In order to address the limitations of traditional seven-sample algorithms for phase calculation in the measurement of silicon sphere diameter, this article proposes an improved seven-sample algorithm. This algorithm retains all the advantages of traditional methods while effectively eliminating algorithmic errors arising from positioning deviations in step size. Through comprehensive analysis and numerical simulation, the algorithm’s performance has been thoroughly evaluated. The results demonstrate that the improved algorithm not only eliminates or reduces algorithmic errors caused by phase-shifting linear and nonlinear errors but also significantly reduces the impact of intensity errors related to multi-beam interference. Even in the presence of a significant step deviation, the improved algorithm can minimize its adverse impact on the measurement accuracy of the silicon sphere diameter.

The kilogram prototype will be gradually replaced by the quantum datum according to the new definition of kilogram adopted by the 26th International Conference on Measurement. This paper discusses the atomic counting method to reproduce kilogram unit. It briefly introduces the research progress to measure Avogadro constant by X-ray crystal density method (XRCD), namely atomic counting method. It discusses the essential technical route of reproducing mass unit kilogram by atomic counting method and its uncertainty based on the current research of National Institute of Metrology (NIM). The mass of silicon sphere can be determined by measuring sphere diameter and oxide layer thickness according to the new results concerning the measurement of Avogadro constant. Phase shift interferometry is used to measure the diameter of silicon sphere, and the realization of phase shift is the key technology of phase shift measurement. A two-channel precision phase shift generator based on high elastic quartz monomer structure is used to generate the phase shift which is required by interferometry. Its foundation is the characteristics of tiny angular deformation and self-recovery of quartz material, which eliminate the empty path and friction in the process of phase shift and establish a monomer phase shift generator with strong stiffness and ultra-high displacement resolution. And a new five-phase shift algorithm is worked out for the phase solution with a high accuracy. It ensures the excellent accuracy of the algorithm when the step positioning error is less than 20 nm, and transforms the control process of phase shift into measurement, and reduces the application difficulty of the interferometry. Based on the two key technologies mentioned above, an interferometer to measure silicon sphere diameter was established in NIM. The stability of the spherical interferometer were tested many times in the period of two months in 2019. The results show that the maximum difference is 0.5 nm, which indicates the ultra-high precision of the spherical interferometer. The measurement of the thickness of oxide layer not only directly affects the mass of oxide layer, but also causes phase delay in the diameter measurement. The measurement results are also used to correct the diameter of silicon spheres. The thickness measurement of oxide layer by ellipsometry and X-ray reflectivity method is a classical method. The ellipsometer can measure the surface layer quickly and accurately, and its absolute thickness needs to be calibrated by X-ray reflection. The National Institute of Metrology uses the spectral ellipsometer of model SE800DUV produced by Sentech, Germany. To eliminate the aliasing effect caused by spherical divergence, an experimental device of spectral ellipsometer suitable for silicon sphere measurement is established by using the aperture filter method. The optimal accuracy of the measurement system for the oxide layer on the surface of silicon spheres can reach 0.2 nm with this device. The standard uncertainty of mass reproduction of silicon sphere is 2.2x10(-8) kg based on our current technology. The major source of uncertainty comes from the measurement error of the thickness of the oxide layer, which is the essential work in future if the kilogram reproduction is finally carried out with atomic counting method in China.

The standard near-silicon liquid (2329kg/m3) is a mixture liquid of tribromopropane and dibromoethane in a certain proportion. This liquid is used to measure the density of single crystal silicon spheres by a static suspension method and the analysis of the difference in the micro density between two silicon spheres. Measuring the difference in the micro-density of the silicon spheres is of great significance for the new definition of the new mass of kilograms. In order to obtain the micro-density difference of the silicon spheres, it is necessary to calculate the static pressure value and the temperature by separately adjusting the single-crystal silicon spheres to the same suspension state and the compression coefficient of the near-monocrystalline silicon density liquid. Through the adjustment of the same hydrostatic suspension state of a single silica ball in different suspension states, the linear constants measured by the linear model are analyzed to calculate the liquid compression coefficient. For this purpose, a static suspension measuring device for a single crystal silicon ball was designed to maintain the water bath within a range of +/- 0.1mk within 3 hours, and the position control of the silicon ball was determined by controlling the pressure of the upper computer.

When the kilogram is redefined in terms of the fixed numerical value of the Planck constant h,the X-ray crystal density (XRCD) method,among others,is used for realizing the redefined kilogram.The XRCD method has been used for the determination of the Avogadro constant NA by counting the number of atoms in a 28Si-enriched crystal,contributing to a substantial reduction of uncertainty in the values of NA and h to 2 × 10-8.This method can be therefore used reversely for the mass determination of a 1 kg sphere prepared from the crystal.The key technologies of lattice constant,isotope,concentration of silicon,diameter of silicon sphere and surface oxide layer are described.The definition of atomic counting method and the method of its value reproduction are introduced.The method will be an important reference for the quality value reproduction of China after the reform of the international system of units.

The precision measurement of Avogadro constant and realization of mass unit kg based on atom counting of single crystal silicon require the measurement of the mass and volume of a silicon sphere. The non-homogeneously distributed oxide layer, which is several nanometer thick on the surface of the sphere, is key to the correction value of the above parameters. The coordination system of the Si sphere is determined by Laue crystallography and laser marking. Different driving approaches of the Si sphere are compared. The automatic scanning instrument is set up based on spectroscopic ellipsometer. The repeatability and stability are investigated, with the scanning results of the NIM#3 Si sphere being presented. It is indicated that the short-term repeatability of the ellipsometric scanning of the surface oxide layer reaches 0.04 nm.

以质量比较仪为主要称量设备、机械加载、置于隔离罩内的5～2000L容量新基准装置[1，2]，以制备纯水作为检定介质，采用单次替代称重法测量被检标准金属量器与特种量器的容量。建立容量测量数学模型，研究了使用制备纯水为检定介质条件下，实测空气密度与采用固定值1.2kg/m3、罐壁温度采用新的算法计算与使用水温等对容量测量不确定度的影响。

The basic principIe,apparatus,prOcedure and parameters by the methOd Of hydrOstatic weighing was intrOduced. With the hydrOstatic weighing,the density dessiminatiOn frOm the sOIid density primary standard—siIicOn sphere tO the secOnd primary standard—a grOup Of 137 hydrOmeters has been reaIized. The measuring uncertainty in fuII range has been evaIuated in detaiI.

Single crystal silicon (Si) sphere method is an important scheme for precise measurement of Avogadro constant and redefinition of kilogram. The surface oxide layer thickness is related to the correction of the measured mass and diameter of the single crystal sphere, and contributes a large proportion of the relative uncertainty of the Avogadro constant. We discuss several basic problems in measuring the sphere surface by ellipsometer, i.e., the influence of the crystalorientationdependent optical constants and surface curvature induced ellipsometric light beam scattering. And the uncertainty components for the adopted indirect method are analyzed. The study provides both experimental and theoretical bases for the measurement research in surface layer on Si sphere.

The density standard liquid at 2329 kg/m3 close to single crystal silicon (DSL-2329) is widely used in the precise machining of silicon single crystal material, and the accurate measurement of the volume compression coefficient of this liquid plays an important role in the quality control of silicon single crystal machining. To improve the measurement accuracy of the existing measurement method, a measurement method based on hydrostatic suspension principle is discussed to determine the compression coefficient of DSL-2329 liquid. The single crystal sphere is immersed into a sealed vessel full of DSL-2329.The density of the liquid can be adjusted through changing the liquid temperature and static pressure, and the hydrostatic suspension of the silicon single crystal sphere is achieved. The silicon single crystal sphere could be suspended at different temperatures and static pressures, where the temperature and static pressure parameter comply with a linear mathematical model. The compression coefficient is calculated using the data of temperature and static pressure at the suspension state. A hydrostatic suspension experimental system was designed with maximal temperature control error ��1.0��10-4��C within 3 h, and the static floating of the silicon single crystal sphere could be achieved through static pressure regulation with a PID control system. In the experiment, the mixture of 1,2,3-tribromopropane and 1,2-dibromoethane was used as the DSL-2329 liquid. The compression coefficient was measured, and its value is 5.15��10-10 Pa-1, which verifies the effectiveness of the proposed measurement method and experimental system.

液体静力称量法是固体密度测量最常用也是测量准确度较高的一种方法.基于阿基米德原理,研究了表面张力对固体密度测量结果的影响.实验选取纯水和纯酒精2种液体作为工作介质,采用一套高准确度液体静力称量装置测量同一固体样品的密度值.实验结果表明,在表面张力小的液体(纯酒精)中固体样品密度测量结果的分散性明显优于在表面张力大的液体(纯水)中固体样品密度测量结果的分散性,为今后提高固体密度测量准确度提供参考方向.

为了克服单晶硅球密度测量静力称重法精度受液体表面张力的影响,研究了压浮法进行单晶硅球密度精密比较测量方法和测量系统.在一定的温度下,调节压力,利用液体压缩系数控制液体密度使标准单晶硅球和被测单晶硅球稳定悬浮于工作液体中,通过温度、压力和悬浮高度的测量,计算出二者之间的密度差值.通过双层控温系统保证了液体温度长期波动在±0.25 mK内,利用标准单晶硅球在不同温度-压力悬浮条件线性关系计算出液体压缩系数.试验证明,压浮法测量装置实现了单晶硅球密度差值的精密测量,标准测量相对不确定度为2×10-7.

We report an algorithm for searching and tracking the center of the circular interference fringes. The algorithm was programmed by VB.NET for processing the interference images captured by CCD camera. Images were changed into binary gray-level format by the Otsu method. The circular scanning method was used to extract the outline of circular interference fringes, and then the coordinates of the perpendicular subtenses were used to remove noise pixels. Finally, the coordinate of the center was calculated by statistical method. The experimental results are in good agreement with the simulation images. The algorithm had subpixel accuracy and anti-noise ability. Thus, the algorithm can be used in accurate measurement for its automatic processing ability.

The absolute density measurement of the single crystal silicon sphere is decisive procedure to determine Avogadro constant.In this review paper,we introduced the current status of the density measurement of the single crystal silicon sphere,including measurement principles,measurement fields,influence factors,measuring devices and the best ability for the diameter measurement,analyzed the main difficulties and key technologies of density measurement,and predicted the development trend and technology prospect in related fields.

对铂电阻温度计在冰水混合物和真空中的自热效应进行了实验研究,提出应用多电流法修正自热效应引起的测量误差.与传统的二电流法和改进的二电流法相比大大降低了自热效应修正给测量结果引入的不确定度.该研究成果对提高真空环境中温度测量的准确度具有重要意义.

The progress in the determination of the Avogadro constant(N A) is reviewed. The x-ray crystal density method is considered as one of the most accurate route to determine N A. According to this method, the molar mass, density and lattice parameter of the single crystal silicon could be measured accurately, then a relative measurement uncertainty 2×10 -8of N A is achievable. The determination of the molar mass, the diameter of the silicon sphere, and the thickness of the oxide layer on the silicon sphere are key issues that affect the measurement accuracy of N Acurrently, and the focal points for further research of the determination N A is presented.

针对测长绝热真空腔内温度场测量困难的特点,提出应用ANSYS有限元仿真与实验研究相结合的方法进行二维热分析.详细介绍了真空腔的ANSYS有限元建模、参数确定、网格划分、施加载荷和求解过程.仿真结果表明外界环境温度变化1℃,绝热真空腔内温度将变化0.085℃.对仿真结果进行了实验验证,实验结果证明利用该仿真技术可准确、可靠地分析绝热真空腔内的温度场,并且提高实验效率的同时降低了实验成本.

基于ISO、OIML以及API和EI阐述体积和密度计量常用水密度的表达方式,并对其公式的应用提出建议.

以相移干涉测长为应用背景,提出了一种基于“机械扫描”的相移测长方法.利用超高弹性石英材料研制出了干涉测长所需的单体3路相移装置,并利用该相移装置建成了相移测长装置,成功地将位移传感器的量值在线溯源到光学频率标准,从而实现了对3路相移的准确测量.介绍了一种引入步长控制误差的“新五幅相移”实现相位解算方法,算法准确度达到0.01％.对不确定度的定量分析结果表明,基于该机械扫描式相移技术构建的绝对长度测量系统准确度可达0.5 nm.

By the mathematic models of flexible hinge, the accurate relationship between the phase-shifting and pressure acting on the hinge is deduced and verified by experimental results. Through the optimization of the geometric parameter of flexible hinge, a phase-shifting generator is developed to determine the length of an object precisely by interferometry. The experiments show that the triple phase-shifting produced using this generator is up to 1 μm. With this generator, an example for the application in length measurement is introduced. The result shows the length uncertainty is 0.5 nm when the temperature uncertainty is limited in 2 mK. This paper provides a novel technique to measure the dimension of an object, especially to the diameter of a silicon sphere for Avogadro constant project.

Avogadro constant (NA) is a fundamental physical constant which constructs the relationship between the microscopic and macroscopic world. The accurate determination of NA can be used for redefining the base units, e.g. kilogram and mole, so that can promote the development of the International System of Units. An effective route to determine NA directly is the modern X-ray crystal density method, in which several parameters of the single crystal silicon, such as molar mass, density and lattice parameter should be measured accurately. The key technologies related to this method includes: the growth of highly pure silicon crystals, the manufacture of the silicon sphere, determination of the atomic mass of the silicon isotopes, X-ray interferometry, precision optical interferometry, and the determination of the thickness as well as the chemical composition of the ultra-thin film. The recent progress and potential direction in future of this research is reviewed in this paper. The significance of NA in the fundamental metrology is also demonstrated by the case of the kilogram redefinition.