The phase optical time domain reflector (Φ?OTDR) can quantitatively measure the external perturbation information by extracting the phase signals from the coherent Rayleigh curve. During solving the phase, the arctangent operation result is limited in [-π, π]. Phase unwrapping is inevitable to obtain a correct signal waveform. However, the traditional phase unwrapping algorithms require that the absolute difference between adjacent phase values does not exceed π. In Φ?OTDR, increasing the emission frequency of the optical pulse can enhance the sampling rate of the perturbation signals, thereby reducing the absolute difference. Nevertheless, the total optical fiber length is determined by the measured object. Once this length is determined, the emission frequency of the optical pulse is limited, which means that the sampling rate of the perturbation signal cannot be further increased. At this point, if the external perturbation signal changes fast, the phase signal cannot be correctly acquired. Therefore, the time-division dual-frequency light is introduced into coherent Φ?OTDR. However, the initial phases in the directions of both pulse time and fiber length are inconsistent, the introduction of time-division dual-frequency light cannot directly enhance the sampling rate of the perturbation signal, which influences the precise reconstruction of phase signals. Additionally, optical pulses with different frequencies amplify the number of fading positions, thereby heightening the challenge of choosing the reference position which is adopted to eliminate the inconsistency of the initial phase in the pulse time direction. Therefore, in coherent Φ?OTDR with the time-division dual-frequency light, a new method is needed to eliminate the inconsistency of the initial phase in the directions of both pulse time and fiber length and thus truly obtain sampling rate multiplication of the perturbation signal and precise reconstruction of phase signals.

The introduction of time-division dual-frequency light into coherent Φ?OTDR satisfies the requirement of sampling rate multiplication for uniform sampling on the sampling sequence of the pulse. However, the probe pulses of different frequencies complicate the distribution of coherent Rayleigh curves, phase curves, etc. Therefore, the true implementation of sampling rate multiplication requires more complex processing. To conveniently select the reference position of coherent Φ?OTDR with the time-division dual-frequency light, we calculate the distance of modulus value at each fiber sampling position for each frequency component, multiply and normalize the distance value at each fiber sampling position, and confirm the location of the perturbation signal based on the normalized curve. Then, we calculate the minimum value of the modulus at each fiber sampling position for each frequency component, and then multiply and normalize the minimum values of the modulus at each fiber sampling position. The reference position is just the fiber sampling position where the maximum value of the normalized curve is closest to the left side of the perturbation source. Correspondingly, the wrapped differential phase is obtained based on the reference position. Since two different frequency lights make the inconsistency of the initial phase more complex, it is best to eliminate the inconsistency of the initial phase caused by two different frequency lights spontaneously. Therefore, in coherent Φ?OTDR with the time-division dual-frequency light, for each frequency component, we select the pulse time when the perturbation is equal to a static event and the perturbation begins to change. Additionally, the wrapped differential phase at this pulse time is chosen as the reference phase. Then, the wrapped differential phase at each pulse time is subtracted by the reference phase of the same frequency pulse light. Meanwhile, the phase change after unwrapping at the pulse time of the reference phase is again adopted as the new reference phase to eliminate the noise and corresponding phase unwrapping error introduced by the reference phase. The unwrapped phase change at each time is subtracted by the new reference phase of the same frequency component.

Two different frequency lights with a pulse interval of 10 μs and an emission frequency of 50 kHz are introduced into coherent Φ?OTDR, and a Burst perturbation signal acts on the optical fiber. To obtain intermediate frequency signals of two frequency components, we filter the collected coherent Rayleigh scattering curves by 40 MHz and 80 MHz bandpass filters respectively. Based on the intermediate frequency signals, the modulus values of the two frequency components are calculated separately. Then, based on the product of the distance of modulus value [Fig. 8(b)], the left side of the perturbation position is accurately determined to be 1.036 km. Based on the product of the modulus minimum value, the reference position is quickly determined to be 1015.68 m [Fig. 8(b)]. For each frequency component, a wrapped differential phase at the pulse time closest to the perturbation change is selected as the reference phase, and then the wrapped differential phase of the same frequency component is subtracted from the reference phase. The difference values are cross-recombined into a new sequence. After unwrapping, it is just the phase change [Fig. 8(b)]. Furthermore, the phase change at the pulse time of the original reference phase is taken as the new reference phase, and the phase change of the same frequency component is subtracted from the new reference phase to obtain a new phase change. The new phase change exhibits a continuous linear profile along the fiber [Fig. 9(b)]. Finally, the precise Burst signal is extracted, and the maximum difference between adjacent phases is 4.5105 rad if the signal is down sampled. The fitting chi-square coefficient of the sinusoidal part is 0.9998, and the root mean square error is only 0.3872 rad.

In the phase optical time domain reflectometry, the traditional phase unwrapping algorithms require that the absolute difference between adjacent phases does not exceed π. It makes the sampling rate increase of perturbation signals crucial for precise reconstruction of the phase signals. However, the optical fiber length limits the increase in the sampling rate of the perturbation signals. Therefore, the time-division dual-frequency light is introduced into coherent Φ?OTDR. To eliminate the phase distortion caused by inconsistent initial phases in direct unwrapping, we perform the new method of choosing the reference position and dual static compensation. In the experiment, when the external perturbation is a Burst signal with a frequency of 700 Hz, the absolute difference between adjacent phases of the single-frequency probe pulse reaches 4.5105 rad. By the proposed method, the Burst signal is accurately retrieved, and the root mean square error of the sinusoidal part is only 0.3872 rad, which means that the sampling rate of perturbation signals is doubled and the phase signal is precisely reconstructed in coherent Φ-OTDR with the time-division dual-frequency light.