An approach of phase-shift transform is proposed and demonstrated to suppress the interference fading in phase sensitive optical time domain reflectometry (-OTDR). The phase-shift transform is executed in the digital domain and the complicated frequency modulation is not required. The operation principle is carefully analyzed and a signal with complementary amplitude can be obtained with this method. Through synthesizing the complementary signals, the false phases can be corrected. Benefiting from the flexibility of this approach, multiple transforms are implemented to make sure that all phases are retrieved accurately. Experimental results show that the intensity fluctuation over 60 dB is reduced to 15 dB, which decreases the standard deviation of differential phase to 0.0224. Besides, 30 dynamic measurements are tested and all distorted phases have been corrected, indicating the high reliability of this method.

An adaptive image restoration algorithm based on 2-D bilateral filtering has been proposed to enhance the signal-to-noise ratio (SNR) of the intrusion location for phase-sensitive optical time domain reflectometry (Φ-OTDR) system. By converting the spatial and time information of the Φ-OTDR traces into 2-D image, the proposed 2-D bilateral filtering algorithm can smooth the noise and preserve the useful signal efficiently. To simplify the algorithm, a Lorentz spatial function is adopted to replace the original Gaussian function, which has higher practicability. Furthermore, an adaptive parameter setting method is developed according to the relation between the optimal gray level standard deviation and noise standard deviation, which is much faster and more robust for different types of signals. In the experiment, the SNR of location information has been improved over 14 dB without spatial resolution loss for a signal with original SNR of 6.43 dB in 27.6 km sensing fiber. The proposed method has the potential to precisely extract intrusion location from a harsh environment with strong background noise.

Phase-sensitive optical time domain reflectometry (Φ-OTDR) realizes quantitative measurement of the dynamic strain employing phase demodulation. Unfortunately, it is difficult to measure the large dynamic strain with the conventional Φ-OTDR due to the restriction of the unwrapping algorithm. In this work, an approach based on two-wavelength probe is proposed and demonstrated to improve the measurable range of the dynamic strain in Φ-OTDR. By utilizing the difference between the two phases acquiring with two different lasers, the large dynamic strain can be recovered. In experiments, dynamic strains with peak values from 10.32 uɛ to 24.08 uɛ are retrieved accurately, which cannot be recovered with the conventional Φ-OTDR. Moreover, the tunable sensitivity is also demonstrated through adjusting the wavelengths of the probe. With the increment of the wavelength interval from 9.06 nm to 23.06 nm, the normalized sensitivity increases from 0.4 to 1 accordingly. That agrees well with the theoretical prediction. Foreseeably, the proposed method will extend the scope of application fields for Φ-OTDR, which requires large dynamic strain recognition.

A phase demodulation algorithm in phase-sensitive optical time domain reflectometry (Φ-OTDR) with self-interference balance detection is proposed. With a simple differentiate-and-cross-multiply (DCM) operation to acquire the perturbation waveform, and a further second-order operation to compensate the amplitude fluctuation of the phase, the phase can be extracted accurately. The self-interference balance detection structure can equivalently achieve the function of dual-pulse detection, but avoid the negative impact of the common-mode noise and the difference between the dual pulses on the demodulation. In experiment, several types of vibrations are retrieved correctly under the condition of single channel and low sampling rate, which demonstrates the validity of this demodulation approach.

In phase-sensitive optical time domain reflectometry (Φ-OTDR), false phase peaks caused by interference fading have been observed experimentally; however, the statistical law has not yet been disclosed. In this work, after clarifying that the false phase peaks originate from the phase hopping of demodulated phase noise during the unwinding process, we define the phase hopping rate (PHR) to evaluate the degree of fading and study the quantitative relationship between the PHR and signal-to-noise ratio (SNR) of the measured signal through theoretical derivation and experimental verification. In addition, a moving rotated-vector-average (MRVA) method is proposed to suppress the fading and eliminate the false phase peaks. In the experiment, after MRVA processing with a 25 ns sliding window, the lowest SNR is pulled from 0.003 to 14.9, and the corresponding PHR is reduced from 0.237 to less than 0.0001, which is consistent with the theoretical analysis.

A novel multi-frequency decomposition (MFD) scheme is proposed to achieve a fading-free phase-sensitive optical time-domain reflectometry ( $\Phi $ -OTDR). By performing short-time Fourier transform (STFT) on the detected signal, the spectrum contents of the normal probe pulse can be fully utilized and decomposed in time-frequency domain without sacrificing more spatial resolution. Through employing the rotated-vector-average (RVA) method to synthesize the decomposed signals, the demodulated phase noise is greatly suppressed and the false phases caused by fading are cleanly eliminated. In experiments, two simultaneous vibrations along the 9.6-kilometer-long fiber are clearly detected without fading for 50 measurements.