Precision measurement of the refractive index of air using a phase modulated homodyne interferometer with a variable length vacuum cavity

Abstract

Precision measurement of the refractive index of air (RIA) using a phase modulated homodyne interferometer with a variable length vacuum cavity is proposed. In this method, to realize precise measurement of RIA, the vacuum cavity is pushed to generate a continuous optical path change between air and vacuum, and the resulting phase change of the interferometer is demodulated with an ellipse-fitting PGC-Arctan algorithm. In order to demodulate the interference phase accurately, a hybrid phase modulation is realized by applying a sinusoidal modulation to an electro optical modulator and a triangular modulation to a piezoelectric transducer. The feature of this individual modulation is that it can guarantee sufficient data for elliptical fitting without sacrificing the modulation depth. The significant advantage of the proposed method is that it can correctly count the integral fringes during the vacuum cavity pushing even with vibrating and air fluctuation as well as precisely demodulate the phase before and after the pushing by calibrating the ellipse parameters in real time. The measurement principle and phase demodulation are described in detail. The static signal processing experiment was carried out to evaluate the accuracy of the phase demodulation scheme. Two RIA measurement experiments were performed, and the results are compared with those obtained with Edlén equations to validate the feasibility and effectiveness of the proposed method. Experimental results show that the standard deviation of RIA is better than 2.6 × 10−8 in 20 min and 4.6 × 10−8 in 8.5 h.