阿伏伽德罗常数测量中硅球直径测量的若干关键问题研究
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摘要
质量单位“千克”是目前国际单位制七个基本量中唯一用实物复现的基准,而标准单晶硅球直径的精密测量是实现阿伏伽德罗常数精确测定,进而建立质量自然基准的关键技术。为完善我国标准单晶硅球直径精密测量系统的不足,进一步提高测量结果的准确度,以及为新直径测量系统的构建提供理论支持,本文在总结国内外标准硅球直径精密测量系统发展现状及其特点的基础上,对我国直径测量系统的测量光路优化调整、光束质量影响、干涉图像处理方法等若干问题进行了研究。
标准硅球直径测量系统利用光学干涉基本原理实现测量,其关键组成包括相移发生系统、硅球位置控制系统、真空绝热及温控测量系统、Fabry-Perot干涉系统、计算机控制及数据处理系统等,论文对各个部分进行了研究,并给出了部分重要的实验结论。
直径测量系统具有纳米级高精度和对称双光路的特点,确定合适的光路结构参数以及光路调整方法是保证测量系统精度的关键。从条纹对比度定义出发,对图像具有最佳对比度条件进行了理论分析和数值模拟。建立了光路对准误差分析模型,详细推导了光路对准对测量结果的影响,结合测量光路特点,提出了“虚拟平行平板法”对入射光的垂直度进行精确调整的方法,实验验证结果表明了该方法的可行性。
由于系统采用的是激光光源,需要根据高斯光束的特点对其影响进行研究。在阐述高斯光束的特性及变换理论、平面波干涉理论基础上,对正入射时高斯光束反射光中心的多光束干涉和双光束干涉进行了分析,然后深入研究了高斯光束相位因子φ(z)在硅球与标准板间距测量,以及两标准板间距测量中引入的误差,最后对不同条件下高斯光束反射光中心的干涉光强进行了数值模拟,并分析了高斯光束对五步相移算法的影响。
结合本系统干涉圆环图像的特点,对干涉图处理方法进行了改进,提出了精确确定硅球顶点与标准板内表面间距的新方法,引入了波面拟合技术。首先对干涉图像中所有点进行相位解算并展开,然后采用Zernike多项式对波面进行拟合,将离散的相位值变为连续的相位分布,最后通过确定相位的极值得到真正的圆环中心位置。数值模拟结果表明,此方法可以消除系统误差,进一步提高系统测量精度。
The unit of mass, the kilogram, is now the only base unit of the International System of Units (SI) being still defined in terms of a material artefact. The precision measurement for the diameter of a single crystal silicon sphere is one of the key techniques for the accurate determination of Avogadro constant, which aims at the realization of mass natural standard. In order to improve the accuracy of the diameter measurement system established by our country and give theoretical support for the establishment of the new measuring system, the present status and characteristics of the diameter measuring system for the single-crystal silicon sphere are summarized at home and abroad. In the thesis, some important aspects are studied, such as the optical path optimization and adjustment, the influence of the beam quality, and the processing method of interferograms.
The basic principle of the diameter measuring system is the optical interferometry, and the key components include the phase-shifting system, the position control system of the silicon sphere, the vacuum insulation and temperature control system, the Fabry-Perot interferometric system, the computer control and data processing system, and so on. Each part of the system is studied, and also some important experiment results are given.
The diameter measuring system has two significant characteristics, nano-meter accuracy and symmetric optical path. So the suitable optical structure and the adjustment methods are of great importance to insure the measurement accuracy. Based on the definition of the fringe contrast, the optimum contrast condition of the interference fringes is theoretically analyzed and numerically simulated. The mathematical model of the optical alignment error is established, and the influence on the measuring results is deduced. Considering the characteristics of the optical path, a novel method is proposed for accurately adjusting the incident angle of laser beam relative to the plate, which is called virtual parallel plate method. In addition, the results of the verification experiment are finished.
Because the light source of the system is He-Ne laser, the influence of Gaussian beam on the diameter measurement needs to be studied. The characteristics and the transform theories of Gaussian beam and the plane-wave interfeorence theories are expounded, and multiple beam interference and dual beam interference of the central reflected light of a Gaussian beam with normal incidence are analyzed. Furthermore, the distance measurement errors between silicon sphere and the plate and the space measurement of two parallel plates are studied, which are caused by phase factorφ(z). Then, the numerical simulations of the central reflected light of a Gaussian beam in different situations are performed,and the impact of Gaussian beam on five-step phase-shifting interferometry is shown.
According to the characteristic of the circular interferogram, the improvement of the processing method is performed. A new method with the wavefront fitting technique is proposed to determine the accurate distance between the sphere and the inner face of the plate. Firstly, the phases of all the discrete points in the interference image must be calculated and unwrapped. Then the continuous phase distribution can be obtained by Zernike polynomials fitting at all discrete points. Lastly, the real center of the circular fringes can be calculated from analytic representation at the location of the extremum on the phase map. Numerical simulation results show that this method can eliminate the system errors, and the measuring accuracy can be improved.
标准硅球直径测量系统利用光学干涉基本原理实现测量,其关键组成包括相移发生系统、硅球位置控制系统、真空绝热及温控测量系统、Fabry-Perot干涉系统、计算机控制及数据处理系统等,论文对各个部分进行了研究,并给出了部分重要的实验结论。
直径测量系统具有纳米级高精度和对称双光路的特点,确定合适的光路结构参数以及光路调整方法是保证测量系统精度的关键。从条纹对比度定义出发,对图像具有最佳对比度条件进行了理论分析和数值模拟。建立了光路对准误差分析模型,详细推导了光路对准对测量结果的影响,结合测量光路特点,提出了“虚拟平行平板法”对入射光的垂直度进行精确调整的方法,实验验证结果表明了该方法的可行性。
由于系统采用的是激光光源,需要根据高斯光束的特点对其影响进行研究。在阐述高斯光束的特性及变换理论、平面波干涉理论基础上,对正入射时高斯光束反射光中心的多光束干涉和双光束干涉进行了分析,然后深入研究了高斯光束相位因子φ(z)在硅球与标准板间距测量,以及两标准板间距测量中引入的误差,最后对不同条件下高斯光束反射光中心的干涉光强进行了数值模拟,并分析了高斯光束对五步相移算法的影响。
结合本系统干涉圆环图像的特点,对干涉图处理方法进行了改进,提出了精确确定硅球顶点与标准板内表面间距的新方法,引入了波面拟合技术。首先对干涉图像中所有点进行相位解算并展开,然后采用Zernike多项式对波面进行拟合,将离散的相位值变为连续的相位分布,最后通过确定相位的极值得到真正的圆环中心位置。数值模拟结果表明,此方法可以消除系统误差,进一步提高系统测量精度。
The unit of mass, the kilogram, is now the only base unit of the International System of Units (SI) being still defined in terms of a material artefact. The precision measurement for the diameter of a single crystal silicon sphere is one of the key techniques for the accurate determination of Avogadro constant, which aims at the realization of mass natural standard. In order to improve the accuracy of the diameter measurement system established by our country and give theoretical support for the establishment of the new measuring system, the present status and characteristics of the diameter measuring system for the single-crystal silicon sphere are summarized at home and abroad. In the thesis, some important aspects are studied, such as the optical path optimization and adjustment, the influence of the beam quality, and the processing method of interferograms.
The basic principle of the diameter measuring system is the optical interferometry, and the key components include the phase-shifting system, the position control system of the silicon sphere, the vacuum insulation and temperature control system, the Fabry-Perot interferometric system, the computer control and data processing system, and so on. Each part of the system is studied, and also some important experiment results are given.
The diameter measuring system has two significant characteristics, nano-meter accuracy and symmetric optical path. So the suitable optical structure and the adjustment methods are of great importance to insure the measurement accuracy. Based on the definition of the fringe contrast, the optimum contrast condition of the interference fringes is theoretically analyzed and numerically simulated. The mathematical model of the optical alignment error is established, and the influence on the measuring results is deduced. Considering the characteristics of the optical path, a novel method is proposed for accurately adjusting the incident angle of laser beam relative to the plate, which is called virtual parallel plate method. In addition, the results of the verification experiment are finished.
Because the light source of the system is He-Ne laser, the influence of Gaussian beam on the diameter measurement needs to be studied. The characteristics and the transform theories of Gaussian beam and the plane-wave interfeorence theories are expounded, and multiple beam interference and dual beam interference of the central reflected light of a Gaussian beam with normal incidence are analyzed. Furthermore, the distance measurement errors between silicon sphere and the plate and the space measurement of two parallel plates are studied, which are caused by phase factorφ(z). Then, the numerical simulations of the central reflected light of a Gaussian beam in different situations are performed,and the impact of Gaussian beam on five-step phase-shifting interferometry is shown.
According to the characteristic of the circular interferogram, the improvement of the processing method is performed. A new method with the wavefront fitting technique is proposed to determine the accurate distance between the sphere and the inner face of the plate. Firstly, the phases of all the discrete points in the interference image must be calculated and unwrapped. Then the continuous phase distribution can be obtained by Zernike polynomials fitting at all discrete points. Lastly, the real center of the circular fringes can be calculated from analytic representation at the location of the extremum on the phase map. Numerical simulation results show that this method can eliminate the system errors, and the measuring accuracy can be improved.
引文
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