Long-Range Distributed Vibration Sensing Based on ... - IEEE Xplore

Long-Range Distributed Vibration Sensing Based on Phase Extraction From Phase-Sensitive OTDR Volume 8, Number 3, June 2016 Guangyao Yang Xinyu Fan Shuai Wang Bin Wang Qingwen Liu Zuyuan He

DOI: 10.1109/JPHOT.2016.2552820 1943-0655 Ó 2016 IEEE

IEEE Photonics Journal

Vibration Sensing Based on Phase Extraction

Long-Range Distributed Vibration Sensing Based on Phase Extraction From Phase-Sensitive OTDR Guangyao Yang, Xinyu Fan, Shuai Wang, Bin Wang, Qingwen Liu, and Zuyuan He State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China DOI: 10.1109/JPHOT.2016.2552820 1943-0655 Ó 2016 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Manuscript received February 23, 2016; revised April 5, 2016; accepted April 7, 2016. Date of current version April 26, 2016. The work was supported by the National Natural Science Foundation of China under Grant 61575001, Grant 61275097, Grant 61307106, and Grant 61307107 and by the Shanghai STCSM Scientific and Technological Innovation Project under Grant 15511105401. Corresponding author: X. Fan (e-mail: [email protected]).

Abstract: Distributed fiber-optic vibration sensors based on phase-sensitive optical timedomain reflectometry (-OTDR) have found many applications in various fields. In this paper, we analyze the phase noise of -OTDR, which is the main limiting factor of the measurement range. We found that the laser phase noise and phase extraction error caused by the intensity noise in photodetection contribute to the total phase noise. By introducing a series of auxiliary weak reflection points along the fiber, we develop a phase-noise-compensated -OTDR and realize a long-range distributed vibration sensing based on the phase extraction. Furthermore, a statistical analysis was proposed to maintain the vibration measurement sensitivity along the whole fiber. In the experiment, vibrations at 30 km were measured with a linear response, which confirmed the validity of our proposed system. Index Terms: Fiber-optics sensors, Rayleigh scattering, remote sensing and sensors.

1. Introduction Distributed optical fiber sensing is a powerful technology when parameters along thousands of continuous positions need to be analyzed. Compared with conventional sensors, the optical fiber sensor has more desirable characteristics such as passivity, anti-electromagnetic interference and low cost. A distributed optical fiber sensor can currently perform various measurements, such as temperature or strain, at any specific segment of a fiber [1]. Among different optical fiber sensors, -OTDR using a narrow linewidth laser as a light source is sensitive to external disturbances and thus is applied to distributed vibration sensing such as intrusion detection [2], [3]. In -OTDR, highly coherent pulses from a narrow linewidth laser are launched into the fiber under test (FUT), and the Rayleigh backscattering (RBS) lightwaves from individual scattering centers within a pulse length interfere coherently, resulting in RBS traces in a jagged form [4]. With a frequency stabled laser and an undisturbed fiber, a stable RBS trace can

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be obtained, since the phase of backscattered lightwave from each scattering center is dependent on the wavelength of laser source and the distance of scattering centers [5]. However, any external disturbance leads to the strain of fiber, which changes the scattering centers’ distance considerably and finally results in a variation of RBS intensity. Therefore, by detecting and comparing the successive RBS intensity traces, external vibration can be obtained [6]. Many efforts have been made on improving the performance of distributed vibration sensing with -OTDR. A polarization-maintaining fiber configuration was introduced into -OTDR for improving the spatial resolution to 1 m [7]. In [8], a semiconductor optical amplifier (SOA) was used to provide a pulse with a high extinction ratio for decreasing the coherent noise. As an experimental result, the vibration sensor can measure the vibration of up to 39.5 kHz with a 5-m resolution and a 600-m measurement range. Peng et al. combined coherent detection and bidirectional Raman amplification and successfully extended the measurement range to 131 km while keeping an 8-m resolution [9]. However, the intensity variation of RBS lightwave is not linearly dependent on the external vibration, which is undesirable in vibration sensing since it may cause the higher-order harmonics, and the sensitivity of optical intensity to vibration is rather low at a long distance. On the other hand, the optical phase of RBS lightwave was introduced into vibration sensing, since the optical phase variation has a directly proportional relationship to the vibration amplitude [10]. There were some researches to obtain the phase signal of RBS lightwave through the interference among RBS lightwaves from different pulses or different positions [11]–[14]. However the measurement range is limited with the interferometric phase extraction, since the RBS lightwave power is extremely weak. The optical phase can also be obtained from the beat frequency of coherent detection, but suffers from the phase noise of laser source. Pan et al. extracted phase signals from the beat frequency in -OTDR [15], and a more than 360 Hz vibration detection bandwidth was achieved with a 10 kHz interrogation repetition rate in a 4 km measurement range, which was limited by the phase noise. Tu et al. used a differential process to prevent signal deterioration caused by the phase noise and realized a measurement range of 25 km with a 10-m spatial resolution [16]. The signal-to-noise ratio (SNR) is very limited since they only use the optical intensity information to locate the vibration. The laser phase noise is a common trouble in distributed fiber sensing technologies which limits the measurement range. In optical frequency domain reflectometry, an auxiliary interferometer is used for providing the information of phase noise [17], [18]. But in -OTDR, the phase noise is produced by the time delay difference of the probe pulse and the local oscillated lightwave, which is difficult to measure with an interferometer. Recently, we find that it is possible to measure the laser phase noise with some auxiliary weak reflection points [19]. In this paper, we analyze the phase noise in the phase extraction from coherent -OTDR and propose a novel scheme to locate and measure the vibration with the optical phase signal extracted from coherent -OTDR. The total phase noise consists of the phase extraction error introduced by the RBS intensity noise in the phase extraction process, and the phase noise introduced by the characteristics of laser source. These are analyzed and experimentally demonstrated in this paper. For compensating the phase noise, several auxiliary weak reflection points are set into the FUT and protected from external disturbances to provide the reference phase. By correcting the RBS lightwave phase signals using the reference phase signal, the laser phase noise can be compensated to a very low level. Finally, taking the statistical characteristics of the phase noise into consideration, we propose a statistical analysis for locating the vibration based on the phase signal extraction, which is more sensitive than the intensity based locating method. This paper is structured as following. In Section 2, the phase noise in -OTDR is analyzed, and in Section 3 we present the principle of phase noise compensation and phase signal based vibration locating method. In Section 4, we describe our experimental investigation, and the conclusion is given in Section 5.

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Fig. 1. Conceptional schematic of coherent -OTDR. CIR: circulator; AOM: acoustooptic modulator; BPD: balanced photodector; FUT: fiber under test.

2. Principle Fig. 1 shows a conceptional schematic of coherent -OTDR. In coherent -OTDR, a narrow linewidth laser is used as a light source, and its electrical field output can be expressed as E ðt Þ ¼ E0 cosð!t þ ðt ÞÞ

(1)

where ! is the optical frequency, and ðt Þ is the optical phase that follows a random walk process. Here, the intensity fluctuation of laser is neglected in the equation. The highly coherent lightwave from the laser is divided into two beams by using an optical coupler: the probe lightwave for launching into the FUT, and the local reference lightwave for coherent detection. An acousto-optic modulator (AOM) is then used to modulate the probe lightwave into a pulse with a frequency shift of fb . The RBS lightwave returned from FUT is mixed with the local lightwave in another 3 dB coupler and the beat signal is detected by using a balanced photodetector (BPD). The detected intensity output in a single measurement can be described as follows: Iðt Þ / ELO Rðt Þcosð2fb t þ ðt0 Þ þ FUT ðt Þ ðtÞÞ

(2)

where t0 is the optical pulse generated moment, Rðt Þ and FUT ðt Þ stand for the reflectivity and the phase change at FUT, respectively. With a Hilbert Transform, the beat signal experiences a 90° phase shift as described in the following expression: H ½Iðt Þ ¼ ELO Rðt Þsinð2fb t þ ðt0 Þ þ FUT ðt Þ ðt ÞÞ: Then the phase signal and intensity signal can be extracted by 8 < ’ðt Þ ¼ arctan H ½Iðt Þ 2fb t Iðt Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : Rðt Þ ¼ I 2 ðt Þ þ H ½Iðt Þ2 :

(3)

(4)

Here, the beat frequency term 2fb is eliminated to simplify the result. It is obvious that the extracted phase signal consists of two important parts: the first part of FUT ðt Þ reflects the external vibration to be extracted, while the second part of ðt0 Þ ðt Þ is derived from the phase noise of the laser source. Since the laser phase noise follows a random walk process, the term of ðt0 Þ ðt Þ is a random variable that follows the Gaussian distribution. The relativity of ðt0 Þ and ðt Þ decreases as the time difference jt0 tj grows, which means that the variance of ðt0 Þ ðt Þ grows with distance. As a result, the phase extraction is disturbed by the laser phase noise, and the influence gets serious when the measurement range is extending. On the other hand, the white noise from the photodetection also affects the phase extraction in -OTDR. The model of signal and noise in -OTDR is described as Sðt Þ ¼ A cosð!t þ ’Þ þ Nðt Þ

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(5)

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where A is the signal amplitude, ’ is the phase term to be extracted, and Nðt Þ is the white noise in the system. Since the bandwidth of RBS signal is narrow, a bandpass filter is usually employed to achieve better performance. The output of bandpass filter is Sðt Þ ¼ A cosð!t þ ’Þ þ NBPF cosð!t þ Þ

(6)

where NBPF is the noise amplitude after bandpass filter, is a random variable following uniform distribution in [0, 2]. According to the linearity of Hilbert Transform, the error of phase extraction can be derived as ! sin ’ þ NBPF A sin ¼ arctan ’: (7) cos ’ þ NBPF A cos Since NBPF is an insignificant value when comparing with the signal amplitude, we use the first order approximation of Taylor expansion, and then the phase extraction error can be approximately expressed by ( NBPF A ðsin cos tan ’Þ; jtan’j < 1 NBPF (8) else: A ðcos sin cot ’Þ; Then, the noise level is evaluated by the variance of phase extraction error. After applying a logarithmic process to this equation, the relationship between the phase extraction error and SNR of photodetection can be directly summarized as A ¼ SNR: (9) log10 ½VARðÞ / 10 log10 NBPF As a conclusion, the phase signal extraction in coherent -OTDR is affected by the phase noise from the laser source as well as the noise in photodetection system. Without any compensation, the laser phase noise is the main limiting factor. The phase noise becomes unbearable at several kilometers even with a narrow linewidth laser whose linewidth is only several kHz. After using phase noise compensation, the noise in photodetection becomes the primary limiting factor, which can only be improved by enhancing the SNR of the system.

3. Phase Signal Based Vibration Measurement 3.1. Phase Noise Compensation It is well known that when extracting the phase signal of -OTDR from several kilometers away, the laser phase noise deteriorates the results. Multiple averaging is necessary to obtain the vibration information, which greatly affects the vibration detection bandwidth. The laser phase noise grows when the time delay difference jt0 t j grows. Specifically, the variance of laser phase noise is directly proportional to the time delay difference. If the time delay difference is shortened to a much shorter value, the phase noise can be suppressed and the phase extraction can obtain much better results. After the phase extraction, we can calculate the difference of phase signals between two arbitrary points along the FUT. Note that the result still contains the phase noise, whose expression is ’ðt1 ; t2 Þ ¼ FUT ðt1 Þ FUT ðt2 Þ ½ðt1 Þ ðt2 Þ

(10)

where t1 and t2 stand for the time delay corresponding to these two points. The noise level of the phase difference only depends on the time delay difference of chosen points. For compensating the phase noise, we set several auxiliary weak reflection points along FUT. These auxiliary weak reflection points is carefully chosen so that the reflection points can be distinguished from RBS signals while the power loss caused by the reflection points is

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Fig. 2. Principle of phase noise compensation with auxiliary weak reflection points.

negligible. These points are protected from the environmental disturbance to obtain the information of laser phase noise exactly. Describing the phase of k th reflection point as ’k , for the fiber near the k th reflection point, we use the new phase term ’0 ðt Þ instead of the original phase ’ðt Þ ’0 ðt Þ ¼ ’ðt Þ ’k ¼ FUT ðt Þ þ ðtk Þ ðt Þ

(11)

where tk is the round trip time delay of the k th reflection point. After the phase noise was compensated, the time delay difference is reduced to jt tk j. The noise compensation ratio is then jt tk j=jt t0 j, as illustrated in Fig. 2. The auxiliary weak reflection points can be set at any position along the fiber. The distance of reflection points should be set according to the coherent length of laser source and the requirement on the noise level. By compensating the phase noise into a very low level, we can easily locate and analyze the vibration.

3.2. Phase Signal Based Locating Method In a RBS intensity based vibration sensing system, the vibration is located by subtracting consecutive intensity-distance traces. But the fading noise influences the locating sensitivity, as the vibration can hardly be detected at some fading positions [20]. If we employ the same method in phase-distance traces extracted from -OTDR, the fading noise still badly influences the result. To solve this problem, we propose a vibration locating method based on statistically analyzing the phase signal. The phase noise level is a monotonically increasing function of distance. With a narrow linewidth laser, the noise level of adjacent points (with a distance of detection resolution) along the fiber is nearly equivalent. Supposing that there are N phase-distance traces obtained, we may describe the phase as follows: ’i ðnÞ ¼ FUT;i ðnÞ þ i ðn0 Þ i ðnÞ;

i ¼ 1; 2; . . . ; N

(12)

where ’i means the ith phase signal, n is the discrete distance after sampling. Here we employ statistical analysis on this group of phase signals. For each point on the fiber, the variance of N phase signals of one group is calculated as DðnÞ ¼ VAR FUT;n ðiÞ þ n0 ðiÞ n ðiÞ (13) where DðnÞ means the variance-distance trace of the given group. As a basic assumption, the phase noise of an ideal laser source follows a random walk process, and the difference of phase noise n0 ðiÞ n ðiÞ is a Gaussian distributed white noise; therefore, the variance-distance trace contains two independent parts: (14) DðnÞ ¼ VAR FUT;n ðiÞ þ VAR½n0 ðiÞ n ðiÞ:

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Fig. 3. Principle of phase-signal-based locating method by statistical analysis.

Fig. 4. Vibration locating with the influence of fading noise.

Each vibration event on the fiber leads to a step change of the first part. By examining the step change of variance-distance trace, vibration can be located with uniform sensitivity along the fiber, because the phase noise and the vibration have no correlation. When the statistical independence exists in different vibration events, which is a reasonable assumption, multi-vibration events can be successfully located. As illustrated in Fig. 3, each vibration event leads to an independent step change, which can be easily observed. The fading noise influences the variance-distance trace, resulting in many spikes. However, since the variance-distance trace is a monotonically increasing function of distance, we can connect the minimum values of variance-distance trace within one spatial resolution to eliminate the influence of fading noise, as illustrated in Fig. 4. We find that this vibration locating method is free of fading noise, since the fading noise related area is always shorter than the spatial resolution.

4. Experimental Setup and Results 4.1. Experimental Setup The experimental setup of coherent -OTDR is shown in Fig. 5. A fiber laser is employed as a coherent light source with a linewidth of 1 kHz to meet the requirement of the long measurement range. The output power of the fiber laser is 10 dBm, and the output wavelength is 1550.0 nm. The lightwave from the fiber laser is then divided into two parts by the 3 dB optical coupler 1 (OC1). The AOM produces pulsed lightwave with 100 ns duration and a 3 kHz repetition rate, and also introduces an 80 MHz frequency shift for heterodyne detection. The pulsed lightwave is amplified by an EDFA, and then launched into the fiber under test (FUT) through a circulator (CIR). The peak power of the amplified pulse is around 23 dBm, which is the threshold of nonlinear effects. A polarization controller (PC) is used for adjusting the polarization state of local reference lightwave to achieve a high performance. The RBS lightwave and local reference lightwave are mixed in the 3 dB optical coupler 2 (OC2), and detected by a balanced photodetector (BPD) (Thorlabs PDB460C-AC) for obtaining the beat signal while blocking the DC component. The bandwidth of BPD is 200 MHz. The electric signal from BPD is sampled

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Fig. 5. Experimental setup of coherent -OTDR. OC: optical coupler; PC: polarization controller; AOM: acoustic optical modulator; AWG: arbitrary waveform generator; EDFA: erbium-doped fiber amplifier; BPF: band-pass filter; ADC: analog-to-digital convertor; PZT: piezoelectric transducer.

by an analog-to-digital converter (ADC) (NI-5154) with a sampling rate of 500 MS/s and an accuracy of 8-bit. The sampled signal then passes a digital band-pass filter to eliminate the out-of-band noise, whose center frequency and bandwidth are 80 MHz and 20 MHz, respectively. Finally, the phase signal is extracted from the filtered signal. Since the auxiliary weak reflection points should be set according to applications, the structure of FUT changes in different experiments, which is described in different paragraphs accordingly.

4.2. Phase Noise Analysis The phase noise introduced by the laser source and the photodetection noise are investigated by experiments respectively. Firstly, a coherent -OTDR with high SNR is designed to explore the laser phase noise, since a high SNR can suppress the disturbance of phase extraction error. We also demonstrate the phase noise compensation method in this part. After that, since the laser phase noise is compensated, we investigate the relationship between the noise in photodetection and the phase extraction error. To demonstrate the influence of laser phase noise and the phase noise compensation method, a 10 km FUT is employed, with five auxiliary weak reflection points which consist of four mated FC/PC-FC/PC connectors and one open FC/APC connector at far end of the FUT. In experiments, the environmental disturbance is shielded by putting the FUT into a sound-proof box. The structure of FUT is shown in Fig. 6(a). Fig. 6(b) shows one corresponding intensity-distance trace of RBS lightwave. The intensities of auxiliary weak reflection points are higher than the RBS lightwave for preventing from the interference effect. The phase signals are extracted from the sampled signals according to (4). The phase variance is used to characterize the noise level, since the phase signal varies at [0, 2] so that the SNR is not applicable. In order to measure the noise level, we acquired 100 consecutive phasedistance traces, and calculated the trace of phase variance versus distance. Fig. 6(c) shows the noise level with and without the laser phase noise compensation, respectively. When there is no compensation, the phase variance accumulates with the distance growing, as predicted in Part 3. However, after the laser phase noise compensation, the phase variance is kept at a very low level. The experimental results match well with theory, which is shown in Fig. 2. After the laser phase noise is compensated, the phase extraction error due to the noise in photodetection, in another word, the SNR of the system, becomes the major limiting factor of measurement range. We investigate the theory about the relationship between the phase extraction error and the RBS intensity noise, and demonstrate it with an experiment. After eliminating the environmental disturbance and the laser phase noise completely, we change the optical

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Fig. 6. Phase noise analysis and compensation result. (a) FUT structure. (b) Corresponding intensity of RBS lightwave. (c) Phase variance-distance trace with phase noise compensation and without compensation, respectively.

Fig. 7. Relationship between SNR of RBS intensity and extracted phase noise level.

power and extract the phase signal under different SNR from 0 dB to 17 dB. Fig. 7 shows the experimental result. The phase noise level of 0 dB corresponds to the mean phase noise extracted from the photodetection noise. When SNR is higher than 5 dB, the result shows a linear characteristic, but the scatters do not converge to a line since the slope is a random variable, as predicted by (8). The points where SNR is lower than 5 dB do not show a linearity because the noise is close to the level of RBS intensity signals, and the first order approximation of Taylor expansion in (8) is invalid in this case. The result implies that the SNR of RBS intensity should be high enough to keep the performance of phase extraction.

4.3. Vibration Measurement The vibrations at 30 km are measured for validating the system. For simplifying the system, the FUT consists of five parts: one 25 km single mode fiber (SMF) for extending the total fiber

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Fig. 8. Experimental results of vibration measurement. (a) FUT structure. (b) Corresponding intensity of RBS lightwave. (c) Phase variance-distance trace in a group with compensation and without compensation, respectively. (Inset) Detail of phase variance trace from 23 to 31 km.

length, two 2 km SMFs, and two 1 km SMFs for experimentally demonstrating the technology. The two 1 km SMFs are fusion spliced for reducing the loss and avoiding connector reflection. Three mated pairs of FC/PC-FC/PC connectors and one open FC/APC connector work as auxiliary weak reflection points. Each auxiliary weak reflection point is only 35 dB higher than RBS lightwave so that the insertion loss can be neglected. A piezoelectric transducer (PZT) is used as the vibration source in our experiment, with a 20 n" strain accuracy. The PZT is set near the splice fusion point between two 1 km SMFs. Around 1 m fiber is tied on the PZT so that the strain introduced by the PZT can be set precisely. We use the strain on fiber as the unit of vibration, and the peak-to-peak value of strain as the vibration magnitude. In the experiment, every 100 phase-distance traces are merged into a group to take a statistical analysis and a phase variance-distance trace is obtained every 0.033 second. By examining the phase variance-distance trace and the phase signal, we obtain the information of external vibration. Fig. 8(a) shows the FUT structure and Fig. 8(b) shows one intensity-distance trace of RBS lightwave. The measurement range is 31 km, and the SNR at the end of FUT is about 8 dB. Longer measurement range is also achievable, but lower SNR means a higher phase extraction error, which deteriorates the accuracy of phase extraction. The four auxiliary weak reflection points can be easily located in the RBS intensity-distance trace since their intensities are apparently higher than the RBS lightwave. They are protected by a sound-proof box for avoiding the external disturbance. With the help of auxiliary weak reflection points, we can compensate the phase noise at the fiber around these points. Fig. 8(c) shows the compensation effect on the whole FUT. It is obvious that due to the laser phase noise, the variance of phase signals increases with the increase of distance, resulting in the deterioration of the phase signal. The phase variance-distance trace begins to fluctuate severely at around 10 km, which may badly influence the vibration locating accuracy, since the monotonicity of phase variance-distance trace is damaged. By the compensation using the phase signals provided from the auxiliary reference points, we see a clear improvement around these reference points. Without the phase noise compensation, the variance of phase noise goes to a quite large value, and after the phase noise compensation, the variance is kept to be less than 0.15 rad2 around reference points so that we can locate the vibration precisely, as shown in the

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Fig. 9. Locating result. (a) Phase-based locating result with different vibration magnitudes. (b) Intensity-based locating result with 180-n" peak-to-peak vibration.

inset of Fig. 8(c). The compensation results match well with the theory. Note that there are some spikes along the fiber since the SNR is poor at these points due to the Rayleigh fading phenomena, so that the phase extraction error overwhelms the signal. When we use the statistical analysis to locate the vibration, these spikes can be neglected as we introduced in Part 3 and illustrated in Fig. 4. By detecting the step change of phase variance-distance trace, vibration could be located precisely. However, when the fiber influenced by vibration is much shorter than spatial resolution, the intensity based locating method may be insensitive. Fig. 9(a) shows the phase based vibration locating result. The vibration locating accuracy is 10-m as the same as the spatial resolution. The phase variance-distance trace has some jags due to low SNR or Rayleigh fading phenomena, but the step change can be seen clearly. Vibrations with different magnitude are set on fiber for testing the sensitivity, and the results imply that smaller vibration can also be located. The amplitude of step change is proportional to the square of vibration magnitude, which is discussed in a later paragraph. For comparison, Fig. 9(b) shows the intensity based vibration locating result with the same method in [8] when a 180 n" dynamic strain is applied, and the result means that no vibration is detected, which implies that the RBS intensity signal is much less sensitive to vibration than the phase signal. As stated before, the vibration magnitude has a linear relationship with the phase signal, therefore the step change of phase variance-distance trace should be proportional to the square of vibration magnitude. An experiment has been carried out for verifying the relationship between the step change and the vibration magnitude. Vibrations with seven different magnitudes are exerted on the FUT, and 10 groups of phase-distance traces are acquired for each vibration magnitude. Due to the quadric relationship between vibration magnitude and the step change amplitude, we use the square root of step change for obtaining a linear fitting curve. Fig. 10 shows the experimental results with the average values and error bars, and the linear fitting curve, which matches well with the theory. The phase signals can be used for directly measuring the external vibration on fiber. To eliminate the influence of the environmental disturbance, the differential phase is obtained by calculating the phase difference between two neighboring points with 10 m distance, which is equal to the spatial resolution. The vibrations with different frequency and same magnitude are measured for investigating the system performance. In our experiment, two kinds of sinusoidal vibration signals are generated by PZT: 1000 Hz with 300 n" magnitude, and 100 Hz with 300 n" magnitude. Fig. 11 shows the time domain measurements of different vibrations. Some noise exists due to the low SNR at 30 km, but there is no obvious distortion. The measured result of 1000 Hz vibration seems to be somewhat away from the sinusoidal wave, since the sample rate to vibration is only 3 kS/s, which is not enough to show the vibration in detail.

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Fig. 10. Average values, error bars, and the linear fitting curve of the experimental results. Square root of step change with vibrations of different magnitudes.

Fig. 11. Vibration signals measured at 30 km of (a) 1000- and (b) 100-Hz signals with a 300-n" magnitude.

For the vibration sensing technology, the frequency information is also important. The spectra of above experimental results are shown in Fig. 12. In the spectrum, we cannot find the higher order harmonics, which are a key excellent performance of vibration sensing. The SNR of measured results is around 20 dB, and the primary noise source is supposed to be the phase extraction error, as the Rayleigh intensity signal has only about 8 dB SNR at 30 km.

5. Conclusion In this paper, we analyzed the phase noise in phase-extracted coherent -OTDR, and proposed a distributed vibration sensing technology based on phase-extracted coherent -OTDR with phase noise compensation using auxiliary reference points. The vibration locating method based on a statistical analysis of optical phase signal is demonstrated. By using this technology, a linear response of the vibration intensity is realized with a long measurement range of about 30 km, a 10-m spatial resolution and a 3 kS/s sampling rate to the vibration signals. This new technology improves the performance of phase-extracted coherent -OTDR for distributed fiber vibration sensing.

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Fig. 12. Measured spectrum of two vibrations with same magnitude and different frequencies.

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