Digitalized Polarization Fading Suppression and Phase Demodulation Scheme of Phase-Sensitive Optical Time-Domain Reflectometry Based on Polarization Diversity Virtual Coherence

Abstract

In this paper, a digitalized polarization fading suppression and phase demodulation technique for a phase-sensitive optical time-domain reflectometry (φ-OTDR) sensing system utilizing polarization diversity virtual coherence is proposed, in which virtual cross-coherence between the polarization diversity digital signals is employed for simultaneous fading noise suppression and phase demodulation. The principle of the proposed demodulation algorithm is presented and analyzed. Based on this, the practicability and validity of the proposed demodulation method for fading noise suppression and distributed vibration sensing are confirmed through experiments. The experimental results indicate that the proposed demodulation scheme can effectively reduce the polarization fading noise caused by the polarization mismatch between the probe light and the reference light, and the phase changes induced by external interference can also be accurately recovered with a signal-to-noise ratio (SNR) of vibration signal localization of 27.14 dB and an SNR of vibration signal phase demodulation of 47.88 dB, which provides a simplified method for simultaneous polarization fading suppression and the phase demodulation of the φ-OTDR system.

1. Introduction

φ-OTDR is a fully distributed vibration-sensing technology that enables a fast response and high sensitivity for small disturbances or strain change detection by measuring the phase variation in the Rayleigh backscattering (RBS) signal along the optical fiber [1,2,3], which can be used in many fields, such as intrusion prevention monitoring [4,5,6], pipeline leakage detection [7,8,9,10], geological exploration [11,12,13], submarine cable fault location [14,15,16,17], and so on. Due to these profound application values of the $\mathsf{\phi }$-OTDR system, it has gained intensive attention and developed rapidly in recent years.

However, for the $\mathsf{\phi }$-OTDR system, polarization fading noise is one of the main problem restricting the demodulation performance of the system. Polarization fading refers to the phenomenon of interference signal intensity reduction or even disappearance due to the mismatch of the polarization states of two coherent beams of light, which is manifested in the random rise and fall of the amplitude of the beat frequency signal that causes the distortion of the demodulation result, and thus seriously affects the vibration signal localization, phase demodulation SNR, as well as the disturbance identification of the system [18]. In recent years, different polarization fading noise suppression technology has been investigated. Qin et al. proposed an all-polarization-maintaining optical path method to avoid the occurrence of polarization fading by using polarization-maintaining fibers and devices [19], in which the all-polarization-maintaining optical path usually needs repeated calibration. Dorize et al. proposed to apply the Gray code technique in optical communication to distributed fiber optic sensing by using the orthogonality of Gray’s complementary code to reduce the effect of polarization mismatch [20], which is greatly inconvenient in signal processing. Wang et al. [21] proposed an area-to-area signal aggregation method with a Rayleigh gray-scale pattern, where the algorithm achieves signal demodulation with an SNR of 15.83 dB for the localization curve and an average fading ratio (FR) of 2.10%. Jiang et al. [22] proposed a fading-free fiber sensor structure by incorporating an acousto-optic frequency shift (AOFS) loop into the light source in dual-pulse $\mathsf{\phi }$-OTDR, by which the FR is reduced to 0.32%, but the sensing distance in the experiment is only 700 m.

Processing the signal at the optical transmitter is a common approach to suppressing polarization fading. Jiang et al. proposed a polarization switching method to obtain four combinations of pulse pairs through a polarization switch that increases the complexity and the processing process of the system [23], and consequently leads to a reduction in demodulation efficiency. Wang et al. proposed a method using a composite dual-probe pulse that allows for the combined consideration of the two orthogonally polarized states [24], in which usually high-performance hardware and a complicated demodulation algorithm are needed. However, there are various ways to perform polarization fading suppression at the optical receiver terminal. Yan et al. proposed a scheme for coherent detection of a 3 × 3 coupler, in which intrinsically oscillating light is divided into two orthogonal components by a polarizing beam splitter (PBS), and then enters the two ports of the 3 × 3 coupler, respectively [25]. Although this scheme realizes the integrated consideration of the P and S polarized states, there is a risk of demodulation phase discontinuity, which will lead to a considerable problem in practical applications. Cao et al. used three polarizers with different angles to analyze the detected signals and reduce the probability of polarization fading [26]. However, the polarizers need to be manually adjusted to control the direction of the polarization state, which is a cumbersome operation. Zhong et al. proposed that after noise reduction in the phase in both temporal and spatial directions, the polarization fading point does not affect the phase demodulation of other non-fading regions, but this does not address the phase demodulation of the fading point itself [27]. In addition, the polarization diversity reception technique proposed by Frigo et al. [28] has also been employed for polarization fading suppression. Polarization diversity reception uses a polarization beam splitter to split the incident light into two orthogonal polarization states, and then detects the signals from these two polarization states separately, thereby reducing the effects of signal degradation due to there being a single polarization state. However, few systematic and comprehensive studies have been carried out on how to combine the two independent outputs of the $\mathsf{\phi }$-OTDR system based on the polarization diversity reception scheme to improve the system performance.

In this paper, a digital polarization fading suppression and phase demodulation scheme utilizing polarization diversity virtual coherence is proposed, in which polarization fading can be suppressed by employing analog cross-coherence between the P and S polarized beat signals to achieve orthogonal polarization state synthesis, and the phase change can be calculated digitally. For the proposed scheme, only a PBS and two balanced photodetectors (BPDs) are used compared with other polarization fading suppression approaches that greatly simplify the phase demodulation system; meanwhile, the noise induced by a hardware system can also be effectively avoided. The results demonstrate that the proposed scheme can efficiently suppress the polarization fading noise in the $\mathsf{\phi }$-OTDR system and enhances the accuracy of vibration localization and the SNR of the system; meanwhile, the phase change along the sensing fiber can also be demodulated, which provides an effective but low-cost solution for simultaneous polarization fading suppression and the phase demodulation of the $\mathsf{\phi }$-OTDR system.

2. Demodulation Principles and Analysis

The proposed polarization fading suppression and phase demodulation scheme is based on the heterodyne coherent detection of the $\mathsf{\phi }$-OTDR system, in which a beat signal is generated through the interference between the probe light and a reference light. In this case, the probe light is split into P and S polarization states through a PBS, and then detected by two BPDs separately.

The outputs of two BPDs can be described as follows [29,30]:

$$I_1=E\cos \theta \cos [2\pi ft+{\phi }_L]$$

(1)

$$I_2=E\sin \theta \cos [2\pi ft+{\phi }_L]$$

(2)

where I₁ is the photo-current of the P polarization signal and I₂ is the photo-current of the S polarization signal, in which E = E_S∙E_L, E_S, and E_L are the amplitude of the probe light and the reference light; θ is the difference angle between the polarization state of the probe light direction and the reference light direction; f is frequency shift produced by the acousto-optic modulator (AOM); and ${\phi }_L$ refers to the phase of the interference field.

It can be seen from Equations (1) and (2) that when θ is 0 or π/2, the intensity of one of the beat signals will decay to 0, and the signal will be flooded with noise, leading to the failure of demodulation. To solve this problem, a digitalized polarization fading suppression and phase demodulation technique based on polarization diversity virtual coherence is proposed. In order to obtain two corresponding signals with the same and non-zero amplitude based on signals I₁ and I₂, the digitalized complete process is shown below.

The simulation generates two orthogonal signals with adjacent pulse periods to the above signals, which have the same frequency and differ in time by ∆t:

$$I_1^{\prime }=E^{\prime }\cos {\theta }^{\prime }\cos [2\pi f(t+\Delta t)+{\phi }_L^{\prime }]$$

(3)

$$I_2^{\prime }=E^{\prime }\sin {\theta }^{\prime }\cos [2\pi f(t+\Delta t)+{\phi }_L^{\prime }]$$

(4)

where E’ is the amplitude of the adjacent, next RBS signals; ${\phi }_L\prime$ is the interference field phase of the adjacent next RBS signals; and θ′ is the difference angle between the polarization state direction of the probe light and the reference light at this moment.

Signals I₃ and I₄ are obtained by applying Hilbert transform to signals I₁ and I₂. Hilbert transform is a linear integral transform that generates the orthogonal signals of the original signals by shifting their frequency domain phase by 90° [31]. As a result, signals I₃ and I₄ can be expressed as follows:

$$I_3=E\cos \theta \sin [2\pi ft+{\phi }_L]$$

(5)

$$I_4=E\sin \theta \sin [2\pi ft+{\phi }_L]$$

(6)

Similarly, the orthogonal signal of signal I₂′ can be derived by applying Hilbert transform:

$$I_4\prime =E^{\prime }\sin \theta \prime \sin [2\pi f(t+\Delta t)+{\phi }_L^{\prime }]$$

(7)

The signals described above can be subjected to analog cross-coherence using the following steps:

$$I_5=I_1\cdot I_1^{\prime }+I_4\cdot I_4^{\prime }=(\cos \theta \cos {\theta }^{\prime }+\sin \theta \sin {\theta }^{\prime })E{E}^{\prime }\cos \Delta \phi$$

(8)

$$I_6=I_3\cdot I_1^{\prime }-I_2\cdot I_4^{\prime }=(\cos \theta \cos {\theta }^{\prime }+\sin \theta \sin {\theta }^{\prime })E{E}^{\prime }\sin \Delta \phi$$

(9)

in which $∆\phi ={\phi }_L-{\phi }_L$’ is the phase change caused by external disturbances. In addition, I₅ and I₆ do not contain high-frequency term components.

Since the polarization state within both the reference light and the RBS light pulse change randomly in single mode sensing fiber, if the polarization states between the reference light and the RBS light mismatch, coherence cannot be generated, which ultimately leads to the random distribution of polarization fading within the beat signal pulse, which means that θ is 0 or π/2. It is obvious that cosθ and sinθ in Equations (1) and (2) cannot both be 0 by the nature of trigonometric functions, which means that in the proposed φ-OTDR system based on polarization diversity, two beat signals with polarization states orthogonal to each other will not decay at the same time, and when the intensity of one of the beat signals decays to 0, the other one will not. Signals I_1′ and I_2′ have a time difference for adjacent pulses with signals I₁ and I₂, which means that Δt is extremely short, so that θ and θ’ are nearly equal. Consequently, I₅ and I₆ in Equations (8) and (9) are not 0, and the suppression of polarization fading can be avoided, leading to the successful demodulation of the phase.

On the basis of the above steps, the phase change is calculated through differential cross multiplication (DCM) arithmetic. Smoothing filtering is also used in the demodulation process to reduce high-frequency fundamental noise. The process of the polarization fading suppression and phase demodulation scheme is shown in Figure 1, where signals I₁ and I₂ are the outputs of the two BPDs, and the other signals are obtained digitally within the demodulation unit (DU). The solid blue lines in Figure 1 indicate addition operations and the dashed red lines indicate subtraction operations.

And amplitude is expressed as follows:

$$I_S=\sqrt{(I_5^2+I_6^2)}$$

(10)

Derivation in I₅ yields I₇, and derivation in I₆ yields I₈. Then, Δφ is calculated by the DCM algorithm and can be expressed as follows [32]:

$$\Delta \phi ={\displaystyle \int \frac{I_5{I}_8-I_6{I}_7}{I_S}}dt$$

(11)

Therefore, polarization fading suppression and phase demodulation can be realized simultaneously by the above scheme.

3. Experiments and Results

3.1. Experimental Setup

We set up relevant experiments to confirm the practicability of the proposed scheme. The φ-OTDR experimental setup used in this experiment is shown in Figure 2. A narrow linewidth laser with a wavelength of 1550.12 nm and a frequency width of 5 kHz is injected into a fiber coupler (FC) with a splitting ratio of 9:1. Lights with energies of 10% and 90% are used as reference and probe lights, respectively. The probe light passes into an acoustic-optic modulator (AOM, T-M200) driven by an arbitrary waveform generator (AWG, T-M200) to generate laser pulses with a 200 MHz frequency shift. Then, the probe light passes into sensing optical fiber via a circulator (CIR) after being magnified by an erbium-doped fiber amplifier (EDFA, PDB435C), where the output power of the EDFA is set to 180 mW. In addition, in order to remove amplifier spontaneous emission (ASE) noise, a bandpass filter is inserted between the EDFA and the CIR with a bandwidth of 0.3 nm. RBS light from the sensing fiber is divided into mutually orthogonal S and P polarized probe light by a PBS; meanwhile, the reference light is also divided into two parts through a 3 dB coupler, and then interferes with P polarized probe light and the S polarized probe light, respectively, through two 2 × 2 couplers to generate two beat frequency signals. The two signals are converted, respectively, to electrical signals through two BPDs (PDB435C) with a bandwidth of 350 MHz, and then collected by a four-channel oscilloscope (DHO4000, Rigol Technologies, SuZhou, China), whose sampling rate is 1 GS/s. Finally, the data are processed through the proposed digitalized polarization fading suppression and DU proposed in this paper. In the system, 5 km of single mode fiber is employed as the sensing fiber. The pulse width is set to 100 ns, which determines the spatial resolution to be 10 m. During the experiment, a piezoelectric transducer (PZT) is used to generate vibration signal with a sensitivity around 1.55 μm/V. In Figure 2, the red line connecting the PBS outlet indicates the P polarized RBS signal and the blue line indicates the S polarized RBS signal. The red line connecting the FC2 outlet indicates the P polarized beat signal and the blue line indicates the S polarized beat signal.

3.2. Results and Analysis

The two beat signals with a pulse repetition frequency of 10 kHz are captured and observed through the oscilloscope. Figure 3a,b demonstrates the whole beat curves of the P polarized signal and the S polarized signal along the 5 km sensing fiber, respectively. Figure 3c,d illustrates the local magnification of the two beat signals within the regions of 1.35~1.37 km and 3.51~3.52 km, respectively. As shown in Figure 3a,b, it is clear that the pulse width is about 50 μs, which is consistent with a 5 km of fiber and a sampling frequency of 1 GS/s. It can be seen from Figure 3c,d that the beat signal period is about 5 ns, which corresponds to a beat frequency of 200 MHz. As shown in Figure 3c, the S polarized signal fades in the area between 1.35 km and 1.37 km, while the P polarized signal does not fade in the same area. Comparatively, Figure 3d shows that when the P polarized signal fades in the area between 3.51 km and 3.52 km, the S polarized signal does not fade in the same area.

In summary, the polarization fading locations occur randomly along the sensing fiber. It is clear from Figure 3c,d that the two RBS signals with orthogonally polarized states do not decay simultaneously within same regions that can be utilized by the proposed scheme for polarization fading suppression.

For the purpose of comparison, the vibration sensing performance of the system without polarization fading suppression is evaluated through the experiment, in which the phases of the P polarized signal and the S polarized signal are used separately for phase demodulation through digitalized orthogonal demodulation [33]. We apply a drive signal with a voltage of 1 V to the PZT to induce vibration on the coiled fiber, and the demodulation results are shown in Figure 4a,b. As illustrated in Figure 4a,b, showing the calculated standard deviation of phase change, obvious vibration activity can be detected that is located at the end of the 5 km sensing fiber, which is in accordance with the actual distance of vibration on the fiber coiled on the PZT. On the other hand, spikes in polarization fading noise can also been observed that are distributed randomly along the phase std variance trace line, which are mainly caused by polarization fading. It can be seen from Figure 4a,b that the maximum calculated standard deviation can even reach 2.3 rad or 2.2 rad, respectively, which means that it can hardly be distinguished from the actual vibration event.

Figure 4c illustrates the trajectory of phase standard deviation by employing the proposed polarization fading suppression and phase demodulation scheme, and the calculated SNR is 27.14 dB. When severe polarization fading occurs, the random rise and fall of the intensity of the beat frequency signal can lead to significant phase noise in the non-vibrational regions. As a result, phase spikes appear in certain non-vibrational regions, which can confuse the true vibrational signal localization spike. While the proposed scheme normalizes the intensity of the beat frequency signal in the fading region, and therefore greatly reduces phase noise, as shown in Figure 4c, there are no noise spikes other than the localization spike of the vibration signal. Comparatively, it can be seen that vibration can be detected; meanwhile, fading noise along the fiber can be suppressed effectively, which demonstrates the practicability of the proposed scheme.

Furthermore, the fading suppression effect of the proposed algorithm is measured in terms of the FR [22], which is defined as the percentage of the intensity of the beat signal normalized to be below 10% of maximum intensity. As shown in Figure 5, the normalized intensity of the beat signals within a sampling time of 10 μs for the three cases is demonstrated, and the red dashed lines indicate the boundaries distinguishing between the fading and non-fading regions, with the respective fading rates calculated. The FR of the P polarized signal is 10.21%, the FR of the S polarized signal is 12.30%, and the amplitude of a few sampling points even completely fades to 0. The FR of the beat signal after digitization using the proposed scheme is 0.25%, and there is no case of intensity decay to 0 at all. Therefore, it can be seen that the proposed scheme is extremely effective in suppressing polarization fading.

The capability of the proposed scheme for fading noise suppression is further confirmed by demodulating the phase over the entire sensing range. The phase state within 50 ms along a 5000 m sensing fiber is measured, and the noise level of the demodulation results before and after the application of the proposed scheme is also calculated, as shown in Figure 6. According to the literature [34], the phase noise level of the -OTDR system can be evaluated by root mean square of the phase noise as RMSt and RMSp. Therefore, the RMSt and RMSp before and after the proposed fading noise suppression scheme are calculated. Figure 6a demonstrates that the single polarization demodulation RMSt reaches up to 0.1 rad, while the RMSt of the proposed scheme is below 0.05 rad. As illustrated in Figure 6b, the probability of the single-polarization-state demodulation RMSp being greater than 0.05 rad is counted separately, which is about 20% for the P-polarized-state demodulation result and 24% for the S-polarized-state demodulation result, while the RMSt of the proposed scheme all remain below 0.05 rad, indicating that the proposed phase demodulation algorithm has a suppression effect on the overall phase noise of the fiber optic link, which is helpful to realize the vibration signals recovered with high fidelity.

To evaluate the effectiveness of the digital polarization diversity virtual coherence algorithm for phase demodulation, vibration signals with different frequencies and waveforms are applied through PZT. Figure 7a shows the demodulated phases that correspond to the sinusoidal driving signals of 500 Hz and 1 kHz. And the demodulated signal exhibits a standard sinusoidal waveform that is consistent with the driving voltage applied to the PZT. To indicate the capability of the proposed scheme for vibration signal recovery, the spectrum of the demodulated vibration signal is also calculated, as shown in Figure 7b. It demonstrates that the background noise level is around −81.06 dB with an SNR of 47.88 dB for 500 Hz sine vibration signals (red line) and is approximately −80.64 dB with an SNR of 47.04 dB for 1 kHz signals (blue line). The dynamic sensitivity of the proposed $\mathsf{\phi }$-OTDR system is obtained according to the literature [35,36], which is approximately 5.51 nε/rad.

The capability of the proposed scheme to demodulate complex frequency signals is also verified by changing the driving signal to a triangular wave and a square wave, and Figure 8a shows the demodulated results for 500 Hz (red line) and 1 kHz (blue line) triangular wave signals. It is obvious from Figure 8a that the waveform and the spectrum are significantly disparate from that of the sine wave, in which the waveform presents a standard triangular waveform, meanwhile both the fundamental and odd harmonics in the spectrum can also be observed, which is in accord with the characteristics of a triangular wave. Figure 8b shows the demodulated results for 500 Hz (red line) and 1 kHz (blue line) square wave vibration signals, in which the frequency spectrum contains high-frequency components specific to a square wave signal, and both the waveform and the spectrum are also consistent with the square wave signal exerted on the PZT. It can be seen that the square wave signal tends to be smoothed, which results in a trapezoidal waveform, as shown in Figure 8b. The distortion of the square wave may be affected by the material properties of the PZT from two aspects. First, the electric field–strain relationship of PZT is nonlinear, meaning that the piezoelectric effect has hysteresis, and thus the rapid jumps of the square wave are smoothed by the nonlinear effect, resulting in the flattening of the waveform edges [37]. Secondly, the mechanical response speed of the PZT is limited by its intrinsic resonance frequency and damping characteristics, and it cannot instantaneously follow the high-frequency components of a square wave signal [38]. Moreover, a smoothing filter is used to eliminate high-frequency fundamental noise in the phase demodulation process [39]. As a result, the high-frequency components of the square wave are suppressed, and the waveform is smoothed to a trapezoidal shape. Therefore, it is verified that the proposed scheme can efficiently suppress polarization fading noise and realize the demodulation of phase changes.

In order to verify the performance of the proposed scheme to achieve phase demodulation for long-distance and high-resolution sensing, the length of the sensing fiber is set to 20 km, the pulse width is set to 20 ns, and the sinusoidal vibration signals of 500 Hz (red line) and 1 kHz (blue line) are loaded at the end of the fiber, respectively. The demodulation results of the vibration signals at 19,980 m are shown in Figure 9, and it can be seen that the waveform does not show obvious distortion, and the spectrum is very accurate, so the proposed scheme can successfully realize the demodulation in the case of a sensing distance of 20 km and a spatial resolution of 2 m.

Finally, we use a comparative table to reflect the performance of the proposed algorithm. It can be seen from

Table 1. Performance comparison of our scheme with those of other representative schemes.

Scheme	Fading Ratio	Localization SNR	Sensing Distance	Demodulation SNR	Spatial Resolution
Rayleigh Gray-Scale Pattern [21]	2.10%	15.83 dB	6.2 km	—	20 m
Frequency Multiplexed [22]	0.32%	—	700 m	—
MRC Algorithm [29]	—	18.19 dB	10 km	29.76	2.5 m
Polarization-Maintaining Configurations [19]	—	—	400 m	—	1 m
Our Scheme	0.25%	27.14 dB	20 km	47.88	2 m

that the proposed scheme has an FR of 0.25% and a localization SNR of 27.14 dB, which reflects an obvious advantage in polarization fading suppression compared to those of the other schemes. Compared to the complex hardware configurations in the traditional schemes, the proposed scheme not only reduces the hardware cost, but also reduces the system noise introduced by multiple components. Moreover, the sensing distance can reach 20 km at a spatial resolution of 2 m, and the SNR of the demodulated signal is much larger than those of the other schemes. As a result, it can accurately locate vibration sources and maintain signal integrity over long distances, which satisfies high-precision requirements, such as pipeline leakage detection or submarine cable fault monitoring. Since the demodulation process is realized by real-time digitization, computation is speedy and takes only a few seconds. Therefore, the proposed scheme has the potential to be applied in real engineering at a low cost.

4. Conclusions

In summary, a digital polarization fading suppression and phase demodulation scheme for an $\mathsf{\phi }$-OTDR sensing system utilizing polarization diversity virtual coherence is proposed. The proposed scheme has an FR of 0.25% and a localization SNR of 27.14 dB, and an SNR of vibration signal phase demodulation of 47.88 dB. It provides a simple and efficient method for phase demodulation and polarization fading noise suppression. Therefore, the proposed scheme can enhance the performance and simplify the system configuration of the $\mathsf{\phi }$-OTDR system, and it has the potential to be applied in real engineering at a low cost.