Study On Several Key Problems Of A Single-Crystal Silicon Sphere Diameter Measuring System For Determination Of Avogadro Constant

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.