本文結合螺旋正交轉換與光流法應用於條紋投影法，建構出一套能即時量測的單拍條紋投影表面形貌量測系統，其架設主要是將傳統相位移法中所設置的CCD改為彩色相機，並將傳統投影的黑白條紋改為紅綠相間的彩色條紋，然後透過彩色相機擷取一張彩色條紋影像並取出紅、綠兩種顏色頻道的條紋影像，再利用螺旋正交轉換與光流法計算出相位差90度的條紋影像，進而求得條紋相位，接著透過相位展開法來得到連續相位，最後獲得試件的表面形貌。而本文分為系統分析與實驗兩個部分，在分析的部分是透過投影不同間距之條紋來分析條紋間距對系統量測結果的影響，其結果得知條紋間距越小，均方根誤差(Root-Mean-Square error, RMSE)減少了0.034mm ~ 0.087mm，RMSE百分比減少了0.49% ~ 4.18%。此外，將設置參數、實際條紋間距與量測高度極限值帶入理論中計算，從結果得知上升高度所造成的相位差極限值不到理論的2π，因此計算系統實際量測高度極限值若以2π來計算，則結果會產生錯誤。實驗部分則是量測四組不同試件，並將量測值與SMS-300M與四步相位移條紋投影法之量測值進行比較，來驗證本系統之準確性，結果顯示在量測高度達0.5mm ~ 5mm的試件時，RMSE大約為17μm至55μm；平均絕對誤差(Mean-Absolute error, MAE)大約為13μm至28μm。

In this thesis, we would apply the spiral phase quadrature transform and optical flow method to the fringe projection method to construct the single-shot fringe projection surface profile measurement system which can measure in real time. The experiment could be fulfill by these step: first, change the CCD of phase-shift method to color camera, and the black and white fringe into the red and green one. Second, get a color fringe image by color camera and extracting out the red and green channel fringe images. And then with spiral quadrature transform and optical flow method we could obtain the fringe pattern with a phase difference of 90 degrees. Last, the surface profile of the specimen could be issued from the unwrapping phase and the algorithm of fringe projection method.
This thesis is divided into two parts-- system analysis and experiment. In the former one, we study the impact of pitch on the system measurement results by analyzing the projecting fringe of different pitch. The result reveals that the smaller the pitch, RMSE reduced by 0.034mm ~ 0.087mm, RMSE percentage reduced by 0.49% ~ 4.18%. Furthermore, bring the setting parameters, the actual pitch of fringe and the limit height of measurement into the theory for calculation will show that the phase difference limit value caused by the rising height is less than 2π. That means when calculated the actual measurement height limit value by phase difference 2π, the result will be an error.
For the experiment part, we measured four groups of different specimens, and compared the measured values with the measured values of SMS-300M and four-step-phase-shifting fringe projection method to verify the accuracy of the system. The results show that the root-mean-square error of the specimens with height 0.5mm ~ 5mm is about 17μm to 55μm, and the mean-absolute error is about 13μm to 28μm. The RMSE percentage of the specimens with height 13mm is about 3.6% to 3.8%, and the MAE percentage is about 2.8% to 3.0%.

1. V. Srinivasan, H.C. Liu, and M. Halioua, “Automated Phase-measuring profilometry of 3-D diffuse objects,”Applied Optics, Vol.23, No.18, pp.3105-3108, 1984.
2. Xian-Yu Su, Wen-Sen Zhou, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,”Optics Communication Vol.94, pp.561-573, 1992.
3. C. Quan, X.Y. He, C.F. Wang, C.J. Tay, H.M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,”Optics Communication Vol.189, pp.21-29, 2001.
4. C. Quan, C.J. Tay, X.Y. He, X. Kang, H.M. Shang, “Microscopic surface contouring by fringe projection method,”Optics & Laser Technology Vol.34, pp.547-552, 2002.
5. 張柏毅，“應用條紋投影法及條紋反射法量測物體表面形貌”，國立成功大學機械工程學系碩士論文，2005。
6. 黃奕棠，“高反射性表面形貌之光學量測研究”，國立成功大學機械工程學系碩士論文，2006。
7. L. Chen and X. Nguyen, “Real-time 3-D robot vision employing novel color fringe projection,”4th International Conference on Autonomous Robots and Agents 2009, pp.177-181.
8. M. Dai, F. Yang, and X. He,“Single-shot color fringe projection for three-dimensional shape measurement of objects with discontinuities,”Appl. Opt. 51(12), 2062–2069, 2012.
9. M. Takeda, and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,”Appl. Opt. 22, 3977-3982, 1983.
10. Qian K.M., Wang H.X., Gao W.J., “Windowed Fourier transform for fringe pattern analysis: theoretical analyses,”Appl Opt 2008;47:5408–19.
11. B. Li, Y. An and S. Zhang,“Single-shot absolute 3D shape measurement with Fourier transform profilometry,”Appl. Opt. 55, 5219-5225 (2016).
12. Larkin, K.G., “Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform,”Journal of the Optical Society of America A, 2001. 18(8): p. 1871-1881.
13. Larkin, K.G., D.J. Bone, and M.A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,”Journal of the Optical Society of America A, 2001. 18(8): p. 1862-1870.
14. Vargas, J., Quiroga, J. Antonio., Sorzano, C. O. S., Estrada, J. C. Carazo, J. M., “Two-step interferometry by a regularized optical flow algorithm,”Optics Letters, 2011. 36(17): p. 3485-3487.
15. Du, H., H. Zhao, and B. Li, “Fast phase shifting shadow moiré by utilizing multiple light sources,”in SPIE Advanced Lithography. 2013. International Society for Optics and Photonics.
16. Xu, J., and J. Gao, “Phase Extraction by Spiral Phase Transform in Digital Shearography,”in Fringe 2013: 7th International Workshop on Advanced Optical Imaging and Metrology, W. Osten, Editor. 2014, Springer Berlin Heidelberg: Berlin, Heidelberg. p. 217-220.
17. Y. Lu, R. Li, and R. Lu, “Fast demodulation of pattern images by spiral phase transform in structured-illumination reflectance imaging for detection of bruises in apples,”Computers and Electronics in Agriculture, 127 (2016), pp. 652-658.
18. 李家成，“單拍陰影疊紋法於表面形貌之量測之研究”，國立成功大學機械工程學系碩士論文，2017。
19. 程法彥，“單拍陰影疊紋表面形貌量測系統之研發”，國立成功大學機械工程學系碩士論文，2018。
20. Thomas Klinger, “Image Processing with LabVIEW and IMAQ Vision,”Pretice Hall PTR, 2003.
21. Gonzalez, Rafael C., and Richard E. Woods., “Digital image processing prentice hall,”Upper Saddle River, NJ (2002).
22. Hariharan, P., B.F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,”Applied Optics, 1987. 26(13): p. 2504-2506.
23. Lin J., and Su X., “Two-dimensional Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,”Opt. Eng. 34 3297-302, 1995.
24. Gómez-Pedrero, J.A., Quiroga, Juan A., José Terrón-López, M., Crespo, Daniel., “Measurement of surface topography by RGB Shadow-Moiré with direct phase demodulation,”Optics and Lasers in Engineering, 2006. 44(12): p. 1297-1310.
25. Quiroga, J.A., Gómez-Pedrero, José A., Terrón-López, M. José., Servin, Manuel., “Temporal demodulation of fringe patterns with sensitivity change,”Optics Communications, 2005. 253(4-6): p. 266-275.
26. Felsberg, M. and G. Sommer, “The monogenic signal,”IEEE Transactions on Signal Processing, 2001. 49(12): p. 3136-3144.
27. Horn, B.K.P., and B.G. Schunck, “Determining optical flow. Artificial Intelligence,”1981. 17(1): p. 185-203.
28. Macy, W.W., “Two-dimensional fringe-pattern analysis,”Applied Optics, 1983. 22(23): p. 3898-3901.