SNR dependence of measurement stability of heterodyne phase-sensitive optical time-domain reflectometry

Phase-sensitive optical time-domain reflectometry (Φ-OTDR) implements distributed vibration measurements by demodulation of vibration-induced phase of Rayleigh backscattered light waves (RBLs), and suffers from measurement instability. The weak intensities of RBLs and the resulting low signal-to-noise ratios (SNRs) of intensity measurements are the dominating factors that cause the instability of vibration measurements. In this paper, dependence of the measurement stability of heterodyne Φ-OTDR on the SNR of the intensity measurement is investigated analytically and experimentally. An analytical solution of the probability density function of the demodulated phase as a function of SNR is obtained through rigorous derivation, and the dependence of the measurement stability on the SNR is investigated by analyzing the probability density function distribution of the demodulated phase. Both the theoretical predictions and experimental results reveal the impact of SNR on the measurement stability of heterodyne Φ-OTDR. This study fulfills the Φ-OTDR theory and would lead to an effective approach to stabilizing vibration quantization.