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Abstract
A novel distributed fiber-optic localization algorithm with high sensitivity and precision based on merged Michelson-Sagnac interferometer is proposed and demonstrated. By performing simple addition and subtraction processing on the two phase differences of the two interferometers, two superimposed signals with a fixed delay can be obtained. The time delay can be calculated by a cross-correlation algorithm. Combined with the polynomial fitting interpolation, the disturbance location resolution is significantly improved. The total sensing distance can reach 120 km, and the localization errors are within ±35 m and ±160 m in the contact and non-contact disturbance experiment, respectively.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Distributed fiber-optic sensors have been studied widely for decades due to their advantages of large-scale monitoring, good concealment, excellent flexibility, and immunity to electromagnetic interference [1]. They have application values in many aspects, such as optical communication links security, oil and gas pipeline leaking monitoring, structural health monitoring, and perimeter security [2].
Two possible methods for the detection of phase sensitive events are phase optical time domain reflectometry (Φ-OTDR) and interferometry. The interferometric systems have very high real-time and sensitive performance in detecting the disturbance signals. In general, Mach-Zehnder interferometer (MZI), Michelson interferometer (MI) and Sagnac interferometer (SI) are used to establish the distributed fiber-optic sensor monitoring system. The possible configurations can be unidirectional MZI [3], or line-based SI [4], or a combination of SI and MZI [5,6], or dual-MZI [7,8], or dual-SI [9,10], or dual-wavelength line-based SI [11], or dual-MI [12], or a combination of Φ-OTDR and MZI [13].
A sensor concept using a combination of MI and SI was presented by Udd [14]. A merged SI-MI sensor for distributed disturbance detection was presented by Spammer et al [15]. The experimental results showed that the measurement precision is approximately ±3 m over a sensing fiber length of 0.2 km. Afterwards, a novel signal processing and localization scheme to further improve the performance of merged SI-MI was presented by Kondrat et al [16]. The experimental results showed that the measurement precision was approximately ±40 m over a sensing fiber length of 6.5 km. After that a SI-MI based sensor system to detect, classify and locate phase sensitive events in fiber optic cables, with precision of ±200 m for a monitoring length of 40 km was presented by Mohanan et al [17]. It is shown that the sensing distance and spatial resolution of a single system are mutually restricted. In addition, algorithms of approximate substitution are all used in the above three proposed papers of sensors based on merged MI-SI, which will affect the localization precision. Their algorithms are based on the assumption of the phase of the lights transmitted in the MI are modulated only once by a disturbance. In fact, the sensing lights of MI are transmitted back and forth in the optical fiber, and its phase will be modulated twice at different time. Moreover, the algorithms in the previous papers have not discussed the differential effect of SI, which will cause an issue that it is difficult to use the low-frequency vibration signals for disturbance localization.
In this paper, we propose and demonstrate a novel distributed fiber-optic localization algorithm with high sensitivity and high localization precision based on merged MI-SI. Due to the different operation principle of the two kinds of interferometers, the disturbance will cause different outputs. By performing simple addition and subtraction processing on the two phase differences of the two interferometers, two superimposed signals with a fixed delay can be obtained. Disturbance distance is proportional to the time of delay which can be accurately obtained by the combination of cross-correlation and polynomial fitting. Because the signals used for cross-correlation are the sum of the disturbance signals with different time delays, the sensor system has high detection sensitivity. Due to the unique localization algorithm without differential effect of SI, the frequency response range of the distributed fiber-optic sensing system is expanded, and the sensing and localization of non-contact disturbance such as buried fiber-optic cable is realized. The total sensing distance can reach 120 km, and the localization errors of contact disturbance are within ±35 m. In the non-contact disturbance experiment with a buried depth of 20 cm fiber-optic cable, the localization errors are within ±160 m.
2. Experimental setup and operation principle
2.1 Experimental setup
The schematic diagram of the proposed merged Sagnac-Michelson Interferometer sensor is shown in Fig. 1. A superluminescent diode (SLD) with a coherence length of tens of micrometers and a distributed feedback (DFB) laser with a coherence length of several meters are served as the light sources of this system. SLD and DFB laser are connected to the reflect port and the pass port of the wavelength division multiplexer1 (WDM1) respectively. An optical isolator (OI) is used to prevent light from entering the lasers and four photo-detectors (PDs), PD1, PD2, PD3, and PD4, are used for photoelectric transformation. Between the reflect ports of WDM2 and WDM3 there is a time-delay fiber (TDF) which is at the center of the fiber loop to ensure that SI gives a high response to a common disturbance. The polarization controller (PC) is used to control the interference stability of SI. The length difference between sensing optical fiber1 (SOF1) and SOF2 is within 50 cm to ensure good interference visibility of MI. The two beams output from DFB laser are out from pass ports of WDM2 and WDM3 and then enter Faraday rotator mirror1 (FRM1) and FRM2 and be reflected back to optical coupler (OC) through the original path. A 3×3 OC is used to close the Sagnac loop to provide passive biasing of the interferometer. The demodulation scheme utilizing a 3×3 OC has the advantage of passive detection and low cost as it requires no phase or frequency modulation in the reference arm or in the laser source, and so there are no active components in the optical domain.
The two beam paths of MI (M1 and M2) are as follows:
The two beam paths of SI (S1 and S2) are as follows: Finally, lights interfere when they are combined at 3×3 OC. The signals of MI output from the pass ports of WDM4 and WDM5 are received by PD1 and PD3 respectively. The signals of SI output from the reflect ports of WDM4 and WDM5 are received by PD2 and PD4 respectively.2.2 Principles of disturbance detection and localization
Assuming that a time-varying disturbance is acted at the point where the distance from TDF is Lx, the signals of MI detected by PD1 and PD3 are:
where E01 and E03 are the amplitudes of the sensing light, ΔφMI(t) is the phase difference of MI generated by the disturbance, and φ01 and φ03 are the initial phase introduced by 3×3 OC. The signals of SI detected by PD2 and PD4 are: where E02 and E04 are the amplitudes of the sensing light, ΔφSI(t) is the phase difference of SI generated by the disturbance, and φ02 and φ04 are the initial phase introduced by 3×3 OC.The phase differences ΔφSI(t) and ΔφMI(t) generated by the same disturbance can be expressed as followed:
The phase differences ΔφMI(t) and ΔφSI(t) generated by the same disturbance are combined by a simple signal processing algorithm to produce ϕ1(t) and ϕ2(t) with a fixed time-delay. In this algorithm, ϕ1(t) is got by ΔφMI(t) plus ΔφSI(t), and ϕ2(t) is got by ΔφMI(t-τ0) subtract ΔφSI(t). There is a time delay 2τx between ϕ1(t) and ϕ2(t) which can be accurately obtain by the correlation method and polynomial fitting. If the disturbance is acted on SOF1, the results of ϕ1(t) and ϕ2(t) are as followed:
3. Simulation results
We first study the localization performance of the proposed distributed fiber-optic vibration sensing system by simulation. This part mainly studies the factors that affect the localization precision which include fiber-optic vibration frequency, noise coefficient of system and algorithms of searching for cross-correlation peak value. The simulation sampling rate of the signal processing is set as 500 KS/s, the total length of sensing fiber-optic is 120 km and the TDF is set as about 10 km.
3.1 Vibration frequency and noise standard deviation
Noise terms in fiber-optic arise not only from random fluctuations of the electron density in the electronic amplifiers devoted to signal processing of the photo-detected current but also from random photon fluctuations in the detected optical field [20]. Here we study the influences of these noises on the fiber-optic sensing system which employs time delay estimation algorithm. The noise that reduces the system SNR is mainly divided into two categories. One is the random disturbance of the transmission optical phase at any point on the sensing fiber path. These noise will decrease the correlativity of the ϕ1(t) and ϕ2(t), leading to an increase in the error of the peak of the cross-correlation curve.
The other one is the high-frequency noise caused by scattered light and photoelectric conversion. As shown in Figs. 3(a) and 3(b), the vibration frequency of the SOF at 60 km are simulated to be 10 Hz and 200 Hz respectively. Generally, external disturbance lasts for a short period of time. Therefore, we use the Gaussian window with a standard deviation of 0.1 to simulate the signals of short-term disturbance. As shown in Fig. 3, the influences of the same noise on the disturbance signal of the two frequencies are different. As shown in Fig. 3(a), the Gaussian white noise with a standard deviation of 0.01 rad makes the two signals of 10 Hz partially overlapped. However, it has less effect on 200 Hz signals as shown in Fig. 3(b). In fact, the higher the frequency of vibration, the smaller the impact of high-frequency noise.
Fig. 3. Simulation of (a) 10 Hz and (b) 200 Hz vibration signals with noise of the same standard. (c) and (d) are local amplification of (a) and (b), respectively.
As shown in Fig. 4, we estimate the localization errors when the vibration frequencies range from 10 Hz to 200 Hz. And the standard deviation of applied Gauss white noise is from 0 rad to 0.01 rad. When the frequency is 10 Hz, the localization precision will be significantly affected once the standard deviation of noise is greater than 0.0003 rad. When the signal frequency is 200 Hz, the localization precision will be significantly affected once the noise standard deviation is greater than 0.005 rad. It can be seen that the higher the disturbance frequency, the stronger the anti-interference ability of the localization system. The requirement of SNR of the system can refer above simulation results in order to obtain high localization precision.
3.2 Search the peak of cross-correlation curves
For practical system, the detected signals are discrete in the time domain due to the operating principle of data acquisition card. No matter how high the sampling rate is, there is always a time interval between two sample points. The sampling rate used in this system is 500 KS/s, so the time interval between the two points is 2 us. The corresponding length of light transmission in fiber-optic is about 400 meters. Higher localization precision can be achieved by increasing the sampling rate. For example, when the sampling rate is increased to 4 MS/s, the localization precision can reach within ±25 meters. Generally, the actual time delay is not just an integral multiple of the sampling interval, so the estimation precision of correlation method depends on the sampling interval. The discrete implementation of cross-correlation sequence H(j) is shown in the following equation:
Generally, the method to improve the localization precision is to increase the sampling rate of the acquisition card. However, the price of the data acquisition card would increase accordingly. At the same time, larger amount of data processing brings higher demands on computers. Here we propose a method to improve the localization precision without increasing any hardware cost. The cross-correlation function obtained by using the time delay estimation algorithm is polynomial fitted to obtain the accurate peak value. So, the peak part of the cross-correlation curve is interpolated to make the cross-correlation curve smoother. The peak resolution is improved correspondingly.
As shown in Fig. 5, the cross-correlation function with time delay of 0 s, 0.2 us, 0.4 us, 0.6 us, 0.8 us, and 1 us are simulated. Because these time delays do not reach one sample point corresponding to 2 us, it can be seen in the Fig. 5 that the peak position is at 499999 in all six cases. So we use polynomial fitting to find accurate position of peak value. The errors are related to the number of samples of fitting, and the number of samples in this experiment is 1000. The pentagrams in the figure show the peak value obtained by fitting curves, and the errors are all less than 0.01 us. Ideally, the higher the number of interpolation sampling points, the higher the resolution. In fact, due to the existence of various noises in the real signal, there will be no practical significance when the number of sample points reaches a certain value. In practical applications, the signal-to-noise ratio (SNR) of the system determines the appropriate interpolation samples.
Fig. 5. Cross correlation peak value under different time delay. The pentagrams in the figure show the peak value obtained by fitting curves.
As shown in Fig. 6, errors of time delay obtained by polynomial fitting are within ±0.005 us when the total number of interpolation between each two points is 200, and errors obtained by taking the maximum value directly are within ±1 us for the sampling rate of 500 KS/s. The results show that the localization precision can be improved from ±200 m to ±1 m by using this algorithm when there is no other extra noise.
4. Experimental results
A proof-of-concept experiment has also been demonstrated to verify the proposed long distance fiber vibration sensing and localization method. As shown in Fig. 1, an experimental setup with the total length of SOF loop up to 120 km and TDF of 10 km is built. A 3 mW continuous-wave SLD source with central wavelength of 1550.12 nm and a 2 mW continuous-wave DFB source with line-width of about 10 MHz at the center wavelength of 1550.12 nm are employed. The light generated by the DFB can completely pass through the pass ports of the WDMs with pass-band of ±0.37 nm at center wavelength of 1550.12 nm. To reduce effects from acoustic pickup of noise, the sensing fibers and TDF are placed in an acoustically shielded box, with only a few short sections exposed for testing purposes. A data acquisition board of 16 bits is used for A/D conversion, and the data sampling rate is 500 KS/s. The length difference between SOF1 and SOF2 is adjusted within ±20 cm. A LabVIEW program is developed to realize the disturbance signals acquisition and processing.
4.1 Contact disturbance source localization
The performance of the MI-SI sensor proposed here for real-time contact disturbance localization is examined. A hammer is acted on the SOF1 to generate a series of disturbances and the interference signals are acquired. Output of the MI and SI for disturbance acted at near 40 km from the loop center is shown in the Fig. 7.
The phase differences ΔφSI(t) and ΔφMI(t) generated by the same disturbance are shown in the Fig. 8(a). The external environment can introduce a slow change in phase for each position of the cable, which will have an impact on the output signal. Moreover, the error of localization by using the ultra-low frequency signals is larger than that by using the higher frequency signals. So high-pass filtering (HPF) of low cut-off frequency 100 Hz is used, and the results are shown in the Fig. 8(b). The signals of ϕ1(t) and ϕ2(t) obtained by the Eqs. (7) and (8) are shown in the Fig. 8(c). The results of the cross-correlation and polynomial fitting are shown in Fig. 8(d). Where, the black points are the sequence H(j) obtained by discrete cross-correlation of ϕ1(k) and ϕ2(k) as shown in Eq. (12), and the red line is the curve obtained by polynomial fitting equation. By looking for the peak value of the fitting curve, we can see that the time delay between ϕ1(t) and ϕ2(t) is 392.47 us. According to Eq. (9), the disturbance location can be calculated as 40.021 km with error of 15 m.
Fig. 8. Signals processing of disturbance localization. (a) Demodulation of phase difference. (b) High pass filtering results of signals of (a). (c) Two signals obtained with time delay. (d) Cross-correlation of the two signals in (c). The pentagram in the figure show the peak value obtained by fitting curve.
The signals when the disturbance is acted on SOF1 and SOF2 are shown in Figs. 9(a) and 9(b), respectively. According to the positive and negative of the beginning signals amplitude, the sensor arm on which the disturbance acted can be identified. As can be seen in the Fig. 9(a), when the disturbance is acted on the SOF1, the beginning amplitude is positive. As shown in the Fig. 9(b), when the disturbance is acted on the SOF2, the beginning amplitude is negative.
In order to estimate the localization precision of each point on the sensor arm and verify whether there is a sensing blind zone, we tested from the first point to the end point of the sensing arm. 30 times of disturbances are repeated nearby 0 km, 10 km, 20 km, 30 km, 40 km, 50 km, and 60 km at one arm, respectively. The localization errors are demonstrated in Fig. 10, which are all within ±35 m. The experimental results using the method of the cross-correlation combined polynomial fitting are better than the results of the direct acquisition method, that is, ±200 m. It was not found that the error in a certain section was significantly increased compared to other sections.
Here we experimentally study the modulating frequency response of the system with a piezoelectric transducer. As show in Fig. 11, when the modulating frequency of piezoelectric (PZT) modulator at 60 km of the SOF1 is lower than 200 Hz, the localization errors are within ±18 m due to the low-frequency noise produced by the environment. When the frequency of disturbance is higher than 200 Hz, the localization errors are within ±10 m. The phase change of the optical fiber caused by external disturbance is more complicated, and the frequency and amplitude of the phase change caused by each disturbance are different. The factors include the magnitude, direction, and duration of the external force acting on the fiber and the external conditions of the fiber optic cable. Therefore, the localization error obtained by hammering the fiber optic cable experiment is greater than the error caused by the PZT simulation disturbance experiment. In this experiment, the load voltage of PZT modulator is 1 V, and the peak-to-peak value of the phase change that is modulated is about 50 rad.
4.2 Non-contact disturbance source localization
In order to prove the high sensitivity of the sensing and localization of system, we tested the ability of the buried optical cable to detect and locate the disturbance of the same impact force as the previous part of the experiment. In this experiment, the buried depth of optical cable is 20 cm and the buried medium is ordinary soil. The signals of ϕ1(t) and ϕ2(t) obtained when the disturbance is acted on the soil above SOF1 and SOF2 are shown in the Figs. 12(a) and 12(b) respectively. The maximum amplitude of ϕ1(t) and ϕ2(t) decreased from 90 rad to 10 rad compare with the contact disturbance experiment for attenuation of soil to impact force. That is due to the existence of vibration damping from the surface to underground [21].
As shown in Fig. 13, we analyze the power spectrum of vibration signal generated by contact disturbance and non-contact disturbance. It can be seen that the non-contact disturbance is about 25 dB lower than the contact disturbance in the frequency range from 600 Hz to 2000Hz. In this case, the frequency components of the signals we use are mainly concentrated below 600 Hz. This is because the damping force is proportional to the vibration speed [22], and the vibration signals above 600 Hz attenuate more.
Because of the low vibration amplitude and frequency of buried cables, it is very important to determine the cut-off frequency of HPF. As shown in the Fig. 14, the effect of the low cutoff frequency of the HPF on SNR and localization precision is studied. The frequency range whose amplitude is higher than -25 dB is approximately 50-200 Hz. Therefore, when the low cut-off frequency is higher than 200 Hz, most of the signal components will be filtered out, resulting in a significant decrease in the SNR.
The standard deviations of localization errors are less than 100 m when the low cut-off frequency is within 100-200 Hz. When the low cut-off of high pass filter is 100 Hz, the localization error is within ±160 m. For different conditions, such as thickness and hardness of soil, different filtering range should be used to ensure high SNR and high localization precision.
5. Conclusions and discussions
The high sensitivity and high localization precision of the proposed fiber-optic sensor based on MI-SI is demonstrated theoretically and experimentally. Compared with localization method of null-frequency, this method has the same high precision in every point of the sensing fiber-optic, and there is no blind area or insensitive area. Time delay estimation based on MI-SI has higher low frequency response ability compared with two wavelength SI-SI. Two arms of MI are distinguished by a unique method, and the total sensing length is up to 120 km. Theoretical and experimental results show that the localization precision of each point on the 120 km sensing optical cable is the same, and there is no blind area. Due to the unique localization algorithm without differential effect of SI, the frequency response range of the distributed fiber-optic sensing system is expanded, and the sensing and localization of non-contact disturbance such as buried fiber-optic sensing is realized. When the sampling rate is 500 KS/s, the localization errors of contact disturbance are within ±35 m. In the non-contact disturbance experiment of 20 cm buried fiber-optic cable, the localization errors are within ±160 m.
The factors that affect the localization precision mainly include: 1. The low-frequency disturbance signal of the whole sensing optical cable caused by environmental factors; 2. The influence from the signal acquisition system, such as electronic noise in the digital circuit, A/D converter, etc., which will affect the SNR of the system; 3. The scattering light noise in the fiber-optic, laser phase noise, laser intensity noise and other factors to reduce the SNR. In fact, these factors have less influence on the high frequency signals. Therefore, HPF can reduce the effect of these factors and improve the localization precision. The vibration frequency of buried optical cable is mainly below 600 Hz. In this experiment the best cutoff frequency of HPF range is 100 Hz to 200 Hz. It is useful to utilize polarization characteristics of scattered light to filter out partial scattered light in MI to improve SNR and the precision of disturbance localization [23]. The frequency of environmental disturbance is close to the vibration frequency of buried optical cable, which will greatly affect the localization precision. How to further improve the precision of disturbance localization using buried optical cable is important and worth studying in the future.
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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