Research On Relative Position Measuring Methods Of Coils Assembly In Joule Balance For Mass Quantum Metrology

In the International System of Units（SI）,kilogram kg is the only basic unit without a quantum standard.Redefining the kilogram with a quantum standard is quite meaningful but especially challenging in scientific research,therefore it was list as one of the six tough scientific experiments in the world by the journal Nature.The National Institute of Metrology in China has proposed the joule balance method to measure Plank constant,whose basic principle is that an electromagnetic force arised from two electrified coils（coil assembly）balances with the gravity of a standard mass,and then quantum standard of mass can be connected with other quantuam standards including time,electrical units,and meter.During this progress,the relative position measuring system plays a key role in joule balance,which contributes the joule balnce to tracing the quantum standard of meter,and maintains a constant integrating range during the measurement.The relative position measuring system of coil assembly can be devided into the relative displacment measuring system,and relative zero position measuring system.The joule balance uses the heterodyen Michelson laser interferometry to measure the relative displacement,which has a large measurment range,sub-nanometer resolution,and strong anti-interference capacity,but because of the periodic nonlinearity error,this method cannot meet the demands of the 2 ×10-8 relative measurement uncertainty of joule balance.As to the absolute zero position measurment demand,joule balance uses mechanical limit at present to set the zero positon and there is not a effective absolute zero position method with sub-micrometer resolution for joule balance.Lack of an absolute zero position method does harm to the constant integrationg range during the measurement,and will bring a 10-7 or even larger relative measurement uncertainty.By researching the principle of joule balance,this paper established error models of relative displacement and relative zero positon.According to those models,this paper proposed the method to restrain nonlinearity errors and the method to measure the zero position.Then this paper estimated the measurement uncertainy of those two methods.The paper has studied the principle and experiments of the methods,the main contents and results are as follows:As to the periodic nonlinearity error in relative displacement system,this paper proposed a method based on a input and output（I/O）lights common path heterodyne interferometer with spatially separated beams.This method utilized a special I/O common path heterodyne with spatially separated beams,so that the nonlinearity error from double-frequency mixing can be eliminated,in addition,the nonlinearity error from multi-order DFS phase mixing can also be restrained by analyzing the souce of multi-order ghost beams and their light intensity.The specially designed I/O common path interferometer contributes to the measuement in vacuum by superposing the input and output lights,so that optical path can be obviously simplied and easy to be adjusted.Both the theory and simulation result show that the nonlinearity can be restrained below 0.2 nm.As to deficiency of absolute zero position measurement,this paper proposed a differential capacitance sensing method based on a single grounded shield window.This method linearly contacted the relative posions with the output differential capacitance values by using shield window to change the effective overlap area,so that the sensitivity can be guaranted and immune to coil waggling.This paper establised a mathematical model for this method by conformal transformation,and theoretically varify its sentivity,and anti-disturbance ability.The simulation results showed that the nonlinearity of this sensor is within 0.2 μm,and the measurement uncertainties from the distrubance along x,y axes are 0.17 μm and 0.08 μm respectively.According to the research above,this paper firstly experimentally verified the nonlinearity model based on multi-order DFS phase mixing.The experiment results showed that the nonlinearity amplitude caused by multi-order DFS can reach to 1 nm,which must be restrained in joule balance.In order to validate the nonlinearity restrain method,this research has established the relevant optical path of heterodyne interferometer.The experiment results show that the nonlinearity amplitude can be restrained to 0.16 nm,which fulfills the uncertainty demands of 0.2 nm.In order to validate the absolute zero position measuring method,this research has calibrated the differential capacitance sensor we proposed.The experiment results showed that the measurement uncertainty caused by this measuring system is 0.2 μm.In conclusion,the methods proposed in this paper have met the relative uncertianty demands of 2×10^-8 in joule balance.