物理学报2016，Vol.65Issue(11)：110601-1-110601-9,9.DOI:10.7498/aps.65.110601
计算电容中Fabry-Perot干涉仪测量位移的相位修正方法∗
Metho de of phase correction of displacement measurement using Fabry-Perot interferometer in calculable capacitor
摘要
Abstract
The calculable capacitor is a classical and fundamental experimental apparatus in precision electromagnetic mea-surements. 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 interfer-ometer, 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 propaga-tion, 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 toλ/2, 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 Gaus-sian beam field, the complex amplitude of the partial beam transmitted through the interferometer is obtained, and its phase versus the longitude propagation distance is analyzed. The amplitude and phase of the total transmitted beam, which is the coherent superposition of all the partial beams, are presented. Since the Fabry-Perot interferometer in the calculable capacitor is actively locked to a stabilized laser at two different cavity lengths, the phase of the transmitted beam at each cavity length is calculated individually. The phase difference between the two transmitted beams versus the longitude propagation distance is also analyzed numerically. The simulation result demonstrates that the minimum value of the displacement correction can be obtained by actively detecting the laser light at a distance of 560 mm from output mirror, when the Fabry-Perot interferometer moves from the cavity length of 111.3 mm to 316.3 mm, and it means that a displacement correction value of 0.7 nm, with a relative value of|δL|/|∆L|=3.4 × 10−9, should be added to the measured displacement of the guard electrode.关键词
Gouy相位/位移修正/Fabry-Perot干涉仪/计算电容Key words
Gouy phase/displacement correction/Fabry-Perot interferometer/calculable capacitor引用本文复制引用
王建波,钱进,刘忠有,陆祖良,黄璐,杨雁,殷聪,李同保..计算电容中Fabry-Perot干涉仪测量位移的相位修正方法∗[J].物理学报,2016,65(11):110601-1-110601-9,9.基金项目
国家重大科学仪器设备开发专项(批准号:2012YQ10022503)和质检公益性行业科研专项(批准号:20150002)资助的课题.@@@@* Project supported by the National Key Scientific Instrument and Equipment Development Project (Grant No.2012YQ10022503), and the Special Scientific Research Fund of Quality Inspection of Public Welfare Profession of China (Grant No.20150002) （批准号:2012YQ10022503）
