## Abstract

In order to solve fading problem and realize sub-meter spatial resolution in DAS, this paper proposes a novel configuration of time-gated digital optical frequency domain reflectometry (TGD-OFDR) based on optical intensity modulator (IM). IM has a large modulation bandwidth and the positive and negative harmonics can be fully used to suppress fading while the spatial resolution remains unchanged. In experiments, with fading suppressed, the spatial resolution of DAS is 0.8 m and the strain resolution is about 245.6 *pε*√Hz along the total 9.8-km sensing fiber. The response bandwidth of vibration is 5 kHz, only/limited by the fiber length.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

The phases of highly coherent light and its Rayleigh backscattering (RBS) traveling in optical fiber are sensitive to external perturbations occurring along the fiber. Distributed fiber-optic acoustic sensor (DAS) is developed from this feature, combined with reflectometry techniques. DAS is a very useful tool having been widely applied in many fields in recent years, such as intrusion detection [1], railway monitoring [2], pipeline surveillance [3], oil exploration [4], and structural health monitoring [5]. This is mainly owing to its long sensing length, the capability of high-density multiplex of acoustic sensors, the strong robustness against harsh environments [6], and so on.

Most of DAS are based on phase-sensitive optical time domain reflectometry (*φ*-OTDR) and lots of important researches about *φ*-OTDR have been reported in the past few years [7–12]. In some applications, such as oil exploration and structural health monitoring [13], the spatial resolution of DAS is expected to be better than 1 m, and meanwhile the sensing length of a few kilometers is required, which is a challenge for *φ*-OTDR. According to the principle of *φ*-OTDR, the width of the optical pulse has to be shorter than 10 ns to achieve sub-meter spatial resolution. As a result, the sensing length and the strain resolution deteriorate severely. The response bandwidth of vibration decreases too, since temporal average method has to be adopted to improve the signal-to-noise ratio (SNR). Additionally, fading noise is a fatal problem in *φ*-OTDR. Fading includes interference fading [14] and polarization fading [15]. They both result in the drastic fluctuation of the intensity of RBS along the fiber. At the points where the RBS intensity is extremely weak, the phase of RBS is dominated by fading noise and can’t be used for sensing any more, since its phase is calculated from the intensity by I/Q demodulation [16]. In 2017, B. Lu et al. reported a DAS system with 30-cm spatial resolution and 19.8-km sensing length [17], but fading noise wasn’t discussed; In 2016, H. F. Martins et al. reported a DAS with 2.5-cm spatial resolution by using the backreflection of live PSK data, and polarization fading was solved by polarization diversity receiver (PDR) [18], but the sensing length is only 500 m in the experiment.

In 2015, we proposed a novel DAS based on time-gated digital optical frequency domain reflectometry (TGD-OFDR) [19]. Both its sensing length and strain resolution are independent with the spatial resolution, since the probe is optical linear-frequency-modulated (LFM) pulse, of which the frequency sweeping range decides the spatial resolution. In our previous reports, the spatial resolution is meter-scale, because the maximum effective frequency sweeping range is only 60 MHz, limited by the bandwidth of acousto-optic modulator (AOM) [20]. We have also proposed methods to solve the fading noise problem [21], which are very effective, but they degrade the spatial resolution, making it harder to realize sub-meter spatial resolution.

The electro-optic modulators (EOM) have already been widely applied in optical fiber communication and sensing to modulate the lightwave with a large frequency bandwidth up to tens of GHz. They can also function as optical frequency shifters, providing a larger frequency bandwidth than AOM. However, unlike the AOM, the monochromatic lightwave becomes polychromatic after the EOM, and many unwanted harmonics arise together with the required one. In order to suppress the unwanted harmonics, optical bandpass filter, injection locking technique [17] and single-side band modulation are used. These techniques make systems more complicated and the potential of harmonics is wasted.

In this paper, we introduce a novel DAS system based on TGD-OFDR configuration and LiNbO_{3} intensity modulator (IM). High spatial resolution is realized owing to the large modulation bandwidth of the IM, and harmonics induced by the IM are fully used to suppress fading noise by matched filter and rotated-vector-sum method, while the spatial resolution remains unchanged. In experiments, with fading noise suppressed well, the spatial resolution of DAS is 0.8 m, and the sensing length is about 9.8 km. The response bandwidth of vibration is 5 kHz, only limited by the length of the sensing fiber. Two vibration events are detected with high SNR by the phase traces of RBS. The strain resolution is about 245.6 *pε*/√Hz along the whole sensing fiber. Due to competitive performances of high strain resolution, high spatial resolution, linear response, broad bandwidth, and fading suppression, the proposed DAS system is capable of high-quality reproduction of the acoustic signal under detection, and thus it is named as high-fidelity DAS.

## 2. System and principle

The system is shown in Fig. 1. The power and frequency of the laser are constant. The highly coherent light from the laser is split into two parts by a polarization-maintaining (PM) coupler. One part is sent to a 90° hybrid & PDR and acts as the local oscillator (LO). The other part is sent into an optical IM as the probe. In the 90° hybrid & PDR, the LO is divided into two beams with two orthogonal polarization states, and then each beam is divided again into two quadrature beams [22]. An arbitrary waveform generator (AWG) generates a LFM pulse sequence to drive the IM. The width of each LFM pulse is *τ _{p}*, and the period of the sequence is

*T*. A ratio-frequency amplifier is used to change the modulation depth of the IM and a direct-current (DC) source is used to adjust the bias point of the IM. An erbium-doped fiber amplifier (EDFA) is implemented to boost the optical power of probe pulses. The sensing fiber is commercial single mode fiber without any special treatment. The RBS reflected by the sensing fiber enters the 90° hybrid & PDR and is divided into four beams too. These beams from the RBS beat with their corresponding beams from the LO and four beating signals are converted into four photocurrent signals by balanced photo-detectors (BPDs), marked as

_{p}*i*(

_{XI}*t*),

*i*(

_{XQ}*t*),

*i*(

_{YI}*t*) and

*i*(

_{YQ}*t*) respectively. A 4-channel oscilloscope is used to acquire the photocurrent signals and the data is processed by a personal computer off-line. The system parameters are listed in detail in Section 3.

The IM is based on a Mach-Zehnder interferometer configuration. The optical phase change induced to either arm of the interferometer is expressed as

*α*is the modulation depth of the IM;

*β*is the normalized bias point of the IM;

*f*

_{0}is the initial frequency, and

*κ*is the sweeping rate. For shorthand,

*φ*(

*t*) is used to represent (2

*πf*

_{0}

*t*+

*πκt*

^{2}) hereinafter. The electric fields of optical pulses entering the fiber [23] is

*ω*is the center angular frequency of the laser. Unimportant scale factors are normalized.

_{c}We assume there are vast independent scattering points randomly distributed along the sensing fiber [6]. The total RBS in X polarization state reflected from all scattering points is expressed as

where*i*represents the

*i*-th scattering point in the fiber model;

*τ*is the round trip time of optical pulse traveling from the fiber’s incident end to the position of the

_{i}*i*-th point;

*a*is the amplitude coefficient, determined by the reflectivity of the

_{i}*i*-th point and the attenuation along the light path;

*θ*is the polarization angle. The RBS enters the 90° hybrid & PDR and the outputs from BPDs are

_{i}*i*(

_{XI}*t*),

*i*(

_{XQ}*t*),

*i*(

_{YI}*t*), and

*i*(

_{YQ}*t*), as described above. We combine two quadrature signals with the same polarization state into a complex signal as follows,

*j*is imaginary unit. Since the distance between two adjacent scattering points is of the order of optical wavelength and is extremely small, the summation above can be rewritten as an integral,

*s*(

*t*)] is expanded as

*J*() is the

_{n}*n*-order Bessel function. cos[

*s*(

*t*)] has multiple LFM components as shown in Eq. (7), but only the positive and negative first-order LFM components are considered here, since the other components can be suppressed by adjusting the values of

*α*and

*β*and can be further filtered by non-matched filters mentioned below. Eq. (7) can be simplified as

Then, ${\overrightarrow{i}}_{X}(t)$ is processed by two different matched filters respectively [24] and the outputs, called complex RBS profiles, are

*W*(

*t*)| which is the production of a

*sinc*function and a triangular windows function, and the full width at half maximum (FWHM) of the profile is regarded as the spatial resolution of TGD-OFDR, where

*v*is the light speed in the fiber. It is noted that the spatial resolution will be doubled if the window function in Eq. (1) is replaced by Hanning window. The amplitude of the complex RBS profile is the intensity trace of RBS, and the phase part is the phase trace of RBS.

_{g}Since the frequencies and phases of ${\overrightarrow{R}}_{+}(t)$ and ${\overrightarrow{R}}_{-}(t)$ are opposite, the complex RBS profiles, ${\overrightarrow{r}}_{X+}(t)$ and ${\overrightarrow{r}}_{X-}(t)$, are different. *E _{Y}*(

*t*), ${\overrightarrow{i}}_{Y}(t)$, ${\overrightarrow{h}}_{Y}(t)$, ${\overrightarrow{r}}_{Y+}(t)$, and ${\overrightarrow{r}}_{Y-}(t)$ are similar to those in X polarization state, and the difference is that cos[

*θ*(

*t*)] is replaced by sin[

*θ*(

*t*)]. The complex RBS profiles with different polarization states are different too. Therefore, complex RBS profiles, ${\overrightarrow{r}}_{X+}(t)$, ${\overrightarrow{r}}_{X-}(t)$, ${\overrightarrow{r}}_{Y+}(t)$, and ${\overrightarrow{r}}_{Y-}(t)$, are different from each other. If they are combined by an optimal algorithm, the fading phenomenon in intensity traces can be relieved well and fading noise in phase traces are suppressed.

The DAS totally injects *K* probes into the fiber, and we mark the four groups of complex RBS profiles demodulated from the *k*-th probe pulse as ${\overrightarrow{r}}_{X+}(k,t)$, ${\overrightarrow{r}}_{X-}(k,t)$, ${\overrightarrow{r}}_{Y+}(k,t)$, and ${\overrightarrow{r}}_{Y-}(k,t)$ respectively. For simplicity, they are rewritten as ${\overrightarrow{r}}_{1}(k)$, ${\overrightarrow{r}}_{2}(k)$, ${\overrightarrow{r}}_{3}(k)$ and ${\overrightarrow{r}}_{4}(k)$ respectively. Due to additive white Gaussian noise, they become ${\overrightarrow{x}}_{1}(k)$, ${\overrightarrow{x}}_{2}(k)$, ${\overrightarrow{x}}_{3}(k)$, and ${\overrightarrow{x}}_{4}(k)$, and

*ϕ*(

_{m}*k*) is the phase constant; Δ

*ϕ*(

_{m}*k*) is fading noise due to ${\overrightarrow{n}}_{m}(k)$ [21, 25]. The variance of fading noise is inversely proportional to the SNR of $\left|{\overrightarrow{r}}_{m}\right|$ according to Fig. 2 and Eq. (18) provided in [21], therefore phase variance, or phase standard deviation (SD), is still large at the position where the intensity SNR is small, although there is no vibration occurring. Rotated-vector-sum method proposed in [21] is adopted here,

*ϕ*(

_{a}*k*) is fading noise after averaging. The theory and experimental results in [21] prove that rotated-vector-sum method is effective and the variance of Δ

*ϕ*(

_{a}*k*) can be reduced here. More importantly, the spatial resolution is still determined by Eq. (13) and doesn’t degrade after Eq. (15).

In order to further suppress fading noise and improve the SNR, moving average method [26] are used here too. Moving average method can be realized easily by

*τ*

_{0}is the width of moving average. However, the spatial resolution of TGD-OFDR after moving average degrades by $\frac{{v}_{g}{\tau}_{0}}{2}$, and hence

*τ*

_{0}should be considered carefully according to the application. After fading noise suppression, differential phase method is employed to obtain the vibration information as described in [21, 27]. The spatial interval of differential phase is set to 0.8 m here, which means the theoretical spatial resolution of DAS is 0.8 m.

## 3. Results and discussion

The system parameters are listed here. The sensing fiber is commercial single mode fiber without any special treatment and the total length is about 9.8 km. Two piezoelectric transducers (PZTs) are placed at the far end of the fiber, and they are 1.5 meter apart. There is about 0.5-m fiber wrapped around the first PZT and about 10-m fiber wrapped around the second PZT. Two PZTs are driven by a 2-channel signal generator (SG) to excite vibrations. The whole experimental system is directly exposed to laboratory environment without isolation. The light source is a fiber laser (NKT, E15) with the linewidth less than 1 kHz. The period of the LFM pulse sequence generated by the AWG (Keysight, M8195A) is 100 *µ*s, and the width of each LFM pulse is 20 *µ*s. The frequency sweeping range is from 100 MHz to 1.1 GHz. Hanning window is applied to the optical probe pulse, in order to suppress the crosstalk [24]. The modulation bandwidth of the IM (Thorlabs, LN82S) is 10 GHz. *β* is set to 1, and *α* is about 0.8. The bandwidth of the BPD (Thorlabs, PDB480C) is from 30 kHz to 1.6 GHz. The sampling rate of the oscilloscope (Keysight, DSOS204A) is set to 2.5 GSa/s per channel, and the resolution is set to 10 bit. The total sensing time in one measurement is 20 ms, which is limited by the memory size of the oscilloscope, so there are totally 200 probe pulses injected into the fiber in each measurement.

In the first experiment, the first PZT continuously excites a 200-Hz sinusoidal vibration, and meanwhile the second PZT excites a 800-Hz sinusoidal vibration. The RBS intensity trace demodulated from the first probe is plotted in red line in Fig. 2(a) and 2(b). Due to the interference fading and polarization fading, it fluctuates sharply and the intensities are extremely low at some positions. For contrast, the intensity trace after fading suppression is plotted in blue line in the same figures. It is shown that all weak points are removed and the minimum intensity SNR along the entire fiber is approximate 30 dB. Phase SDs are calculated from 200 RBS phase traces and phase SD traces are plotted in Fig. 2(c) and 2(d). The red line is the phase SD trace of an undisturbed area before fading suppression. Since no strain signal is applied to the fiber, the phase fluctuation is caused by fading noise. The phase SD is large exactly at the position where RBS is weak. Due to the large fading noise, it is impossible to detect and locate true vibrations from the phase SD trace. However, after fading suppression, as plotted in blue color, the phase SD trace is integrally reduced and the maximum phase SD is less than 0.14 *rad* along the whole fiber except for the vibration area. Such a noise level of phase makes it possible to detect vibrations directly by the phase SD trace, as shown by Fig. 3.

The total frequency sweeping scale of each LFM pulse is 1 GHz and the pulse shape is Hanning window, so the theoretical spatial resolution of TGD-OFDR is 0.2 m before fading suppression methods are used. We focus on the Fresnel peak caused by the connector 1 as displayed in red in Fig. 2(e), and we find its FWHM is about 0.2 m, agreeing well with the theory. After fading suppression, the spatial resolution of TGD-OFDR becomes 0.4 m, as shown in 2(f). The degradation is due to moving average method, and the moving average window is set to 0.2 m, which also agrees well with the theory. The phase traces focusing on the vibration area are enlarged in Fig. 3. The theoretical spatial resolution of DAS is 0.8 m, as stated above. In Fig. 3(a), both the rising and falling edges of each vibration area are about 0.8 m, which proves the actual spatial resolution of DAS [28].

The period of injecting probes is 100 *µ*s and the acquisition is single-shot, therefore the measurable vibration bandwidth of our system is 5 kHz according to sampling theory. In order to further test the performances of our system, the first PZT excites a 200-Hz sinusoidal vibration and the second PZT excites a 4.6-kHz sinusoidal vibration simultaneously. The detected waveforms are shown in Fig. 4(a) and 4(b), which is a high-quality reproduction of the applied strain signal. The envelope of waveform in 4(b) seems to be amplitude modulated, because the signal frequency 4.6 kHz is close to the Nyquist frequency. Their single-side power spectra are displayed in Fig. 4(c). The frequencies are correct and there are no harmonic and crosstalk observed, which means our system has high linearity. The noise level is about −55 dB rad^{2}/Hz, i.e., 1.78 × 10^{−3} rad/√Hz. According to the relationship between the phase shift of the RBS and the amplitude of the strain [27], the strain resolution is about 245.6 *pε*/√Hz with a 0.8-m spatial resolution. The SNR of both measured vibrations are over 30 dB as shown in Fig. 4(c).

## 4. Conclusion

In this paper, we reported a competitive DAS system based on TGD-OFDR configuration and intensity modulator (IM). The IM has a large modulation bandwidth, which can realized the high spatial resolution. More importantly, the simultaneous positive and negative frequency components are fully used to suppress fading noise while the spatial resolution remains unchanged. In experiments, with fading noise suppressed well, a spatial resolution of 0.8 m is achieved. The strain resolution is about 245.6 *pε*/√Hz along the total 9.8-km sensing fiber. The vibration bandwidth is 5 kHz, only limited by the sensing length. Two vibration events are located correctly with high SNR by the phase trace of RBS in experiments, and the waveforms of vibrations are retrieved with high fidelity. The proposed system is named as high fidelity DAS due to the competitive performance, and it is promising in applications such as oil exploration and structural health monitoring.

## Funding

National Key R&D Plan of China (2017YFB0405500).

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