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Abstract
In this paper, we propose and experimentally demonstrate a novel quasi-distributed fiber-optic vibration sensing system, which can achieve vibration measurement with a wide frequency response over a long distance. The system is based on phase-sensitive optical frequency domain reflectometry (ϕ-OFDR). The sensing part is a single-mode fiber (SMF) with auxiliary weak reflection points along it. By detecting the auxiliary weak reflection points, we can obtain the waveform of the vibration signal. In the experiments, single-point and multi-point vibrations with a wide-frequency response at 100 km are successfully measured, which validated the proposed system. To the best of our knowledge, this is the first time to realize a wide-band vibration waveform measurement over such a long range by using reflectometry-based sensing system.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The vibration sensing system based on optical reflectometry, with advantages of long-range, high-sensitivity and distributed measurement capability, has attracted considerable attentions in recent years [1–7]. Optical reflectometry is based on measuring Rayleigh backscattering in the fiber core, and there are mainly two types of realization methods: pulse wave based method and continuous wave based method. The representative reflectometry of the pulse wave based method is optical time domain reflectometry (OTDR), which is widely used for the diagnosis of fiber links nowadays. However, OTDR suffers from an inherent trade-off relation between the maximum measurable distance and the spatial resolution. We can increase the pulse duration to improve its maximum measurable distance, while the spatial resolution becomes worse as the pulse duration increases. Recently, a new scheme of pulse wave based reflectometry called time-gated digital optical frequency domain reflectometry (TGD-OFDR) is proposed [8]. By employing a frequency-chirped pulse as a probe, TGD-OFDR overcomes the trade-off relation between the maximum measurable distance and the spatial resolution, since its spatial resolution is determined by the frequency-chirped range. However, the spatial resolution is still limited since the requirements of the receiver bandwidth are very strict. For the continuous wave based reflectometry, optical frequency domain reflectometry (OFDR) plays a primary role with the capability to realize a high spatial resolution and high sensitivity by employing a frequency-swept continuous-wave (CW) lightwave as a probe. However, the maximum measurable distance of OFDR is limited by the laser coherence length since the laser phase noise causes serious degradation to the signal-to-noise ratio (SNR) as the measurement distance approaches the laser coherence length [9]. The laser phase noise also affects the repeatability of OFDR, which is the main noise for sensing application [10]. For this reason, OFDR-based sensing application is restricted to a relatively short range of several tens to hundreds of meters [1,2,11]. In this respect, pulse wave based reflectometry is immune to laser phase noise to some extent [8,12,13]. This is the dominant advantage in the sensing application, for which the vibration sensing is mainly based on the pulse wave based methods nowadays. To elongate the measurement range, phase-noise-compensated OFDR (PNC-OFDR) is introduced to mitigate the effect of laser phase noise in OFDR [14]. By mitigating the laser phase noise along the whole fiber, the repeatability of OFDR is improved greatly [15].
Among various demodulation techniques of reflectometry-based vibration sensing system, phase-sensitive methods have the highest sensitivity. The phase term of the backscattered signal directly reflects the external vibration and provides a linear response [5]. In recent years, distributed vibration sensing system achieved by pulse wave based reflectometry combined with phase-sensitive methods has shown a rapid development trend [5,6,16]. However, there are still some difficult problems in these schemes. Firstly, it suffers from an inherent trade-off relation between the maximum measurable distance and the vibration bandwidth, limited by Nyquist theorem [17,18]. Secondly, although Rayleigh backscattering based method achieves a distributed measurement theoretically, the deadzones caused by polarization mismatch and coherence fading phenomenon limited the realization of the full-distributed measurement [3,7]. Thirdly, the SNR in Rayleigh backscattering based methods is not high enough at the long distance since the signal power is largely attenuated and the Rayleigh signal is very weak there [8]. For the above reasons, schemes based on the fiber with auxiliary weak reflection points along it have been proposed and the advantage over the Rayleigh backscattering based schemes is verified [4,16,19]. However, the trade-off relation between the maximum measurable distance and the vibration bandwidth still exists. Some researches have focused on this problem and some solutions are proposed [20,21], however, the common problem of these schemes is the difficulty to achieve multi-point measurements.
In this paper, we propose a quasi-distributed vibration sensing system based on phase-sensitive OFDR ($\phi$-OFDR), in which the trade-off relation between the maximum measurable distance and the vibration bandwidth is overcome. We employ the auxiliary weak reflection points as the demodulation units to achieve vibration waveform measurement. In the experiment, single-point vibration measurements with frequency of 20 kHz are realized. The measurement of two-point vibrations with frequency of 15 kHz and 20 kHz at 100 km are successfully demonstrated. The ability of arbitrary-waveform vibration measurement is also verified.
2. Measurement principles
2.1 Vibration measurement via the auxiliary weak reflection points by using $\phi$-OFDR
In OFDR, after the coherent detection by interfering with the local lightwave, the detected electrical signal of the Rayleigh backscattering from a certain distance can be expressed as [20]:
where $R$ is the reflectivity from the fiber under test (FUT), $E_0$ is the electrical field amplitude of the probe, $\gamma$ is the linear frequency sweep slope of the probe, $\tau _F$ is the delay time experienced by the reflection of the probe lightwave relative to the local lightwave, $\theta (t)$ is the randomly fluctuating optical phase at time $t$ which is related to the limited laser coherence length, and the phase of the lightwave is modulated by $\phi (t)$ which is the signal to be measured.From Eq. (1), we may see that the main noise comes from the phase noise $\theta (t)-\theta (t-\tau _F)$, which has to be eliminated to obtain $\phi (t)$. Therefore, the PNC algorithm is introduced. After the phase noise compensation, the time-domain expression of OFDR signal is [14]:
Here the phase noise term of $I(t)$ is compensated from $\theta (t)-\theta (t-\tau _F)$ to $\Theta (t)$ and approaches zero. As a result, it has little effect to obtain the disturbance signal of $\phi (t)$ after the phase noise compensation. To obtain the exact form of $\phi (t)$, we firstly calculate the complex amplitude of the backscattering signal as a function of distance by Fourier transforming $I(t)$. Then the corresponding sensing position of each auxiliary weak reflection point can be selected by windowing the distance-domain data and its time-domain data is obtained by the inverse Fourier transform. Considering that a narrow-band signal has been obtained after the inverse Fourier transform, we calculate its 90$^\circ$ phase-shifted signal by using Hilbert transform to obtain the signal shown below: Then the phase signal can be extracted by using the following expression: and we can ignore the term $\Theta (t)$ since it is close to zero.By using the above method, $\phi (t)$ can be measured by measuring the next nearest weak reflection phase signal behind the position where the disturbance signal exists, since the lightwave backscattered by the scatters behind the disturbance are all modulated by $\phi (t)$.
For the vibration sensing system based on the pulse-wave reflectometry, the measurable vibration bandwidth is limited by the travel time of the probe [17,18]. The advantage of OFDR is that the probe is a continuous wave which makes it possible to record the fiber status continuously, therefore the trade-off relation between the measurable vibration bandwidth and the sensing range is broken.
The proposed scheme can not be realized using Rayleigh scattering since the sideband, which contains the measured vibration signal, will overlap with each other, and results in a failure of the vibration signal extraction. Contrarily, the sideband of a weak reflection point can be clearly identified over the Rayleigh scattering level. Compared with the Rayleigh backscattering based schemes, by measuring the weak reflection points, we could just focus on the intensity of the weak reflection points and ignore whether or not the SNR is high enough at the specific position where the disturbance occurrs. Therefore, the problem of deadzone caused by polarization mismatch and coherence fading in the Rayleigh backscattering based schemes can also be avoided effectively.
2.2 Measurement of multiple vibration events
Since the lightwave backscattered by all the scatters behind the position where disturbance occurs is modulated by $\phi (t)$, a subtraction method is effective for measuring multi-point vibrations. When two vibrations occur at different positions simultaneously, we firstly obtain the front event by measuring its next nearest weak reflection point. The time-domain expression of electrical signal after interfering with the local lightwave is
where $\phi _1(t)$ is the phase change caused by the front vibration signal and we can obtain it by For the second event, we also measure its next nearest weak reflection point. The time-domain expression is where $\phi _2(t)$ is the phase change caused by the second vibration signal and we can obtain $\phi _2(t)$ by a subtraction of $\phi _1(t)$ as described below:2.3 Measurement of vibration with a large amplitude
For the limited sampling rate of the pulse-wave reflectometry based vibration sensing system, not only the maximum measurable vibration frequency is restricted, but also the maximum measurable vibration amplitude has a limitation. In the phase demodulation based scheme, errors will be induced when the phase change between two adjacent samples is greater than $\pi$, which makes it difficult to obtain a linear response [22]. Therefore, the following assumptions have to be satisfied for two adjacent sampling points
where $A_{former}$ and $A_{latter}$ are two adjacent sampling points of the vibration signal. For OFDR-based scheme, benefiting from breaking the trade-off relation between the measurement distance and vibration bandwidth, the proposed scheme can provide a high-enough sampling rate to overcome this limitation. In this scheme, the ultimate limitation of maximum measurable frequency is caused by the bandwidth of the receiver.3. Experiment
The experimental setup is shown in Fig. 1. A narrow-linewidth fiber laser (NKT, Adjustik E15, linewidth < 1 kHz) is employed as the optical source and then connected to an intensity modulator (IM). We adjust the bias voltage of the modulator in the nonlinear range to suppress the carrier. A polarization controller is used to guarantee the correct polarization direction for the lightwave injected into the IM. The instantaneous optical frequency is modulated by sweeping the radio frequency and the frequency-swept range is 1 GHz, which corresponds to a theoretical two-point spatial resolution of 10 cm if the laser phase noise is not taken into account. Then the desired sideband is selected by utilizing a fiber Bragg grating (FBG). The frequency-swept lightwave is then fed to a 10/90 optical coupler, with a small amount of lightwave launched into the auxiliary interferometer for compensating the laser phase noise. A 100-km single mode fiber (SMF) is used as the sensing part, and at the end of the fiber, three weak reflection points are embedded into it as the demodulation units. Considering the linewidth of the laser uesd in the experiment is less than 1 kHz, the length of the delay fiber in the auxiliary interferometer is chosen to be 25 km to ensure an acceptable SNR. Therefore, the trace may be divided to 8 sections and the first to the eighth reference signals are calculated to carry out the phase noise compensation [14]. The separation between two adjacent weak reflection points is about 100 m. Two balanced photodetectors (Thorlabs PDB480C-AC) are used to receive the signals of the auxiliary reference interferometer and the reflectometry, respectively. The electrical signals are sampled by using a two-channel analog-to-digital converter (ADC) (NI-5171R), and then processed by using a personal computer. Phase noise compensation and vibration demodulation are accomplished by digital algorithms.
Fig. 1. Experimental setup. FL: fiber laser; IM: intensity modulator; RF synthesizer: radio frequency synthesizer; FBG: fiber Bragg grating; PC: polarization controller; OC: optical coupler; BPD: balanced photodetector; ADC: analog-to-digital converter.
In the experiments, we exert the disturbance by using a piezo-electric transducer (PZT) at the fiber end to simulate the vibrations as shown in Fig. 2.
Fig. 2. Configuration of the sensing part. FUT: fiber under test; SG: signal generator; PZT: piezo-electric transducer.
Figure 3 shows the three weak reflection points measured by OFDR and the red boxes indicate the sensing positions for each demodulation unit. We firstly exert one disturbance and then demodulate it by using the method described above. Vibrations with different frequencies of 500 Hz and 20 kHz are applied to the FUT respectively. The measured waveforms of the vibrations and their corresponding power spectra are shown in Fig. 4. We may see that the amplitude of the 500-Hz vibration is about 10 rad, which is much larger than the maximum measurable vibration amplitude $\pi$ by pulse-wave reflectomotry at 100-km sensing distance. The ability of large-amplitude vibration measurement is verified.
Fig. 3. Three weak reflection points at the fiber end and the red areas show the corresponding sensing sections.
Fig. 4. Measurements of single disturbance with frequencies of 500 Hz and 20 kHz, respectively. The two curves on the left are time-domain waveforms and their corresponding power spectra (logarithmic coordinates) are on the right.
To demonstrate the validity of the wide-band response, a broadband signal whose frequency varies linearly between 5 kHz to 10 kHz, is excited by PZT and measured. The obtained waveform and the time-frequency diagrams are shown in Fig. 5. For multi-point vibrations, we exert two disturbances by PZT at different positions of the FUT as shown in Fig. 2. The two different vibration signals have frequency of 15 kHz and 20 kHz, respectively, and the experimental results (power spectra) are shown in Fig. 6. We may observe a clear measurement without any crosstalks.
Fig. 5. The measured time-domain waveform of the frequency-swept signal and its time-frequency diagram.
Fig. 6. The measured power spectra (logarithmic coordinates) of two vibrations at two different positions.
4. Discussion
In this scheme, the spatial resolution, namely the separation of two adjacent weak reflection points, needs to be wider as the vibration frequency becomes higher, since the sidebands of the adjacent weak reflection points can not overlap with each other. For a certain amplitude of the vibration, the relationship between the maximum measurable frequency and two parameters of the system (spatial resolution $d$ and the linear frequency sweep slope of the probe $\gamma$) is
where $f$ is the maximum measurable frequency of the vibration. Therefore, we could adjust $\gamma$ to make the system to be adapted to different requirements of vibration bands.Rayleigh backscattering is the main noise in this system. When we window the distance-domain data which corresponds to one demodulation unit, the undesired Rayleigh backscattering is inevitably included. It will reduce the accuracy of the phase demodulation, and also influence the sensing resolution. A higher reflectivity of the weak reflection point and a better spatial resolution will increase the phase demodulation accuracy, since they could provide a higher SNR. We analyze the sensing resolution by the numerical simulation with the typical reflectivity of −70 dB/m for Rayleigh backscattering in SMF. The result is shown in Fig. 7 and we may see that the phase resolution, namely the sensing resolution, is decided by the reflectivity of the weak reflection point and the spatial resolution. A higher reflectivity of the weak reflection point and a better spatial resolution provide better phase demodulation resolution, however, they may result in a relatively short sensing range and a limited frequency response bandwidth. The spatial resolution is also a key parameter, and it is decided by the distance of two adjacent weak reflection points. The design principle is to avoid the crosstalks from the two points which depend on the parameters including the vibration frequency, and the vibration amplitude which determines the number of sidebands.
Fig. 7. Numerical simulation results: the relation of the phase resolution and the reflectivity of weak reflection points with three different spatial resolutions.
It is worth noting that the fiber connectors are used as the weak reflection points for the demodulation in the experiments as shown in Fig. 2. Actually, other types of weak-reflection structures can also be used as the demodulation unit, such as the weak-reflection FBG array. Two requirements should be satisfied for the unit: its reflection bandwidth should cover the spectrum range of the frequency-swept probe lightwave, and it has a suitable reflectivity. From the perspectives of convenience and cost-effectiveness, the weak reflector array is a more suitable sensing unit than FBG array.
5. Conclusion
In this work, we demonstrate a long-range and wideband-response quasi-distributed vibration sensing system based on $\phi$-OFDR. It provides a linear response of vibration and overcomes the trade-off between the sensing distance and the maximum measurable vibration frequency compared with the conventional methods. In the experiments, vibrations with frequencies of 500 Hz and 20 kHz at the distance of 100 km are measured, respectively. The ability of multi-point vibrations measurement is also demonstrated. The proposed method has a prospect to be applied in practical applications such as intrusion monitoring for large structures.
Funding
National Key Research and Development Program of China (2017YFB0405500); National Natural Science Foundation of China (61620106015, 61735015, 61775132).
Disclosures
The authors declare no conflicts of interest.
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