A phase-optical time domain reflectometer (Φ-OTDR) can quantitatively reflect the external perturbation signal according to the change in extracted phase. Therefore, they have been widely used and actively studied in the fields of perimeter security monitoring, performance monitoring of dredged pipelines, cable partial discharge monitoring, and seismic wave detection. In Φ-OTDR, there are various types of noise, including photoelectric noise of the detector, electronic noise of the data acquisition card, phase noise of the reference light, polarization fading, interference fading. These noises not only affect the signal-to-noise ratio of the detected result, but also induce distortion of the signal waveform. This implies that they degrade the accuracy of the phase signal, thereby affecting the correctness of event discrimination. Moreover, the phase of Φ-OTDR is extracted from its detected intensity or amplitude curve. It implies that the noise of coherent Φ-OTDR is in the form of both amplitude and phase. Given that Φ-OTDR measures the perturbation signal at every sampling position of the fiber, the extracted phase, including the noise, is distributed in the direction of both “fast time axis” and “slow time axis”. Therefore, a three-stage noise suppression method is required to retrieve a more accurate phase signal.

For obtaining a more accurate measurement result, a dual-layer processing method, which suppresses the noise in the form of both amplitude and phase, was adopted in coherent Φ-OTDR. Furthermore, the noise in the form of phase was suppressed in the direction of both “slow time axis” and “fast time axis”. First, low-pass filters were used to reduce the noise in the form of amplitude separately for the vertical and orthogonal components during the digital orthogonal demodulation process. This enhanced the visibility of the modulus to correctly solve the phase. Then, for the noise in the form of phase, the processing of denoising was performed in the direction of “fast time axis” and “slow time axis”. In the direction of “slow time axis”, the method of wavelet decomposition and reconstruction was used for noise suppression. Based on the characteristic of the linear distribution of phase change in the undisturbed region of the fiber and randomness of noise in coherent Φ-OTDR, the approximate components of phase changes after wavelet decomposition at different sampling positions of the fiber were used for correlation calculation. The number of decomposed layers for wavelet denoising was then automatically determined by the maximum value of the correlation coefficient. This avoided errors due to manual decisions. In the direction of “fast time axis”, according to the linear profile of phase change of each pulse, data fitting with the method of total least squares was performed. Correspondingly, the fitting process effectively reduced noise in the form of a phase.

In the orthogonal demodulation process, low-pass filtering is applied to both the orthogonal and vertical components to suppress noise in the form of amplitude, resulting in a clear visibility of the modulus [Fig.4(c)]. Based on the correlation calculation of the approximate components, obtained via the wavelet decomposition of the phase changes, the highest value of the correlation coefficient is obtained when the number of decomposed layers is four [Fig.5(c) and Fig.5(d)]. Therefore, four is automatically chosen as the decomposition level for subsequent wavelet denoising. Then, the process of wavelet denoising in the direction of “slow time axis” and data fitting in the direction of “fast time axis” are performed. The root mean square error of the sinusoidal waveform of the final extracted phase signal is only 0.17832 rad [Fig.6(d)], which is 23.3% lower than that obtained using the two-stage denoising method without wavelet denoising in the direction of the “slow time axis”. This indicates that the three-stage denoising method with wavelet denoising in the direction of the “slow time axis” achieves more accurate measurements. Additionally, the results of the discussion with respect to the effect of polarization show that in coherent Φ-OTDR using a highly coherent and high-stability frequency laser, the effect of polarization fading on the correct extraction of phase signal can be approximately ignored (Fig.8).

In the process of orthogonal demodulation in coherent Φ-OTDR, the digital low-pass filter is used to reduce the noise in the form of amplitude. Correspondingly, a reference position is selected to retrieve the phase. Then, for the unwrapped phase changes, the method of wavelet decomposition and reconstruction is used to remove the noise in the direction of “slow time axis”. Based on the spatial profile of the phase change and the randomness of noise, the number of decomposed layers of wavelet denoising is obtained via a correlation calculation of the approximate component of the wavelet coefficient. Finally, the data fitting of total least squares for the phase change of each pulse is performed in the direction of “fast time axis” for suppressing the influence of the noise in the form of phase. For the final calculated phase signal, the R-square coefficient and root-mean-square error of fitting with unknown parameters of the sinusoidal function correspond to 0.99996 and 0.17832 rad, respectively. Compared to the results obtained by the data processing method without wavelet denoising, the R-square coefficient increases by 0.00003 and root mean square error decreases by 23.3%. Further studies demonstrate that the phase information obtained using the three-stage denoising method is closer to the true value. Consequently, the newly proposed method is more helpful in achieving an accurate measurement in coherent Φ-OTDR.