基于双波长干涉的微表面形貌测量的算法和实验研究
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摘要
随着微细加工技术的不断发展进步和微电路、微光学元件、微机械等微表面的不断出现,对微表面三维形貌测量技术也提出了更高的要求,迫切需要微表面三维形貌测量的技术。在众多微表面形貌测量方法中,相移干涉法以其高精度和非接触的优点,得到了广泛的应用。本文在相移干涉法基础上,提出了一种双波长干涉测量方法,该方法可以直接得到真实相位分布,不需要解包裹的过程。用双波长干涉测量重建微表面形貌的算法和实验是本文研究的关键。围绕这一主要内容,所做的主要工作如下：
1.从干涉的基本原理出发,对相移干涉的基本理论进行了研究,在此基础上提出了一种利用双波长干涉的微表面形貌检测方法。研究了双波长干涉的相位提取算法,其关键是初始点的相位计算和判别。该方法不需要解包裹的过程,同时也避免了由相移器引入的附加误差。
2.用软件模拟了基于双波长干涉进行微表面检测的过程。首先建立理想三维物体模型,基于双波长干涉理论制作干涉图,利用本文提出的相位提取算法获取相位的真实值,获得了表面形貌。并且在干涉图上加入不同程度的高斯噪声和椒盐噪声,来评估相位提取算法的可行性和鲁棒性。
3.设计了基于双波长干涉重建物体表面形貌的系统。根据系统的要求,分别给出了针孔滤波系统,扩束准直系统,干涉系统和数据接收系统的参数。
4.搭建了基于双波长干涉重建物体表面形貌的实验系统,分别以平面反射镜和凹面反射镜为被测物,利用两个不同波长的激光器获得了双波长干涉图,利用本文提出的相位提取算法,提取了被测物的真实相位,获得了微表面的三维形貌。从而从实验上证明了双波长干涉方法的可行性。
With the development of micro-fabrication technology, it is necessary for micro-three-dimensional surface measurement. Phase-shifting interferometry has been widely used in micro-surface topography measurement with the advantages of high precision and non-contact. In this paper, a dual-wavelength interferometry algorithm which can get the real phase distribution directly without unwrapping is presented. Theoretical and experimental studies of the algorithm based on the dual wavelength interferometry are the focus on this research. The main work as follows has been done according to this main content.
1. Based on the interference theory, the principle of dual-wavelength interfere was introduced. And the phase extraction algorithm based on two-wavelength interferometry was presented. This algorithm not only got rid of unwrapping but also avoided the additional errors from phase shifter.
2. The process of surface reconstruction was simulated. Firstly, the ideal model of a three-dimensional object was established, and its interferograms were made based on the dual-wavelength interference theory. Then, the value of the phase can be obtained using the algorithm mentioned above. Additionally, different levels of Gaussian noise, salt and pepper noise were added in the interferograms to analyze the noise insensitive of the algorithm, and the results showed that the algorithm was insensitive to these kinds of noise which proved the feasibility of the algorithm.
3. The surface morphology reconstruction system with dual-wavelength interferometry was designed. According to the actual requirements of the system, the parameters of the pinhole filter, the collimated beam expander, the interferometer and the data receiving system were calculated.
4. An experimental system was carried out to get the interferograms of flat mirror and concave mirror, and further more got the true values of the phases. The results show that the dual wavelength interference theory and algorithm was correct.
1.从干涉的基本原理出发,对相移干涉的基本理论进行了研究,在此基础上提出了一种利用双波长干涉的微表面形貌检测方法。研究了双波长干涉的相位提取算法,其关键是初始点的相位计算和判别。该方法不需要解包裹的过程,同时也避免了由相移器引入的附加误差。
2.用软件模拟了基于双波长干涉进行微表面检测的过程。首先建立理想三维物体模型,基于双波长干涉理论制作干涉图,利用本文提出的相位提取算法获取相位的真实值,获得了表面形貌。并且在干涉图上加入不同程度的高斯噪声和椒盐噪声,来评估相位提取算法的可行性和鲁棒性。
3.设计了基于双波长干涉重建物体表面形貌的系统。根据系统的要求,分别给出了针孔滤波系统,扩束准直系统,干涉系统和数据接收系统的参数。
4.搭建了基于双波长干涉重建物体表面形貌的实验系统,分别以平面反射镜和凹面反射镜为被测物,利用两个不同波长的激光器获得了双波长干涉图,利用本文提出的相位提取算法,提取了被测物的真实相位,获得了微表面的三维形貌。从而从实验上证明了双波长干涉方法的可行性。
With the development of micro-fabrication technology, it is necessary for micro-three-dimensional surface measurement. Phase-shifting interferometry has been widely used in micro-surface topography measurement with the advantages of high precision and non-contact. In this paper, a dual-wavelength interferometry algorithm which can get the real phase distribution directly without unwrapping is presented. Theoretical and experimental studies of the algorithm based on the dual wavelength interferometry are the focus on this research. The main work as follows has been done according to this main content.
1. Based on the interference theory, the principle of dual-wavelength interfere was introduced. And the phase extraction algorithm based on two-wavelength interferometry was presented. This algorithm not only got rid of unwrapping but also avoided the additional errors from phase shifter.
2. The process of surface reconstruction was simulated. Firstly, the ideal model of a three-dimensional object was established, and its interferograms were made based on the dual-wavelength interference theory. Then, the value of the phase can be obtained using the algorithm mentioned above. Additionally, different levels of Gaussian noise, salt and pepper noise were added in the interferograms to analyze the noise insensitive of the algorithm, and the results showed that the algorithm was insensitive to these kinds of noise which proved the feasibility of the algorithm.
3. The surface morphology reconstruction system with dual-wavelength interferometry was designed. According to the actual requirements of the system, the parameters of the pinhole filter, the collimated beam expander, the interferometer and the data receiving system were calculated.
4. An experimental system was carried out to get the interferograms of flat mirror and concave mirror, and further more got the true values of the phases. The results show that the dual wavelength interference theory and algorithm was correct.
引文
[1]殷纯永主编,现代干涉测量技术,天津,天津大学出版社,1999：290-297
[2]周明宝,林大键,郭履容,郭永康,微结构表面形貌的测量,光学精密工程,1999,7(3)：7-13
[3]H.Dagnall. Exploring Surface Texture.2nd Edition. London:Rank Taylor Hobson Limited,1986:5-8
[4]李艳军,左洪福等,显微观测技术的新进展及其应用,光学仪器,2002,24(2)：32-37
[5]K.J.Stout, L.Blunt, Nanometres to micrometres:therr-dimensional surface measurement in bio-engineering, Surface and Coatings Technology,71(1995) 69-81
[6]Song J F, Vorburger T V. Stylus profiling at high resolution and low force. Appl Opt,1991,30:42-50
[7]Stedman M, Lindsey K. Limits of surface measurement by stylus instruments. Proc SPIE,1988,1009:56-61
[8]Whitehouse D J. Instrumentation for measuring finish, defects and gloss. Proc SPIE,1985,525:106-123
[9]K D Vernon-parry, Scaning Electron Microscopy:an introduction, Analysis, Ⅲ-Vs Review·Vol.13 No.4 2000
[10]T.G.Lenihan, A.P.Malshe, W.D.Brown, L.W/Schaper, Artifacts in SPM measurements of thin films and coatings, Thin Solid Films 270(1995) 356-361.
[11]包学诚,周志尧,非接触式表面微观形貌光学测量技术的进展,现代科学仪器,1999(6)：8-10
[12]高志山,陈进榜,表面微观形貌的显微干涉检测原理及干涉显微镜发展现状,光学仪器,1999,21(6)：36-42
[13]惠梅,表面微观形貌测量中相移干涉术的算法与试验研究,中国科学院西安光学精密机械研究所博士论文,2001年
[14]许谊,徐毓娴,惠梅等,微分相衬干涉显微镜定量测量表面形貌,光学精密工程,9(3)：221-230
[15]卓永模,杨甬英,徐敏,张为权,双焦干涉表面微观轮廓检测,仪器仪表学报,1993,14(2)
[16]钱克矛,光学干涉计量中的位相测量方法研究,中国科学技术大学博士学位论文,2000年7月
[17]钱克矛,续伯钦,伍小平,光学干涉计量中的位相测量方法,实验力学,2001,16(3)：239～249
[18]James C.Wyant, Phase shifting interferometry,1998,pp1-40
[19]K.A.Ngoi, K.Venkatakrishnan, N.R.Sivakumar, T.Bo, Instantaneous Phase Shifting Arrangement for Microsurface Profiling of Flat Surface, Opt. Comm. 2001,190:109-116
[20]R.Escalona, E.lglesias, J.Vicens, Realization of a Phase Shifting interferential Microscope and its Application to the High Resolution Profilometry, Instrumentation and Development,1994,3(4):53-58
[21]Halioua M and Liu H, Optical three-dimensional sensing by phase measuring profilometry, Optics and Lasers in Engineering,1989,11 (2/3):787-793
[22]Michael B. North-Morris, Jay VanDelden, and James C. Wyant, Phase-shifting birefringent scatterplate interferometer, Appl. Opt.,2002,41(4):668-677
[23]Hariharan P, Phase-stepping interferometry with laser diodes:effect of changes in laser power with output wavelength, Appl. Opt.,1989,28(1):27-29
[24]洪佩智,计量光学,北京：兵器工业出版社,1992年第一版p203-216
[25]S.Ishikawa, G.Bonck, h.Bohme. Phase-shifting interferometry with a coupled interferometer:Application to optical roughness of gauge blocks. Optik,1992,91:103-108.
[26]R.A.Nicolas. Precise method to determine systematic erros in phase-shifting interferometry on Fizeau interferences. Applied Optics,1993,32(31);6380-6386.
[27]J.C.Wyant, interferometric optical metrology:basic principles and new systems, Laser Focus,1982,14(5):65-71.
[28]M.J.downs, measurement of the profiles of super-smooth surfaces using optical interferometer, proc. SPIE,1988,vol.1009:14-19.
[29]薛实福,李庆祥,王伯雄等,显微干涉系统测量微细图形的台阶高度,清华大学学报,1990,30,(5)：38-44
[30]v.Srinivasan, H.C.liu, Maurice halioua, Automated phase-measuring profilometry: a phase mapping approach,Appl:Opt.1985,24(2):85-187.
[31]Phillion,D.W,. "General methods for generating phase-shifting interferometry algorithms," Appl. Opt.36,8098(1977).
[32]Nagaski Ohyama, Takeshi Shimano, Jumpei Tsujijushi and Toshio Honda, An analysis of systematic phase errors due to nonlinearity in fringe scanning systems, Opt. Comm..1986,58(4):223-225
[33]赵宏,薛实福,李庆祥等,光学轮廓仪测量原理及其误差分析,清华大学学报,1992,32(2)：42-47
[34]Cheng, Y.-Y. and J.C. Wyant, "Phase Shifter Calibration in Phase-Shifting Interferometry," Appl. Opt.,24,3049(1985)
[35]J.S.Sirkis, Ym.Chen, h.Singh, and A.Y.Cheng, computerized optical fringe pattern analysis in photomechanics:a review, Opt. Eng.1992,31,304-314
[36]徐先锋,广义相移数字全息干涉术相移提取及波前再现算法的理论及实验研究,山东大学博士学位论文,2008年.
[37]Stoilov g, dragcstinov T. Phase-stepping Interferometry:Five-frame Algorithm with an Arbitrary step[J]. Optics and Lasers in Engineering,1997(28):61-69
[38]N. A. Ochoa and J. M. Huntley, Convenient method for calibrating nonlinear phase modulators for use in phase-shifting interferometry[J], Opt. Eng.,1998, 37(9):2501-2505.
[39]C. Wei, M. Chen, and Z. Wang, General phase-stepping algorithm with automaticcalibration of phase steps [J], Opt. Eng.,1999,38(8):1357-1360.
[40]Y.Surrel, Phase stepping:a new self-calibrating algorithm [J], App. Opt., 1993,32(19):3598-3600.
[41]P. L. Wizinowich, Phase-shifting interferometry in the presence of vibration:a new algorithm and system [J], App. Opt.,1990,29(22):3271-3279.
[42]Y. Ishii and R. Onodera, Phase-extraction algorithm in laser diode phase-shifting interferometry [J], Opt.Lett.,1995,20(18):1883-1885.
[43]K. G. Larkin, Natural demodulation of two-dimensional fringe patterns:Ⅱ. Stationary phase analysis of the spiral phase quadrature transform [J], J. Opt. Soc. Am.A,2001,18(8):1871-1881.
[44]T. Kreis, Digital holographic interference-phase measurement using the Fourier transform method [J], J.Opt. Soc. Am. A,1986,3(6):847-855.
[45]J. Masajada, A. Popiolek-Masajada, and D. M. Wieliczka, The interferometric system using optical vortices as phase markers [J], Opt. Commun. 2002,207(2):85-93.
[46]K. A. Goldberg and J. Bokor, Fourier-transform method of phase-shift determination [J], App. Opt.,2001,40(17):2886-2894.
[47]L. Z. Cai, Q. Liu, and X. L. Yang, Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps [J], Opt. Lett.,2003,28(19):1808-1810.
[48]X. F. Meng, X. Peng, L. Z. Cai, A. M. Li, P. Guo, and Y. R. Wang, Wavefront reconstruction and three-dimensional shape measurement by two-step dc-term-suppressed phase-shifted intensities, Opt. Lett.,2009,34(8):1210-1212
[49]X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, Two-step phase-shifting interferometry and its application in image encryption, Opt. Lett.,2006,31(10):1414-1416
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[59]李晓静,相移干涉微表面形貌检测仪的数据处理与实验研究,天津大学,2007
[2]周明宝,林大键,郭履容,郭永康,微结构表面形貌的测量,光学精密工程,1999,7(3)：7-13
[3]H.Dagnall. Exploring Surface Texture.2nd Edition. London:Rank Taylor Hobson Limited,1986:5-8
[4]李艳军,左洪福等,显微观测技术的新进展及其应用,光学仪器,2002,24(2)：32-37
[5]K.J.Stout, L.Blunt, Nanometres to micrometres:therr-dimensional surface measurement in bio-engineering, Surface and Coatings Technology,71(1995) 69-81
[6]Song J F, Vorburger T V. Stylus profiling at high resolution and low force. Appl Opt,1991,30:42-50
[7]Stedman M, Lindsey K. Limits of surface measurement by stylus instruments. Proc SPIE,1988,1009:56-61
[8]Whitehouse D J. Instrumentation for measuring finish, defects and gloss. Proc SPIE,1985,525:106-123
[9]K D Vernon-parry, Scaning Electron Microscopy:an introduction, Analysis, Ⅲ-Vs Review·Vol.13 No.4 2000
[10]T.G.Lenihan, A.P.Malshe, W.D.Brown, L.W/Schaper, Artifacts in SPM measurements of thin films and coatings, Thin Solid Films 270(1995) 356-361.
[11]包学诚,周志尧,非接触式表面微观形貌光学测量技术的进展,现代科学仪器,1999(6)：8-10
[12]高志山,陈进榜,表面微观形貌的显微干涉检测原理及干涉显微镜发展现状,光学仪器,1999,21(6)：36-42
[13]惠梅,表面微观形貌测量中相移干涉术的算法与试验研究,中国科学院西安光学精密机械研究所博士论文,2001年
[14]许谊,徐毓娴,惠梅等,微分相衬干涉显微镜定量测量表面形貌,光学精密工程,9(3)：221-230
[15]卓永模,杨甬英,徐敏,张为权,双焦干涉表面微观轮廓检测,仪器仪表学报,1993,14(2)
[16]钱克矛,光学干涉计量中的位相测量方法研究,中国科学技术大学博士学位论文,2000年7月
[17]钱克矛,续伯钦,伍小平,光学干涉计量中的位相测量方法,实验力学,2001,16(3)：239～249
[18]James C.Wyant, Phase shifting interferometry,1998,pp1-40
[19]K.A.Ngoi, K.Venkatakrishnan, N.R.Sivakumar, T.Bo, Instantaneous Phase Shifting Arrangement for Microsurface Profiling of Flat Surface, Opt. Comm. 2001,190:109-116
[20]R.Escalona, E.lglesias, J.Vicens, Realization of a Phase Shifting interferential Microscope and its Application to the High Resolution Profilometry, Instrumentation and Development,1994,3(4):53-58
[21]Halioua M and Liu H, Optical three-dimensional sensing by phase measuring profilometry, Optics and Lasers in Engineering,1989,11 (2/3):787-793
[22]Michael B. North-Morris, Jay VanDelden, and James C. Wyant, Phase-shifting birefringent scatterplate interferometer, Appl. Opt.,2002,41(4):668-677
[23]Hariharan P, Phase-stepping interferometry with laser diodes:effect of changes in laser power with output wavelength, Appl. Opt.,1989,28(1):27-29
[24]洪佩智,计量光学,北京：兵器工业出版社,1992年第一版p203-216
[25]S.Ishikawa, G.Bonck, h.Bohme. Phase-shifting interferometry with a coupled interferometer:Application to optical roughness of gauge blocks. Optik,1992,91:103-108.
[26]R.A.Nicolas. Precise method to determine systematic erros in phase-shifting interferometry on Fizeau interferences. Applied Optics,1993,32(31);6380-6386.
[27]J.C.Wyant, interferometric optical metrology:basic principles and new systems, Laser Focus,1982,14(5):65-71.
[28]M.J.downs, measurement of the profiles of super-smooth surfaces using optical interferometer, proc. SPIE,1988,vol.1009:14-19.
[29]薛实福,李庆祥,王伯雄等,显微干涉系统测量微细图形的台阶高度,清华大学学报,1990,30,(5)：38-44
[30]v.Srinivasan, H.C.liu, Maurice halioua, Automated phase-measuring profilometry: a phase mapping approach,Appl:Opt.1985,24(2):85-187.
[31]Phillion,D.W,. "General methods for generating phase-shifting interferometry algorithms," Appl. Opt.36,8098(1977).
[32]Nagaski Ohyama, Takeshi Shimano, Jumpei Tsujijushi and Toshio Honda, An analysis of systematic phase errors due to nonlinearity in fringe scanning systems, Opt. Comm..1986,58(4):223-225
[33]赵宏,薛实福,李庆祥等,光学轮廓仪测量原理及其误差分析,清华大学学报,1992,32(2)：42-47
[34]Cheng, Y.-Y. and J.C. Wyant, "Phase Shifter Calibration in Phase-Shifting Interferometry," Appl. Opt.,24,3049(1985)
[35]J.S.Sirkis, Ym.Chen, h.Singh, and A.Y.Cheng, computerized optical fringe pattern analysis in photomechanics:a review, Opt. Eng.1992,31,304-314
[36]徐先锋,广义相移数字全息干涉术相移提取及波前再现算法的理论及实验研究,山东大学博士学位论文,2008年.
[37]Stoilov g, dragcstinov T. Phase-stepping Interferometry:Five-frame Algorithm with an Arbitrary step[J]. Optics and Lasers in Engineering,1997(28):61-69
[38]N. A. Ochoa and J. M. Huntley, Convenient method for calibrating nonlinear phase modulators for use in phase-shifting interferometry[J], Opt. Eng.,1998, 37(9):2501-2505.
[39]C. Wei, M. Chen, and Z. Wang, General phase-stepping algorithm with automaticcalibration of phase steps [J], Opt. Eng.,1999,38(8):1357-1360.
[40]Y.Surrel, Phase stepping:a new self-calibrating algorithm [J], App. Opt., 1993,32(19):3598-3600.
[41]P. L. Wizinowich, Phase-shifting interferometry in the presence of vibration:a new algorithm and system [J], App. Opt.,1990,29(22):3271-3279.
[42]Y. Ishii and R. Onodera, Phase-extraction algorithm in laser diode phase-shifting interferometry [J], Opt.Lett.,1995,20(18):1883-1885.
[43]K. G. Larkin, Natural demodulation of two-dimensional fringe patterns:Ⅱ. Stationary phase analysis of the spiral phase quadrature transform [J], J. Opt. Soc. Am.A,2001,18(8):1871-1881.
[44]T. Kreis, Digital holographic interference-phase measurement using the Fourier transform method [J], J.Opt. Soc. Am. A,1986,3(6):847-855.
[45]J. Masajada, A. Popiolek-Masajada, and D. M. Wieliczka, The interferometric system using optical vortices as phase markers [J], Opt. Commun. 2002,207(2):85-93.
[46]K. A. Goldberg and J. Bokor, Fourier-transform method of phase-shift determination [J], App. Opt.,2001,40(17):2886-2894.
[47]L. Z. Cai, Q. Liu, and X. L. Yang, Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps [J], Opt. Lett.,2003,28(19):1808-1810.
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