纳米精度测量与校准系统关键技术研究
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摘要
论文开展的创新性工作包括以下几个方面：
1．相位偏移干涉移相误差补偿技术研究。在研究相位偏移干涉测量技术基础上，重点研究了五幅算法计算精度及移相误差对计算结果的影响；提出了四幅算法及五幅算法移相误差补偿方法，理论分析及模拟仿真结果显示，该方法可以补偿移相过程中一阶移相误差及二阶移相误差对相位偏移干涉测量精度的影响。采用相位偏移干涉仪试验验证了上述补偿方法的有效性
2．相位偏移干涉测量技术在纳米精度测量与校准系统中的应用研究。将相位偏移干涉测量技术应用于测量与校准系统运动转角误差测量，初步试验验证了该方法的可行性。
3．外差式激光干涉仪非线性误差分析研究。从理论上研究了双频激光干涉仪非线性误差产生的原因；分析了直流偏量、等幅性偏差、正交误差对比相法相位测量结果的影响；
4．外差式激光干涉仪非线性误差补偿技术研究。在研究干涉测量非线性误差补偿原理的基础上，提出一种基于待检偏测量信号参数估计原理的非线性误差补偿方法。设计了试验验证方案，采用改变密封玻璃腔内气体压力的方法模拟纳米级微位移。试验结果表明，该补偿方法可以较好地修正双频激光干涉仪由于频率泄漏造成的非线性测量误差，使测量不确定度减少二分之一。
5．柔性铰链结构参数分析。研究了二维复合式悬臂梁柔性铰链模态频率、静态特性与铰链结构参数之间的关系；建立了结构参数和力学特性
西北工业大学博士论文
之间的对应关系;研究了基于复合式悬臂梁柔性铰链的二维十字对称柔性
铰链结构，对其模态频率以及位移应力特性进行仿真试验;结果表明此种
结构形式的运动对称性很好;其驱动位移与结构体最大拉压应力值之间接
近线性关系，而且这种结构可以得到100林m以上的运动位移。
6.基于二维十字对称柔性铰链结构的微位移工作台试验测试。利用
单频激光干涉仪测试其运动定位误差特性，相位偏移干涉法测试运动转角
误差，光电自准仪测试其运动偏摆误差。该研究为纳米精度校准技术系统
中位移驱动与定位装置研究提供了基础，试验数据为测量数据综合误差补
偿技术研究奠定了基础。
With the increasing of the accurate of the modern manufacture, research on nanometer measurement method and establishing of nanometer calibration systems has been one important domain. This dissertation is based upon the project "the Research on Nanometer Calibration" (No. 60102102), and the "Study of Micro-position Systems for Nanometer Precision Calibration Technology" (No. 01153077) supported by the Aeronautic Science foundation of China. This paper mainly includes the following aspects:
1. The deviation introduced by reference phase shifting errors on four-steps and five-steps algorithm are analyzed. Based on the principle of phase algorithm, a novel compensation method of reference phase-shifting error is described for four-steps algorithm and the five-steps algorithm. The theoretic analysis and data simulation indicate that the phase deviation arising from the first and the second harmonic reference phase-shifting errors can be eliminated using this method. By using a phase shifting interferometer with resolution of 0.1nm, the compensation method was experimentally verified.
2. The application of the phase shifting interferometry in Nanometer Accuracy Measurement and Calibration Systems (NAMCS) is studied. The measuring system to measure the dimensional rotation errors of the NAMCS is configured. The principium experiment verified this method.
3. The non-linearity errors in the heterodyne interferometry is investigated. For the heterodyne interferometer used within the nanometer and sub-nanometer region, the frequency leakages due to the imperfect optical elements and the thermal non-linearity drift restrict its uncertainty to about 20nm.A more comprehensive theoretic analysis for this non-linearity of heterodyne interferometer is given. The contribution of the phase quadrature error, the variable gains and the mean levels to the uncertainty of the phase meter are discussed.
4.The compensation technology for non-linearity errors in heterodyne
interferometry is studied. One novel non-linearity compensation method is proposed based on the parameters estimation of the discrete interference signals. The effectiveness of the compensation method considering phase-quarter errors, unequal amplitude and the DC components are simulated. The experiments setup is founded, in which the micro-displacement is simulated by the variation of the gas's refractive index in the closed glass cavity. The results show that this method makes it possible to reduce the uncertainty from 20nm to less than 10nm.
5. The structure of the cantilever flexure hinges is analyzed. The relations between the mode frequency, static characteristic and the framework parameters are studied. A two dimension crossed symmetric cantilever flexure hinge is investigated using finite elements method. The simulation of the mode frequency and the study of the relation between the displacements and the stress indicate that this flexure hinge has good flexibility and linearity between the displacement and the maximum stress. Moreover its motion range reaches to more than 100μm×00μ m.
6. Experimental investigation of the motion specifications of two dimension stage based on above crossed symmetric flexure hinge. The position errors are measured by two dimension single-frequency laser interferometer, the pitch and yaw errors are tested using phase shifting interferometer with a resolution of 0.1nm, the linearity along motion axis is investigated by autocollimator with 0.01" uncertainty. These experiments establish the foundation for the orientation system in the subject of "Nanometer Accuracy Measurement And Calibration Systems" (NAMCS) and the data provide the information for the synthesize compensation technology.
1．相位偏移干涉移相误差补偿技术研究。在研究相位偏移干涉测量技术基础上，重点研究了五幅算法计算精度及移相误差对计算结果的影响；提出了四幅算法及五幅算法移相误差补偿方法，理论分析及模拟仿真结果显示，该方法可以补偿移相过程中一阶移相误差及二阶移相误差对相位偏移干涉测量精度的影响。采用相位偏移干涉仪试验验证了上述补偿方法的有效性
2．相位偏移干涉测量技术在纳米精度测量与校准系统中的应用研究。将相位偏移干涉测量技术应用于测量与校准系统运动转角误差测量，初步试验验证了该方法的可行性。
3．外差式激光干涉仪非线性误差分析研究。从理论上研究了双频激光干涉仪非线性误差产生的原因；分析了直流偏量、等幅性偏差、正交误差对比相法相位测量结果的影响；
4．外差式激光干涉仪非线性误差补偿技术研究。在研究干涉测量非线性误差补偿原理的基础上，提出一种基于待检偏测量信号参数估计原理的非线性误差补偿方法。设计了试验验证方案，采用改变密封玻璃腔内气体压力的方法模拟纳米级微位移。试验结果表明，该补偿方法可以较好地修正双频激光干涉仪由于频率泄漏造成的非线性测量误差，使测量不确定度减少二分之一。
5．柔性铰链结构参数分析。研究了二维复合式悬臂梁柔性铰链模态频率、静态特性与铰链结构参数之间的关系；建立了结构参数和力学特性
西北工业大学博士论文
之间的对应关系;研究了基于复合式悬臂梁柔性铰链的二维十字对称柔性
铰链结构，对其模态频率以及位移应力特性进行仿真试验;结果表明此种
结构形式的运动对称性很好;其驱动位移与结构体最大拉压应力值之间接
近线性关系，而且这种结构可以得到100林m以上的运动位移。
6.基于二维十字对称柔性铰链结构的微位移工作台试验测试。利用
单频激光干涉仪测试其运动定位误差特性，相位偏移干涉法测试运动转角
误差，光电自准仪测试其运动偏摆误差。该研究为纳米精度校准技术系统
中位移驱动与定位装置研究提供了基础，试验数据为测量数据综合误差补
偿技术研究奠定了基础。
With the increasing of the accurate of the modern manufacture, research on nanometer measurement method and establishing of nanometer calibration systems has been one important domain. This dissertation is based upon the project "the Research on Nanometer Calibration" (No. 60102102), and the "Study of Micro-position Systems for Nanometer Precision Calibration Technology" (No. 01153077) supported by the Aeronautic Science foundation of China. This paper mainly includes the following aspects:
1. The deviation introduced by reference phase shifting errors on four-steps and five-steps algorithm are analyzed. Based on the principle of phase algorithm, a novel compensation method of reference phase-shifting error is described for four-steps algorithm and the five-steps algorithm. The theoretic analysis and data simulation indicate that the phase deviation arising from the first and the second harmonic reference phase-shifting errors can be eliminated using this method. By using a phase shifting interferometer with resolution of 0.1nm, the compensation method was experimentally verified.
2. The application of the phase shifting interferometry in Nanometer Accuracy Measurement and Calibration Systems (NAMCS) is studied. The measuring system to measure the dimensional rotation errors of the NAMCS is configured. The principium experiment verified this method.
3. The non-linearity errors in the heterodyne interferometry is investigated. For the heterodyne interferometer used within the nanometer and sub-nanometer region, the frequency leakages due to the imperfect optical elements and the thermal non-linearity drift restrict its uncertainty to about 20nm.A more comprehensive theoretic analysis for this non-linearity of heterodyne interferometer is given. The contribution of the phase quadrature error, the variable gains and the mean levels to the uncertainty of the phase meter are discussed.
4.The compensation technology for non-linearity errors in heterodyne
interferometry is studied. One novel non-linearity compensation method is proposed based on the parameters estimation of the discrete interference signals. The effectiveness of the compensation method considering phase-quarter errors, unequal amplitude and the DC components are simulated. The experiments setup is founded, in which the micro-displacement is simulated by the variation of the gas's refractive index in the closed glass cavity. The results show that this method makes it possible to reduce the uncertainty from 20nm to less than 10nm.
5. The structure of the cantilever flexure hinges is analyzed. The relations between the mode frequency, static characteristic and the framework parameters are studied. A two dimension crossed symmetric cantilever flexure hinge is investigated using finite elements method. The simulation of the mode frequency and the study of the relation between the displacements and the stress indicate that this flexure hinge has good flexibility and linearity between the displacement and the maximum stress. Moreover its motion range reaches to more than 100μm×00μ m.
6. Experimental investigation of the motion specifications of two dimension stage based on above crossed symmetric flexure hinge. The position errors are measured by two dimension single-frequency laser interferometer, the pitch and yaw errors are tested using phase shifting interferometer with a resolution of 0.1nm, the linearity along motion axis is investigated by autocollimator with 0.01" uncertainty. These experiments establish the foundation for the orientation system in the subject of "Nanometer Accuracy Measurement And Calibration Systems" (NAMCS) and the data provide the information for the synthesize compensation technology.
引文
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【3】 赵克功，计量仪器仪表与计量科学的现状和发展趋势及其在21世纪工业中的作用，
仪器仪表学报，1997，Vol．18(5)：92～98
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【7】 Wetzels S.F.C.L., Schellekens P.H.J. Development of a traceable laser based displacement calibration systems with nanometer accuracy, Annals of the CIRP, 1997,Vol.46:481～484
【8】 Andrew Yacoot and Michael J. Downs,The use of X-ray interferometry to investigate the linearity of the NPL differential Plane Mirror Optical Interferometer, Meas. Sci. and Technol. 2000,Vol.11:1126～1130
【9】 Hou, W. and Wilkening G., Investigation and compensation of the nonlinearity of heterodyne interferometer, Precision Engineering,1992,Vol.1491～98
【10】 王林、曹芒、李达成，用于纳米测量的扫描X射线干涉技术，光学精密工程，1998，Vol．6(1)：47
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【12】 Dai Xiaoli and SetaKatuo, High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry, Meas. Sci. Terchnol. 1998,Vol.9: 1031～35
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【2】 T. V. Vorburger, J.A. Dagata, G. Wilkening and K. Lizuka, Industrial Uses of STM and AFM, Annals of CIRP,1997,Vol.46(2):597～620
【3】 赵克功，计量仪器仪表与计量科学的现状和发展趋势及其在21世纪工业中的作用，
仪器仪表学报，1997，Vol．18(5)：92～98
【4】 BobroffN. Recent advances in displacement measuring interferometry [J]. Meas. Sci. Technol. 1995, 4: 907-926
【5】 M. Bienias, K. Hasche, R. Seemann, K. Zhiele, 计量型原子力显微镜，1998，Vol．19(1)：1～8
【6】 Ronald Dixson, Rainer Koning, T. V. Vorburger, Joseph Fu, Measurement of pitch and width samples with the NIST calibrated Atomic Force Microscope, SPIE,1998,VOL.3332:420～432
【7】 Wetzels S.F.C.L., Schellekens P.H.J. Development of a traceable laser based displacement calibration systems with nanometer accuracy, Annals of the CIRP, 1997,Vol.46:481～484
【8】 Andrew Yacoot and Michael J. Downs,The use of X-ray interferometry to investigate the linearity of the NPL differential Plane Mirror Optical Interferometer, Meas. Sci. and Technol. 2000,Vol.11:1126～1130
【9】 Hou, W. and Wilkening G., Investigation and compensation of the nonlinearity of heterodyne interferometer, Precision Engineering,1992,Vol.1491～98
【10】 王林、曹芒、李达成，用于纳米测量的扫描X射线干涉技术，光学精密工程，1998，Vol．6(1)：47
【11】 胡小唐等，用于扫描探针显微技术的空间超精密定位系统，天津大学学报，1996，Vol．29(1)：1～6
【12】 Dai Xiaoli and SetaKatuo, High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry, Meas. Sci. Terchnol. 1998,Vol.9: 1031～35
【13】 Brand U, Herrmann K. A laser measurement system for the high-precision calibration of displacement transducers. Meas. Sci. Technol. 1996, 7: 911-917
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