Fundamental limits on the digital phase measurement method based on cross-correlation analysis

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 × 10−6 rad/Hz1/2@1 Hz. Moreover, the cyclic phase error of about 10−2 rad/Hz1/2, 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.