Accurate phase extraction by phase-closure assisted self-mixing φ-OTDR

Distributed acoustic sensing (DAS) based on phase-sensitive optical time-domain reflectometry (φ-OTDR) has been widely used for distributed vibration monitoring because of its high sensitivity, distributed measurement, and electromagnetic immunity. Self-mixing φ-OTDR extracts phase from the interference among multiple probe pulses, providing a stable direct-detection approach for long-distance sensing. However, its self-referencing configuration, in which the phase is recovered from the beating of Rayleigh backscattering (RBS) fields, makes beat-channel demodulation jointly dependent on the quality of both RBS responses, so degradation of either response can reduce phase-extraction accuracy and eventually lead to phase distortion. In this work, we propose a phase-closure assisted compensation (PCAC) method for the accurate phase extraction of self-mixing φ-OTDR. By extending the self-mixing scheme from dual-pulse to triple-pulse, three strongly correlated pairwise beat channels are generated. These beat channels form a closed phase loop, in which the ideal beat phases satisfy a phase-closure relation. Therefore, deviations from this closure relation provide an inter-channel consistency metric for identifying phase-distortion regions. Experimental results demonstrate that PCAC improves the vibration response signal-to-noise ratio (SNR) in distortion-prone boundary regions while preserving the response in the central vibration region. At a representative distorted position near 9026.8 m, the noise-buried 500 Hz vibration is recovered with 25.6 dB SNR. The results in this study confirm the effectiveness of the proposed scheme in improving phase extraction accuracy in self-mixing φ-OTDR.