Yu-Rong Liang, Hui-Zong Duan, Hsien-Chi Yeh, and Jun Luo
MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physics, Huazhong
University of Science and Technology, 1037 Luo Yu Road, Wuhan 430074, People's Republic of China
(Received 2 July 2012; accepted 26 August 2012; published online 19 September 2012)

Ultra-precision phase measurement is a key technology for state-of-the-art laser interferometry. In this paper we present a fully digital phase measurement method based on cross-correlation analysis, and analyze the measurement errors caused by sampling quantization, intrinsic white noise and non-integral-cycle sampling. The last error source results in a cyclic error that has not been reported ever. We used a high-performance data acquisition system to carry out the cross-correlation-based phase measurement, and obtained a noise level of 1.2 × 10 ⁻⁶rad/Hz ^1/2@1 Hz. Moreover, the cyclic phase error of about 10 ⁻²rad/Hz ^1/2, caused by non-integral-cycle sampling, had been observed. In order to demonstrate the application of this precision phase measurement method, an ultra-precision heterodyne laser interferometer, consisting of digital phase measurement system and ultra-stable optical bench, was constructed for displacement measurement. The experimental results showed that a measurement resolution of 63 pm had been achieved.