| Planck constant (h) is a fundamental physical constant that links the macroscopicand the microscopic matter.The accurate determination of h can be used to redefine thekilogram and therefore realize a kind of mass quantum stantard.Different from the usualwatt balance approach, National Institute of Metrology, China (NIM)has proposed anovel joule balance method for precisely measuring h.In this method, the displacementof a moving coil should be measured with nanometer uncertainty for the whole range ofseveral tens of minimeters, and the results should be traced to the length standardmetrologically; In addition the moving coil’s attitude parameter must be recordedsimultaneously.We first review the laser interferometrics methods of measuring the velocity of themoving coil in Watt balance such as homodyne,heterodyne and Fabry-Perotinterferometer;We then analyze the specific requirements and characteristics of themoving coil on the basis of the principle and apparatus of Joule Balance.A three-axiallaser heterodyne interferometric measurement method is ultimately proposed to measurethe displacement and the attitude of the moving coil in real time.Further,afrequency-shift folded Fabry-perot cavity interferometric method is developed to tracethe measurement result to the length standard or time and frequency standardmetrologically.A three-axial laser heterodyne interferometric system is constructed to implementthe measurement of the moving coil in Joule Balance.In order to determine the positionand attitude parameters of the moving coil, the relationship between the centroidcoordinates and plane posture of the moving coil and three-axial displacementmeasurement coordinates is analyzed.It is helpful for the adjustment and alignment ofthe mutual inductance coil as well as the measurement of the mutual inductance in JouleBalance. The long term stability and repeatability of the displacement and plane posturemeasurement of the moving coil in ambient air are investigated in the simulated joulebalance by this system, the comparison experiment for the displacement is alsogived.the measurement uncertainty of the displacement is determined to be32nm,8nmfor the change in the refractive index of air of10-7,10-8. Furthermore, a folded Fabry-Perot cavity interferometric system by means offrequency-shift is built for absolute distance measurement and calibration.Acombination of an acousto-optic frequency shifter (AOFS) and an off-set lock laser,which is controlled to stabilize at an offset frequency from Iodine stabilized laser, isworked as a tunable and highly stable light source.Considering the dependence of thebeam’s Bragg diffraction angle on the modulation frequency,AOFS with double-passconfiguration is proposed to eliminate the alignment problem effectively. Therelationship between the modulation bandwidth and the efficiency of Bragg diffractionis analyzed for the optical and acoustic beam having the finite width, and the parameterof the focusing lens are carefully designed to optimize the bandwidth and the efficiencyat the same time.The double bandwidth of AOFS in our double-pass configuration isachieved successfully with the above effort, and the beam quality of the first orderdiffracted light is also ensured.When the displacement of the highly reflected mirror ofthe folded Fabry-Perot cavity is modulated by a piezoelectric transducer (PZT) with asine wave, the sine wave are immerged in the reflected signal of the folded Fabry-Perotinterferometric signal, the amplitude and the phase characteristics of the sine signal areused to discriminate the resonance peak, Dual lock-in amplifers are applied to detect theadjacent resonant peaks of the fold Fabry-Perot cavity.Based on the above experimentalapparatus,the results show that the length of the cavity can be measured with anuncertainty of about1.5×10-7in the whole range of245mm～295mm. |
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