Distributed fiber-optic vibration sensing based on phase extraction from time-gated digital OFDR

Shuai Wang; Xinyu Fan; Qingwen Liu; Zuyuan He

doi:10.1364/OE.23.033301

1. Introduction

Optical fiber based distributed sensors, with series of advantages over other technologies, have been used to measure environmental variations along the sensing fiber, such as temperature, strain, magnetic field and other external disturbances, via backscatterings including Rayleigh scattering, Raman scattering and Brillouin scattering. Among them, distributed vibration sensors can be used to evaluate structural conditions of bridges, airplanes, and pipelines, etc. Many efforts have been made to accomplish such vibration sensing systems based on phase-sensitive optical time domain reflectometry (OTDR) and optical frequency domain reflectometry (OFDR). In conventional phase-sensitive OTDR systems [1–4 ], a modulated optical pulse from a narrow linewidth laser is injected into the fiber under test (FUT), and the backscattered lightwave is collected to form a trace showing a random pattern of Rayleigh backscattering. The random pattern remains the same if the external environment does not change; if an external disturbance occurs, a vibration signal can be extracted from the differences between successive traces. For OFDR systems [5, 6 ], the position and the frequency of the vibration can be obtained by a cross-correlation analysis of the beat signals between the vibrated state and non-vibrated state. Most existing distributed vibration detection systems extract the amplitude term of the backscattered signal but the amplitude signal only partially reflects the external vibration signal.

On the contrary, the phase term of the backscattered signal directly reflects the external vibration signal, and the fact that the response of the phase change to vibration signals is linear gives a better solution to industrial applications. There are many attempts to extract the phase term from phase-sensitive OTDR. However, the SNR is rather low since it does not allow adequate averages, which makes the extracted phase term inaccurate after only several hundred meters of FUT for a relatively high resolution of about 1 m. [7]. As for OFDR, which may have a better SNR than phase-sensitive OTDR, it suffers from laser phase noise when it comes to long distance, and the extracted phase term becomes inaccurate [8].

Recently, a novel time-gated digital optical frequency domain reflectometry (TGD-OFDR) was proposed with a much improved SNR together with a very high spatial resolution [9]. In TGD-OFDR, the light frequency sweeping time is much shorter than the coherent time of the laser source by increasing the frequency sweeping rate, and both the phase noise from the laser source and the phase variation due to environmental disturbance are mitigated greatly. In this paper, we propose a novel long-range distributed dynamic strain sensing technique by use of TGD-OFDR scheme thanks to the mitigated phase noise influence. In this proposal, a linearly frequency-modulated (LFM) pulse is taken as the probe signal and the local reference signal is a CW lightwave. By using a 90 degree optical hybrid, the real and imaginary parts of the backscattered signal are both obtained [10–12 ], and the phase-to-distance mapping is realized in digital domain. Experimental results show that vibration events over a distance of 40 km in a single mode fiber can be measured with a spatial resolution of 3.5 m and a minimal measurable acceleration sensitivity of 0.08g. Meanwhile, the linear relationship between the vibration acceleration and the extracted phase term is verified. To the best of our knowledge, this is the longest measurement range fulfilled by phase extraction for distributed fiber-optic vibration detection.

2. Phase noise consideration

As mentioned above, the measurement range of OFDR is limited by laser’s coherence length because laser phase noise causes serious degradation to the signal-to-noise ratio (SNR) and the extracted phase term of the backscattered signal is inaccurate in long distance detection. On the contrary, TGD-OFDR suffers less from laser phase noise even at long detection distance. In comparison with the phase noise effects on OFDR and TGD-OFDR, a simulation is performed. To obtain a quantitative denotation of the phase noise, we take the power spectrum of the beat signal [13–15 ] to characterize the influence of laser phase noise. The power spectrum of the beat signal of OFDR can be expressed as:

\begin{array}{l} S (f) = e^{- (2 t_{d} / τ_{c})} \frac{2 R (t_{d}) \sin [(f - f_{b}) τ_{p}]}{π (f - f_{b})} + \\ \frac{2 R (t_{d}) τ_{c}}{1 + {[π τ_{c} (f - f_{b})]}^{2}} {1 - e^{- (2 t_{d} / τ_{c})} [\cos [π (f - f_{b})] + \frac{\sin [π (f - f_{b}) t_{d}]}{π τ_{c} (f - f_{b})}]} \end{array}

As for TGD-OFDR, when the measurement distance is longer than the probe pulse length, the power spectrum of the beat signal is given as:

\begin{array}{l} S (f) = \frac{2 R (t_{d}) τ_{c}}{1 + {[π τ_{c} (f - f_{b})]}^{2}} {1 - \\ e^{- (2 t_{d} / τ_{c})} [\cos [π (f - f_{b})] + π τ_{c} (f - f_{b}) \sin [π (f - f_{b}) τ_{p}]]} \end{array}

Figure 1 depicts the numerical simulation of the power spectra of the beat signals of OFDR and TGD-OFDR, respectively, from 1 km to 100 km by assuming that the linewidth of the laser is 5 kHz, the light frequency sweeping time of OFDR and TGD-OFDR is 10 ms and 10 μs, respectively. To make the result more intuitive, the beat frequency is set to zero. Figure 1(a) shows that in OFDR as the measurement distance increases, the power spectrum broadens from a sinc shape to a Lorenzian shape, which means that the effects of laser phase noise increases as the distance grows. On the other hand, as shown in Fig. 1(b), the power spectrum of the beat signal of TGD-OFDR stays same when the measurement length continues to be increased. Actually, the FWHM of the power spectrum is proportional to the laser’s linewidth. Thanks to the fast frequency sweeping rate, the actual spatial resolution of TGD-OFDR is much better than OFDR at long distance according to $Δ z = \frac{c}{2 n} \frac{Δ f}{γ}$ . In simple terms, TGD-OFDR has a faster frequency sweeping rate and a shorter integration time of laser phase noise compared with conventional OFDR. Therefore, the influence of laser phase noise on TGD-OFDR is greatly mitigated in long distance measurements.

Fig. 1 Power spectrum of the beat signal of (a) OFDR and (b) TGD-OFDR.

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3. Operation principle and signal processing

For TGD-OFDR, the lightwave from a narrow linewidth CW laser with an initial optical angular frequency of $ω_{0}$ is divided by a 90/10 coupler into two beams, a measurement beam and a local reference beam. As shown in Fig. 2 , the measurement beam is modulated by an LFM pulse using an acoustic optical modulator (AOM) and is launched into the FUT. Then the Rayleigh backscattering from FUT is mixed with local reference beam in the 90 degree optical hybrid and then converted to electrical signal with the help of a balanced photodetector (BPD). The signals are sampled by an analog-to-digital card (ADC) and collected using a personal computer (PC). In the processing progress, the signals are correlated with a digital matched filter to obtain the reflectometric traces, which are finally used to extract the phase term for vibration measurement.

Fig. 2 Experimental setup of distributed vibration sensing system based on TGD-OFDR. FL: fiber laser; EDFA: erbium-doped optical fiber amplifier; BPD: balanced photodetector; AWG: arbitrary waveform generator; ADC: analog-digital card; PC: personal computer.

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Let us consider a fiber-optic distributed vibration sensing system based on TGD-OFDR as shown in Fig. 2. The backscattered lightwave $E_{s} (t)$ from a certain position of the FUT is a linearly chirped pulse with a constant sweeping rate of $γ$ , and the reference signal $E_{L} (t)$ is directly launched from the fiber laser. The two lightwave can be expressed as:

E_{s} (t) = A (t_{d}) \exp [j ω_{0} (t - t_{d}) - j π γ {(t - t_{d})}^{2} - j θ (t - t_{d}) + j φ_{r a y l e i g h} (t_{d})] rect [\frac{t - t_{d}}{τ_{p}}]

E_{L} (t) = E_{L O} \exp [j ω_{0} t + j θ (t)]

where

A (t_{d})

and

φ_{r a y l e i g h} (t_{d})

are the amplitude and phase term of the backscattered signal respectively,

t_{d}

is the delay time related to the scattered point,

θ (t)

means the laser phase noise,

E_{L O}

is the amplitude of local lightwave,

τ_{p}

is the duration time of pulse,

r e c t [t]

is the rectangular function.

The backscattered signal interferes with the reference signal in the 90 degree optical hybrid and detected by the BPD. After combining the quadrature components at the output of the 90 degree optical hybrid, the system response to the beat signal is:

s_{b e a t} (t) = A (t_{d}) \exp [- j π {(t - t_{d})}^{2} - j ω_{0} t_{d} + j φ_{s c a t t e r} + j θ (t - t_{d}) - j θ (t)] r e c t [\frac{t - t_{d}}{τ_{p}}]

The LFM pulse from the AWG, i.e., a digital pulse, is directly acquired with the expression:

s_{d i g i t a l} (t) = E_{0} \exp (j 2 π f_{m} t - j π γ {(t - t_{d})}^{2} + j φ_{0}) r e c t [\frac{t - t_{d}}{τ_{p}}]

Where

f_{m}

is a frequency shift of the pulse for reducing low-frequency noise,

φ_{0}

is the initial phase of the pulse. Note that no phase noise term is expressed here since it does not exist in digital pulse. After correlating the beat signal and the digital pulse in digital domain, the final beat signal is expressed as:

s (t) = E_{0} A (t_{d}) \exp [j 2 π f_{m} t + j θ (t) - j θ (t - t_{d}) + j φ] r e c t [\frac{t - t_{d}}{τ_{p}}]

Where

φ = φ_{0} + ω_{0} t_{d} + φ_{s c a t t e r}

. After taking the Fourier transform of the beat signal, we can finally obtain the following expression:

S (f) = \int_{0}^{τ_{p}} s (t) d t = R (t_{d}) \frac{sin [π (f - f_{m}) τ_{p}]}{π (f - f_{m})} exp [jφ (f)]

| S (f) |

has a maximum value at

f = f_{m}

which indicates the position of the backscatter corresponding to

t_{d}

; as the full width at half maximum (FWHM) of the sinc function is

Δ f = \frac{1}{τ_{p}}

, the spectral signature of the minimum resolving adjacent backscatters is

| S (f - Δ f) |

. Then the corresponding spatial resolution

Δ z is given by

Δ z = \frac{c}{2 n γ τ_{p}}

where c is the light speed in vacuum, n is the refractive index of FUT, and

γ τ_{p}

means the frequency sweeping range. The result shows that the spatial resolution of TGD-OFDR is the same as that of OFDR in short distance [16].

The phase term of the backscattering corresponding to $t_{d}$ is, $φ (f_{m})$ and it is a combination of Rayleigh backscattering phase term, the delay caused phase term, and the phase noise term. Assuming a sinusoidal vibration signal is coupled to the fiber, it will affect the optical path length, which is equivalent to phase modulation $φ_{v i b r a t i o n} = δ \sin ω_{v} t$ , where $δ$ is the vibration magnitude and $ω_{v}$ is the vibration frequency. The vibration event can be directly observed through the amplitude and phase variation from multiple reflectometry traces while the location of the event can be ascertained using the following relationship: $z = t_{d} \frac{c}{2 n}$ .

In conventional OFDR-based distributed vibration sensing systems, the frequency and the position of the vibration event were calculated by a cross-correlation between OFDR traces of vibration state and of non-vibration state. Therefore, the frequency-response of vibration and the spatial resolution has a trade-off relationship since both the vibration frequency and the location are determined from the OFDR trace, i.e., from the beat frequency. In our proposed system, since the vibration information in time domain is obtained directly from different traces, the repetition rate only depends on the FUT length, and can be much higher.

4. Experiment and results

In the experiment, a narrow linewidth laser (NKT Koheras Adjustik) was used as the light source with a linewidth of ~1 kHz. An AOM driven by a sweeping RF signal was employed to generate the LFM pulse with the sweeping range from 170 MHz to 230 MHz, which is limited by the bandwidth of the AOM, in 20 μs duration time. The sweeping repetition rate wasset to be 2 kHz after considering the FUT length. Two 1.6 GHz BPDs (Thorlabs) were used to receive the signals coming from 90 degree optical hybrid (Kylia). The signals after BPDs were decreased to 0~60 MHz by inserting another AOM into the local lightwave (not shown in the Figure). The data were collected by using an ADC with a sampling rate of 416 MS/s and a 10-bit resolution.

The vibration was excited by a PZT attaching to the FUT, driven by a function generator whose frequency can be adjusted from several Hz to 1 kHz. Meanwhile, an acceleration meter sticking on the PZT also detected the vibration for comparison.

Figures 3 show one part of the measured reflectometry traces of backscattering from FUT. Fifty consecutive traces were recorded here. Figure 3(c)-3(e) show the intensity terms, the unwrapped phase terms, the differential phase traces of adjacent backscattering, while Fig. 3(a) and 3(b) gives a reflection intensity profile of the whole trace of 40 km fiber (50 consecutive traces) and an APC connector at ~30 km showing the spatial resolution.

Fig. 3 (a) Reflection intensity profile of the whole trace of 40 km fiber (50 consecutive traces); (b) Reflection intensity profile of an APC connector showing a spatial resolution of 3.5 m; (c) Measured intensity traces of backscattered lightwave from FUT (50 consecutive traces); (d) Unwrapped phase traces of backscattered lightwave from FUT (50 consecutive traces); (e) Differential phase traces of adjacent backscattered lightwave (50 consecutive traces).

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4.1 Phase extraction

In order to obtain the phase traces, multiple reflectometry traces were recorded. The unwrapped phase terms yielded a matrix ${φ (z_{i}, t_{j}); i = 1 : I, j = 1 : j}$ , where I is the number of samples in a single trace and J is the number of traces. According to the backscatter impulse model [16], the received backscattered wave is a mixed result of different positions interfering with each other, and SNR is quite low at some area as a consequence (circled in blue dash line in Fig. 3). The phase term extracted at these positions is unstable and have a $2 π$ hopping in different traces as shown in Fig. 3. We find that the differential phase term may exceed $2 π$ at some dead zones such as ~40.014 km as shown in Fig. 3(c)-3(e), since the SNR was poor at these points due to Rayleigh fading phenomena [17]. The dead zone was examined to be about 0.5 m, much smaller than the spatial resolution. But it won’t be a big problem for the identification of the vibration event. It is also believed that this problem of existing dead zones can be solved with a multi-wavelength scheme since different wavelengths change the places of low-SNR points [18]. In order to reduce the phase uncertainty, we take a differential phase $Δ φ (z_{i}, t_{j}) =$ $φ (z_{i} - Δ z, t_{j}) - φ (z_{i}, t_{j})$ , then the vibration event can be observed clearly from the vibration phase term (circled in red dash line in Fig. 3).

4.2 Detection of vibration events

In the experiment, the allowable repetition rate of the LFM pulse was 2 kHz which determined the maximum frequency-response of vibration to be ~1 kHz. The FUT used in the experiment is a standard SMF with a length of 40.3 km. The PZT was attached at the position of ~40 km, and 100 reflectometry traces were recorded. The pulse width was 20 μs which means a larger dynamic range than that of conventional OTDR (usually with 100 ns pulse at 10 m spatial resolution) can be obtained and allowing a long-distance detection. Unlike OTDR, the spatial resolution in TDG-OFDR is not determined by the pulse duration but by the frequency sweeping range according to Eq. (9). As shown in Fig. 3(b), the spatial resolution can be seen clearly to be 3.5 m from the reflection peak generated at the position of an APC connector.

As shown in Fig. 4 , a 200 Hz sinusoidal vibration with a minimum acceleration of 0.08g was detected. It is interesting to compare Fig. 4(a)-4(d), where we find that the distance-time mapping of the phase term has a much better sensitivity than that of the amplitude (or intensity) term. Besides, the phase-time curve is quite close to the excitation signal upon PZT verifying that the advantage of vibration detection based on phase extraction over amplitude extraction. Here, the solid line is the extracted phase offset and the dashed line is the excitation signal upon PZT. The first-order differential of length change is its speed while the second-order differential of length change is its acceleration. Since the applied PZT driving voltage has a sine-wave shape, its second-order differential would also have a sine-wave shape.

Fig. 4 Experimental results with a 200 Hz sinusoidal excitation at z = 40.02 km. (a) Distance-time mapping trace of the phase term of backscattering; (b) Extracted phase-time curve of the vibration; (c) Distance-time mapping of the intensity term of backscattering; (d) Extracted intensity-time curve of the vibration.

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To examine the frequency-response, a 600 Hz sinusoidal vibration, quite close to the allowable maximum response frequency of 1 kHz, was detected as well in the experiment as shown in Fig. 5 . The harmonic tone in Fig. 5(c) is supposed to be caused by the high order harmonic wave of the PZT.

Fig. 5 Experimental results with an 600Hz sinusoidal excitation at z = 40.02 km. (a) Distance-time mapping trace of the phase term of backscattering; (b) Extracted phase-time curve of the vibration. (c) The power spectrum of extracted phase signal.

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To verify whether the extracted differential phase has a linear relationship with the vibration intensity, further experiment were designed and the amplitudes of the phase-time curves were counted at vibration acceleration of 0.08g, 0.12g, 0.16g and 0.2g, respectively. Figure 6 shows that the amplitude of the phase-time curve exhibits linear relationship with the vibration acceleration. Therefore, the phase-term extracted from TGD-OFDR directly reflects the external vibrations, showing that our proposed scheme provides a much practical distributed vibration sensing technique for long-range applications.

Fig. 6 (a) Extracted phase-time curves of vibration at different vibration acceleration. (b) The amplitude of phase-time curves versus vibration acceleration.

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5. Conclusions

We proposed and demonstrated a distributed fiber-optic vibration sensing technique based on TGD-OFDR. Both theoretical and experimental results show that the novel technique can improve the SNR considerably while maintaining a high spatial resolution. We demonstrated that vibration measurement based on backscattering phase extraction has a much better sensitivity over conventional methods based on backscattering amplitude extraction. We also showed that TGD-OFDR has a much better SNR than OTDR, and a much better phase noise performance than OFDR, making it possible to achieve long distance vibration sensing based on phase extraction. Our demonstrational experiment realized successfully distributed vibration sensing with a measurement range of over 40 km, a spatial resolution of 3.5 m, a frequency response up to 600 Hz, and a minimal measurable vibration acceleration of 0.08g.

Acknowledgment

This work was supported partially by the National Natural Science Foundation of China under Grant 61275097, 61307106, 61307107. Xinyu Fan acknowledges the support from Doctoral Fund of Ministry of Education of China under Grant 20130073120026, and Shanghai STCSM Scientific and Technological Innovation Project under Grant 15511105401.

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Distributed fiber-optic vibration sensing based on phase extraction from time-gated digital OFDR

Abstract

1. Introduction

2. Phase noise consideration

3. Operation principle and signal processing

4. Experiment and results

4.1 Phase extraction

4.2 Detection of vibration events

5. Conclusions

Acknowledgment

References and links

Cited By

Figures (6)

Equations (9)

Optics Express