本論文提出一種新穎的三維形貌條紋投影輪廓儀之影像融合技術。
由於投影至待測物表面的條紋，在不同的量測位置下，都有相同的相位值(

This paper presents a novel integration technique for segmented 3D profiles measured by projected fringe profilometry. Fringe patterns are projected to the inspected surface. The projected patterns fix their positions relative to the tested object during two segmented measurements. Thus, finding two matched surface points becomes a problem of searching for two identical phases in the fused data sets. This novel integration technique can match images successfully and achieve pixel-to-pixel registration easily even in the presence of geometric deformation, illumination changes, and severe occlusions. It is superior to the other methods because of its:
(1) High matching accuracy;
(2) Improved robustness;
(3) Reduced computational time;
(4) Capability of compensating distortions of the optical system at every
pixel location;
(5) Suitable for images rotating or scaling; and
(6) Suitable for any other projected fringe measurement method.
We also propose a method to design and fabricate a 2-D fringe pattern which can be applied to the integration technique for segmented 3D profiles. Campered with using 1-D fringe patterns for image registration, using a 2-D fringe pattern saves the measurement time and further proveds more tolerence to hand the shadow and noise problems. Tests of the system performance have been carried out that the accuracy of the registration scheme is 5.96% of image pixel size. Therefore, this technique can be extensively used in modern high technology industry. Especially when it requires higher resolution close-up images or overcomes the issue of not every inspected object can be fully expressed just by a single full-field measurement, it is necessary to use this integration technique.

摘要-----------------------------------------------------Ⅱ
英文摘要-------------------------------------------------Ⅲ
致謝-----------------------------------------------------Ⅳ
目錄-----------------------------------------------------Ⅴ
圖目錄---------------------------------------------------Ⅶ
表目錄---------------------------------------------------Ⅸ
第一章 導論
1-1 前言-------------------------------------------------1
1-2 文獻回顧---------------------------------------------5
1-3 研究動機---------------------------------------------7
第二章 相位移條紋投影輪廓儀之量測原理與校正系統
2-1 相位移條紋投影輪廓儀(PSPFP)簡介----------------------10
2-2 PSPFP之量測原理--------------------------------------11
2-2-1 相位展開與相位展開演算法---------------------------16
2-3 PSPFP之校正系統--------------------------------------22
2-3-1 「相位-縱深」的校正--------------------------------23
2-3-2 「側向」的校正-------------------------------------25
2-3-3 三維形貌物體的量測---------------------------------28
第三章 相位移條紋投影輪廓儀之三維形貌影像融合
3-1 圖形配準簡介-----------------------------------------29
3-1-1 Rigid transformation----------------------------30
3-1-2 Affine transformation---------------------------30
3-1-3 Projective transformation-----------------------31
3-1-4 Curved transformation---------------------------32
3-2 結合點之同相位關係-----------------------------------33
3-3 局部量測系統的裝置原理以及圖形配準技術---------------36
3-4 以相位為依據的圖形配準座標轉換關係式-----------------42
第四章 實驗裝置與實驗步驟流程
4-1 實驗裝置---------------------------------------------45
4-2 實驗步驟流程-----------------------------------------50
4-2-1 程式流程----------------------------------------50
4-2-2 校正系統實驗步驟--------------------------------51
4-2-3 圖形配準系統實驗步驟----------------------------52
4-2-4 影像融合系統實驗步驟----------------------------53
第五章 實驗結果
5-1 三維形貌量測實驗誤之誤差值分析-----------------------54
5-2 三維形貌量測實驗結果(1)------------------------------65
5-3 三維形貌量測實驗結果(2)------------------------------71
5-4 圖形配準與影像融合實驗結果---------------------------77
第六章 結論與未來研究工作
6-1 結論-------------------------------------------------87
6-2 未來研究工作-----------------------------------------88
附錄-----------------------------------------------------89
參考文獻-------------------------------------------------92

1. R. E. Brooks and L. O. Heflinger, “Moiré gauging using optical interference patterns,” Applied Optics, 8, 935-939 (1969).

2. D. M. Meadows, W. O. Johnson, and I. B. Allen, “Generation of surface contours by Moiré patterns,” Applied Optics, 9, 942-947 (1970).

3. H. Takasaki, “Moiré topology,” Applied Optics, 9, 1467-1472 (1970).

4. G. T. Reid, R. C. Rixon, and H. I. Messer, “Absolute and comparative measurement of three-dimensional shape by phase measuring Moiré topography,” Optical Laser Technology, 16, No. 6, 315-319 (1984).

5. A. Asundi and C. S. Chan, “Phase shifted projection grid effect of pitch and profile,” Optics and Lasers in Engineering, 21, 31-47 (1994).

6. Mitsuru Baba and Tadataka Konishi, “Range image system with multiplexed structured light by direct space encoding,” Conference Record - IEEE Instrumentation and Measurement Technology Conference, 3, 1437-1442 (1999).

7. S. H. Rowe and W. T. Welford, “Surface topography of non-optical surfaces by projected interference fringes,” Nature, 216, No. 5117, 786-788 (1967).

8. S. H. Rowe, “Projected interference fringes in holographic interferometry,” J. Opt. Soc. Am., 61, No. 12, 1599-1603 (1971).

9. R. Crane, “Interference phase measurement,” Applied Optics, 8, 538 (1969).

10. J. H. Burning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Applied Optics, 13, 2693 (1974).


11. G. W. Johnson and D. T. Moore, “Design and construction of a phase-locked interference microscope,” Proc. SPIE, 103, 76 (1977).

12. V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Applied Optics, 23, No. 18, 3105-3108 (1984).

13. V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry: a phase mapping approach,” Applied Optics, 24, No. 2, 185-188 (1985).

14. S. K. Case, J. A. Jalkio, and R. C. Kim, “3-D vision system analysis and design,” in Three-Dimensional Machine Vision, Takeo Kanade, Ed., Kluwer Academic Publishers, Norwell, MA, pp. 63-95, (1987).

15. G. Lu, S. Wu, N. Palmer, and Hongyu Liu, “Application of phase-shift optical triangulation to precision gear gauging,” Proc. SPIE, 3520, 52-63 (1998).

16. Hongyu Liu, B. A. Bard, Wei-Hung Su, Fei Wu, Shizhuo Yin, and T. S. Yu, “Accuracy enhancement in phase-shifting projected fringe profilometry by microscanning,” Proceedings of Optical Society of America Annual Meeting, Santa Clara, California, September 26 - October 1, (1999).

17. Hongyu Liu, B. A. Bard, Wei-Hung Su, and Fei Wu, “Precision profile measurement by phase-shifting projected-fringe profilometry,” ARL year 2000, The Pennsylvania State University (internal publications).

18. Wei-Hung Su, Hongyu Liu, Karl Reichard, Shizhuo Yin, and Francis T. S. Yu, “Fabrication of digital sinusoidal grating and precisely controlled diffusive flat and their applications to highly accurate projected fringe profilometry,” Optical Engineering, 42, No. 6, 1730-1740 (2003).



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, 216, Issues 1-3, 65-80 (2003).

20. Wei-Hung Su, Karl Reichard, Hongyu Liu, and Shizhuo Yin, “Integration of segmented 3D profiles measured by calibration-based phase-shifting projected fringe profilometry (PSPFP),” Optical Memory & Neural Networks, 12, No. 1, (2003).

21. R. M. Goldstein, H. A. Zebker, and Werner C.L., “Satellite Radar Interferometry: Two-Dimensional phase unwrapping,” Radio Sci., 23,718-720, (1988).

22. E. Kreysig, “Advanced Engineering Mathematics,” Wiley, New York, 700-701, (1966).

23. J.M Huntley and J.R. Buchland, “Characteristization of sources of 2π phase discontinuity in speckle interferograms,” Journal of the Optical Society of America, 12, No.9, 1990-1996, (1995).

24. J. M Huntley, “Noise-immune phase unwrapping algorithm, ”Applied Optics, 28, No. 15, 3268-3270, (1989).

25. D. C. Ghiglia, G. A. Mastin, and L. A. Romero, “Cellular automata method for phase unwrapping,” Journal of the Optical Society of America, 4, No.1, 267-280, (1987).

26. H. Zhao, W. Chen, and Y. Tan , ”Phase-unwrapping algorithm for the measurement of the three-dimension object shapes,” Applied Optics , 33,No.20,4497-4500, (1994).

27. J. Szumowski, W. R. Coshow, F. Li, and S. F. Quinn, ”Phase unwrapping in the three-point Dixon method for fat suppression MR imaging ,”Radiology, 192, No. 2, 555-561, (1994).



28. S. M. song, S. Naple, N. J. Pelc, and G.. H. Glover , ”phase unwrapping of MR phase image using Poisson equation,” IEEE Transaction on Image Processing, 4, No. 5, (1995).

29. J. C. Marron, P. P. Sanchez, and R. C. Sullivan, “Unwrapping algorithm for least-square phase recovery from the modulo 2π bi-spectrum phase,” Journal of the Optical Society of America, A, 7(1), 14-20, (1990).

30. Judg T. R. and P. J. Bryanston-Cross, “ A review of phase unwrapping techniques in fringe analysis,” Optical Laser Techno edge , 21 , 199-239, (1994) .

31. L. G. Brown, “A survey of image registration techniques,” ACM Computing Surveys, 24, No. 4, 325-376, (1992)

32. Chitra Dorai, Gang Wang, Anil K. Jain, and Carolyn Mercer, “Registration and integration of multiple object views for 3D model construction,” IEEE Transactions on Pattern analysis and Macine Intelligence, 20, No. 1, 83-89, (1998).

33. G. Simon and M. O. Berger, “A two-stage robust statistical method for temporal registration from features of various type,” IEEE Computer Vision, Sixth International Conference, 261-266, (1998).

34. Nicola Ritter, Robyn Owens, James Cooper, Robert H. Eikelboom, and Pail P. van Saarloos, “Registration of stereo and temporal images of the retina,” IEEE Transactions on Medical Imaging, 18, No. 5, 404-418, (1999).

35. J. A. Williams and M. Bennamoun, “Evaluation of a novel multiple
point set registration algorithm,” IEEE Pattern Recognition, Proceedings. 15th International Conference, 1, 1007-1010, (2000).

36. H. A Martins, J. R. Birk, and R. B. Kelly, “Camera model based on data from two calibration planes,“ Computer Graphics and Image Processing,17,173-180, (1981).
37. M. Born and E. Wolf, Principle of optics, 7th ed. The Macmillan Company, Place, (1999).

38. Wei-Hung Su, “Advance phase-shifting projected fringe profilometry Techniques,” Ph.D. dissertation (USA PSU Electrical Engineering 2002)

39. Wei-Hung Su, Yi-Ling Hsu, Cho-Yo Kuo, and Hung-Ming Chen
, “Integration of segmented 3D image data measured by projected fringe profilometry,” SPIE's 49th Annual Meeting 2004 Denver, Colorado USA

40. D. G. Bailey and T. H. Lill, “Image Registration Methods for Resolution Improvement,” Proceedings of image and Vision Computing NZ, pp 91-96 (August 1999).

41. T. J. Silva, C. S. Lee, T. M. Crawford and C. T. Rogers, “Inductive measurement of ultra-fast magnetization dynamics in thin-film Permalloy,” JOURNAL OF APPLIED PHYSICS. 85, 7849-7862, (1999).

42. João Carlos Machado, Marco Antônio von Kruger, Eva Maria Almeida Fontes and Márcio Manhães Gomes de Almeida, “Evaluation of an ultrasonic method applied to the measurement of blood coagulation time,” Physiol. Meas. 18, 129-143, (1997).

43. Wei-Hung Su, “Kebin Shi, Zhiwen Liu, Bo Wang, Karl Reichard, and Shizhuo Yin, “A large-depth-of-field projected fringe profilometry using supercontinuum light illumination,” Applied Optics, 13, No. 3, 1025-1032 (2005).