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Abstract
A low-complexity multi-subcarrier pulse generation scheme is proposed to suppress the interference fading in a phase-sensitive optical time-domain reflectometer (Φ-OTDR) based distributed acoustic sensor (DAS) with heterodyne coherent detection. The multi-subcarrier pulse is generated in the digital domain based on the proper clipping operation of a sine signal. The localization and recovery of the disturbance signal are realized by the spectrum extraction and rotated vector sum (SERVS) method. The experimental results show that the occurrences of interference fading can be significantly reduced. The intensity fluctuation is reduced from ∼75 dB to ∼25 dB. Multiple disturbance signals are successfully demodulated to verify the effectiveness of the proposed method.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fiber optic distributed acoustic sensing (DAS) technology based on Rayleigh backscattering (RBS) light has become a hot research topic due to its unique advantages such as high sensitivity, large measurement range and environmental adaptability [1]. It uses the backscattered light along the sensing fiber to detect and analyze the disturbance signals. In recent years, DAS technology has been deployed in many practical applications, such as oil and gas pipeline monitoring [2], seismic monitoring [3], perimeter security [4], traffic and railroad monitoring [5], and maintenance of telecommunication fiber optic cables [6]. Specifically, recent research has considered to use DAS in all dark communication fibers worldwide to enable large-scale environmental sensing [7,8]. Therefore, DAS is becoming an essential sensing technology and the potential market for its application is increasing.
The RBS based DAS is typically realized by the phase-sensitive optical time domain reflectometer ($\Phi$-OTDR) scheme with heterodyne coherent detection. The scheme exploits the interaction of photons with inherent defects within the fiber, which cause fluctuations of the refractive index in the fiber [9]. $\Phi$-OTDR uses a narrow linewidth laser with high coherence as the light source to send optical pulses to the fiber and interrogates the RBS light from the intrinsic fiber defects. The refractive index in each fiber segment changes when the fiber is disturbed. It is noted that the RBS signals carry the information about the disturbance signal. The analysis of the RBS signal can extract how the signal from the scattering point varies in intensity or phase, which in turn enables disturbance localization and vector field reconstruction. The advantage of the phase over the intensity is that the phase can provide a linear response to strain, making a complete reconstruction of the disturbance signal.
However, the sensing performance of $\Phi$-OTDR is affected by signal fading, including both polarization and interference fading. The polarization diversity detection has been widely used in the heterodyne $\Phi$-OTDR to reduce the polarization fading components [10]. Due to the random spatial distribution of the refractive index and the high coherence of the light source, the RBS signal may suffer from interference fading [11]. Fading points, characterized by extremely low intensity backscattering, pose challenges for acquiring accurate external disturbance information in a $\Phi$-OTDR system [12]. This is mainly caused by a reduction in the intensity of the backscattered light in certain regions, resulting in the degradation of signal-to-noise ratio (SNR). If the SNR is severely degraded, the phase cannot be properly demodulated, resulting in localization errors and distortion of the reconstructed signal.
It has explained that the SNR of the extracted phase depends on the intensities of the sampled points [13]. In order to reduce the fading points and increase the SNR, a straightforward thought is to increase the sensitivity from the perspective of sensing fiber itself and the design of the transducer structure. Techniques to enhance the reflectivity of optical fibres have attracted increasing attention [14], which may be a solution to suppress the interference fading. Weak reflector array schemes such as ultra weak fibre Bragg grating (UWFBG) arrays have been proposed to increase the reflectivity and avoid coherent Rayleigh noise without a serious increase in fibre transmission loss [15]. Similarly, consecutive longitudinal microstructured fibers with stronger backscattering coefficient and spacing intervals are an option to eliminate the adverse effects of interference attenuation [16]. However, due to the complex manufacturing process of the sensing units, the technology is expensive to roll out on a large scale.
In addition to changing the scattering rate of the fiber microstructure, the time-domain properties of the backward Rayleigh-scattered signal can be controlled by superposition of multiple statistically independent field components to reduce the number of fading points [12], for example, by using multicore [17] or multimode [18] fibers for sensing. It seems more convenient to use different frequencies to obtain statistically independent Rayleigh channels than the use of special optical fibers. The schemes of multi-frequency source have been proposed to explore the effect of optical frequency on signal amplitude [19]. The location of the interference fading point has been shown to be related to the center frequency of the laser [20]. Therefore, the interference fading can be suppressed by probing optical pulses with different frequencies [21]. Several methods have been proposed to mitigate the interference fading by generating optical pulse signal with multiple frequencies. In 2017, the chirp signal with wide frequency spectrum was used as the probe signal [22]. Spectrum extraction and rotated vector sum (SERVS) method was then proposed to increase the SNR of the demodulated signal and reduce the possibility of interference fading. In 2019, the main and side frequency lobes of a single rectangular pulse were regarded as the multi-frequency probe signal to achieve interference fading mitigation after SERVS method [23]. A scheme of multi-frequency probes generation based on several acoustic optical modulator (AOM) followed by optimal intensity tracking was also presented [24]. In 2022, a scheme with multiple narrow linewidth laser sources and balanced photodetectors was also proposed to effectively eliminate the intensity fading [25]. In 2023, a scheme using random sampling as well as a frequency-division multiplexing probes in coherent $\Phi$-OTDR was proposed [26], realizing quantitative measurements of ultra-high frequency vibration signals with suppressed interference attenuation. In the same year, a phase modulator-based optical frequency comb detection scheme was proposed [27]. By using the detected light generated from an equal amplitude frequency comb, the inverse Rayleigh scattered light with different intensity distributions is obtained to suppress the fading effect. It is also shown that the application of optical frequency combs [28,29] in DAS can significantly improve the spatial resolution of the system [30].Recently, a coherently parallel fiber optic distributed acoustic sensing based on dual Kerr soliton microcomb has been reported [31]. By providing colocked multiple-frequency channels, the dual-frequency comb light source realizes the linear superposition of sensing signals, while the frequency division multiplexing strategy effectively suppresses coherent attenuation and also realizes high-precision phase demodulation, which has a great potential to improve sensitivity.
In this paper, we propose a scheme to generate a multi-subcarrier optical pulse with equally frequency spacing using only one AOM. The interference fading can be effectively mitigated by properly mixing the multi-subcarrier RBS signal via SERVS method. The experimental results show that the intensity fluctuation is reduced from $\sim$7 dB to $\sim$25 dB after mixing five subcarriers. Different disturbance signals have also been retrieved without obviously distortion and frequency response loss.
2. Principle
We design a multi-subcarrier pulse waveform in real-value domain to achieve detection of multiple-frequency RBS signal. The signal generation process is shown in Fig. 1. We first generate a sine wave with an initial phase, which is controlled by the phase of $\varphi$. The phase $\varphi$ can be used to adjust the peak to average power ratio (PAPR) of the signal to avoid the undesired nonlinear distortions. The clipping operation is then applied onto the time domain waveform to induce strong nonlinearities to generate multiple subcarriers. Further, the clipping operation leads to the distortion of the sinusoidal signal, which results in a series of harmonic components in the frequency domain. For the proposed method, the harmonic components will be the desired subcarriers. The clipping operation is described as:
The frequency of the sine signal is determined by the sampling rate of the digital-to-analog converter. In this work, we first use a sampling rate of 1 GSa/s to generate a sine signal with frequency of 20 MHz. If the clipping threshold is appropriately chosen, a multi-subcarrier signals can be generated in a subcarrier interval of 20 MHz. It is noted that the multi-subcarrier pulse is different from the conventional rectangular pulse, whose spectrum also has the characteristic of multiple frequencies [23]. In the spectrum of rectangular pulse, the energy of the side lobes is much lower than the main lobe. And the bandwidth of the side lobes is half of the main lobe, as shown Fig. 2(a). The spectrum of our proposed multi-subcarrier pulse is shown in Fig. 2(b). Compared to the spectrum of rectangular pulses, the energy distribution of our proposed multi-subcarrier pulse spectrum is more uniform. Although the subcarriers far from the center also have energy attenuation compared to the middle subcarrier, the attenuation is smaller and the bandwidth of each subcarrier is the same. It means that the RBS signal are generated at more frequencies, which can be used to enhance the SNR and suppress the interference fading after SERVS method.
Fig. 2. The normalized spectrum of (a) rectangular pulse, (b) proposed multi-subcarrier pulse and (c) RBS signal with same pulse width in frequency domain in the experiment.
For validation, we also provide the normalized spectrum of RBS signal in the experimental demonstration with subcarrier interval of 20 MHz in Fig. 2(c). It can be seen that the spectrum of RBS signal in baseband agrees well with the simulated spectrum in Fig. 2(b).
Since each subcarrier can be extracted to recover the interference information independently, the SERVS method can be then used to eliminate the interference fading after spectrum extraction. The spectrum extraction process is also illustrated in Fig. 2(c), where the dashed boxes indicate the filters to extract the desired subcarriers. Spectrum extraction is performed by designing filters in the digital domain to achieve separation of different subcarriers. It is noted that the proposed method can also work even if the spectrum is overlapped. This is because the sensing information exists throughout the band, and the fading location can maintain different among the five subcarriers if a small portion of the spectrum is overlapped. The central subcarrier with the highest energy is defined as subcarrier $\mathrm{S}_0$. The subcarriers with frequencies higher than $\mathrm{S}_0$ are defined as $\mathrm{S}_{+1}$, $\mathrm{S}_{+2}$ according to the frequency distance to $\mathrm{S}_0$ from near to far. Similarly, the subcarriers with frequencies lower than $\mathrm{S}_0$ are defined as $\mathrm{S}_{-1}$, $\mathrm{S}_{-2}$. The phase information obtained from the extracted subcarriers are then combined via SERVS method to achieve interference fading suppression [23]. To efficiently combine scattered signals with varying carrier frequencies and validate the previously mentioned theoretical outcomes, it is essential to perform phase alignment. This method rotates the phase of each subcarrier frequency backscattering signals to be aligned, ensuring the maximum intensity superposition.
3. Experimental setup
The experimental setup is shown in Fig. 3. The continuous-wave (CW) light from the narrow linewidth laser first passes through a 90:10 coupler, of which 90% is used as the probing light and the rest 10% is used as local oscillator (LO). The narrow linewidth laser has a linewidth of less than 3 kHz to satisfy the system’s requirement for coherence of the probe source, which is not affected by the broadening of the modulated spectrum. An arbitrary waveform generator (AWG) is used to generate the desired multi-subcarrier signal at sampling rate of 1 GSa/s. The generated multi-subcarrier signal has a pulse width of 100 ns and repetition frequency of 1 kHz. The generated multi-subcarrier signal is then added onto the CW light through an AOM with 200 MHz frequency shift to obtain the probing optical signal. The probing optical signal is then amplified by an erbium-doped fiber amplifier (EDFA) followed by an optical band-pass filter (BPF) to suppress the spontaneous emission noise. The amplified optical signal is then launched into the single-mode sensing fiber with length of 1.67 km through an optical circulator. The RBS light from port 3 of the optical circulator then beats with the LO light at a 50:50 optical coupler. The optical-to-electrical conversion is realized in a balanced photodetector (BPD) with a bandwidth of 300 MHz. The obtained electrical signals are digitized by a data acquisition card (DAQ) with a sampling rate of 1 GSa/s, which is sufficient to cover the spectrum of more than five subcarrier signals, enabling the extraction of information from multiple subcarriers proceed smoothly. The RBS signal is then recovered and analyzed offline. The external disturbance is employed by the piezoelectric transducer (PZT) at the position of 1.60 km and fiber length on the PZT is 6.9 m. The disturbance signal is generated by an arbitrary function generator (AFG), which is driven by the electrical signal with adjustable voltage and frequency.
Fig. 3. Experimental setup. AWG: arbitrary waveform generator; OC: optical coupler; AOM: acoustic optical modulator; EDFA: erbium-doped fiber amplifier; BPF: bandpass filters; FUT: fiber under test; PZT: Piezoelectric Tube; PC: polarization controller; BPD: balanced photodetector; DAQ: data acquisition card.
4. Results
The digitized RBS signal is processed segmentally to obtain the intensity traces of the different subcarriers. The time domain intensity of the five-subcarrier signals at the same location is shown in Fig. 4(a). It can be seen that the intensity fluctuations in different subcarriers are not consistent, which shows certain complementary characteristics. We also apply the Pearson product-moment correlation coefficient (PCC) to analyze the correlation between the intensities of different traces at different subcarriers. It is noted that smaller PCC means a lower correlation. The correlation coefficients between each subcarrier calculated using 100 successive acquisitions of the RBS are shown in Fig. 4(b). It can be seen that the PCC is low among the subcarriers, which also confirms the complementary characteristics of the subcarriers. And the corresponding retrieved traces can be regarded as having independent fading locations along the fiber.
Fig. 4. (a) the retrieved intensity traces of extracted subcarriers $\mathrm{S}_{-2}$, $\mathrm{S}_{-1}$, $\mathrm{S}_0$, $\mathrm{S}_{+1}$, $\mathrm{S}_{+2}$. (b) the PCC coefficients among subcarriers in 100 successive RBS traces.
Since the decomposed signal trace in each subcarrier is a complex vector, the SERVS method is used to mix the decomposed signal. To explore the effect of the number of subcarriers on interference fading mitigation, three cases of using only subcarriers $\mathrm{S}_0$ (denoted as SERVS ($\mathrm{S}_0$)), mixing subcarriers $\mathrm{S}_0$, $\mathrm{S}_{-1}$, $\mathrm{S}_{+1}$ (denoted as SERVS ($\mathrm{S}_0$, $\mathrm{S}_{-1}$, $\mathrm{S}_{+1}$)), and mixing subcarriers $\mathrm{S}_0$, $\mathrm{S}_{-1}$, $\mathrm{S}_{+1}$, $\mathrm{S}_{-2}$, $\mathrm{S}_{+2}$ (denoted as SERVS ($\mathrm{S}_0$, $\mathrm{S}_{-1}$, $\mathrm{S}_{+1}$, $\mathrm{S}_{-2}$, $\mathrm{S}_{+2}$)) are considered.
Figure 5(a)-(c) shows the intensity corresponding traces. The intensity trace of beat signal processed by using one subcarrier is shown in Fig. 5(a) with intensity fluctuation of about 75 dB. With five subcarriers synthesis, the intensity fluctuation is reduced and to $\sim$25 dB, and the fading point decreases gradually with the increase of the number of subcarriers. Figure 5(d)-(f) shows the corresponding 800 differential phase traces in one color. It can be seen that when we used five subcarriers for mixing, all the false phases were eliminated and the vibrations were clearly observed at the position of 1.60 km. Furthermore, as the standard deviation (SD) of the differential phases precisely reflects the distribution of phase fluctuations [32,33], we present a comparison of the phase SD for three scenarios in Fig. 5(g)-(i). Before the interference fading is suppressed, there are many unperturbed places where the noise SD values are large, which means that the interference fading causes many error points during phase demodulation. When combined using multiple subcarriers, the phase SD diminishes close to 0 in undisturbed areas and sharply increases at the perturbation site, forming a peak that corresponds to the vibration. This suggests that the phase is flat in the region without perturbations and there is almost no demodulation error throughout the differential phase. In other words, the proposed method can effectively suppress the interference fading, enhance the disturbance localization capability and improve the phase demodulation accuracy of the system. The slight overall increase in the SD of the fiber after the vibration point is attributed to a decrease in the SNR resulting from the insertion loss of the PZT. In addition, it can be seen from the differential phase SD that a final spatial resolution of 8 m can be obtained after using five subcarriers, which is related to the superposition of the time-domain waveforms corresponding to the extracted subcarriers. In this experiment, five subcarriers were used for aggregation, which effectively suppressed the effect of interference fading on phase demodulation. In addition to the effect of the number of aggregated subcarriers [12], the fading suppression effect will also be related to the signal quality of the subcarriers, and selecting subcarriers with higher energy may reduce the possibility of mixing more noise. In practical scenarios, an appropriate number of subcarriers can be selected for aggregation based on the system SNR requirements.
Fig. 5. Intensity of beat signal processed with (a) subcarrier $\mathrm{S}_0$; (b) subcarrier $\mathrm{S}_0$, $\mathrm{S}_{-1}$, $\mathrm{S}_{+1}$; (c) subcarrier $\mathrm{S}_0$, $\mathrm{S}_{-1}$, $\mathrm{S}_{+1}$, $\mathrm{S}_-2$, $\mathrm{S}_{+2}$; and 800 differential phase traces processed with (d) subcarrier $\mathrm{S}_0$; (e) subcarrier $\mathrm{S}_0$, $\mathrm{S}_{-1}$, $\mathrm{S}_{+1}$; (f) subcarrier $\mathrm{S}_0$, $\mathrm{S}_{-1}$, $\mathrm{S}_{+1}$, $\mathrm{S}_{-2}$, $\mathrm{S}_{+2}$; and the SD of of the differential phases processed with (g) subcarrier $\mathrm{S}_0$; (h) subcarrier $\mathrm{S}_0$, $\mathrm{S}_{-1}$, $\mathrm{S}_{+1}$; (i) subcarrier $\mathrm{S}_0$, $\mathrm{S}_{-1}$, $\mathrm{S}_{+1}$, $\mathrm{S}_-2$, $\mathrm{S}_{+2}$.
The essence of fading suppression is to eliminate the low-level points in the intensity traces, which is the basis for acquiring high-quality phase information along the whole sensing fiber [12]. That is to say, the amplitude distributions reflect the possibility of high-quality phase demodulation. The fitting of the amplitude distributions for SERVS ($\mathrm{S}_0$), SERVS ($\mathrm{S}_0$, $\mathrm{S}_{-1}$, $\mathrm{S}_{+1}$), and SERVS ($\mathrm{S}_0$, $\mathrm{S}_{-1}$, $\mathrm{S}_{+1}$, $\mathrm{S}_{-2}$, $\mathrm{S}_{+2}$) are shown in Fig. 6. It can be seen that all the three distributions follow the Rayleigh distribution. With larger number of subcarriers, the overall value of the amplitude becomes larger with more of the amplitude value moving away from the origin. It means that the occurrence of interference fading is gradually reduced. In addition we compare the fitting results of conventional rectangular pulse probing using a pulse width of 100 ns. Due to the ordinary filtering method as well as its main flap bandwidth, the intensity distribution of the obtained backward Rayleigh scattering signal is similar to the result of the single subcarrier $\mathrm{S}_0$ in the scheme proposed in this paper, which can be also more consistent on the image.
Fig. 6. The fitting of amplitude distribution of SERVS ($\mathrm{S}_0$), SERVS ($\mathrm{S}_0$, $\mathrm{S}_{-1}$, $\mathrm{S}_{+1}$), SERVS ($\mathrm{S}_0$, $\mathrm{S}_{-1}$, $\mathrm{S}_{+1}$, $\mathrm{S}_{-2}$, $\mathrm{S}_{+2}$) and the rectangular pulse detection results.
Finally, we conduct several dynamic measurements to demonstrate that the disturbance signal can be restored accurately. In experiment, two sinusoidal vibration signals with frequency of 50 Hz and 200 Hz are applied onto the fiber. The phase recovery waveforms of the 50 Hz and 200 Hz vibrations are shown in Fig. 7(a) and (c), respectively. Figure 7(b) and (d) show the corresponding power spectral density (PSD). It can be seen that the disturbance signal can be accurately recovered. The SNR are calculated to be as high as 30.84 dB and 33.36 dB, respectively. Besides, a chirped waveform with frequency from 1 Hz to 150 Hz is tested and the measured time-domain signal is illustrated in Fig. 7(e). With short-time Fourier transform, the corresponding frequency spectrum is calculated and depicted in Fig. 7(f). It can be seen that all the disturbance signal can be recovered with high accuracy, which demonstrate the effectiveness of the proposed method.
Fig. 7. The dynamic measurements.(a) measured time-domain signal and (b) the corresponding PSD of the 50 Hz vibration; (c) measured time-domain signal and (d) the corresponding PSD of the 200 Hz vibration; (e) measured time-domain signal and (f) the corresponding frequency spectrum of the frequency-chirped vibration.
We believe that the signal acquired in the absence of vibration perturbations can be used as the absolute noise floor. As shown in Fig. 8(a), we acquired the undisturbed phase signal for 0.1 s and took the maximum value of the phase change during this period as the minimum phase change corresponding to detectable external disturbance, i.e., 0.153 rad. In addition, its corresponding PSD will be used as the absolute background noise of the system, as shown in Fig. 8(b), with an average value of -59.60 dB. Although the application of vibration should not affect the noise floor, loading or removing the vibration signal in the experiment still leads to some differences. For example, a small number of harmonics can also be observed in Fig. 7(b). Therefore, we believe that the small differences are within an acceptable margin of error.
5. Discussion
In this paper, the multicarrier signal is generated using a single analogue-based AOM without changing the structure of conventional DAS system. In the digital domain, the digital signal processing (DSP) only involves generation of a single-tone sinusoidal signal and clipping operation. It is noted that other multicarrier signal generation methods may usually require additional optical modualtors [24,27,34] or high resolution digital-to-analog converter (DAC) [22,32]. Therefore, our proposed method has the advantages of low complexity and simply implementation in digital domain. Moreover, the multicarrier signal generation can also be achieved completely in analog domain with even lower cost and complexity. For example, the sinusoidal waveform is first generated by a direct digital synthesis (DDS) module. Then the clipping operation can be achieved by a comparator and high-speed analogue switches in the order of 10 ns [35]. Therefore, it is possible to generate the multicarrier signal in a simple electrical circuit without the requirement of expensive high-speed digital devices.
6. Conclusion
In this paper, an optical multi-subcarrier pulse signal is designed and generated based on a single AOM to mitigate the interference fading in DAS. By extracting and mixing the subcarriers, the amplitude of the synthesized vector increases with the reduction of the possibility of interference fading occurrences. The ability of the proposed method to mitigate the interference fading has been successfully demonstrated. In the experimental demonstration, we show that five subcarriers are sufficient to effectively mitigate the occurrences of interference fading. Moreover, the proposed method can accurately recover the disturbance signal which are applied on the fiber. The SNR of the recovered disturbed signal can be more than 30 dB. It is noted that no additional optoelectrical devices are required for the proposed method, indicating its promising future in practical applications.
Funding
National Natural Science Foundation of China (42327803, 62275097, 62205313); Major Science and Technology Projects of Wuhan (2023010302020030); Guangdong Basic and Applied Basic Research Foundation (2023A1515010965,2024A1515010017); Technology Innovation Project of Hubei Province (2022BEC003); Key R&D Program of Hubei Province (2023BAB062); Postdoctoral Fellowship Program of CPSF (2023M733301); Fundamental Research Funds for Central University China University of Geosciences (Wuhan) (CUGDCJ202204, G1323523064); Open Project Program of Wuhan National Laboratory for Optoelectronics (2023WNLOKF007).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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