计算电容中Fabry-Perot干涉仪测量位移的相位修正方法  

Methode of phase correction of displacement measurement using Fabry-Perot interferometer in calculable capacitor

作　　者：王建波[1,2] 钱进[2] 刘忠有[2] 陆祖良[2] 黄璐[2] 杨雁[2] 殷聪[2] 李同保[1] 

机构地区：[1]同济大学物理科学与工程学院,上海200092 [2]中国计量科学研究院,北京100013

出　　处：《物理学报》2016年第11期40-48,共9页Acta Physica Sinica

基　　金：国家重大科学仪器设备开发专项(批准号:2012YQ10022503);质检公益性行业科研专项(批准号:20150002)资助的课题~~

摘　　要：计算电容是复现电学阻抗单位的基准装置,利用计算电容值和量子霍尔电阻值可以准确计算出精细结构常数α.计算电容的本质是通过高准确度地测量屏蔽电极的位移,实现对电容量值的测量.因此,基于Fabry-Perot干涉仪的精密电极位移测量系统是计算电容装置中最为核心和关键的部分.在Fabry-Perot干涉仪测位移过程中,由于高斯激光束存在轴向Gouy相位,该附加相位将会引起相邻干涉条纹对应位移的变化(大于或者小于λ),导致位移的测量值与实际值存在偏差.本文阐述了高斯激光场的传播特性,利用高斯激光束在自由空间和透过薄透镜复振幅的变换关系,建立了计算电容装置中Fabry-Perot干涉仪透射光束的传输模型;通过对不同腔长的Fabry-Perot干涉仪透射光场相位的分析,获得了高斯激光束轴向Gouy相位修正与传输距离的关系.结果表明,当腔长从111.3 mm移动至316.3 mm时,在接收距离为560 mm的情况下,高斯光束轴向Gouy相位引起的位移修正的绝对值最小为0.7 nm,其相对相位修正量|δL|/|?L|=3.4×10^(-9).The calculable capacitor is a classical and fundamental experimental apparatus in precision electromagnetic measurements.It is the alternating current（AC） impedance primary standard,and an important tool in measuring the fine structure constant.The calculable capacitor provides a way to directly link the capacitance unit to the mechanical unit of length.In the calculable capacitor,the displacement measurement of the guard electrode is an essential part,because the average value of the cross capacitances is directly proportional to the linear displacement of the moving guard electrode.In order to measure the displacement with a high accuracy of 10^（-9） or lower,a Fabry-Perot interferometer,whose cavity length is traceable to a stabilized laser by the phase sensitive detection technique,is employed.Considering that the Fabry-Perot interferometer is irradiated by the Gaussian laser beam,the effect of the phase shift of the Gaussian field,relative to the plane wave,should be carefully considered in the displacement measurement.The amplitude of the Gaussian laser beam disperses out of the region where it can be assumed to be plane-wave propagation,so its wavefronts bend and their spacing is different from that of the plane wave.As a result,the corresponding distance of an interference fringe from the coherent Gaussian laser beams is not strictly equal to λ,and it means that the displacement correction based on the phase shift of the Gaussian laser beam in the Fabry-Perot interferometer is inevitable.Therefore,the measured result should add or subtract the correction value to obtain the actual displacement of the interferometer.In order to determine the Gouy phase correction,an interferometer model based on the calculable capacitor is studied analytically and numerically.Using the free space propagation and lens transformation of the Gaussian beam field,the complex amplitude of the partial beam transmitted through the interferometer is obtained,and its phase versus the longitude propagation distance is analyze

关 键 词：Gouy相位 位移修正 Fabry-Perot干涉仪 计算电容 

分 类 号：TM934.2[电气工程—电力电子与电力传动] TH744.3[机械工程—光学工程]