Accurate Measurement for the Subsequent Perturbation in the Coherent Φ-OTDR System with Small Laser-Frequency-Drift

In the coherent Φ-OTDR system with small laser-frequency-drift less than 50 kHz, the phase change in the quiet region without external perturbation is theoretically deduced to be linear with the fiber length while its waveform in the direction of pulse sequence is highly similar with the external perturbation acting on the fiber before the quiet region. Moreover, the phase information of one position contains the perturbation information of all foregoing positions. Consequently, a simple and accurate solution of differential operation for acquiring the phase information of subsequent perturbation which is behind the initial perturbation occurring on the fiber is proposed. The fitted phase change trace between the foregoing and the subsequent perturbation is extended to the region behind the subsequent perturbation. Then, behind the subsequent perturbation, the extended phase change trace is subtracted by the fitted phase change trace containing two perturbations. Moreover, in order to afford the fitting data with less noise as much as possible, the phase changes at positions where the value of modulus of coherent Φ-OTDR is lower than the set threshold value is firstly eliminated. To verify these methods, an experiment with two PZT vibrations in this paper is described. For the subsequent PZT vibration, the sinusoidal phase signal with a frequency of 50 Hz is perfectly retrieved when the threshold is set to be 10 mV. And the discussion about threshold value shows that it is satisfactory for the accuracy of phase extraction of the subsequent perturbation if the threshold is set as or above the noise level in the form of modulus in the experiment.