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Abstract
A polarization fading suppression technique is proposed for distributed interferometric sensing systems, based on matched interference between polarization switched pulses. For each individual sensor, two sets of interferometric outputs are obtained, one corresponding to the interference between two pulses with initially parallel polarization, the other corresponding to that between two pulses with initially orthogonal polarizations. As such, at least one output presents visibility no less than $\sqrt {2}/2$. By selecting the one with higher visibility for demodulation, the influence of polarization fading can be suppressed significantly, leading to distributed acoustic sensing with notably improved robustness and reliability.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Distributed optical fiber sensing (DOFS) has shown great advantages in terms of monitoring range, environmental adaptability, transmission loss control, and system robustness [1–3]. Among the various types of DOFS technologies, distributed acoustic sensing (DAS) provides an important tool for structural health monitoring of large infrastructure such as railways and roads, hydrophone application, perimeter intrusion detection, resource exploration, seismology research, etc [4,5]. Conventionally, coherent Rayleigh back-scattering, which is highly sensitive to strain, is adopted with optical time-domain reflectometry to achieve DAS, presenting sub-meter spatial resolution and sensing distance over $150$ km [6]. However, the Rayleigh back-scattering coefficient of commercial single-mode fibers is only $\sim -70$ dB/m, resulting in limited signal-to-noise ratio (SNR) that hinders the practical applications of the technique [7]. Based on an ultra-weak fiber Bragg grating (UWFBG) array, a double-beam interferometric sensor array can be formed by pairs of adjacent UWFBGs [8], which is much more stable as compared to the random multi-beam interference in coherent Rayleigh scattering. Consequently, interferometric DAS with improved SNR can be achieved.
In practical applications, environmental disturbances could induce squeeze and twist of the optical fiber, resulting in time-varying fiber birefringence. The pulses reflected by two adjacent UWFBGs or scattered by different fiber sections may have different states of polarization(SOP), even though they originate from the same input pulse. The non-ideal interference leads to reduced signal amplitude, which is referred to as polarization-induced signal fading in interferometric DAS [9,10], or simply polarization fading. In the case of severe polarization fading, the sensor can exhibit very poor SNR, resulting in degradation of the system robustness. With a Faraday rotator, the round-trip transmission of the light in the same fiber compensates for the birefringence-induced polarization rotation. While achieving visibility of 1, the method cannot be implemented in distributed sensing systems [11]. Using feedback polarization control, the SOP of an input signal can be tracked and adjusted, ensuring ideal interference. However, due to the random polarization rotation in different sensing fiber sections, there exists a pulse-to-pulse variation in the SOP of the reflected signal. To ensure ideal visibility, a negative feedback mechanism that responds fast enough is required, which is difficult to realize [12]. With polarization diversity detection, three different SOP components of the interference signal are obtained separately. By selecting the one with better performance, visibility no less than $0.37$ can be maintained [13]. By introducing a high-speed polarization rotator to one arm of the interferometer, the sensing precision can be improved by calculating the weighted average of the data obtained at two orthogonal SOPs, when polarization fading occurs for one of the SOPs [14]. Based on orthogonal polarization switching, an interferometric sensing system presenting visibility of 1 is proposed, achieving $0.838$ visibility in the experimental demonstration [15]. However, since four groups of interferometric signals are required, the demodulation is complicated and relatively time-consuming.
In this work, a polarization fading suppression method is proposed and demonstrated in an UWFBG-array-enhanced distributed interferometric sensing system, based on matched interference between polarization-switched pulses. By obtaining the interferometric outputs of both two parallelly-polarized and two orthogonally-polarized pulses, the one presenting higher visibility can be selected for phase demodulation and vibration signal recovery. Theoretically, visibility no less than $\sqrt {2}/2$ can be achieved. In practice, a threshold slightly smaller is adopted to avoid frequent switching between the two channels when the visibilities of the two are close. By setting the threshold at $0.62$, polarization fading is suppressed significantly, and SNR over $30$ dB can be maintained.
2. Experimental setup
The experimental setup in Fig. 1 is adopted to investigate the proposed polarization fading suppression method. The output of a laser is modulated into an optical pulse train with $30$-ns pulsewith and $30$-kHz repetition rate using a semiconductor optical amplifier (SOA) module, which is triggered by the output of a field-programmable gate array (FPGA). The optical pulse train is then sent to the Pulse Group Generation part, where it is split into three outputs using a $1 \times 3$ fiber coupler (FC). With the path length differences controlled using the delay fibers (DF1 and DF$2$) and the pulse amplitudes balanced using a variable optical attenuator (VOA), the three outputs are combined using a $2 \times 1$ FC and a polarization beam combiner (PBC). With each input pulse, a pulse group containing three pulses is generated, presenting SOPs $X$, $X$, and $Y$, where $X$ and $Y$ are used to denote two orthogonal linearly-polarized states and are indicated by the arrows and dots in Fig. 1, respectively. The time interval between two pulses is controlled at $40$ ns by adjusting the length of DF1 and DF$2$. Note that polarization-maintaining fibers and passive devices, colored orange in Fig. 1, are adopted to guarantee the stability of the polarization states. Meanwhile, the Pulse Group Generation part is packaged inside a box with vibration and sound isolation, to minimize the influence of external perturbation on the path length differences. An erbium-doped fiber amplifier (EDFA) is used to amplify the output pulse train, and a bandpass filter (BPF) is used to reject the out-of-band amplified spontaneous emission (ASE) noise.
Fig. 1. The experimental setup for distributed interferometric sensing with polarization-fading suppression. SOA: semiconductor optical amplifier; FC: fiber coupler; DF: Delay fiber; VOA: variable optical attenuator; PBC: polarization beam combiner; EDFA: erbium-doped fiber amplifier; BPF: bandpass filter; OC: optical circulator; PD: photodetectors; FPGA: Field-Programmable Gate Array; DAQ: data acquisition card; PZT: piezoelectric transducer; PC: polarization controller
An optical circulator (OC) is used to direct the amplified optical pulse train to the UWFBG array, which contains $220$ interferometric sensors formed by $221$ UWFBGs. The UWFBGs are inscribed serially using the phase-mask method while the fiber is fabricated by a fiber drawing tower [16], presenting center wavelength of $1550$ nm, reflection bandwidth of $3$ nm, reflectivity of $-45$ dB, and grating spacing of $15$ m. In Sensor$\#2$, which is constructed by UWFBG$\#2$, UWFBG$\#3$, and the fiber in between, a fiber section is wound around a piezoelectric transducer (PZT) tube to introduce controllable vibration, and a polarization controller (PC) is adopted to change the SOP. The same structure is applied at Sensor $\#42$ and Sensor $\#220$.
The reflected sensing signal is then directed by OC1 to EDFA$2$ for pre-amplification and BPF$2$ for ASE noise rejection. To demodulate the vibration-induced phase shift, the amplified sensing signal is sent to a MI using OC$2$. The MI is constructed by a $3 \times 3$ FC and two Faraday rotator mirrors (FRMs). For clarity, the ports on the right of the $3 \times 3$ FC are numbered 1–$3$ and those on the left are numbered $4$–$6$.
In the conventional UWFBG-array-enhanced distributed interferometric sensing system, the output of the SOA is directly sent to the EDFA for amplification, bypassing the Pulse Group Generation part. The path length difference between the two arms of the MI would be kept at $15$ m, matching the grating spacing. Therefore, the sensing pulses reflected by two adjacent UWFBGs would interfere. The three interferometric outputs from Ports $4$–$6$ are directed to three photodetectors (PDs) for optical-to-electrical conversion and then a data acquisition card (DAQ) for analog-to-digital conversion. The corresponding phase demodulation algorithm is applied to reconstruct the vibration signal [17].
To achieve polarization fading suppression, however, the path length difference between the two arms of the MI is adjusted to $11$ m, so that matched interference can occur. For simplicity, the input pulses with $X$ and $Y$ polarizations are referred to as $X$- and $Y$-pulses in the following. As shown in Fig. 2, the interference between the first $X$-pulse reflected by UWFBG$\#(n+1)$ and the second $X$-pulse reflected by UWFBG$\#n$ generates the first output pulse, which is colored red. For clarity, we use IP$\#(1X,n+1)$ to represent the first $X$-pulse reflected by UWFBG$\#(n+1)$ and IP$\#(2X,n)$ to represent the second $X$-pulse reflected by UWFBG$\#n$. Similarly, IP$\#(Y,n)$ represents the $Y$-pulse reflected by UWFBG$\#n$. The interferometric output of IP$\#(1X,n+1)$ and IP$\#(2X,n)$ is denoted by OP$\#(1,n)$, while that of IP$\#(2X,n+1)$ and IP$\#(Y,n)$ is denoted by OP$\#(2,n)$. The two output pulses are colored red and blue in Fig. 2, respectively.
Fig. 2. Matched interference between two groups of polarization-switched pulses generated by the reflection of two adjacent UWFBGs.
3. Principle
When the sensing fiber between UWFBG$\#n$ and UWFBG$\#(n+1)$ presents no birefringence, the visibility of OP$\#(1,n)$ is $V_{1,n}=1$ and that of OP$\#(2,n)$ is $V_{2,n}=0$. However, due to the environmental disturbances, the sensing fiber could present random birefringence that varies over time, and the influence on $V_{1,n}$ and $V_{2,n}$ is derived in the following.
The optical fields $E_{1X}$, $E_{2X}$ and $E_Y$ of the three pulses at the input of the UWFBG array are expressed as [18]
The optical intensity of OP$\#(1,n)$ is given by
Table 1. The Jones matrices involved in the derivation of visibility
We thus obtain the optical intensities of OP$\#(1,n)$ and OP$\#(2,n)$:
The expression of each parameter in Eq. (4) is given in Supplement 1. The phase changes $\Delta \phi _{1,2}$ are the values of interest in the demodulation. Due to the low transmission loss of the sensing fiber and uniformity of the UWFBGs, $I_n = I_{n+1}$ can be assumed. Therefore, the two interferometric outputs OP$\#(1,n)$ and OP$\#(2,n)$ present visibilities given by
From the derivation above, we can see that the visibility of one of the two interferometric outputs is always no less than $\sqrt {2}/2$. Therefore, by selecting the one with higher visibility for phase demodulation, the influence of polarization fading can be suppressed significantly.
Though the proposed method can tackle the polarization fading due to the polarization rotation induced by random fiber birefringence, it should be noted that vibration could also induce fiber birefringence, leading to a slight difference between $\varphi _1$ and $\varphi _2$, which is assumed the same in this work. The resulting time-varying phase difference would cause crosstalk to the downstream sensors, which the proposed method could not eliminate. Nonetheless, such a crosstalk is generally considered quite small and comparable to the additive circuit noise [19].
4. Experimental results
First, we verify the impact of visibility on the performance of the distributed interferometric sensing system. The results are obtained using the conventional single-pulse input [17]. Accordingly, the fiber length difference between the two arms of the MI is the same as the grating pitch, which is kept at $15$ m, and the $500$ Hz vibration signal applied by the PZTs at the corresponding sensors is demodulated by the arctangent demodulation algorithm. Figure 3(a) shows the SNR of the sensing signal obtained at Sensor$\#42$, which is measured using lasers with linewidths $\Delta \nu =3$ kHz, $100$ kHz, and $40$ MHz, while the visibility of the sensor is varied by adjusting the PC. The results are presented by the red, blue, and black curves. In all three cases, the SNR of the sensing signal decreases as the visibility of the interferometric sensor decreases. In addition, it drops drastically as the visibility decreases to a certain value. In other words, certain visibility should be guaranteed so that the SNR of the sensing signal can be maintained. Meanwhile, the interferometric sensor requires higher visibility to achieve certain SNR when a laser of larger linewidth is used. This is attributed to the stronger laser phase noise, which is translated into more severe amplitude noise by interference. Furthermore, comparing the results obtained with $3$ kHz and $100$ kHz linewidths, the performance improvement by narrower laser linewidth becomes less significant when the amplitude noise is no longer dominated by that converted from the laser phase noise.
Fig. 3. Measured SNR at varied visibility with (a) different laser linewidths at Sensor$\#2$ and at (b) Sensor$\#2$, Sensor$\#42$ and Sensor$\#220$ with laser linewidth of $100$ kHz.
Because of the uniformity of the UWFBGs, all the interferometric sensors in the array should perform similarly. However, as the optical power of the pulses becomes weaker over transmission in the grating arrays, the sensing signals generated by the downstream sensors present lower SNR even though the visibility is the same. As shown in Fig. 3(b), the upstream sensors present higher SNR than the downstream sensors at the same visibility. SNR over $30$ dB can be expected with $0.4$ visibility at Sensor$\#42$, which corresponds to sensing distance of $630$ m. However, at Sensor$\#220$, which corresponds to sensing distance of $3.3$ km, the SNR decreases to $10$ dB as the visibility decreases to $0.4$. It can thus be inferred that the influence of polarization fading becomes more severe if we are aiming at long sensing distance. In other words, polarization fading suppression is imperative in achieving reliable long-distance interferometric sensing.
Polarization-switched pulses depicted in Fig. 2 are then adopted to verify the polarization fading suppression method. The visibilities of OP$\#(1,220)$ and OP$\#(2,220)$, and the sum of the squares of the visibilities, are calculated and plotted in Fig. 4 as red, blue, and black curves, respectively. Within $60$-s time, we manually adjust the PC to change the birefringence of the sensing fiber. As shown in Fig. 4, while $V_1$ and $V_2$ both vary over time due to the manually-induced fiber birefringence, the sum value fluctuates around $0.98$, presenting variance of $0.0044$. The sum value can be lower than the theoretical value of 1, when the two interfering pulses present unequal optical power leaves or there is incoherent noise like ASE noise. Meanwhile, considering the instantaneous value, the fluctuation of the optical power and the low frequency environmental disturbance may affect the interference and result in fluctuation of the sum value.
Fig. 4. Visibilities $(V_1, V_2)$ and Sum of squares of the visibilities $(V_1^2 + V_2^2)$ of the two interferometric outputs.
We then look at the details in Fig. 4 while examining the demodulated signals shown in Fig. 5. At first, $V_1$ remains close to 1, indicating that the interference at OP$\#(1,220)$ does not suffer much from polarization fading. During the same period, a stable signal envelope is observed in Fig. 5(a1), and a $500$ Hz sinusoidal waveform is clearly shown in Fig. 5(a2). However, with the decrease of visibility, the signal envelope starts to fluctuate around the $25$th second. As the visibility decreases to $0.3$ at the $32$nd second, the $500$ Hz vibration signal cannot be restored correctly, as revealed by both Fig. 5(a1) and 5(a3). Nonetheless, the decrease of $V_1$ is always accompanied by an increase of $V_2$. Therefore, successful signal restoration can be achieved at OP$\#(2,220)$, as shown in Fig. 5(b3). Figure 5(b2) presents the demodulated signal at the 1st second, which corresponds to $V_2=0.4$. It is observed that even though the signal amplitude looks normal in Fig. 5(b1), the demodulated signal is already distorted. Based the analysis above, it is expected that stable operation of the vibration sensor can be guaranteed when the fiber birefringence varies over time due to the environmental disturbances, by performing signal demodulation using the interferometric output with higher visibility.
To implement the proposed polarization-fading suppression in practice, an automatic selecting algorithm is designed. To obtain the actual visibility of the sensor, as mentioned previously, the vibration-induced phase change should be no less than $2\pi$, so that ${\rm max}[I_{1,2}(n)]$ and ${\rm min}[I_{1,2}(n)]$ could be measured reliably. In practice, such strong vibration signals may not always present, and the visibilities may be underestimated when the vibration is weak. Nonetheless, since the output presenting a larger value is still the one with larger visibility, Eq. (5) can still be used for the output selection. When the visibilities of the two outputs are close and fluctuating, frequent switching may occur. Due to the path length difference in the Pulse Group Generation part in Fig. 1, the fiber birefringence in the upstream sensing fiber, and the random laser phase noise, there could be a small phase jump if direct switching to the other channel is applied. In practice, to minimize the phase jump, the Pulse Group Generation part is packaged inside a box with vibration and sound isolation. Also, a laser with relatively small linewidth is adopted as the optical source. Meanwhile, when switching to the other output, the phase difference between the two outputs are calculated and compensated, which requires extra processing time. To avoid frequent switching between the two outputs when the visibilities are close and fluctuation, a threshold value $p$ is thus introduced, and the demodulation only switches to the other output when the visibility becomes more than $p\%$ larger. To validate the effect of the threshold, the PC in Sensor$\#220$ is manually adjusted during a $60$-s period and the induced degree of polarization fading would be time-varying. The visibilities of the two outputs are calculated during the same period, while demodulation is performed based on both two outputs. By setting the threshold at different values, the minimum visibility, time of switching, and the average SNR are calculated and presented in Table 2. When no threshold is set ($p=0$), minimum visibility of $0.70$ can be maintained. However, during the $60$ s of operation, switching between the two outputs occurs $33$ times, which requires extra demodulation time. When the two interferometric outputs presenting similar and fluctuating visibilities, even more frequent switching could occur. As the threshold increases, the minimum visibility in the system decreases slightly. Even when the threshold is set at $p=30$, the average SNR of the sensing signal within $60$ s only decreases by $<1$ dB. Meanwhile, the number of switches during demodulation can be reduced by over $90\%$.
Table 2. The impact of threshold on the sensing performance
With the automatic selection, the final output of Sensor$\#220$ is plotted in Fig. 6(a1). By setting the threshold at $p=25$, the visibility remains no less than $0.62$ during the manually-induced disturbance, as shown in Fig. 6(b), guaranteeing the performance of the interferometric sensor. Figure 6(a2) and 6(a3) show the temporal waveforms of the demodulated vibration signals, which present negligible phase jumps when switching the other channel occurs.
Fig. 6. (a1) The final output signal with (a2–a3) the zoom-in view of the two switchings. (b) Visibilities of the two interferometric outputs and the automatically selected output.
The SNRs of the demodulated signals obtained from OP$\#(1,220)$, OP$\#(2,220)$, and the automatically selected output are presented as the red, blue, and black curves in Fig. 7. In general, the trends of the three curves follow those of the visibility results in Fig. 6(b). Due to the induced fiber birefringence, the SNRs of the demodulated signals from OP$\#(1,220)$ and OP$\#(2,220)$ both vary notably over time, but the automatically selected output always presents SNR $>30$ dB. Compared to the case with polarization fading, the SNR improvement can be more than $20$ dB when the visibility drops below $0.3$, which is confirmed by the results between the $25$th and $35$th second in Fig. 6(b) and Fig. 7.
Fig. 7. SNRs of the demodulated signals obtained from OP$\#(1,220)$, OP$\#(2,220)$ and automatic selection
5. Conclusion
In this work, a polarization fading suppression method is proposed and demonstrated in a UWFBG-enhanced distributed interferometric sensing system. By achieving matched interference between polarization-switched pulses, the interferometric outputs of both two parallelly-polarized and two orthogonally-polarized pulses are obtained. In theory, at least one of the two outputs presents visibility $\ge \sqrt {2}/2$. To avoid frequent switching, a threshold is introduced. With a small sacrifice of minimum visibility to $0.62$, the times of switching can be reduced by over $90\%$. With the proposal polarization fading suppression method, a sensing system presenting good and stable SNR is achieved. Compared with the polarization diversity detection scheme, this method presents higher minimum visibility. Meanwhile, the method can also be implemented in distributed interferometric sensing systems based on FBG or reflector arrays, when other demodulation schemes, such as the phase-generated carrier method, are adopted.
Funding
National Natural Science Foundation of China (61735013, 62075171).
Disclosures
The authors declare that there are no conflicts of interest related to this paper.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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