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Abstract
A novel distributed fiber-optic sensor is proposed and demonstrated, in which two Mach-Zehnder interferometers are used to detect the interference signals with different wavelengths, and one 3 × 3 coupler is deployed to demodulate the time-varying phase change caused by vibration. The novel dual Mach-Zehnder interferometer (DMZI) is composed of two wavelength division multiplexers. Then, a time delay estimation algorithm is designed to construct two related signals using the phase difference, and the two constructed signals are used to obtain vibration position through cross-correlation. Experimental results show that the sensing distance can reach 100 km and the location error is within ±25 m.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Distributed fiber optic sensor can detect the time-varying vibration of the whole fiber. Due to the advantages of extreme sensitivities, high dynamic range and long-distance monitoring, it has been widely used in oil and gas pipelines, border security, and bridge health monitoring [1–5].
A variety of configurations based on fiber optic interferometer has been proposed to realize distributed sensing systems, such as Michelson interferometer (MI), Mach-Zehnder interferometer (MZI) and Sagnac interferometer (SI) [6–9]. But there are some disadvantages in practical applications. For example, MI has scattered light, so the sensing distance is limited; the polarization instability of MZI will causes polarization fading and affects demodulation; SI is not sensitive to low-frequency disturbances, and the positioning is inaccurate when the disturbance occurs in the center of the ring. Further, because SI is a ring structure, it is not suitable for the scenes which require straight line laying in engineering applications. To overcome the above shortcomings, some composite interference structures have been studied. A dual-SI interferometer sensor was proposed by Russell et al [10], the sensing system they proposed can correctly locate disturbances acting on a 40 km long sensing loop with a positional sensitivity of ±100 m. An SI-MI interferometer for distributed sensor was proposed by Kondrat et al [11], the experimental results of their work showed that along the 6 km, the position resolution of the disturbance is about ±40 m. A merged MZI and SI distributed sensor for detection and localization of the pipeline leaks was proposed by Huang et al [12] with the minimum detectable phase signal about 3.3×10−4 (rad/√Hz), in which the designed sensor has very wide dynamic range that can be greater than 76 dB. Because of these advantages, the composite structure has gradually become a research hotspot.
A common positioning method is based on the Null-frequency of the phase difference generated by the disturbance [13–15]. The system doesn’t respond the characteristic frequencies of certain disturbances, which means that the intensity of the characteristic disturbance frequency fnull(k) is significantly smaller than the surrounding frequency. There will be a periodic frequency loss, and a series of depressions formed at this time, called Null-frequency points. The relationship between the Null-frequency point and the disturbance location can be expressed as:
where n is the refractive index of the fiber, c is the light speed in vacuum, fnull(k) is the kth Null-frequency of the disturbance. However, when the frequency of vibration signal is less than the first Null-frequency, it would be hardly to find the Null-frequency points. Therefore, the Null-frequency method couldn’t be applicable for low frequency vibration detection. Distributed acoustic sensing (DAS) based on phase-sensitive OTDR (φ-OTDR) can monitor the phase of the Rayleigh backscattered signal to realize the positioning of vibration signal [16,17]. Although φ-OTDR has the advantages of lower deployment cost and compact form factor, it also has some inherent defects restricting its applications. For example, the weak Rayleigh backscattering signal in fiber limits acquisition speed [18], and the fading noise caused by interference fading and polarization fading makes DAS unable to detect the localization of real vibrations and decreases the strain resolution severely [19].In this paper, we propose and demonstrate a distributed fiber optic sensor with high sensitivity and localization based on novel dual Mach-Zehnder interferometer (DMZI). In the proposed DMZI, two independent Mach-Zehnder interferometers are constructed by the wavelength division multiplexer, and the phase signals of the two independent interferometric optical paths is built by a 3 × 3 coupler. Then, we design the time delay estimation algorithm to generate two very similar composite signals by using the phase difference of the two interferometers. The two composite signals have only a time delay difference in the time domain. A cross-correlation operation is performed on the two signals to obtain the delay, which determine the location of the vibration. Time delay estimation algorithm can avoid the defects of Null-frequency, and has higher positioning precision. Faraday rotating mirror and polarization beam splitters are used in the sensing system to eliminate polarization-induced fading and weaken the effect of backscattered light, so that the sensing fiber can be as long as possible. In the process of signal processing, we can judge whether the disturbance occurs in the left arm or the right arm by the positive or negative initial phase difference.
2. Experiment setup and sensing principle
2.1 Sensing system
A schematic diagram of the proposed distributed fiber optic sensor is shown in Fig. 1. Its basic structure is composed of two novel dual Mach-Zehnder interferometers (DMZI). A continuous-wave distributed feedback laser (DFB) is applied in interferometer. The wavelength division multiplexer (WDM1) is to combine two wavelengths of light into fiber. The isolator (ISO) is used to prevent the backscattered light entering the laser and affecting its working state, and to protect the laser. By controlling the polarization controller (PC) to change the polarization state of the transmitted light, and make the split ratio of the two exit ports of polarization beam splitter (PBS1) different. PBS 2 and PBS 3 play an important role in this system because PBS can improve the signal-to-noise ratio (SNR) of the system. Specifically, PBS can separate 2/3 of Rayleigh Backscattering (RB) from the returned light [20]. WDMs (WDM2, WDM3, WDM4, WDM5) is used to separate or combine λ1 and λ2. The time delay fiber (TDF) can guarantee that the phase changes of the two interferometers caused by the same disturbance are different. TDF is also the physical hardware foundation of dual wavelength demodulation algorithm. The function of faraday rotating mirror (FRM) is used to eliminate the effects of polarization-induced fading eliminating and maintain the polarization stability of the system [21,22]. Four beams of light are reflected by FRM1, FRM2, FRM3 and FRM4, then interference forms at the optical coupler (OC). Here, OC is a 3 × 3 coupler with a ratio of 1:1:1. PD1, PD2, PD3 and PD4 are used to detect the four interference signals. A data acquisition card (DAQ) is used to convert the analog signal into a digital signal, and then the digital signal is transferred to the computer for data processing.
Fig. 1. Schematic diagram of distributed fiber-optic sensor based on DMZI. DFB: distributed feedback laser; WDM: wavelength division multiplexer; ISO: isolator; PC: polarization controller; PBS: polarization beam splitters; OC: 3×3 optical coupler; TDF: time delay fiber; FRM: faraday rotating mirror; PD: photodetector; DAQ: data acquisition.
It can be verified from Fig. 1 that the propagation paths of the interferometer with wavelength λ1 are as follows:
- (a) PBS1 → PBS2 → WDM2 → TDF1 → FRM1 → TDF1 → WDM2 → PBS2 → OC
- (b) PBS1 → PBS3 → WDM3 → TDF2 → FRM3 → TDF2 → WDM3 → PBS3 → OC
2.2 Principle
When a disturbance is applied to the position Q of the right arm, interference will be formed at the OC. The interference signals received by PD1, PD2, PD3 and PD4 can be derived as:
The sensing system use wavelength division multiplexing technology to form two Mach-Zehnder interferometers. The phase difference Δφ1(t) and Δφ2(t) caused by the vibration can be expressed as:
Similarly, if the disturbance applied on the left arm, Δφ1(t) and Δφ2(t) can be expressed as:
Therefore, when vibration is applied to different arms, we can judge whether the disturbance occurs on the left arm or the right arm by the positive or negative amplitudes of Δφ1(t) and Δφ2(t).The diagram of time delay estimation algorithm is shown in Fig. 2. Performing a series of mathematical operations on Eq. (6) and Eq. (7), two related signals with very high similarity can be calculated based on the below equations:
Compare Eq. (10) and Eq. (11), there is a time delay Δτ = 2nLx/c between Δϕ1(t) and Δϕ2(t), where Lx is the location of disturbance. The cross-correlation of Δϕ1(t) and Δϕ2(t) is calculated by:
According to previous derivation, the flow chart for obtaining location information is shown in Fig. 3. The main steps are listed as follows:
- (1) Start;
- (2) The data acquisition card converts 4 channels of interference signals from analog signals to digital signals that can be processed by computer;
- (3) Intercept the effective fragment of the four time-domain interference signals for subsequent data processing. The four time-domain interference signals are I1(t), I2(t), I3(t) and I4(t), respectively;
- (4) Phase difference Δφ1(t) is obtained by demodulating the effective fragment interference signals I1(t) and I3(t). Similarly, Δφ2(t) is also obtained in the same way;
- (5) Determine whether the disturbance is in the left arm or the right arm by judging the initial amplitude of the phase difference is positive or negative;
- (6) Apply time delay estimation algorithm to obtain Δϕ1(t) and Δϕ2(t). The two signals are similar in time domain and there exists only one known delay;
- (7) Apply the cross-correlation operation between Δϕ1(t) and Δϕ2(t) to obtain the time delay, which is defined as: Δτ = 2nLx/c;
- (8) The disturbance location is obtained by Lx = c·Δτ /2n;
- (9) End.
3. Experiment and analysis
3.1 Simulation experiment
The feasibility of the time delay location algorithm has been verified by formula deduction. Now, we simulated the positioning performance of the proposed distributed optical fiber sensor system. According to [23], the Rayleigh backscattering in fiber can be described as the vector sum of the backscattering of a series of random reflection elements, the amplitude follows Gaussian distribution, and phase follows uniform distribution. Since the amplitude spectrum of Gaussian white noise follows Gaussian distribution, we use Gaussian white noise to simulate the backward Rayleigh scattering in the fiber. We mainly discuss the influence of disturbance frequency and the noise on location accuracy. The simulation result is shown in Fig. 4.
In Fig. 4, (X) axis represents the frequency of external vibration, Y axis represents the proportion of noise in the signal, and Z axis represents positioning error. The vibration frequency is simulated from 100 Hz - 2000Hz. From Fig. 4, we can see when the noise is constant, as the vibration frequency increases, the positioning error gradually decreases. When the proportion of noise ranges from 0 - 20% and the vibration frequency is fixed, as the noise ratio increases, the positioning error gradually increases. It can be seen that a higher noise ratio can result in a greater positioning error, and a higher vibration frequency can result in a smaller positioning error.
Figure 5 compares the location error under different noise ration. First, as the vibration frequency increases, the location error gradually decreases. Second, the location error with 1% noise ratio is less than the location error with 3%. This means that decreasing noise ration can improve the precision of positioning.
3.2 Location experiment
With the support of simulation results, the proposed sensor is verified by experiments and we demonstrate the experiment set up based on Fig. 1.
The light source in the sensing system is two DFB with bandwidth is about 10 MHz and the output optical power is 12 mW. The only difference between the two light sources is the central wavelength that one is 1548.52 nm and the other is 1550.12 nm. TDF1 and TDF2 are time delay fiber with a length of 10 km (too short will not be able to locate, and too long will introduce unnecessary losses). A 16-bit DAQ (National Instrument Co., Ltd) acquisition card is used to transfer the collected data into the computer, where acquisition frequency is 500 K/s. The sensing fiber used is standard Corning SMF-28 single fiber. A LabVIEW program is used to realize the signal processing and analysis.
Use a hammer to apply a vibration at sensing fiber, the time-domain interference signal received by PDs (PD1, PD2, PD3, PD4) is shown in Fig. 6(a). Here, the PD1 and PD3 detects interference signals with wavelength of 1548.52 nm, PD2 and PD4 detects interference signals with wavelength of 1550.12 nm, respectively. What the detector received is the intensity spectrum of the interference signal, which cannot directly obtain the information about the vibration position. The phase differences Δφ1(t) and Δφ2(t) generated by the vibration are shown in the Fig. 6(b). Note that, from Eq. (6) and Eq. (7), the location information of the vibration has been included in Δφ1(t) and Δφ2(t). Since the sensing fiber is very long, the slow phase change caused by the external environment will affect the phase difference when accumulated. Therefore, in actual signal processing, it is necessary to let Δφ1(t) and Δφ2(t) through a high-pass filter. Usually, the low cutoff frequency is set as 100 Hz. The phase difference signals Δφ1(t) and Δφ2(t) are used to obtain the two high similarity signals Δϕ1(t) and Δϕ2(t), and the time delay of Δϕ1(t) and Δϕ2(t) determines the vibration location. The corresponding result is shown in the Fig. 6(c). The cross-correlation between Δϕ1(t) and Δϕ2(t) is shown in Fig. 6(d), and the time delay can be obtained which is Δτ = 0.2953 ms. According to Eq. (13), the vibration location can be calculated as 30.174 km with an error of 23 m (OTDR measured vibration location is 30.151 km).
Fig. 6. The process results of time delay estimation algorithm with the disturbance position Lx = 30.175 km (a) The signals received by the PDs; (b) The phase difference signals Δφ1(t) and Δφ2(t); (c) The two signals Δϕ1(t) and Δϕ2(t); (d) The cross-correlation of Δϕ1(t) and Δϕ2(t).
3.3 Vibration experiment on left or right arm
This section is the experiment about the vibration is applied at the left arm or the right arm. The experimental diagram is shown in Fig. 7. Since the influence of external temperature and atmospheric pressure on the fiber changes slowly and weakly, it is assumed that the environmental conditions of the two sensing arms are the same, which means that the phase difference between the two arms is zero when there is no vibration.
As shown in Fig. 8, we can know the phase difference is different WITH vibration is applied on the different arms. So it can be judge whether the vibration occurs on the left arm or the right arm. When the vibration is applied at the Q point of the left arm of the interferometer, the signals detected by the PD1 and PD2 are shown in Fig. 8(a) and the phase difference signals Δφ(t) is shown in Fig. 8(b), respectively. When the vibration is applied at the P point of the right arm of the interferometer, the signals detected by the PD1 and PD2 are shown in Fig. 8(c) and the phase difference signals Δφ(t) is shown in Fig. 8(d), respectively. In Fig. 8(a) and Fig. 8(c), the PD detects the intensity signals but it cannot distinguish them in the time domain. Thus it cannot judge whether the interference is applied on the left arm or right arm. However, a clear difference can be seen after phase demodulation, as shown in Fig. 8(b) and Fig. 8(d). That is, when the vibration is applied on the left arm, it can be seen that the initial amplitude of the phase difference is positive. On the contrary, when the vibration is applied to the right arm, the initial amplitude of the phase difference is negative.
Fig. 8. Experimental result: (a) Vibration the left arm at position Q, the signals received by PD1 and PD2; (b) The phase difference signals Δφ(t); (c) Vibration the right arm at position P, the signals received by PD1 and PD2; (d) The phase difference signals Δφ(t).
Based on this relationship, we can use the initial amplitude of the phase difference to judge whether the disturbance is applied at the left arm or the right arm. In other words, both the left arm and right arm of the interferometer can be used for sensing, and the sensing distance extends to doubled. However, it should be noted that in practical applications, the system needs pre-calibration to realize this function. That is, we need to know the corresponding relationship between the initial phase of the left arm and the right arm in advance. When the two arms are deployed in different places, the environment temperature should be taken into consideration. If the temperature difference between the two arms is very large, the optical path difference between the left arm and the right arm will not be equal, which will cause the interference contrast to decrease. As a result, the positioning precision of the system is reduced, and even cannot be located. Therefore, in actual deployment, the environment temperature should be considered.
3.4 Result analysis
To show the superiority of the time delay algorithm, a comparison experiment between time delay algorithm and Null-frequency is done. The frequency spectrum obtained from fast Fourier transform (FFT) for Δφ(t) is shown in Fig. 9. It can be seen that when the vibration is applied at nearby 10 km, there is no obvious effective Null-frequency point in the frequency spectrum which means this is a blind area for Null-frequency and it cannot be located. The location obtained by the time delay algorithm is 10.251 km with an error of 19 m (OTDR measured length is 10.232 km). When the vibration is applied at nearby 30 km, the first-order null frequency fnull(1) is 1679.11 Hz. The location calculated by Eq. (1) is 30.427 km and the error is 276 m (OTDR measured length is 30.151 km). In this case, the location obtained by the time delay algorithm is 30.174 km with an error of 23m. We can conclude when the Null-frequency cannot be located, the time delay algorithm can locate. When the Null-frequency can be located, the time delay algorithm has a higher precision than Null-frequency, and there is no blind zone.
For the convenience of statistics, assuming that the vibration applied at the left arm, the location on the coordinate axis is expressed as a negative value. When the vibration applied at the right arm, the corresponding value is positive. In Fig. 10, vibration is applied at the different positions (near by -40 km, -30 km, -10 km, 0 km, 20 km, 50 km) of the sensing fiber to test the location precision of the system. The location errors are depicted in Fig. 10. The experimental results are shown that the sensing system has high stability with location error ±25 m.
Fig. 10. The location error for 10 times vibration nearby -40 km, -30 km, -10 km, 0 km, 20 km, 50 km, respectively.
4. Conclusion
A novel distributed fiber-optic sensor based on dual Mach–Zehnder interferometer was proposed, and the feasibility of its positioning was demonstrated through derivation and experiments. Compared with the Null-frequency, the proposed time delay estimation algorithm can achieve a higher precision at each point of the sensing fiber without any blind zone. PBS was utilized in the system to separate the backscattered light so that the sensing fiber can reach 50 km. In the signal processing, the positive or negative of the initial phase difference was used to judge the vibration applied at the left or right arm, which means that the sensing distance can achieve double (i.e., extend to 100 km). The experimental results showed that when the sampling rate is 500 K/s, the positioning error of the system is within ±25 m. Therefore, the proposed sensing system can realize real-time monitoring and positioning, which has great potential used in long-distance perimeter security.
Funding
Science and Technology Commission of Shanghai Municipality (19511132200); National Key Research and Development Program of China (2017YFB0803100).
Disclosures
The authors declare no conflicts of interest.
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