Phase Unwrapping Method of Φ-OTDR System Based on Recursive-Branch-Cut Algorithm

Phase unwrapping is a crucial technique in phase-sensitive optical time domain reflectometry ( $\Phi $ -OTDR) systems. Due to the effects of system under-sampling, I/Q imbalance, and environmental noise, the traditional method of unwrapping the phase is prone to wrapping or even distortion. In this work, a 2-D phase unwrapping method based on the recursive-branch-cut (RBC) algorithm is proposed and studied to improve the accuracy of the demodulated phase waveform. The data near the vibration location is expanded into a 2-D wrapped phase map along the time direction. According to the abnormal phase distribution law, the 2-D wrapped phase map is divided into sliding windows of different lengths. Under the constraint of ensuring the global continuity of the phase, the local phase is optimized by selecting an appropriate integration path, and the error is minimized, thereby suppressing the propagation of abnormal noise globally. The experimental results show that in the range of 1–80 Hz, the method can stably increase the upper limit of the system dynamic range by 3.21 dB. At the same time, the system has a good linear strain response capability, and the strain sensitivity is 22.46 rad/ $\mu \varepsilon \times $ m and ${R}^{{2}}$ = 0.9997. In addition, the method greatly improves the demodulation characteristics without increasing the generality and practicability of the system, which is beneficial to the fully digital realization of the heterodyne detection technology.