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This letter proposes a method for predicting the maximum detectable distance of phase-sensitive optical time-domain reflectometry ( $\varphi $ -OTDR). Based on analyzing the noise composition of the output photocurrent signal of $\varphi $ -OTDR, the relationship between the ratio of the standard deviation of the photocurrent signal to the standard deviation of thermal noise and the complete distortion rate of the demodulated signal is obtained from actual measurements. The critical value of the ratio is determined according to the critical value of the complete distortion rate. Finally, based on the known optical fiber attenuation coefficient, the standard deviation of the photocurrent signal at starting position of optical fiber, the balanced photodetector (BPD) output voltage without light and the ratio determined by the complete distortion rate, a formula for calculating the maximum detectable distance is proposed. The results indicate that when the optical fiber length is not greater than 35.7 km, the maximum deviation is only 1.0 km. It can effectively predict the maximum detectable distance of $\varphi $ -OTDR.

To obtain the criterion of whether the optical fiber composite overhead ground wire (OPGW) is iced and to estimate the ice thickness, this letter establishes a three-dimensional temperature field model for OPGW under icing conditions and validates it through the experiments. Based on this, sine function is used to simulate the time-varying ambient temperature, and the lag characteristics of the optical fiber temperature are discovered through the simulation and also the experiment. The concept of phase difference in the curves between optical fiber temperature and ambient temperature is proposed, and the relationships between the phase difference and the mean ambient temperature, fluctuation amplitude of ambient temperature, ice thickness are investigated. It reveals that the influence of mean value and fluctuation amplitude of ambient temperature on the phase difference can be neglected, and the relationship between the phase difference and the ice thickness is obtained. The criterion for determining transmission line icing based on the phase difference is proposed, along with a formula for ice thickness estimation.

To address the issue of frequency drift of the laser in the phase-sensitive optical time-domain reflectometry ( $\varphi $ -OTDR) system, this letter utilizes a combination of whale optimization algorithm and variational mode decomposition (WOA-VMD) to mitigate low-frequency noise induced by frequency drift during $\varphi $ -OTDR demodulation. The results show that the proposed method can effectively mitigate the impact of frequency drift on demodulation: when 1 Hz sinusoidal vibration is applied, the waveform bias is reduced from 2.037 rad to 0.087 rad, which is 78% and 96% lower than the twice differential (TD) method and difference-fitting (DF) method respectively; when 0.2 Hz sinusoidal vibration is applied, the waveform bias is reduced from 7.289 rad to 0.193 rad, which is 95% and 96% lower than the TD and DF methods respectively. This method effectively mitigates the influence of frequency drift on $\varphi $ -OTDR demodulation.

The cross-correlation method has a low computational burden and is less sensitive to noise, but the method may have a long spectra measurement time, especially for Brillouin spectra with an asymmetric frequency sweep span. To improve the real-time performance of spectra measurement, the influence of the frequency sweep span, sweep span deviation, and frequency step on the error in the estimated Brillouin frequency shift (BFS) is systematically investigated. Based on the results, the optimal sweep span and its influencing factors are investigated. The results reveal that when the frequency sweep span is not wide enough and there is a sweep span deviation, the BFS error will not decrease with a decreasing frequency step. The error decreases rapidly with an increasing frequency sweep span, and then it tends to a stable value. The linewidth and sweep span deviation have an important effect on the optimal sweep span. An estimation formula for the optimal sweep span is presented, and an improved cross-correlation method is proposed based on it. The proposed method is compared with existing classic cross-correlation methods. The results reveal that the proposed method can ensure high BFS accuracy and decrease measurement time.