目前進行旋轉物體之量測往往需要拍攝兩張照片，其中需要影像定位，追蹤物體初始位置與最後位置，整個量測過程非常耗時且廢工夫，準確度受限於三維量測與影像對位。而條紋投影技術是用於量測三維物體形貌，經由研究發現物體於曝光時間內移動之影像會影響條紋對比度，而模糊條紋可以還原出形貌之外也可進行物體速度之量測
本論文利用條紋投影技術（Fringe Projection Technique）進行旋轉物體的速度量測，突破以往速度量測之方法，避免障礙物干擾或三維影像因視差造成影像對位之瓶頸，只需拍攝一張動態影像，即可藉由模糊條紋與對比度還原物體的三維形貌並計算其移動速度。
本實驗以傅立葉轉換法（Fourier Transform Method）擷取條紋相位，並利用相位展開法（Phase Unwrapping Technique）取得影像每一像素之相位值，成功還原旋轉物體之三維形貌。同時利用影像對比度之差異，將影像灰階圖進行曲線擬合（Curve Fitting），並藉由對比度演算法計算影像對比度以進行旋轉物體之速度量測。

At present, the measurement of rotating objects often requires taking two photos. In the experiment, image positioning is required to track the initial position and final positions of the object. The whole measurement process is very wasteful. The accuracy is limited by the three-dimensional measurement and image alignment. The fringe projection technology is used to measure the shape of a three-dimensional object. According to research, it is found that the image of the object moving during the exposure time will affect the fringe contrast, and the blurred fringe can reconstruction the shape and also measure the velocity of the object.
The experiment proposed in this study was a breakthrough in the previous velocity measurement method to avoid the optical parallax or obstacle. The image can reconstruct the three-dimensional (3D) profile and measure the velocity of the object by using the one-shot method.
In this study, the 3D profile of the object was reconstructed using the Fourier transform method to obtain the phase of the object, and the phase unwrapping technique was used to obtain the phase value of the image. Meanwhile, by using the different contrast of the image, the curve-fitting algorithm was conducted to calculate contrast. The velocity of the object was calculated by using the algorithm of contrast.

論文審定書 i
致謝 ii
摘要 iii
Abstract iv
目錄 v
圖次 vii
表次 xiii
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 4
第二章 文獻回顧與原理 5
2.1 條紋投影技術 6
2.2 三角量測法 9
2.3 相位擷取技術 12
2.3.1 傅立葉轉換 12
2.3.2 相位轉移技術 16
2.4 相位展開演算法 18
2.5 系統校正 20
第三章 實驗方法與推導 22
3.1 研究流程 22
3.2 速度量測 24
第四章 結果與討論 29
4.1 實驗架構與設備 29
4.2 投影機灰階校正 35
4.3 影像對比度分析之方法 36
4.4 三維形貌量測 41
4.4.1 靜態物體之準確度分析 41
4.4.2 動態物體之準確度分析 44
4.4.3 旋轉物體之三維形貌量測 49
4.4.4 誤差分析 53
4.5 速度量測 54
4.5.1 未移動之速度量測 54
4.5.2 橫向平移之速度量測 66
4.5.3 深度位移之速度量測 78
4.5.4 風扇之速度量測 89
4.5.5 單擺之速度量測 95
4.5.6 誤差分析 101
第五章 結論 102
參考文獻 103

[1] C.J. Peach, R.J. Lisle, (1979). “A fortran IV program for the analysis of tectonic strain using deformed elliptical markers,” Computers and Geosciences, 5, 325-334.
[2] M. Radmacher, (1997). “Measuring the elastic properties of biological samples with the AFM,” IEEE Engineering in Medicine and Biology Magazine, 16, 47-57.
[3] B. Zitová, J. Flusser, (2003). “Image registration methods: a survey,” Image and Vision Computing, 21, 977-1000.
[4] O. Monserrat, M. Crosetto, (2008). “Deformation measurement using terrestrial laser scanning data and least squares 3D surface matching,” ISPRS Journal of Photogrammetry and Remote Sensing, 63, 142-154.
[5] A.J. Croxford, P.D. Wilcox, B.W. Drinkwater, P.B. Nagy, (2009). “The use of non-collinear mixing for nonlinear ultrasonic detection of plasticity and fatigue Finite deformations of an elastic solid,” The Journal of the Acoustical Society of America, 126, 117-122.
[6] R. Dandoš, K. Mozdřeň, H. Staňková, (2018). “A new control mark for photogrammetry and its localization from single image using computer vision,” Computer Standards and Interfaces, 56, 41-48.
[7] S. Zhang, (2010). “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Optics and Lasers in Engineering, 48, 149-158.
[8] T. Yang, G. Zhang, H. Li, Z. Zhang, X. Zhou, (2019). “Theoretical proof of parameter optimization for sinusoidal fringe projection profilometry,” Optics and Lasers in Engineering, 123, 37-44.
[9] M.R. Milind, H.S. Warren, (1990). “Accuracy of a laser doppler velocimeter for instantaneous velocity measurements on rotating solid surfaces,” Optical Sensing and Measurement, 70, 98-112.
[10] A. Nakashima, Y. Tuda, C. Liu, Y. Hayakawa, (2010). “A real-time measuring method of translational/rotational velocities of a flying ball,” IFAC Proceedings Volumes, 43, 732-738.
[11] J. Nanzer, (2012). “Interferometric measurement of the angular velocity of moving humans,” Radar Sensor Technology XVI, 8361, 836102.
[12] S.A. Alexandra, T. Vasilis, P.W. Carsten, (2015). “Laser diode self-mixing interferometry for velocity measurements,” Optical Engineering, 54, 1-9.
[13] A. Treven, M. Saje, (2015). “Integrating rotation and angular velocity from curvature,” Advances in Engineering Software, 85, 26-42.
[14] W.T. Co, (2012). “Inspection to 3-D deformation of a dynamic object using fringe projection techniques,” Master Thesis, National Sun Yat-sen University.
[15] S.H. Rowe, W.T. Welford, (1967). “Surface topography of non-optical surfaces by projected interference fringes,” Nature, 216, 786-787.
[16] H. Takasaki, (1970). “Moiré topography,” Applied Optics, 9, 1467-1472.
[17] H. Takasaki, (1973). “Moiré topography,” Applied Optics, 12, 845-850.
[18] S.H. Rowe, (1971). “Projected interference fringes in holographic interferometry,” Journal of the Optical Society of America, 61, 1599-1603.
[19] M. Takeda, H. Ina, S. Kobayashi, (1982). “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” Journal of the Optical Society of America, 72, 156-160.
[20] M. Takeda, K. Mutoh, (1983). “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Applied Optics, 22, 3977-3982.
[21] V. Srinivasan, H.C. Liu, M. Halioua, (1984). “Automated phase-measuring profilometry of 3-D diffuse objects,” Applied Optics, 23, 3105-3108.
[22] J.L. Li, H.J. Su, X.Y. Su, (1997). “Two-frequency grating used in phase-measuring profilometry,” Applied Optics, 36, 277-280.
[23] X. Su, W. Chen, Q. Zhang, Y. Chao, (2001). “Dynamic 3-D shape measurement method based on FTP,” Optics and Lasers in Engineering, 36, 49-64.
[24] Q.Y. Liu, (2008). “3D shape reconstruction using projected fringe profilometry for an image blurred by linear motion,” Master Thesis, National Sun Yat-sen University.
[25] B.C. Huang, (2015). “Projected fringe profilometry techniques using for specular surfaces,” Master Thesis, National Sun Yat-sen University.
[26] S.Y. Chen, (2017). “Design and fabrication of the multi-functional projected fringe profilometry,” Master Thesis, National Sun Yat-sen University.
[27] T.H. Liu, (2020). “Projected fringe profilometry using 2-D fringe pattern for 3-D,” Master Thesis, National Sun Yat-sen University.
[28] W.H. Su, W.T. Co, (2016). “A real-time, full-field, and low-cost velocity sensing approach for linear motion using fringe projection techniques,” Optics and Lasers in Engineering, 81, 11-20.
[29] Y.H. Lo, (2019). “Measurements of three-dimensional expansion coefficients by fringe projection technique,” Master Thesis, National Sun Yat-sen University.
[30] Z. Ji, M.C. Leu, (1989). “Design of optical triangulation devices,” Optics & Laser Technology, 21, 339-341.
[31] H. Guo, G.A. Sitton, C. Burrus, (1998). “The quick Fourier transform: an FFT based on symmetries,” IEEE Trans. Signal Process., 46, 335-341.
[32] X. Su, W. Chen, (2001). “Fourier transform profilometry: a review,” Optics and Lasers in Engineering, 35, 263-284.
[33] S. Zhang, P.S. Huang, (2006). “High-resolution, real-time three-dimensional shape measurement,” Optical Engineering, 45, 1-8.
[34] Y. Liu, Q. Zhang, X. Su, (2015). “3D shape from phase errors by using binary fringe with multi-step phase-shift technique,” Optics and Lasers in Engineering, 74, 22-27.
[35] N.H. Ching, D. Rosenfeld, M. Braun, (1992). “Two-dimensional phase unwrapping using a minimum spanning tree algorithm,” IEEE Transactions on Image Processing, 1, 355-365.
[36] T.J. Flynn, (1997). “Two-dimensional phase unwrapping with minimum weighted discontinuity,” Journal of the Optical Society of America A, 14, 2692-2701.
[37] M. Servin, J.M. Padilla, A. Gonzalez, G. Garnica, (2015). “Temporal phase-unwrapping of static surfaces with 2-sensitivity fringe-patterns,” Optics Express, 23, 15806-15815.
[38] J.M. Huntley, H. Saldner, (1993). “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Applied Optics, 32, 3047-3052.
[39] H. Zhao, W. Chen, Y. Tan, (1994). “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Applied Optics, 33, 4497-4500.
[40] H.O. Saldner, J.M. Huntley, (1997). “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Applied Optics, 36, 2770-2775.
[41] E. Zappa, G. Busca, (2008). “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Optics and Lasers in Engineering, 46, 106-116.
[42] H. Liu, W.H. Su, K. Reichard, S. Yin, (2003). “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Optics Communications, 216, 65-80.
[43] W.H. Su, H. Liu, R. Karl, S. Yin, T.S.Y. Francis, (2003). “Fabrication of digital sinusoidal gratings and precisely controlled diffusive flats and their application to highly accurate projected fringe profilometry,” Optical Engineering, 42, 1730-1740.
[44] H.Y. Ling, (2005). “Data fusion of 3D profiles measured by projected fringe profilometry,” Master Thesis, National Sun Yat-sen University.
[45] W.H. Su, H.S. Huang, N.J. Cheng, (2020). “One-shot profile measurements for a rotating object using Fourier transform profilometry,” Photonic Fiber and Crystal Devices: Advances in Materials and Innovations in Device Applications XIV, 11498.