Recently, a distributed fiber optic sensor named phase optical time domain reflectometer or phase-sensitive optical time domain reflectometer (Φ-OTDR) has been used in the localization and monitoring of earthquake waves, underwater facilities, etc. Precision in the localization of external perturbations on the fiber is crucial for effective problem resolution. The conversion coefficient between the extracted phase signal detected by Φ-OTDR and the corresponding perturbation signal acting on the fiber significantly impacts localization accuracy. Therefore, the characteristic of parameters relative to the conversion coefficient in Φ-OTDR should be deeply researched. Then, based on the established mathematical model of coherent Φ-OTDR, modulus, statistical phase, phase change, and peak difference of coherent Φ-OTDR with and without the static region is analyzed, respectively. The analysis reveals that when coherent φ-OTDR has perturbations homogeneously distributed along the fiber, there is no static region on the phase change-fiber length plane. At this point, although the waveform like the information of external perturbation still can be found in the retrieved phase change in the direction of pulse sequence, the phase change does not have a strictly linear relationship along the fiber. It is different from what was expected in coherent Φ-OTDR having the static region, which means that coherent Φ-OTDR must have the static region if a higher localization accuracy is needed. A localization case demonstrates that the proposed method with the designed static region enhances localization resolution by 210% compared to the traditional coherent φ-OTDR without the static region. These findings underscore the importance of the conversion coefficient and the relevance of the static region in Φ-OTDR for achieving accurate and effective localization.

The absolute difference (phase jumping) between two adjacent phases should be less than pi in order to accurately recover the phase signal with traditional phase unwrapping algorithm, which limits the capability of quantitative measurement for traditional PHI-OTDR. In this article, a new process of phase unwrapping with an auxiliary light in coherent PHI-OTDR is proposed, so the resolvable phase jumping is extended to a larger value beyond pi and the capability of phase unwrapping is improved. In this PHI-OTDR system, wrapped differential phases between a reference position and the subsequent positions of fiber are firstly acquired for all probe light pulses. And wrapped differential phases of interleaving pulse sequence are unwrapped using the traditional phase unwrapping algorithm. Then, positions where the differential phases are correctly unwrapped are obtained from the discontinuously linear profile of the phase change curves of the original probe light. Based on these positions, the information of perturbation can be correctly retrieved. In experiment, the new process of phase unwrapping with the auxiliary for PHI-OTDR is executed and a perturbation signal which induces a maximum phase jumping of 3.7154 rad is well reconstructed. More experimental results all demonstrate the validity of the proposed method.

In the coherent PHI-OTDR system, the phase signal is retrieved based on the reference point and the observation point which are off and closer to the two sides of step of the phase change. In the experiment, the optical pulse with the changed peak power, width or shape is injected into the fiber for interrogating the change of the quantitative characteristic of the measured phase signal. When the pulse width is fixed at 200 ns and its peak power is adjusted from 14 dBm to -23 dBm, the amplitude is slightly increased from 17.3575 rad to 17.4411 rad as long as the Rayleigh backscattering signal can be found in the electrical signal. Changing the pulse width from 260 ns to 80 ns when the peak power is fixed at 14 dBm, the maximum amplitude and the minimum amplitude of the measured phase signal are 17.4625 rad to 17.4509 rad, respectively. When the arbitrary shape of the optical pulse generated from the MZI structure with a changed delay fiber from 3 m to 6 m, the amplitude varies from 17.4558 rad to 17.4819 rad. For every measurement, the change of frequency is also small. And the small value of standard deviation supports the accuracy of the measurement. All the measurements show that the changed pulse nearly has no impact on the quantitative characteristic of the measured phase signal in the coherent PHI-OTDR system. Moreover, we also find that the phase signal of external event can be correctly extracted as long as the Rayleigh backscattering signal can be detected.