics, vol. 45, no. 13, pp. 2995-3002, 2006.
[26] David W Robinson, Graeme T Reid, and Peter De Groot, "Interferogram analysis: Digital fringe pattern measurement techniques," Physics Today, vol. 47, no. 8, p. 66, 1994.
[27] Christopher Waddington and Jonathan Kofman, "Saturation avoidance by adaptive fringe projection in phase-shifting 3d surface-shape measurement," in 2010 international symposium on optomechatronic technologies, 2010: IEEE, pp. 1-4.
[28] W. H. Su, "Color-encoded fringe projection for 3d shape measurements," Optics Express, Article vol. 15, no. 20, pp. 13167-13181, Oct 2007.
[29] Jason Geng, "Structured-light 3d surface imaging: A tutorial," Advances in Optics and Photonics, vol. 3, no. 2, pp. 128-160, 2011.
[30] Yang Fujun Dai Meiling, "Three-dimensional shape measurement based on single-shot color fringe projection of sinusoidal grating," Acta Optica Sinica, vol. 31, no. 7, p. 0712002, 2011.
[31] X. Y. Su, W. J. Chen, Q. C. Zhang, and Y. P. Chao, "Dynamic 3-d shape measurement method based on ftp," Optics and Lasers in Engineering, Article vol. 36, no. 1, pp. 49-64, Jul 2001.
[32] 劉僑原, "利用條紋投影法進行快速移動物體之瞬間形貌量測技術," 光電工程研究所, 國立中山大學, 高雄市, 2008.
[33] X. Y. Su and Q. C. Zhang, "Dynamic 3-d shape measurement method: A review," Optics and Lasers in Engineering, Review vol. 48, no. 2, pp. 191-204, Feb 2010.
[34] M. R. Luo and B. Cui, "Crosstalk between color channels in a display system," Optical Society of America A, vol. 27, no. 5, pp. 918-921, 2010.
[35] Z. H. Zhang, C. E. Towers, and D. P. Towers, "Time efficient color fringe projection system for 3d shape and color using optimum 3-frequency selection," Optics Express, Article vol. 14, no. 14, pp. 6444-6455, Jul 2006.
[36] C. A. Bouman F. Zheng, and M. A. Neifeld, "Crosstalk mitigation in multi-channel imaging systems using low-rank matrix approximation," Optics Express, vol. 22, no. 17, pp. 19961-19976, 2014.