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Abstract
Wider bandwidth always means better overall performance for an information system. Naturally, this criterion can also be applied to phase-sensitive optical time domain reflectometry (Φ-OTDR), which is a typical distributed optical fiber sensing (DOFS) system. Thus, an indispensable way to enhance the performance of Φ-OTDR is to increase the available system bandwidth, which is usually limited by the electrical components. As a kind of frequency resources, the negative frequency band (NFB) has been used in communication systems based on coherent receivers and high-order modulation, but is still rarely used in DOFS. In this paper, we make a comprehensive study on how to utilize NFB in Φ-OTDR and thus double the available system bandwidth. Moreover, the related improvement of sensing performance is experimentally demonstrated. The positive and negative frequency multiplexing is utilized together with frequency division multiplexing to break the inherent trade-off between sensing distance and scan-rate. As a result, 21.6 kHz scan-rate is experimentally achieved on a 103 km fiber, with $97~p\varepsilon /\sqrt {Hz}$ strain resolution and 9.3 m spatial resolution. To the best of our knowledge, this is the best sensing performance in long distance Φ-OTDR > 100 km. The proposed scheme can also be applied to other DOFS systems with heterodyne-detection, opening up new possibilities for performance enhancement in DOFS systems.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Distributed optical fiber sensing (DOFS) is a research hot area in the recent decade [1–5]. Through time/frequency domain analysis [6,7], distributed measurement of sensing parameters over one hundred kilometers can be achieved [8–11] with high precision. As an important branch of DOFS, phase-sensitive optical time domain reflectometry ($\Phi$-OTDR) based on Rayleigh backscattering (RBS) has attracted intensive interests and has been already used in many real-life applications such as structural health monitoring, vehicle tracking and seismic wave detection [12–14].
In $\Phi$-OTDR, the bandwidth of the key devices (such as signal generator, photo-detector (PD) and analog-to-digital convertor (ADC)) has decisive impacts on the system performance: (1) The spatial resolution mainly depends on the pulse-width in single-pulse/optical-pulse-coding $\Phi$-OTDR [6,15], or relies on the bandwidth of the probing chirped-pulse in pulse-compression (PC) $\Phi$-OTDR [16]. Therefore, to achieve higher spatial resolution, shorter pulse-width or larger bandwidth of the chirped-pulse is needed, which requires larger bandwidth electrical components. (2) The scan-rate $f_{scan}$ of $\Phi$-OTDR is mainly limited by the fiber length, and the relationship between them is $f_{scan} \leq c/2nL$, where L is the fiber length, n is the refractive index of the fiber and c is the speed of light in vacuum. The frequency division multiplexing (FDM) is an effective way to increase the scan-rate [17,18], however, there is an inherent trade-off between the number of FDM channels (i.e., the scan-rate enlargement factor) and the spatial resolution, with a fixed system bandwidth. (3) The interference fading will seriously influence the measurement results of phase-demodulation $\Phi$-OTDR. Therefore, to eliminated interference fading, it is necessary to use multiple frequency bands to synthesize measurement results [16,19,20]. (4) The sensing distance of $\Phi$-OTDR mainly depends on the signal-to-noise ratio (SNR) at the far end of fiber-under-test (FUT) [10]. Distributed Raman amplification (DRA) [21], long-duration chirped pulse [22] and optical pulse coding [15] are effective ways to extend the sensing distance. However, the injected optical power of the probing pulse is limited by the onset of nonlinear effects such as stimulated Brillouin scattering (SBS). Since the threshold of SBS is highly dependent on the bandwidth of the probe pulse, increase the bandwidth of the probe pulse could be an effective way to avoid SBS. From the aforementioned analysis, it can be seen that increasing the available electrical bandwidth of the system is an indispensable way to enhance the overall performance of $\Phi$-OTDR.
Broadband channelization is an alternative way to detect large bandwidth signals through multi-channel detection [23]. However, the channelized receiver needs dual coherent optical frequency combs, which will increase the cost and the complexity of the system.
Another promising way to increase the available electrical bandwidth with only the ordinary components is utilizing the negative frequency band (NFB) [24,25]. In order to utilize the NFB in $\Phi$-OTDR, some preliminary studies based on single sideband (SSB) modulation of the IQ modulator and coherent detection have been done by the authors: (1) In 2017, an experimental demonstration with positive and negative frequency multiplexing (PNM) in optical pulse compression radar was firstly reported [24], realizing the detection of reflection points with doubled repetition rate; (2) In 2018, a further progress assisted by PNM was demonstrated with the ability to realize distributed strain measurement [25]. It should be noted that, there are valuable works using NFB with different arrangements and outcomes. In 2015, the NFB has been used in optical frequency domain reflectometry (OFDR) to make full use of the available sweeping bandwidth and improve the scan-rate to the theoretical bound: $c/2nL$ [26]. The positive/negative frequency signal is generated by selecting the proper processing window. However, this method cannot be used in $\Phi$-OTDR, because the basic sensing principles are different. In 2018, the negative harmonic was used to suppress the interference fading noise in time-gated OFDR [27]. In that scheme, the positive and negative harmonics were generated symmetrically and simultaneously by double sideband (DSB) modulation, which lacks flexibility and the power of the positive/negative harmonic is 3dB lower than that of SSB case.
As for long distance distributed acoustic sensing (DAS), until now there have been only a few reports on DAS beyond 100 km. With the assistance of long-chirped-pulse in PC-$\Phi$OTDR and the DRA, the sensing distance has been extended to more than 100 km with meter-scale spatial resolution [10,11]. Due to the inherent trade-off between scan-rate and sensing distance, the scan-rates of the above systems are both less than 1 kHz, which will seriously limit the application scenarios. In 2020, Z. Zhang et al. proposed a novel quasi-distributed phase-sensitive optical frequency domain reflectometry ($\phi$-OFDR) and realized 20 kHz vibrations measurement at 100 km [28]. However, this scheme can only be used in quasi-distributed sensing system, and the distance between two reflection points is large ($\sim$ 100 m in [28]).
In this paper, the general theory of NFB and the related enabling techniques for PNM $\Phi$-OTDR are elaborated for the first time. Particularly, aiming at the drawback of low scan-rate in long-distance DAS, PNM are combined with FDM to break this bottleneck. As a result, 21.6 kHz scan-rate over 103 km fiber, with $97~p\varepsilon /\sqrt {Hz}$ strain resolution and 9.3 m spatial resolution is experimentally demonstrated. It should be noted that NFB method could be integrated with channelization technology to further enhance the electrical bandwidth of the system, and this method is expected to be applied in other optoelectronics systems, such as distributed sensor based on Brillouin scattering, microwave photonics radar, etc.
2. Principle of NFB
According to the Shannon sampling theorem, the sampling rate of a signal must be twice greater than the maximum frequency of the signal. Assuming that the sample rate is $f_s$, the frequency domain is divided into two parts: positive frequency band (PFB) $[0, f_s/2]$ and NFB $[-f_s/2, 0)$. For a real signal $s(t)$, according to the nature of the Fourier transform, one can get:
It can be seen that the signal in NFB is the conjugation of it in PFB, which means the information contained in these two bands are the same. Therefore, extra efforts are needed to explore the value of NFB in DOFS. Assuming that the PFB and NFB of the signal $h(t)$ are $h_p(\omega )$ and $h_n(\omega )$, respectively, then the frequency domain expression of $h(t)$ is:3. Utilizing NFB in $\mathbf {\varPhi }$-OTDR
3.1 General system configuration
The general system configuration is shown in Fig. 1. The ultra-narrow linewidth laser is utilized as the light source. The continuous-wave (CW) from the laser is modulated into high quality probe signal by the IQ modulator driven by arbitrary waveform generator (AWG), and then be injected into FUT through a circulator. The RBS signal is collected in the port3 of the circulator, and is mixed with the local oscillator (LO) by $90^\circ$ optical hybrid. A variable optical attenuator (VOA) and a polarization controller (PC) are used to adjust the power and polarization state of LO, respectively. The in-phase and quadrature-phase output signals of the optical hybrid are converted to electrical signals by two balanced photodetector (BPD), and then be sampled by two ADCs.
Fig. 1. The general system configuration utilizing NFB. (UC: up-conversion; DC: down-conversion; NFB: negative frequency band; PFB: positive frequency band.)
3.2 General principle of using NFB in $\Phi$-OTDR
The principle of using NFB in $\Phi$-OTDR can be summarized as three steps. First, generating the up-conversion (UC) and down-conversion (DC) signals through IQ modulation. Second, converting the UC and DC bands into NFB and PFB respectively through coherent detection using 90$^\circ$ optical hybrid. Third, separating the positive and negative frequency signals in the frequency domain, demodulating them separately, and then combining the demodulation results.
Assuming that the outputs of AWG are $I(t)$ and $Q(t)$, then the probe signal generated by IQ modulator with predistortion process [29] can be expressed as:
The probe signal $E_m(t)$ is injected into FUT, and the RBS signal can be seen as the summation of the contributions of each relevant scatterers [30]:
where $\overline {a_i}=a_i\exp \left [(-\alpha c\tau _i)/n \right ]$; $a_i$ and $\tau _i$ are the amplitude and delay of the $i$th scatterer, respectively; $N_s$ is the total number of the scatterers of the whole sensing fiber; $\alpha$ is the fiber attenuation coefficient; $c$ is the velocity of light in vacuum; $n$ is the refractive index of the fiber.Then the RBS signal is mixed with LO: $E_L(t) = A_L\exp \{j \omega _c t\}$, and the signals of the I-channel and the Q-channel of the 90$^\circ$ hybrid are detected by two BPDs [6,31–33], and can be expressed as:
In general, to obtain the RBS signals of PFB and NFB, $E_{RSC}(t)$ is first converted into frequency domain, and then the positive part and the negative part of the frequency domain are converted into time domain, respectively. While in some special cases, such as PC-$\Phi$OTDR, the RBS signals of PFB and NFB can be separated by the different matched filters [18], and then are separately demodulated through traditional $\Phi$-OTDR phase demodulation algorithm in our earlier paper [6]. The demodulation results are combined through a certain way as follows: (1) For SNR enhancement, the demodulation results of PNM can be directly averaged or rotated then summated [27]; (2) For improving the scan-rate, the demodulation results of PNM are re-arranged according to the time sequence of the received PFB and NFB, and thus the scan-rate becomes the reciprocal of the time interval between PFB and NFB signals [25].
3.3 Impact of PNM on SNR
When only the positive frequency band is used, $I(t)$ and $Q(t)$ should satisfy the orthogonal relationship ($\hat {I}(t)=Q(t)$) to produce the single-band probing signals, combined with Eq. (7), we can get the RBS signal in this case:
The RBS signal in this case only has positive frequency parts. It should be noted that the negative frequency parts of $n(t)$ can be removed by the KK relation [34], so Eq. (9) only contains the negative frequency parts of $n(t)$.In general, the output signal power of the IQ modulator is limited by the amplitude of the signal from AWG and the $V_\pi$ of the modulator, which means the output power of the IQ modulator will be not doubled when the UC band and DC band are simultaneously generated by DSB modulation. However, in most schemes of $\Phi$-OTDR, the probe signals are independent pulses or pulse sequences. As shown as an example in the upper left corner of Fig. 1, we can generate the UC band and DC band at the different time-slots. Therefore, the signal energy in the PFB/NFB of Eq. (7) is equal to the signal energy in Eq. (9). That is to say, using PNM will not degrade the intensity SNR of the system. In $\Phi$-OTDR, the SNR of differential phase is proportional to the intensity SNR [19,35], so PNM will also not affect it.
The strain sensitivity of $\Phi$-OTDR can be evaluated by the noise floor of the PSD [11,25,30] whose expectation can be expressed as [36]
where $f_{scan}$ is the scan-rate of the system; $\delta _\varepsilon ^2$ is the variance of the strain demodulated when the fiber is not disturbed, and its value is the same with/without PNM because of the same SNR of the differential phase. In our manuscript, the PNM is used to double the scan-rate. That is to say, $E[PSD]$ will be decreased by 3dB, and the strain sensitivity will be improved by $\sqrt {2}$ times.In order to verify the above conclusion experimentally, the experiments using PNM and only PFB were implemented based on the setup reported in our previous work (the short-distance case) [25]. In PNM case, the demodulation results are combined according to the time sequence of the received PFB and NFB. The expectations of PSD ($E[PSD]$) along the fiber in different cases were measured, and its probability density function (PDF) are shown in Fig. 2.
Fig. 2. The statistical results of $E[PSD]$ in different cases; (a) positive-only vs. PNM; (b) positive-only vs. PFB of PNM; (c) positive-only vs. NFB of PNM.
The statistical results show that the signal qualities of both PFB and NFB in PNM scheme are very close to that of positive-only case. Moreover, since the scan-rate is doubled in PNM case, the PSD along the fiber is smaller than that of the positive-only case. The mean values of $E[PSD]$ in different cases are shown in Table 1. Compared with the positive-only case, the mean values in PFB/NFB of PNM are slightly larger, and the improvement introduced by PNM is slightly less than 3dB. This phenomenon is caused by the imperfection of the 90$^\circ$ optical hybrid and the finite inter-band suppression ratio of the IQ modulator, although some compensations have been applied.
Table 1. The mean value of statistical results in different cases.
4. Increasing scan-rate for long range PC-$\varPhi$OTDR
Pulse-compression (PC) $\Phi$-OTDR is a promising technology, which can break the trade-offs among sensing range, spatial resolution and strain sensitivity. So far, the sensing distance of PC-$\Phi$OTDR has been extended to more than 100 km [10,11]. However, the upper bound of the scan-rate decreases with the increase of sensing distance. For example, when the sensing range is 100 km, the upper bound of scan-rate is only 1 kHz. This limitation severely restricts the application of existing long distance PC-$\Phi$OTDR, since it is not suitable for applications where high frequency disturbances need to be detected, such as distributed acoustic sensing. On the other hand, for the low frequency disturbances detection scenarios such as seismic wave detection [14], the low scan-rate will significantly deteriorate the detected signal. The reason is as following: The ambient/environmental noises can be regarded as broadband noises. When the scan-rate is low, low-frequency ($\leq f_{scan}/2$) signals and noises can be collected naturally, while high frequency ($> f_{scan}/2$) noises will also be aliased to the low frequency band, and these aliased noises cannot be removed by the digital filter. However, those noises can be easily filtered out when the scan-rate is large enough. In summary, breaking the upper bound of scan-rate is very important for long range PC-$\Phi$OTDR.
FDM technology is an effective way to break the upper bound of scan-rate. However, the use of FDM will increase the bandwidth requirements of the electrical components, such as PD, ADC, etc, or sacrifice other parameters [18]. In this manuscript, FDM and PNM are combined to alleviate the bandwidth requirements of electrical components. Assuming that the period of the probe pulse is $T$, and the FDM number is $N$, the modulator’s driving signals of I and Q channel are set as:
Combining Eq. (7) and Eq. (11), one can get the RBS signal with coherent detection in this case, and can be expressed as:
4.1 Experimental setup and pulse-sequence design
The experimental setup is shown in Fig. 3. The basic structure of the experiment is as the same as Fig. 1. The linewidth of the laser is $100~Hz$. A 1455 nm Raman pump (a semiconductor laser with 25.9 dBm output power) was used for distributed amplification. The sensing fiber is about $103~km$. A calibrated piezoelectric ceramic transducer (PZT) wound with a $12.3~m$ fiber is placed at the end of the sensing fiber to generate disturbance, and there is another $100~m$ SMF attached to the PZT. The bandwidth of the two BPDs is 1.6 GHz, and the sample rate and the vertical resolution of the two ADCs are 3.2 GSa/s and 12-bits, respectively.
In order to take full advantage of the bandwidth of BPD and ADC, FDM with 12 channels and PNM are combined. The schematic diagram of probe pulse sequences is shown in Fig. 3. Each FDM channel has UC band and DC band. The repetition period of pulse-sequences and the duration of UC/DC bands are 1110 $\mu$s and 35 $\mu$s, respectively. The start frequency is set as 15 MHz. The bandwidth and the frequency interval of each FDM channel are 120 MHz and 5 MHz, respectively. Moreover, each UC/DC band contains five sub-chirped-pulses for interference fading eliminating [16,19,20]. The frequency interval of the adjacent sub-chirped-pulses is also 5 MHz, so the bandwidth and the duration of them are 20 MHz and 7 $\mu$s, respectively.
In order to verify the suppression ratio of the positive and negative frequencies band, the probe pulse sequences as shown in Fig. 3 are directly fed into the 90$^\circ$ optical hybrid for IQ demodulation. At this time, the UC/DC band signals will be converted into negative/positive frequency signals. Fig. 4(a) shows the real parts of the pulse sequences after the IQ demodulation. The PFB signals are selected as an example to analyze the suppression ratio (The switching between PFB/NFB signal generation only needs to change the initial phase from -90$^\circ$ to 90$^\circ$, so the suppression ratios are the same). The PSDs of the PFB signals are plotted on the same figure, and is shown in Fig. 4(b). The inset of Fig. 4(b) is the enlarged results of PSD around the first frequency band. It can be seen that the suppression ratios of each positive and negative bands are over 23 dB.
Fig. 4. The measurement results of the pulse sequences; (a) The real parts of the pulse sequences after the IQ demodulation; (b) The PSDs of PFB.
4.2 Experimental results
The RBS signal is first acquired and the short-time Fourier transform (STFT) result shown in Fig. 5. It can be seen that 3.02 GHz bandwidth has been utilized in a system with 1.6 GHz photodetector and 3.2 GHz digitizer.
To improve the SNR at the far end of the fiber, a 1455 nm Raman pump is used for distributed amplification. The probe pulse sequences are firstly amplified by co-pumping Raman amplification; and then the RBS signal are amplified by counter-pumping Raman amplification. The feature of accumulated Raman gain along fiber was analyzed in [37], showing that the signal reflected (by either Rayleigh backscattering or fiber-fault) at a far-end location will experience larger accumulated gain. Fig. 6 shows the comparison of the intensity responses of single pulse with and without DRA. It can be seen that with DRA, the intensity SNR at the fiber far-end is increased to 17.6 dB. Therefore, the interference-fading phenomenon can be well suppressed by the rotated-vector-sum method [16]. This improvement is enough for PC-$\Phi$OTDR to demodulate the phase information with good SNR at the end of 103 km sensing fiber.
After performing the separation and demodulation of the Rayleigh scattering signal of each channel, and recombining the demodulation result, the phase demodulation result of the system with high scan-rate can be obtained. A sinusoidal wave with 100 Hz frequency and 3 V peak-to-peak amplitude was applied on the PZT to generate disturbance. The phase demodulation results are shown in Fig. 7. The phase-distance map is shown in Fig. 7(a) and the disturbance zone at the far end of 103 km fiber can be easily recognized. The corresponding time domain signal in the disturbance zone is shown in the inset of Fig. 7(a); where the blue dots is the experimental data, and the red line is the fitting curve. In the phase demodulation process, a Hann window was used to suppress the crosstalk, so the width of the compression window of the chirped pulse is 8.3 m. The differential phase is proportional to virtual gauge length [30]. To ensure the quality of the demodulated signal, the gauge length was set as slightly larger than the width of the compression window, which is 9.3 m. Thus, the spatial resolution of our system is 9.3 m [38]. Fig. 7(b) shows the variance of the differential phase along the fiber, and the rising edge is 9.3 m, which is equals to the expected spatial resolution. In order to evaluate the crosstalk, the PSDs along the end of the fiber were calculated and are shown in Fig. 7(c). Fig. 7(d) is the PSD value at 100Hz (the frequency of the disturbance signal) along the fiber. It can be seen that the crosstalk is less than -40 dB.
Fig. 7. (a) The phase-distance map at the far end of FUT; (b) The variance of the differential phase along the fiber; (c) The PSDs along the end of the fiber; (d) The PSD value at 100Hz.
The strain resolution is an important parameter for $\Phi$-OTDR and usually be evaluated by the noise floor of the PSD [11,22,30,39]. Diverse sinusoidal waves with 1 V amplitude and different frequencies are applied to PZT, and the PSD is shown in Fig. 8. The noise floor is defined as secondary maximum peak here, which is about -41.71 $dB~rad^2/Hz$, corresponding to 97 $p\varepsilon /\sqrt {Hz}$ strain resolution.
The scan-rate of this system is multiplied by 24 times with PNM and FDM, which results in the 10.8 kHz of the measurable bandwidth of vibrations. In order to test the vibration frequency response range, a linear frequency modulated signal was applied on the PZT, whose frequency is increased from 100 Hz to 10.5 kHz in 30 ms and then decreased back in 30 ms. The STFT of the obtained waveform is shown in Fig. 9, which shows that the chirped vibration is measured correctly. In general, by making full use of the frequency band resources, the proposed scheme has demonstrated unprecedented overall performance. Compared with the recently reported DAS over 100km [11] (bi-directional DRA was used), this system is a single-ended system, which is more suitable for practical applications. Moreover, this system achieves a scan-rate of up to 21.6 kHz, which can greatly expand the application scenarios of long-distance DAS.
5. Conclusions
In this paper, the negative frequency band is proposed to increase the measurement bandwidth of $\Phi$-OTDR, without increasing the requirement of hardware’s bandwidth. The general principle of negative frequency band and its implementation in $\Phi$-OTDR are theoretically analyzed in detail. The positive and negative frequencies multiplexing is combined with frequency division multiplexing to increase the scan-rate of PC-$\Phi$OTDR by more than 20 times. As a result, $97~p\varepsilon / \sqrt {Hz}$ strain sensitivity in 103 km sensing range with 9.3 m spatial resolution is experimentally realized. The proposed scheme can also be applied to other DOFS systems with heterodyne-detection.
Funding
National Natural Science Foundation of China (41527805, 61731006, 62075030); Sichuan Provincial Project for Outstanding Young Scholars in Science and Technology (2020JDJQ0024); 111 project (B14039).
Acknowledgments
The authors would like to thank Dr. Yun Fu of the University of Electronic Science and Technology of China for English polishing.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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