True Phase Measurement of Distributed Vibration Sensors Based on Heterodyne $\varphi $-OTDR

We demonstrate a method to truly measure the phase change originated from external vibration by heterodyne phase-sensitive optical time-domain reflectometer (φ-OTDR). The method of differential phase between sections of a sensing fiber is explored. In order to truly measure the phase change induced by external vibration, we point out that such sections of the fiber to calculate differential phase must cover at least the whole vibration region together with a section of fiber spaced by a pulse duration. The resultant differential phase is theoretically found to be twice the value of the real phase induced by external vibration. We further experimentally investigate a distributed sensor with a sensing fiber of 41.2 km based on φ-OTDR system. The experimental results are well consistent with the simulation results, which provides a general guidance for quantitative phase measurement of the external excitation such as slow variations based on heterodyne φ-OTDR technique.