Research On Determining The Diameter Of Silicon Sphere By Laser Interference Method

The high-precision measurement of the gravitational constant G has always been one of the difficult and hot issues in the world.The current status of measuring G is that the results of the various groups do not match within the error range.Scientists suspect that there may be unknown systematic errors in the experiment.In 2018,the team of the Center of Gravitational Experiments of Huazhong University of Science and Technology measured the G value through the time-of-swing method and the angular-acceleration-feedback method,reaching the international leading level.In the two experiments,the distance between the center of the attracting mass is the main factor that limits the measurement accuracy,while the roundness and diameter of the sphere are the main sources of error in the measurement of the distance between the centers of the sphere.In order to reduce the influence of the distance between the centers of the sphere,it is an effective way to use single crystal silicon spheres with smaller roundness and more uniform density to measure G.In order to solve the problem of measuring the diameter of silicon spheres,this subject uses laser interferometry to carry out related theoretical and experimental research.In the experiment,the two optical wedges are fixed to the ultra low expansion glass surface in parallel,and the distance between the two optical wedges is L.Then put the single crystal silicon sphere to be measured between the two optical wedges,and the gap between the silicon sphere and the optical wedge is 1dand ^d2.The diameter of the silicon sphere can be determined by measuring L and ^d1⁽¹⁰⁾d2respectively.In order to determine the absolute value of the distance,a three-coordinate measuring machine is first used to determine the value range of the integral order of interference,and then two lasers with wavelengths of 633 nm and 532 nm are used to measure the fractional order of interference.According to the initial measurement results of the three coordinates and the fractional order of interference obtained by two-wavelength laser,The method of exact fractions is used to finally determine the integral order of interference.The frequency of the laser is measured by the beat frequency based on the fine spectrum of the iodine molecule,and the refractive index of the air is measured by the Edlen formula.Combining integral and fractional order of interference,laser frequency,and air refractive index the measurement result of the diameter of the single crystal silicon sphere is 127.226429(20)mm.The experimental error is analyzed in detail:For the experimental optical path,the laser frequency is traced to the fine spectrum of the iodine molecule,and the He-Ne laser,which measures the fractional order of interference,has a frequency uncertainty of 11.3MHz within 300 s and the contribution of the diameter measurement uncertainty is 1.6 nm.The total uncertainty of alignment is less than 235?rad,resulting in a diameter measurement uncertainty less than 4.0 nm.The Gouy phase shift of the Gaussian beam results in a diameter measurement uncertainty of 0.9 nm;For the measurement environment,the Edlen formula measures the air refractive index with an accuracy of 3.9×10^-8,resulting in a diameter measurement uncertainty of 5.6 nm.Temperature fluctuation of 20 m K in the experiment results in a diameter measurement uncertainty of 6.4 nm.The thermal expansion coefficients of silicon sphere and ultra low expansion glass contribute 0.3 nm and 2.2 nm to the uncertainty of diameter measurement,respectively Based on the current experimental errors,the uncertainty of the silicon sphere diameter measurement is 20 nm.The measurement accurency of the sphere diameter meet the requirement of the team for the subsequent high-precision measurement of G.