條紋投影輪廓測儀(Projected Fringe Profilometry簡稱PFP)搭配相位轉移技術為一量測三維形貌的有名技術，此技術主要將條紋圖案投影到待測物體上，並由影像擷取系統擷取條紋分佈影像，原理為被投影之條紋受待測物體表面輪廓而扭曲，其條紋資訊需應用arctan運算，因此須將不連續相位分佈展開成一連續性相位分佈，進而分析待測物體之表面輪廓。
目前已有許多研究提出相位轉移技術擷取條紋資訊方法，但大多數方法需額外投影條紋圖案進而辨識條紋序列進行相位展開，故擷取條紋資訊影像數量將大於一般相位資訊所需。
本研究提出使用對比度編碼的方法設計條紋圖案，條紋本身編碼效果極佳，因此在有限的五張影像中即可獲得待測物體之絕對相位資訊，進行相位展開時不需額外擷取條紋影像，可直接進行相位展開，此編碼方法使得三維形貌量測有效縮短數據分析時間以及降低量測所需成本。

Phase-shifting projected fringe profilometry (PSPFP) is a powerful tool for 3D shape measurements. It projects a fringe pattern onto the inspected object and records the fringe distribution at another point of view. Phase of the projected fringes is distorted by the surface profile, and hence is analyzable retrieve the surface profile. Phases are extracted with the phase-shifting method. It evaluates phases with the arctangent operation, leading to their principle values constrained within the interval (–π, π). Unwrapping is therefore required to restore the continuity of the phase map.
Most fringe-projection methods based on phase-shifting techniques require additional projected patterns to identify the fringe order for the task of phase unwrapping. The total number of projections is usually more than that used for phase extraction.
In this paper, a contrast-encoded scheme is presented. There is no need to take additional projections for phase unwrapping. The fringe patterns used for phase extraction can be analyzed for unwrapping directly. This makes it more efficient to perform high speed, real time, and low cost 3-D shape measurements.

論文審定書 i
誌謝 ii
摘要 iii
Abstract iv
目錄 v
圖目錄 vii
表目錄 xi
第一章 簡介 1
1.1前言 1
1.2文獻回顧 3
1.3研究動機與目標 4
1.4論文架構 5
第二章 條紋輪廓儀原理 6
2.1簡介 6
2.2光學三角量測法 8
2.3相位擷取技術 11
2.3.1相位轉移技術（五步相位移） 11
2.3.2傅立葉轉換法 13
2.4相位展開及其演算法 15
第三章 編碼條紋之特性 17
3.1編碼條紋圖案設計 17
3.2 編碼條紋應用於相位移轉換技術 24
3.3 二進位制編碼條紋應用之模擬 27
第四章 實驗與分析 32
4.1 實驗儀器與架構 32
4.2編碼條紋圖案之形貌量測-塊規 35
4.3實驗參數分析 46
4.4三進位制編碼條紋圖案量測表面複雜物體之形貌輪廓還原 53
4.5四進位制編碼條紋圖案量測表面複雜物體 63
4.6 GAMMA校正 65
第五章 結論 70
參考文獻 72

[1] S. H. Rowe, W. T. Welford,“Surface topography of non-optical surfaces by projected interference fringes,”Nature, 216, 786-788 (1967).
[2] H. Takasaki,“Moire topography,”Applied Optics, 9, 1467-1472 (1970).
[3] S. H. Rowe,“Projected Interference Fringes in Holographic Interferometry,”Journal of the Optical Society of America, 61, 1599-1603 (1971).
[4] M. Takeda, H. Ina, S. Kobayash,“Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,”Journal of the Optical Society of America, 72, 156-160 (1982).
[5] V. Srinivasan, H. C. Liu, M. Halioua,“Automated phase-measuring profilometry of 3-D diffusive objects,”Applied Optics, 23, 3105-310 (1984).
[6] J. L. Li, H. J. Su, X.Y. Su,“Two-frequency grating used in phase-measuring Profilometry,”Applied Optics, 36, 277-280 (1997).
[7] X. Su, W. Chen, Q. Zhang, Y. Chao,“Dynamic 3-D shape measurement method based on FTP,”Optics and Lasers in Engineering, 36, 49-64 (2001).
[8] W. Su, K. Reichard, H. Liu, S. Yin,“Integration of segmented 3D profiles measured by calibration-based phase-shifting projected fringe profilometry (PSPFP),”Optical Memory & Neural Networks, 12, 51-63 (2003).
[9] S. Zhang,“Recentprogressesonreal-time3Dshapemeasurementusingdigitalfringe
Projectiontechniques,”Optics and Lasers in Engineering, 48, 149-158 (2010).
[10] 蕭智鴻,“全像術應用在於體腔內部之三維形貌量測”國立中山大學材料科學研究所碩士論文，中華民國九十七年八月.
[11] 柯韋廷,“利用條紋投影技術進行物體表面之三維形變量量測”國立中山大學材料科學研究所碩士論文,中華民國一百零一年月七月.
[12] 黃俊善,“條紋投影輪廓儀從事動態微小元件之研究” 國立中山大學材料科學研究所碩士論文,中華民國九十六月七月.
[13] 徐一麟,“條紋投影輪廓儀之三維型貌影像融合分析”國立中山大學材料科學研究所碩士學位論文,中華民國九十四年六月.
[14] 陳煒仁,“以繞射元件從事三維形貌量測技術之研究”國立中山大學材料科學研究所碩士論文,中華民國九十五年六月.
[15] K. G. Larkin, B. F. Oreb,“Design and assessment of symmetrical phase-shifting algorithms,”Journal of the Optical Society of America, 9, 1740-1748 (1992).
[16] H. Liu, W. H. Su, K. Reichard, S. Yin,“Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,”Optics Communications, 216, 65-80 (2003).
[17] X. Su, W. Chen,“Fourier transform profilometry: a review,”Optics and Lasers in Engineering, 35, 263-284 (2001).
[18] M. Takeda, K. Mutoh,“Fourier transform profilometry for the automatic measurement of 3-D object shaped,”Applied Optics, 22, 3977-3982 (1983).
[19] E. Zappa, G. Busca,“Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,”Optics and Lasers in Engineering, 46, 106-116 (2008).
[20] J. Geng,“Structured-light 3D surface imaging: a tutorial,”Journal of the Optical Society of America, 3, 128–160 (2011).
[21] M. Minou, T. Kanade, T. Sakai,“A method of time-coded parallel planes of light for depth measurement,”The Institute of Electronics, Information and Communication Engineers 64, 521-528 (1981).
[22] G. Sansoni, S. Corini, S. Lazzari, F. Docchio,“Three-dimensional imaging based on Gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications,”Applied Optics, 36, 4463-4472 (1997).
[23] C. Brenner, J. Boehm, J. Guehring,“Photogrammetric calibration and accuracy evaluation of a cross-pattern stripe projector,”Proceedings of International Society for Optics and Photonics, 3641, 164-162 (1998).
[24] G. Sansoni, M. Carocci, R. Rodella,“Three-dimensional vision based on a combination of gray-code and phase-shift light projection: analysis and compensation of the systematic errors,”Applied Optics, 38, 6565-6573 (1999).
[25] Y. Wang, S. Zhang,“Novel phase-coding method for absolute phase retrieval,”Optics Letters, 37, 2067–2069 (2012).
[26] D. Zheng, F. Da,“Phase coding method for absolute phase retrieval with a large number of codewords,”Optics Express, 20, 24139–24150 (2012).
[27] X. Chen, Y. Wang, Y. Wang, M. Ma, C. Zeng,“Quantized phase coding and connected region labeling for absolute phase retrieval,”Optics Express, 24, 28613-28624 (2016).
[28] K. Creath,“Step height measurement using two-wavelength phase-shifting interferometry,”Applied Optics, 26, 2810-2816 (1987).
[29] J. M. Huntley, H. O. Saldner,“Temporal phase-unwrapping algorithm for automated inteferogram analysis,”Applied Optics, 32, 3047-3052 (1993).
[30] J. M. Tribolet,“A new phase unwrapping algorithm,”Proceeding of Institute of Electrical and Electronics Engineers Transactions on Acoustics, Speech and Signal Processing, 25, 170-177 (1977).
[31] H. Zhao, W. Chen, Y. Tan,“Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,”Applied Optics, 33, 4497-4500 (1994).
[32] D. C. Ghigila, L. A. Romero,“Robust two-dimensional weighted and unweighted phase unwrapping that use fast transforms and iterative methods,”Journal of the Optical Society of America, 11, 107-117 (1994).
[33] U. Spagnolini,“2-D phase unwrapping and instantaneous frequency estimation,”Journal of the Optical Society of America, 33, 579-587 (1995).
[34]H. O. Saldner, J. M. Huntley,“Temporal phase unwrapping : application to surface profiling of discontinuous objects,”Applied Optics, 36, 2770-2775 (1997).