本論文使用三種波形(餘弦波、方波、三角波)的數位條紋結構光，再加上七步相位移法、相位展開技術、參考平面扣除法來量測不同的三維表面輪廓，量測試件包含半圓形、內凹半圓、方形、三角形等形狀。量測系統是將數位結構光法投影至待測物上，然後以數位攝影機擷取條紋影像，最後使用多步相位移技術計算出物體表面的三維輪廓。實驗結果顯示，不同波形的結構光在量測不同樣式的待測物時會達到不同的效果。餘弦波對於半圓形試件有較小的量測誤差(1.27%)，方波則對於方形試件有較小的量測誤差(15.66%)，而三角波則對於三角形試件有較小的量測誤差(10.18%)。未來應用於產品的即時檢測時，可針對輪廓形狀來選擇較適合的條紋結構光進行量測，以獲得最小誤差的三維表面輪廓。

In this thesis, different three-dimensional surfaces were measured by three kinds of waveforms (cosine wave, square wave, triangular wave) of digital structured light projection, seven-step phase shifting, phase unwrapping, reference plane subtraction method. The measured objects include semi-circular, concave semi-circular, square and triangle. In this system, digital structured light is projected onto the objects, and then the fringe pattern images are captured with CCD. Finally, the three-dimensional surfaces of the objects are calculated by multi-step phase-shifting. As the results, different objects achieved different effect by using different kinds of waveforms of digital structured light. The semi-circular objects measured by cosine wave have smaller measurement error (1.27%). The square objects measured by square wave have smaller measurement error (15.66%). The triangular objects measured by triangular wave have smaller measurement error (10.18%). In order to get the minimum error of the three-dimensional surfaces profile, it is selected more appropriate fringe pattern structured light to measure according to objects profile, which is used for product immediate detection.

目錄
第1章 緒論	1
1.1 前言	1
1.2 文獻回顧	4
1.3 研究動機和目的	10
1.4 研究方法	11
1.5 論文架構	12
第2章 相位移干涉術原理	13
2.1 前言	13
2.2 結構光理論	14
2.3 相位量測技術	18
2.3.1 傅立葉轉換法	18
2.3.2 相位移法	19
2.4 相位移法之相位計算公式	22
2.4.1 七步相移法	23
2.5 相位展開技術	25
2.6 相位高度值換算	27
第3章 相位移量測系統	30
3.1 系統架構	30
3.1.1 DLP投影機	31
3.1.2 CCD 攝影機	32
3.1.3 運動機構	33
3.2 實驗步驟	34
第4章 多步相位移量測之結果	35
4.1 量測系統的尺寸校正	35
4.2 消除待測物表面之反射光	37
4.3 待測物的印製─3D列印機	39
4.4 直徑一公分半圓	40
4.5 直徑三公分半圓	45
4.6 邊長一公分的正方形	50
4.7 邊長三公分的正方形	55
4.8 邊長一公分的正三角形	61
4.9 邊長三公分的正三角形	66
4.10 直徑一公分的內凹圓	72
4.11 直徑三公分的內凹圓	77
第5章 結論與未來展望	82
5.1 結論	82
5.2 未來展望	83
參考文獻	84


 
圖目錄
圖1 1三維量測技術分類圖	2
圖1 2傳統條紋產生之架構	4
圖1 3利用 LDF (Long distance microscope) 的數位條紋投影法	5
圖1 4電阻器外型偵測結果。(a) 原始影像。(b) 重建之2.5D外型。	5
圖1 5影像還原重建後之3D模型: (a)3D影像上色(b)抓取相似之色澤[6]	6
圖1 6三維形狀量測之系統架構[6]	6
圖1 7利用RGB表示三色相位的彩色數位條紋投影法。	7
圖1 8三維量測之硬體設備架構圖[5]	8
圖1 9計算後之最佳三條紋術: (a)25 (b)24 (c)20 (d)相位展開圖[5]	8
圖1 10投影綠色條紋之最佳三條紋數： (a)25 (b)24 (c)20 [5]	9
圖2 1 (a) 餘弦條紋圖 (b)條紋剖面圖	15
圖2 2 (a) 三角條紋圖 (b)條紋剖面圖	16
圖2 3 (a) 方形條紋圖 (b)條紋剖面圖	17
圖2 4餘弦條紋亮度分布示意圖	21
圖2 5七步相移條紋圖	24
圖2 6反正切函數之分子分母正負號求得2π模數示意圖 (a)象限判別圖 (b)π模數轉換2π模數[39]	26
圖2 7相位包裹及相位展開示意圖	26
圖2 8條紋投影系統之光學幾何關係	27
圖3 1系統架構圖	30
圖3 2  Acer K132 LED Projector之DLP投影機	31
圖3 3 CCD攝影機	32
圖3 4運動機構	33
圖4 1量測之相位值與校正塊規	35
圖4 2SKD-S2消光劑	37
圖4 3 3D印表機ATOM 2.0	39
圖4 4七步相位移之各相移截圖(a)~(g)為相位量測實際圖(h)為擷取原圖	40
圖4 5 餘弦波相位包裹圖	40
圖4 6 方波相位包裹圖	41
圖4 7 三角波相位包裹圖	41
圖4 8 相位還原圖(a)餘弦波(b)方波(c)三角波	42
圖4 9 三維曲面影像(a)餘弦波(b)方波(c)三角波	43
圖4 10 直徑為一公分的半圓之三種波剖面圖	44
圖4 11七步相位移之各相移截圖(a)~(g)為相位量測實際圖(h)為擷取原圖	45
圖4 12 餘弦波相位包裹圖	45
圖4 13 方波相位包裹圖	46
圖4 14 三角波相位包裹圖	46
圖4 15 相位還原圖(a)餘弦波(b)方波(c)三角波	47
圖4 16 三維曲面影像：(a)餘弦波，(b)方波，(c)三角波	48
圖4 17 直徑為三公分的半圓之三種波剖面圖	49
圖4 18七步相位移之各相移截圖(a)~(g)為相位量測實際圖(h)為擷取原圖	50
圖4 19 餘弦波相位包裹圖	50
圖4 20 方波相位包裹圖	51
圖4 21 三角波相位包裹圖	51
圖4 22 相位還原圖：(a)餘弦波，(b)方波，(c)三角波	52
圖4 23 三維曲面影像：(a)餘弦波，(b)方波，(c)三角波	53
圖4 24 邊長為一公分的正方型之三種波剖面圖	54
圖4 25 七步相位移之各相移截圖(a)~(g)為相位量測實際圖(h)為擷取原圖	55
圖4 26 餘弦波相位包裹圖	56
圖4 27 方波相位包裹圖	56
圖4 28 三角波相位包裹圖	57
圖4 29 相位還原圖：(a)餘弦波，(b)方波，(c)三角波。	58
圖4 30 三維曲面影像：(a)餘弦波，(b)方波，(c)三角波。	59
圖4 31邊長為三公分的正方形之三種波剖面圖	60
圖4 32 七步相位移之各相移截圖(a)~(g)為相位量測實際圖(h)為擷取原圖	61
圖4 33 餘弦波相位包裹圖	61
圖4 34 方波相位包裹圖	62
圖4 35 三角波相位包裹圖	62
圖4 36 相位還原圖：(a)餘弦波，(b)方波，(c)三角波。	63
圖4 37 三維曲面影像：(a)餘弦波，(b)方波，(c)三角波。	64
圖4 38 邊長為一公分的正三角形之三種波剖面圖	65
圖4 39 七步相位移之各相移截圖(a)~(g)為相位量測實際圖(h)為擷取原圖	66
圖4 40 餘弦波相位包裹圖	67
圖4 41 方波相位包裹圖	67
圖4 42 三角波相位包裹圖	68
圖4 43 相位還原圖：(a)餘弦波，(b)方波，(c)三角波	69
圖4 44 三維曲面影像：(a)餘弦波，(b)方波，(c)三角波。	70
圖4 45 邊長為三公分的正三角形之三種波剖面圖	71
圖4 46七步相位移之各相移截圖(a)~(g)為相位量測實際圖(h)為擷取原圖	72
圖4 47 餘弦波相位包裹圖	72
圖4 48 方波相位包裹圖	73
圖4 49 三角波相位包裹圖	73
圖4 50 相位還原圖：(a)餘弦波，(b)方波，(c)三角波。	74
圖4 51 三維曲面影像：(a)餘弦波，(b)方波，(c)三角波。	75
圖4 52 直徑為一公分的內凹半圓之三種波剖面圖	76
圖4 53 七步相位移之各相移截圖(a)~(g)為相位量測實際圖(h)為擷取原圖	77
圖4 54 餘弦波相位包裹圖	77
圖4 55 方波相位包裹圖	78
圖4 56 三角波相位包裹圖	78
圖4 57 相位還原圖：(a)餘弦波，(b)方波，(c)三角波。	79
圖4 58 三維曲面影像：(a)餘弦波，(b)方波，(c)三角波。	80
圖4 59直徑為三公分的內凹半圓之三種波剖面圖	81
表目錄
表1 1研究步驟	11
表3 1投影機規格	31
表3 2運動機構之步進馬達規格	33
表4 1消光劑規格表	38
表5 1誤差值表	83

[1]林詩瑀,蔡裕祥,“精密量測及檢驗,”全華科技圖書,2002.
[2]B. Bidanda, S. Motavalli,and K. Harding, “Reverse engineering: an evaluation ofprospective non-contact technologies and application in manufacturing system,”International Journal of Computer Integrated Manufacturing, Vol.4, No. 3,pp.145-156, 1991.
[3] P. J. Besl, “Active optical range imaging sensors,” Machine Vision and Applications, Vol. 1, No. 2, pp.127-152, 1988.
[4]Z. Zhang, S. Huang, Y. Xu, C Chen, Y. Zhao, N. Gao, andY. Xiao, “3D palmprint and hand imaging system based on full-field composite color sinusoidal fringe projection technique,” Applied Optics, Vol. 52, No. 25, pp. 6138-6145, 2013.
[5] S. Huang, Z. Zhang, Y. Zhao, J. Dai, C. Chen, Y. Xu, E. Zhang, and L. Xie, “3Dfingerprint imaging system based on full-field fringe projection profilometry,” Optics and Lasers in Engineering, Vol. 52, pp. 123-130, 2014.
[6]S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Optics and Lasers in Engineering, Vol. 48, No. 2, pp. 149-158, 2010.
[7]蔡宇軒, “疊紋式晶圓翹曲量測技術之開發,”國立臺灣科技大學機械工程系碩士論文,2014.
[8]H. Schreiber, and J. H. Bruning, “Phase shifting interferometry,”Optical Shop Testing, pp. 547-666, 2006.
[9]J.Aizenberg, J. A. Rogers, K. E. Paul, and G. M. Whitesides, “Imaging profiles of light intensity in the near field: applications to phase-shift photolithography,”Applied Optics, Vol. 37, No. 11, pp. 2145-2152, 1998.
[10]P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Applied Optics, Vol. 26, No. 13, pp. 2504-2505, 1987.
[11]K. Creath, “Phase-shifting speckle interferometry,” Applied Optics, Vol. 24, No. 18, pp. 3053-3058, 1985.
[12]Y. Cheng, and J. C. Wyant, “Phase shifter calibration in phase-shifting interferometry,”Applied Optics,Vol. 24, No.18, pp. 3049-3052, 1985.
[13]A. Twitto, J. Shamir, A. Bekker, and A. Notea, “Detection of internal defects using phase shifting holographic interferometry,” NDT & E International, Vol. 29, No. 3, pp. 163-173, 1996.
[14]G. Lai, and T.Yatagai, “Generalized phase-shifting interferometry,”Journal of the Optical Society of America A, Vol. 8, No. 5, pp. 822-827, 1991.
[15] W. Chung, and L. Wen, “Measurement of warpage of electronic packagings after machining by phase-shifting shadow moire method,” Proceedings of SPIE4537, Third International Conference on Experimental Mechanics, China, Vol. 4537, pp. 20-24, 2002.
[16] J. A. Quiroga, A. Gonz’alez-Cano, and E. Bernabeu, ”Phase-unwrapping algorithm based on an adaptive criterion,” Applied Optics, Vol. 34, No. 14, pp. 2560-2563, 1995.
[17] Y. Xu, and C. Ai, “Simple and effective phase unwrapping technique,”Proceedings of SPIE 2003, Interferometry VI: Techniques and Analysis, San Diego, Vol. 2003, pp. 254-263, 1993.
[18] D. C. Ghiglia, G. A. Mastin, and L. A. Romero, “Cellular-automatamethod for phase unwrapping,” Journal of the Optical Society of America A, Vol. 4, pp. 267-280, 1987.
[19] D.C. Ghiglia, and M.D. Pritt, “Two-dimensional phase unwrapping: Theory, algorithms and software,” Wiley-Interscience, 1998.
[20] D. J. Bone, “Fourier fringe analysis: the Two-dimensional phase unwrapping problem,” Applied Optics, Vol. 30, No. 25, pp. 3627-3632, 1991.
[21] R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry : two-dimensional phase unwrapping,” Radio Science, Vol. 23, No. 4, pp. 713-720, 1988.
[22] K.G. Larkin, and B.F. Oreb, “Design and assessment of symmetrical phase-shifting algorithms,” Journal of the Optical Society of America A, Vol. 9, No.10 , pp. 1740-1748, 1992.
[23]J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Applied Optics, Vol. 22, No. 21, pp. 3421-3432, 1983.
[24]Srinivasan, V., H. C. Liu, and M. Halioua, "Automated phase-measuring profilometry of 3-D diffuse objects," Applied Optics, vol.23, pp.3105-3108, 1984.
[25] P. S. Huang, F. Jin, and F. P. Chiang, “Quantitative evaluation of corrosion by a digital fringe projection technique,” Optics and Lasers in Engineering, Vol. 31, No. 5, pp.371-380, 1999.
[26]Pavageau, S., R. Dallier, N. Servagent, and T. Bosch, "A new algorithm for large surfaces profiling by fringe projection," Sensors and Actuators, vol.115, no.2-3, pp.179-184, 2004.
[27]Quan, C., X. Y. He, and C. F. Wang, "Shape measurement of small objects using LCD fringe projection with phase shifting," Optics Communications, vol.189, no.1-3, pp.21-29, 2001.
[28]Y. Surrel, “Phase stepping: a new self-calibrating algorithm,”Applied Optics, Vol. 32, No. 19, pp. 3598-3600,1993.
[29] P. Carré, “Installation etutilisation du comparateurphotoelectrique et interferentiel du Bureau International des Poids et Mesures,”Metrologia, Vol. 2, No. 1,pp. 13-23, 1966.
[30]J. E. Gallagher, and D. R. Herriott, “Wavefront measurement,” U. S. PatentNo. 3, 694, 088, 1972.
[31]P. Hariharan, B.F. Oreb, and T. Eiju, “Digital phase-shift interferometry:a simple error-compensating phase calculation algorithm,” Applied Optics, Vol.26, No. 13 , pp.2504-2506, 1987.
[32]A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Optical Engineering, Vol. 36, No. 9, pp. 2466-2472, 1997.
[33]J. Pan, P. S. Huang, and F. P. Chiang, "Color-encoded digital fringe projection technique for high-speed 3D shape measurement: color coupling and imbalance compensation," Photonics Technologies for Robotics, Automation, and Manufacturing, vol.5265, pp.205-212, 2004.
[34]P. S. Huang, Q. Hu, F. Jin, and F. P. Chiang, "Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring," Optical Engineering, vol.38, no.6, pp.1065-1071, 1999.
[35]蔡怡庭, “光學相位量測暨影像處理技術在電子構裝之應用,” 國立台灣大學應用力學研究所碩士論文,2000.
[36]D.Malacara, “Optical shop testing,” John Wiley & Sons, 2007.
[37]W. W. Macy, “Two-dimensional fringe-pattern analysis,” Applied Optics, Vol.22, No. 23, pp.3898-3901, 1983.
[38] P. Sandoz, “An algorithm for profilometry by white-lightphase-shifting interferometry,” Journal of Modern Optics, Vol. 43, No. 8, pp. 1545-1554, 1996.
[39]高斌栩, “創新式平行性相位還原法應用於剪切平面之研究,”國立中興大學機械工程研究所碩士論文,2005.
[40]陳怡光, “表面電漿共振移相干涉儀之影像處理系統,”國立中央大學機械工程研究所碩士論文, 2003.
[41] 顏子評,“多步相位移干涉術應用於三維複雜曲面量測”, 淡江大學機械與機電工程學系碩士班學位論文(pp. 1-121), 2015