干涉儀相位移動器之精密校正法

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：49

、訪客IP：18.223.206.84

姓名

周厚丞(Hou-Cheng Chou) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

干涉儀相位移動器之精密校正法
(The precise calibration of the phase-shifting adapter in interferometer)

相關論文

★ 嵌入式繼光鏡顯微超頻譜影像系統應用在口腔癌切片及活體之設計及研究	★ 新型液晶電視與背光模組的探討分析
★ 高動態範圍雷射測距系統之研製	★ 雙燈投影裝置運用於遠距教學之研究
★ 膠囊內視鏡之照明系統設計	★ 任意頻率調變式雷射測距儀
★ 膠囊內視鏡之成像鏡頭設計	★ 色域映對理論應用於顯示器色彩調校之研究
★ 多原色顯示器之色域探討與亮度優化設計	★ 相位移動器校正之研究
★ 色彩調校技術與顯示器構色原理之分析	★ 顯示器色彩之視覺疲勞研究
★ 新型灰階編碼於全像儲存系統之研究	★ 多主色顯示器之研製
★ 電校式電阻感測器校正方法之研究	★ 利用色彩原理之新型儲存技術

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

現今高精密度的製造業要求更加準確、精確和迅速的量測學，而相移干涉學正是目前許多工業所倚重的一門量測的學問，相移精度對於相移干涉術之量測，是最可代表樣品之可靠度。對利用相移干涉術來量測樣品之干涉儀而言，不準確的相移會在計算物體相位上而產生誤差，如此，無法準確的得到物體的表面資訊。
本系統之相位移動器由三個壓電致動器所構成，由於壓電致動器本身之差異與結構上受到不同應力的影響，在移動的過程中會產生移動不均勻的問題；為了提高其精準度，本文章提出一種有效提升精確度的校正方法，從理論推導出壓電致動器位移與條紋斜率之關係，接著主要是利用傅立葉轉換後，在空間頻率座標上之訊號為兩個脈衝函數值，並藉由兩點之連線求得其斜率，再由輸入電壓與條紋斜率變化之關係，得知各PZT之間的差異，來完成校正各PZT之工作，再藉由五步相移將其相位值計算出來，可發現此方法的確改善移動不均勻的現象，未經校正時，相位移誤差之RMS值為3.492 deg，約為0.0194λ，而經校正後，相位移誤差之RMS值最好可降低至0.062 deg，約為0.0034λ，證明出此方法有效的提升相位移動的精確度。

摘要(英)

The precision of phase-shift to the measurement of phase-shift interferometry may most represent reliability of a sample. It is represented the reliability of the sample that the measurement of the phase-shift accuracy for the phase-shift interferometry.
In this thesis, a method to calibrate a phase-shifting adapter (PSA) with three piezoelectric ceramics based on the relationship between the displacement of PZT and the slope of interference fringe is proposed to increase the testing precision of phase-shifting interferometer. The unequal movement of the PSA is improved by this method.
The paper proposed that the relations between shifting and the slope of interference fringe for phase-shifting adapter. Subsequently used flat plate interferogram as a sinusoidal wave and transferred from Fourier transform. Signals in frequency domain were two values of pulse functions, and calculated the slope by connecting the points. Before the phase-shifting adapter is calibrated, the RMS of phase shift error is 0.3492 deg, which is equal to 0.0194λ. After the phase-shifting adapter is calibrated, the RMS of phase shift error is 0.0621 deg, which is equal to 0.00004λ.It is found that this method really improved the phenomenon of moving unevenness, and advanced precision of phase-shift effectively.

關鍵字(中)

★ 誤差分析
★ 相移校正
★ 快速傅立葉轉換
★ 相移干涉術

關鍵字(英)

★ noise analysis
★ phase shift calibration
★ phase shifting interferometry
★ fast fourier transform

論文目次

中文摘要................................................................................................................I
英文摘要..............................................................................................................II
誌謝.....................................................................................................................III
目錄.....................................................................................................................IV
圖目錄..............................................................................................................VIII
表目錄..............................................................................................................XIV
第一章緒論.......................................................................................................1
1.1 前言..........................................................................................................1
1.2 研究目的與動機......................................................................................2
第二章相移干涉系統.......................................................................................4
2.1 基本干涉原理..........................................................................................4
2.1.1 光干涉原理......................................................................................5
2.1.2 相移干涉技術..................................................................................7
2.1.3 各式相移演算法..............................................................................9
2.1.3.1 三步相移演算法......................................................................9
2.1.3.2 四步相移演算法....................................................................10
2.1.3.3 Carré演算法..........................................................................10
2.1.3.4 五步相移演算法....................................................................11
2.1.4 相移量與CCD之誤差分析...........................................................12
2.1.4.1 三步相移理論誤差................................................................12
2.1.4.2 四步相移理論誤差................................................................14
2.1.4.3 五步相移理論誤差................................................................15
2.1.4.4 CCD之理論誤差...................................................................16
2.1.5 相位展開與重建技術....................................................................17
2.2 壓電致動器之工作原理........................................................................19
2.2.1 壓電材料........................................................................................19
2.2.2 壓電原理及現象............................................................................21
2.2.3 壓電應用........................................................................................23
2.3 干涉條紋之分析....................................................................................23
2.3.1 光學像差分析................................................................................23
2.3.2 影像快速傅立葉轉換....................................................................26
2.3.3 濾波器的分析................................................................................29
2.3.4 條紋斜率計算................................................................................29
第三章相移精度文獻探討.............................................................................32
3.1 各演算法之比較....................................................................................32
3.1.1 線性誤差分析................................................................................32
3.1.2 非線性誤差分析............................................................................33
3.2 校正相位移動裝置................................................................................35
3.2.1 光學條紋投射器之步進馬達........................................................35
3.2.2 干涉儀之相位移動器....................................................................37
3.3 計算相位變化........................................................................................38
第四章提升相位移動器精確度之理論.........................................................40
4.1 建立壓電致動器之空間分佈................................................................40
4.1.1 一般分佈情形................................................................................40
4.1.2 特殊分佈情形................................................................................43
4.2 條紋斜率分析........................................................................................51
4.2.1 傅立葉空間分析............................................................................51
4.2.2 分析條紋斜率之極限....................................................................53
4.3 提升相位移動器精確度之方法............................................................57
第五章模擬之研究.........................................................................................59
5.1 模擬光學雜訊........................................................................................59
5.1.1 雜訊分析........................................................................................59
5.1.2 光學像差之影響............................................................................66
5.2 模擬PZT移動情形................................................................................69
5.3 模擬五步相移法....................................................................................70
第六章實驗與分析.........................................................................................72
6.1 實驗系統與架構....................................................................................72
6.2 實驗步驟................................................................................................77
6.3 實驗結果................................................................................................82
6.3.1 校正分析........................................................................................86
6.3.2 校正後結果....................................................................................90
6.4 實驗誤差分析........................................................................................92
6.4.1 空氣擾動與環境振動....................................................................92
6.4.2 非線性移動現象與磁滯現象........................................................94
6.4.3 其他誤差影響..............................................................................100
第七章結論與未來展望...............................................................................103
7.1 實驗結論..............................................................................................103
7.2 未來展望..............................................................................................104
參考文獻...........................................................................................................106
附錄一...............................................................................................................112
附錄二...............................................................................................................115
附錄三...............................................................................................................116

參考文獻

[1] 張良知, ”光干涉學及其應用-光之干涉,” 科儀新知, 第四十九期 (第十卷第五期), pp. 54-65, 1989.
[2] 張良知, ”光干涉學及其應用-雙光束干涉,” 科儀新知, 第五十期 (第十卷第六期), pp. 25-36, 1989.
[3] K. Creath and A. Morales, “Contact and noncontact profilers,” Chap. 17 in Optical Shop Testing, D. Malacara, Ed., pp. 697-700, Wiley, New York, 1992.
[4] J. Ojeda-Castaneda, “Foucault, wire, and phase modulation tests,” Chap. 8 in Optical Shop Testing, D. Malacara, Ed., pp. 265-299, Wiley, New York, 1992.
[5] I. Ghozeil, “Hartmann and other screen tests,” Chap. 10 in Optical Shop Testing, D. Malacara, Ed., pp. 367-385, Wiley, New York, 1992.
[6] D. K. Cheng, Field and wave electromagnetics, pp. 306-317, Addison-wesley, Reading, Massachusetts, 1983.
[7] M. V. Klein and T. E. Furtak, “Interference,” Chap. 5 in Optics, pp. 263-272, Wiley, New York, 1986.
[8] 張良知, ”光干涉學及其應用-光之干涉,” 科儀新知, 第五十一期 (第十一卷第一期), pp. 8-16, 1989.
[9] J. E. Greivenkamp and J. H. Bruning, “Phase Shifting Interferometry,” Chap. 14 in Optical Shop Testing, D. Malacara, Ed., pp. 501-589, Wiley, New York, 1992.
[10] Gallagher, J. E. and D. R. Herriott, “Wavefront Measurement” U. S. Patent3,694,088, 1972/1972.
[11] Creath, K., “Phase-Measurement Interferometry Technique,” in Progress in Optics. Vol. XXVI, E. Wolf, Ed., Elsevier Science Publishers, Amsterdam, 349-393, 1988.
[12] J. C. Wyant, C. L. Koliopoulos, B. Bhushan and O. E. George, “An Optical Profilometer for Surface Characterization of Magnetic Media,” ASLE Trans., 27, 101, 1984.
[13] J. C. Wyant, “Interferometry optical metrology: basic principles and new systems,” Laser Focus, 65–71, 1982.
[14] Carré, P. “Installation et Utilisation du Comparateur Photoelectrique et Interferentiel du Bureau International des Poids de Mesures,” Metrologia 2, 13, 1966.
[15] P. Hariharan, B. F. Oreb, and T. Eiju, ‘’Digital Phase-Shifting Interferometry: a Simple Error-Compensating Phase Calculation Algorithm,” Appl. Opt. 13, 2504, 1987.
[16] 吳朗, ”電子陶瓷壓電,” 全欣資訊圖書股份有限公司, 1995.
[17] 池田拓郎, ”基本壓電材料學”, 復漢出版社, 1985.
[18] http://www.cs.pu.edu.tw/~ychu/class951/ImageProcessing/vendor/Ch05.ppt
[19] D. W. Robinson and G. T. Reid, Interferogram Analysis, 2nd Ed., pp. 123-126, Institute of Physics Publishing, Bristol and Philadelphia, 1993.
[20] J. Schwider, R. Burow, K. E. Elssner et al., “Digital wave-front measuring interferometry: some systematic error. sources,” Appl. Opt. 22, 3421-3432, 1983.
[21] K.G. Larkin and B.F. Oreb, “Design and assessment of symmetrical phase-shifting algorithms,” J. Opt. Soc. Am. A 9, 1740-1748, 1992.
[22] J. B. Hayes, “Linear methods of computer controlled optical figuring” PhD Dissertation Optical Sciences Center University of Arizona Tucson AZ, 1984.
[23] C. Ai and J. C. Wyant, “Effect of piezoelectric transducer nonlinearity on phase shift interferometry,” Appl. Opt. 26, 1112–1116, 1987.
[24] M. Jiang, H. Y. Tam, X. Y. He, “Phase shifting calibrated with digital image correlation method,” Proc. SPIE 5852, 599-607, 2005.
[25] Yu Zhu, Jingbang Chen, Hui Liu, Rihong Zhu and Yuling Xiao, “Nonlinear calibrating for phase-shifting adapter with three pztz,” Microwave and Optical Technology Letters, vol. 23, no. 6, 413-414, 1999.
[26] Bernd Gutmann and Herbert Weber, “Phase-shifter calibration and error detection in phase-shifting application: a new method,” Appl. Opt. Vol. 37, 7624-7631, 1998.
[27] Xin Chen, Maureen Gramaglia, and John A. Yeazell, “Phase-shift calibration algorithm for phase-shifting interferometry,” J. Opt. Soc. Am. A, Vol.17, No.11, 2061-2066, 2002.
[28] Kieran G. Larkin, “A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns,” Opt. Express 9, 236-253, 2001.
[29] Kemao Qian, Seah Hock Soon and Anand Asundi, “Calibration of phase shift from two fringe patterns,” Measurement Science and Technology, 15, 2142-2144, 2004.
[30] Improving the linearity of piezoelectric ceramic actuators, Electron Lett, 442-444, 1982.
[31]陸懋宏，吳政芳，”利用雙波長相移干涉術量測三維表面輪廓”，國立交通大學光電工程研究所，民國八十八年。
[32]曾垂拱，葉格銘，“菲索干涉儀與壓電材料之晶圓表面量測”，國立台灣科技大學機械工程技術研究所碩士學位論文，民國九十二年。
[33] P. Abhijit, R. Langoju, and P. Rastogi, "A state space approach in phase shifting interferometry," Optics Communications, vol. 263, no. 2, pp. 281-288, 2006.
[34] D. J. Bone, H. A. Bachor, and R. J. Sandeman, "Fringe-pattern analysis using a 2-D Fourier transform," Appl. Opt, vol. 25, no. 10, pp. 1653-1660, 1986.
[35] M. Chen, H. Guo, and C. Wei, "Algorithm immune to tilt phase-shifting error for phase-shifting interferometers," Appl. Opt, vol. 39, no. 22, pp. 3894-3898, 2000.
[36] Y. Y. Cheng and J. C. Wyant, "Phase shifter calibration in phase-shifting interferometry," Applied Optics, vol. 24, no. 18, pp. 3049-3052, 1985.
[37] K. A. Goldberg and J. Bokor, "Fourier-transform method of phase-shift determination," Appl. Opt, vol. 40, no. 17, pp. 2886-2893, 2001.
[38] K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, "Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts," J. Opt. Soc. Am. A, vol. 14, no. 4, pp. 918-930, 1997.
[39] K. Hibino, K. G. Larkin, B. F. Oreb, and D. I. Farrant, "Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts: reply to comment," Journal of the Optical Society of America A, vol. 15, no. 5, pp. 1234-1235, 1998.
[40] Q. Kemao, "Windowed Fourier transform for fringe pattern analysis: addendum," Applied Optics, vol. 43, no. 17, pp. 3472-3473, 2004.
[41] Q. Kemao, "Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations," Optics and Lasers in Engineering, vol. 45, no. 2, pp. 304-317, 2007.
[42] H. J. Kim and B. W. James, "Two-dimensional Fourier-transform techniques for the analysis of hook interferograms," Applied Optics, vol. 36, no. 6, pp. 1352-1356, 1997.
[43] R. Langoju, A. Patil, and P. Rastogi, "Super-resolution Fourier transform method in phase shifting interferometry," Optics Express, vol. 13, no. 18, pp. 7160-7173, 2005.
[44] R. Langoju, A. Patil, and P. Rastogi, "Estimation of multiple phases in interferometry in the presence of nonlinear arbitrary phase steps," Optics Express, vol. 14, no. 17, pp. 7686-7691, 2006.
[45] R. Langoju, A. Patil, and P. Rastogi, "Chirp estimation in phase-shifting interferometry," Optics Letters, vol. 31, no. 13, pp. 1982-1984, 2006.
[46] R. Langoju, A. Patil, and P. Rastogi, "A novel approach for characterizing the nonlinear phase steps of the PZT in interferometry," Optics and Lasers in Engineering, vol. 45, no. 2, pp. 258-264, 2007.
[47] W. S. Li and X. Y. Su, "Real-time calibration algorithm for phase shifting in phase-measuring profilometry," Optical Engineering, vol. 40, no. 5, pp. 761-766, 2001.
[48] J. B. Liu and P. D. Ronney, "Modified Fourier transform method for interferogram fringe pattern analysis," Applied Optics, vol. 36, no. 25, pp. 6231-6241, 1997.
[49] J. H. Massig and J. Heppner, "Fringe-pattern analysis with high accuracy by use of the Fourier-transform method: theory and experimental tests," Applied Optics, vol. 40, no. 13, pp. 2081-2088, 2001.
[50] R. A. Nicolaus, "Evaluation of Fizeau Interferences by Phase-Shifting Interferometry," Optik, vol. 87, no. 1, pp. 23-26, 1991.
[51] A. Patil, B. Raphael, and P. Rastogi, "Generalized phase-shifting interferometry by use of a direct stochastic algorithm for global search," Optics Letters, vol. 29, no. 12, pp. 1381-1383, 2004.
[52] A. Patil and P. Rastogi, "Approaches in generalized phase shifting interferometry," Optics and Lasers in Engineering, vol. 43, no. 3-5, pp. 475-490, 2005.
[53] A. Patil and P. Rastogi, "Nonlinear regression technique applied to generalized phase-shifting interferometry," Journal of Modern Optics, vol. 52, no. 4, pp. 573-582, 2005.
[54] A. Patil and P. Rastogi, "A min-norm approach for estimating phase distribution in an interferogram," Journal of Modern Optics, vol. 53, no. 3, pp. 283-293, 2006.
[55] A. Patil, R. Langoju, and P. Rastogi, "Constraints in dual phase shifting interferometry," Optics Express, vol. 14, no. 1, pp. 88-102, 2006.
[56] K. Qian, Y. Fu, Q. Liu, H. S. Seah, and A. Asundi, "Generalized three-dimensional windowed Fourier transform for fringe analysis," Optics Letters, vol. 31, no. 14, pp. 2121-2123, 2006.
[57] K. M. Qian, H. S. Seah, and A. Asundi, "Fault detection by interferometric fringe pattern analysis using windowed Fourier transform," Measurement Science & Technology, vol. 16, no. 8, pp. 1582-1587, 2005.
[58] C. Quan, S. H. Wang, and C. J. Tay, "Nanoscale surface deformation inspection using FFT and phase-shifting combined interferometry," Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology, vol. 30, no. 1, pp. 23-31, 2006.
[59] J. A. Quiroga, D. Crespo, J. Vargas, and J. A. Gomez-Pedrero, "Adaptive spatiotemporal structured light method for fast three-dimensional measurement," Optical Engineering (Bellingham, Washington), vol. 45, no. 10, p. 107203, 2006.
[60] P. D. Ruiz, J. M. Huntley, and G. H. Kaufmann, "Adaptive phase-shifting algorithm for temporal phase evaluation," Journal of the Optical Society of America A-Optics Image Science and Vision, vol. 20, no. 2, pp. 325-332, 2003.
[61] P. D. Ruiz, J. M. Huntley, and G. H. Kaufmann, "Adaptive phase-shifting algorithm for temporal phase evaluation," Journal of the Optical Society of America A, vol. 20, no. 2, pp. 325-332, 2003.
[62] P. D. Ruiz, G. H. Kaufmann, and J. M. Huntley, "New adaptive phase-shifting algorithm for temporal phase evaluation," Proceedings of SPIE, vol. 4777, p. 251, 2003.
[63] Y. J. Shen and J. M. Huntley, "Simple method to calibrate phase modulators for use in dynamic phase-shifting interferometry," Optical Engineering, vol. 43, no. 12, pp. 2998-3002, 2004.

指導教授

歐陽盟(Mang Ou-Yang)

審核日期

2007-7-24

推文