1. INTRODUCTION

With intensive research for more than three decades, optical fiber has fully established its advantages in distributed measurements of physical quantities, such as temperature, strain, pressure, magnetic field, and electric field [1–3]. Realization of distributed fiber sensing is generally based on the natural scattering processes presented in optical fibers, such as Rayleigh scattering [4,5], spontaneous Raman scattering [6,7], and spontaneous or stimulated Brillouin scattering [8–10]. In the case of Brillouin scattering, the backscattered signals can be interrogated in the time domain [11–15], frequency domain [16–18], or correlation domain [19–22], resulting in different types of distributed Brillouin fiber sensors with their respective sensing properties, such as ultra-long sensing distance [12], ultra-high spatial resolution [22], and ultra-low measurement uncertainty [23].

The performance of a Brillouin fiber sensor is mainly determined by the signal-to-noise ratio (SNR) of the Brillouin gain (or phase). Besides optimizing Brillouin scattering between pump and probe waves as well as Brillouin response detection schemes, the use of digital denoising offers another important way for SNR enhancements. Early studies focused on one-dimensional (1D) digital denoising, i.e., removing noises in either the horizontal dimension [corresponding to gain distribution versus distance [23,24]; see Fig. 1(a)] or the vertical dimension [corresponding to gain distribution versus scanning frequency or time at a fiber position [25]; see Fig. 1(a)]. Later, it was found that the redundancies contained in both dimensions of the measured raw data matrix can be used together to enhance the SNR [26]. This motivates the use of advanced two- and three-dimensional image denoising methods for noise removal, such as non-local means [26], block-matching and 3D filtering [27], and convolutional neural networks [28–30], resulting in impressive SNR enhancements of more than 10 dB. However, with a deeper understanding of the image denoising methods, it was recently found that the newly added image denoising action is nearly useless [31,32] [see Fig. 1(a)]. The reason is related to the fact that the image denoising action is redundant with the conventional signal processing that is composed of horizontal-dimension low-pass filtering and vertical-dimension spectrum fitting. Therefore, although the denoised Brillouin gain spectrum appears much “cleaner” than the raw one, the reduction of BFS measurement uncertainty is in fact marginal.

Fig. 1. Performance of image denoising for spectrum-fitting-based and slope-assisted Brillouin frequency shift (BFS) estimation methods. (a) Brillouin gain spectrum fitting for BFS estimation. For a Brillouin fiber sensor, the raw gain data measured at different scanning frequencies and positions forms an image. Recently, numerous image denoising methods have been used to denoise the raw data. Although image denoising can make the gain spectrum much “cleaner”, the BFS measurement uncertainty is not reduced no matter how much SNR enhancement is gained from image denoising. The image denoising is redundant with conventional signal processing, which is composed of horizontal-dimension low-pass filtering and vertical-dimension spectrum fitting. (b) Slope-assisted analysis of Brillouin phase-gain ratio for BFS estimation. The Brillouin phase-gain ratio is directly mapped to the BFS, thus the noise reduction via image denoising can directly reduce the measurement uncertainty.

Here, in order to make Brillouin fiber sensing truly benefit from image denoising, we employ the slope-assisted analysis of the Brillouin phase-gain ratio for BFS estimation, which relies on the direct mapping of the Brillouin phase-gain ratio to the BFS [33,34]. This approach, in contrast, reduces the measurement uncertainty as shown in Fig. 1(b). Compared to other slope-assisted methods based on the mapping via either Brillouin gain or phase, the mapping via the Brillouin phase-gain ratio can demodulate the BFS more precisely and robustly, being insensitive to pump power variations, pump depletions, or polarization-, temperature-, and strain-related gain (or phase) variations [33–37]. To implement the Brillouin phase-gain ratio measurement, both Brillouin gain and phase are needed. Since the SNR of the denoised data is determined not only by the image denoising methods but also the SNR of the raw data, it is essential to minimize the noise levels of raw Brillouin gain and phase before image denoising. In the case of Brillouin gain extraction, the balanced direct detection (BDD) provides the most precise raw Brillouin gain so far via common-mode noise subtraction [24]. Besides, in the case of Brillouin phase extraction, coherent detection is needed since direct detection throws away all the phase information while coherent detection provides both gain and phase information [38–43]. In recent years, coherent detection has been optimized, being robust to the phase noises introduced by group velocity dispersion (GVD) [40] and group delay jitter [41–43]. These advances in Brillouin gain and phase extraction reveal that ultra-precise raw Brillouin gains (phases) can be obtained by differentiating two signals with different Brillouin gains (phases) but the same noises [24,41,43]. The remaining challenge is how to design an optimal system for simultaneous differential Brillouin gain and phase extraction. The direct combination of the BDD with a coherent detection scheme increases the system complexity as well as raw data size. A digital coherent detection approach [43] has been demonstrated to extract differential Brillouin gain and phase simultaneously. Yet, it is quite computationally intensive compared to conventional analog coherent detection schemes [38–42], requiring a higher sampling rate as well as more complicated digital signal processing.

In light of these facts, we then propose an advanced coherent detection scheme, called a microwave-photonic interferometer (MPI), to realize ultra-precise raw differential Brillouin gain and phase detection. The MPI converts some amplitude and phase noises into common-mode noises contained in two microwave signals by means of a four-wavelength microwave-photonic link transmission. Those common-mode noises are further eliminated through an analog destructive interference process between the two microwave signals. The MPI does not need to increase the data sampling rate nor employ additional digital signal processing compared to a conventional analog coherent detection scheme. We verify the proposed method in a Raman-assisted Brillouin optical time domain analyzer (BOTDA) with a sensing distance of 117.39 km. Benefiting from the beating-noise-dominated ultra-precise raw Brillouin gain and phase extracted by the MPI, as well as the 11.2-dB (or 13 times) SNR enhancement realized by the image denoising, a measurement uncertainty of <2MHz over a measurement range of 80 MHz with a spatial resolution of 2 m is achieved for a single probe frequency scanning. We compare our MPI-based, slope-assisted, and image-denoising-enhanced sensing approach with the state-of-the-art scheme based on the BDD and conventional signal processing. A sensing speed acceleration of more than 20 times is achieved. We also replace the MPI by a state-of-the-art analog coherent detection scheme {i.e., phase-noise-insensitive coherent detection (PNI-CD) [10]}; the comparison results clearly show that the sensing speed cannot be accelerated because of the low raw data quality offered by the PNI-CD. Our work indicates that the slope-assisted method translates any dB SNR enhancement resulting from image denoising into measurement uncertainty reduction. As such, any powerful image denoising method developed for computer vision and artificial intelligence may be employed to boost the sensing performance. Furthermore, the MPI plays an important role in making a slope-assisted, image-denoising-enhanced Brillouin fiber sensor outperform the state-of-the-art.

2. RESULTS

A. Operation Principle of the MPI

For a coherent detection Brillouin fiber sensor, a microwave signal ?0(?) with a frequency of ?LO is transmitted over the sensing fiber, which resembles a microwave-photonic link [38,44]. Ideally, the amplitude and phase of ?0(?) should only change due to Brillouin scattering. However, in fact, many other factors would also modify the amplitude and phase of ?0(?), such as group delay, GVD, and RIN transfer. Here, these amplitude and phase changes are treated as noises. In Supplement 1 Table S1, we list the main noise sources in Brillouin fiber sensors. These noises can be classified into three categories: (1) amplitude noises ?(?), (2) phase noises ?(?), and (3) extra noises ?(?). The operation principle of the proposed MPI for eliminating amplitude and phase noises is shown in Fig. 2(a). A four-wavelength Brillouin probe counter-propagates with the Brillouin pump in the fiber under test (FUT). The generation of the probe using ?0(?) is detailed in the experimental setup as shown in Fig. 2(b). The longest and shortest probe wavelengths interact with the pump through stimulated Brillouin scattering (SBS) in the FUT. After transmission through the FUT, the upper and lower two optical wavelengths of the probe are separated by a dense wavelength division multiplexer (DWDM). Two replicas of ?0(?) are recovered from the beatings between the upper and lower two optical wavelengths in the photodetector1 (PD1) and PD2, respectively. They can be written as (see Supplement 1 Section 1.1)

where ?(?) is the amplitude noise, ?1(?) and ?2(?) are the phase noises induced by fiber GD jitter and GVD, ?SBS(?) and ?SBS(?) are the Brillouin gain and phase, respectively, ?P12−A1(?) and ?P34−A2(?) denote extra beating noises between probe wavelengths 1-2 and additive noise ?A1(?) and between probe wavelengths 3-4 and additive noise ?A2(?), respectively. In a microwave-photonic link, the phase noise is mainly caused by fiber group delay jitter and GVD and thus ?1,2(?)=?GD(?)+?GVD1,2 with ?GD(?)=2??1??LO, ?GVD1=−?GVD2=−2?2?2??LO(2?S+?LO), where ?1 is the inverse of group velocity, ?2 is the GVD parameter, ? is the sensing distance, and ?S is the scanning frequency [41,42].

Fig. 2. Operation principle and experimental setup. (a) Operation principle of the MPI. The probe composed of four optical wavelengths interacts with the pump through stimulated Brillouin scattering (SBS) in the sensing fiber. Two microwave signals (?1(?) and ?2(?)) resulting from the beatings between the upper and between the lower two optical wavelengths of the probe destructively interfere with each other, after equalizing their amplitudes meanwhile adjusting their phase difference being ?. Such a destructive interference process effectively eliminates a multitude of amplitude and phase noises and thus results in ultra-precise raw Brillouin gain and phase measurements. (b) Experimental setup of a Raman-assisted BOTDA based on the MPI. TLS: tunable laser source; PC: polarization controller; IM: intensity modulator; MG: microwave generator; SOA: semiconductor optical amplifier; PG: pulse generator; BPF: bandpass filter; DRP: depolarized Raman pump; WDM: wavelength division multiplexer; FUT: fiber under test; EDFA: erbium-doped fiber amplifier; PS: polarization scrambler; CIRC: circulator; DWDM: dense wavelength division multiplexer; PD: photodetector; MPS: microwave phase shifter; MA: microwave attenuator; LNA: low-noise amplifier; I/Q Dem.: in-phase/quadrature demodulator; LBF: low-pass filter.

Equation (1) indicates that ?PD1(?) and ?PD2(?) can be phase synchronized to a level independent of group delay, which fluctuates randomly due to environmental perturbations [45–47]. In addition, GVD leads to a ?S-dependent phase difference between ?PD1(?) and ?PD2(?). By amplitude and phase tuning to make the amplitudes of ?PD1(?) and ?PD2(?) equal while their phase difference is ? at a given ?S, the resulting two microwave signals ?1(?) and ?2(?) are then combined (destructively interfered) to get a differential signal ?Δ(?). The output of the interferometer, i.e., ?Δ(?), is sent to the radio frequency (RF) port of an I/Q demodulator as the RF input ?RF(?); meanwhile ?PD2(?) serves as the local oscillator ?LO(?) of the I/Q demodulator for demodulation. The Brillouin gain and phase can be demodulated by

where ?IMPI(?) and ?QMPI(?) are the output I-trace and Q-trace of the I/Q demodulator, respectively; ?LR is a constant phase offset introduced by electrical cable length difference (i.e., the difference between the cable lengths from the PD2 to the LO port and from the PD2 to the RF port of the I/Q demodulator). Further, ??MPI(?)=?IMPI(?)cos?(?LR)+?QMPI(?)sin?(?LR) and ??MPI(?)=−?IMPI(?)sin?(?LR)+?QMPI(?)cos?(?LR) are the noises contained in the demodulated Brillouin gain and phase, respectively, where ?IMPI(?) and ?QMPI(?) are noises contained in ?IMPI(?) and ?QMPI(?), respectively, and both of them originate from beating noises ?P12−A1(?) and ?P34−A2(?). Equation (2) clearly illustrates that the MPI is insensitive to both amplitude noise ?(?) and phase noises ?(?), resulting in ultra-precise raw Brillouin gain and phase measurements limited mainly by the beating noises.

B. High-Quality Raw Data Acquisition

Considering that the combination of the distributed Raman amplification and BDD provides state-of-the-art single-pulse Brillouin fiber sensing performance [24,48], we elaborately test our MPI-based sensing scheme in a Raman-assisted BOTDA. The experimental setup is shown in Fig. 2(b) (detailed in Appendix A). In order to maximally eliminate amplitude noises, ?01−?02=?0/2 is needed, where ?01 and ?02 are the transmission time delays from ?0(?) to ?1(?) and from ?0(?) to ?2(?), respectively; ?0 is the period of ?0(?). Clearly, destructive interference requires stable phase difference between ?1(?) and ?2(?) for each ?S. The measured phase difference between ?1(?) and ?2(?) in 100 consecutive measurements with a 5-s interval when ?S=8.41GHz is shown in Fig. 3(a). Note that the average phase difference is set to zero. As seen there, the stable phase difference condition is guaranteed by using the four-wavelength probe and recovering ?0(?) from the longer two and the lower two wavelengths, respectively. Further, the recovered two replicas ?1(?) and ?2(?) are chopped into pulse signals (detailed in Supplement 1 Section 1.1); ?01=?02 is achieved when the envelopes of ?1(?) and ?2(?) overlap with each other as shown in Fig. 3(b). This is realized mainly by matching the electrical cable lengths. Moreover, the microwave phase shifter (MPS) is finely adjusted to guarantee ?0/2 time delay between ?1(?) and ?2(?). Therefore, as shown in Fig. 3(b), the amplitude of their interference signal ?Δ(?) is largely reduced with respect to ?1(?) or ?2(?). In addition to the time-domain observation, the destructive interference is also confirmed in the frequency-domain measurement via an electrical spectrum analyzer. ?1(?) and ?2(?) are restored to continuous microwave signals in this case. As shown in Fig. 3(c), the carrier power suppression reaches 46.97 dB. The results observed in both time-domain and frequency-domain imply that the common-mode amplitude noise ?(?) is suppressed effectively. It is noteworthy that there always exist slight amplitude and phase mismatches between ?1(?) and ?2(?) even with precise calibration of transmission time delays. For example, the phase difference between ?1(?) and ?2(?) varies with ?S because of fiber GVD as shown in Fig. 3(d). A detailed discussion in Supplement 1 Section 2 shows that these amplitude and phase mismatches would only give rise to additional direct current (DC) components in the acquired I-traces and Q-traces. As such, their impacts can be eliminated simply by using DC-component-subtracted I-traces and Q-traces to calculate the Brillouin gain and phase through Eq. (2).

For a long-distance Raman-assisted BOTDA, the amplitude noise added to the probe is dominated by the RIN [49]. In addition, the additive noises are mainly composed of the double Rayleigh scattering (DRS) noise and amplified spontaneous emission (ASE) noise. The DRS noise is located near the carrier frequency [50] while the ASE noise spreads over the whole frequency band [51]. Thus, the optical spectra of the probe wave and the additive noises can be schematically represented by the red and blue lines in Fig. 4(a). For the coherent detection, the beating between the probe and the eight regions (marked by #1−#8) generates beating noises with a central frequency of 2.45 GHz and a bandwidth of 100 MHz, which affects the SNR since they are within the passbands of the BPF2 and BPF3. We denote the RIN, the beating noise between a probe wavelength and the DRS noise within a region, and the beating noise between a probe wavelength and the ASE noise within a region as ?RIN(?), ?P−DRS(?) and ?P−ASE(?), respectively.

Fig. 3. Destructive interference results. (a) Phase difference between ?1(?) and ?2(?) when ?S=8.41 GHz in consecutive 100 measurements with a 5-s interval. (b) Time domain and (c) frequency domain observation of the destructive interference. ?1(?) and ?2(?) are chopped into 20-ns pulses for the time-domain observation, and they are continuous waves for the frequency-domain observation. (d) Phase difference between ?1(?) and ?2(?) versus ?S. The blue curve is the theoretically predicted result, i.e., ?GVD1−?GVD2, and the red curve is the measured data.

Fig. 4. Precise raw Brillouin gain and phase measurements via the MPI. (a) Schematic of the spectra of the four-wavelength probe and the additive noises ?A1(?) and ?A2(?) after the transmission of the probe wave through the sensing fiber. RIN is the main amplitude noise added to the probe amplitude. In addition, DRS and ASE noises are the two main additive noises. Measured (b) Brillouin gain and (c) Brillouin phase versus distance traces for the phase-noise-insensitive coherent detection (PNI-CD) and the proposed MPI. The PNI-CD provides the best performance for a current analog coherent detection BOTDA. (d) Spectra of the noises contained in measured raw Brillouin gain for the PNI-CD and MPI. The green and black curves show the smoothed results. (e) Derived spectra of RIN ?RIN(?), probe-ASE beating noise ?P−ASE(?), probe-DRS beating noise ?P−DRS(?), and phase noise ?LO(?) [the noise term induced by the noises contained in ?LO(?) to the Brillouin phase for the PNI-CD]. The starting frequency is 2.45 GHz for ?P−ASE(?) and ?P−DRS(?) and is 0 Hz for ?RIN(?) and ?LO(?). (f) Spectra of the noises contained in measured raw Brillouin phase for the PNI-CD and MPI, along with the predicted results.

To measure ?RIN(?) introduced by the distributed Raman amplification, the PNI-CD scheme [10] as shown in Fig. S2 is performed. It provides the state-of-the-art performance for a current analog coherent detection BOTDA, as it is insensitive to fiber GD jitter and GVD. However, it suffers from RIN in measuring Brillouin gain [10]. The main difference between the MPI and PNI-CD is that the RF input of the I/Q demodulator [i.e., ?RF(?)] is ?Δ(?) for the MPI while is ?1(?) for the PNI-CD. The measured raw Brillouin gain and phase versus distance (or spatial-domain) traces at the pump-probe frequency difference of 10.86 GHz with 2048 averages for the PNI-CD and MPI is shown in Fig. 4(b) and Fig. 4(c), respectively. The MPI doubles the Brillouin gain with respect to the PNI-CD owing to the destructive interference. The notable variations of the Brillouin phase in the distance range of 0–40 km are caused by the variations of the BFS due to fiber coiling. Figure 4(d) shows the spectra of the noises contained in raw Brillouin gain spatial-domain traces for the two coherent detection schemes, which are calculated by performing fast Fourier transform to 10000-point raw gain data in the absence of SBS. All the spectra in Fig. 4 are normalized to the peak spectral amplitude of ??PNI(?) (the noise contained in the raw Brillouin gain for the PNI-CD). The MPI reduces the noise spectral amplitude compared to the PNI-CD in the whole 0–50 MHz frequency range because of RIN cancellation. As a result, the standard deviation of ??MPI(?) is reduced by 5.8 times with respect to ??PNI(?). The spectral amplitude of ??MPI(?) in the 2–50 MHz frequency range is nearly flat, thus indicating that it is govern by white ?P−ASE(?). In addition, ?P−DRS(?) dominates in the 0–2 MHz frequency shift range. Theoretically, ??PNI(?)=?P−ASE(?)+?P−DRS(?)/2+?RIN(?) and ??MPI(?)=2?P−ASE(?)+?P−DRS(?) (detailed in Supplement 1 Section 1.4.2). As a result, ??PNI2=??MPI2/2+?RIN2, where ??PNI, ??MPI, and ?RIN are the spectra of ??PNI(?), ??MPI(?), and ?RIN(?), respectively. Based on ??PNI and ??MPI [green and black curves in Fig. 4(d)], ?RIN can be derived [blue curve in Fig. 4(e)]. Besides, since the spectral amplitude of ?P−ASE(?) is flat versus frequency, we can represent its spectrum, say, ?P−ASE, by the red curve in Fig. 4(e). Then, the spectrum of ?P−DRS(?), say, ?P−DRS, can be derived according to ??MPI2=2?P−ASE2+?P−DRS2 [green curve in Fig. 4(e)].

In the case of Brillouin phase demodulation, the noises contained in ?LO(?) introduce an extra noise term ?LO(?) to the demodulated Brillouin phase for the PNI-CD. Based on the operation principle of the mixers, the spectrum of ?LO(?), say, ??LO, is deduced and shown as the black curve in Fig. 4(e) (see Supplement 1 Section 1.4.3). Then, the spectra of ??PNI(?) and ??MPI(?), i.e., the noises added to raw Brillouin phases for the PNI-CD and MPI, can be predicted according to ??PNI2=?P−ASE2+?P−DRS2/2+??LO2 and ??MPI2=2?P−ASE2+?P−DRS2 (see Supplement 1 Section 1.4.3), where ??PNI and ??MPI are the spectra of ??PNI(?) and ??MPI(?), respectively. The predicted results [the green and black curves in Fig. 4(f)] match well with the experimental results (the blue and red curves), indicating that the derived spectra of different noises shown in Fig. 4(e) are valid. The MPI enhances the SNR of raw Brillouin phase by ∼1.1dB compared to the state-of-the-art PNI-CD since it is insensitive to the noises contained in ?LO(?) (detailed in Supplement 1 Section 1.4.3). Therefore, the MPI achieves the best SNR performance in both Brillouin gain and phase extraction.

C. Static Sensing Scenario

In order to denoise a newly measured 1D 1×150000raw Brillouin gain or phase spatial-domain trace, we follow [26] to form 2D images by stacking together spatial-domain traces and the sliding temporal window is randomly set to 25 since we found that its change nearly does not affect the denoising performance. The denoising convolutional neural network (DnCNN) is used for image denoising, which is trained by following the training settings used in [52] for DnCNN-S. The noises used for training come from measured real noises instead of random Gaussian noises. The time cost of denoising a 2-D 25×150000 raw data image to get a denoised 1-D 1×150000 trace is only ∼0.55s because of GPU acceleration (NVIDIA GeForce RTX3090).

The raw Brillouin gain and phase spatial-domain traces along with the denoised traces in one measurement are shown in Figs. 5(a) and 5(b), respectively. The insets of the two figures show that the DnCNN does not blur the signal edges owning to its high-fidelity feature [28], such that the spatial resolution is not degraded. The spectra of the noises contained in raw and denoised data (only showing the gain case as an example) are shown as the blue and red curves in Fig. 5(c). Since the DnCNN can recognize and remove both probe-DRS and probe-ASE beating noises, it reduces the noise spectral amplitudes in the whole 0–50 MHz frequency range. As a result, the denoised data exhibits excellent short-term (determined by the high-frequency noises) and long-term (determined by low-frequency noises) stability as shown in Fig. 5(d), which is a magnified view of the gain traces in the distance range of 120–121 km as shown in Fig. 5(a). The strong low-frequency variation induced by probe-DRS beating noise is considerably eliminated, so that the denoised data varies much more smoothly versus distance compared to the raw data. The SNR enhancements gained by the DnCNN for the Brillouin gain and phase along the whole sensing fiber are further shown in Figs. 5(e) and 5(f), respectively. The SNRs are enhanced by ∼11.2dB for both Brillouin gain and phase in the 40–117 km range. Besides, in the 0–40 km range, the polarization-dependence of SBS causes non-negligible Brillouin gain and phase fluctuations, which cannot be recognized and removed by the DnCNN (detailed in Supplement 1 Fig. S13). Thus, the SNR enhancements in this distance range are smaller, which decrease from 11.2 dB to 5 dB when sensing position varies from 40 km to 0 km for both Brillouin gain and phase cases.

Fig. 5. Signal-to-noise ratio (SNR) enhancements via the DnCNN. Raw and denoised (a) Brillouin gain and (b) Brillouin phase versus distance. (c) Spectra of noises contained in raw and denoised Brillouin gain (normalized to peak spectral amplitude of the raw noise). (d) Magnified view of the gain traces in 120–121 km. The denoised data exhibits excellent short-term and long-term stabilities since the DnCNN can remove both low-frequency and high-frequency noises as shown in (c). SNRs of raw and denoised (e) Brillouin gain and (f) Brillouin phase versus distance. The SNR enhancements for both Brillouin gain and phase reach 11.2 dB.

The measured Brillouin phase-gain ratio versus pump-probe frequency difference at the beginning of the sensing fiber is shown in Fig. 6(a). This curve is first measured with a probe frequency scanning step of 4 MHz and further interpolated with a frequency grid of 0.01 MHz to offer a sufficient frequency resolution for BFS mapping. The phase-gain ratio does not change linearly versus frequency difference for a 20-ns pump [35,36]. Figure 6(b) shows the linewidth of the measured Brillouin gain spectrum along the sensing fiber. The linewidth remains nearly constant around 60 MHz [49]. Hence, we use the phase-gain ratio curve shown in Fig. 6(a) to demodulate the BFS for every sensing position. By fixing the pump-probe frequency difference at 10.86 GHz and using the slope-assisted analysis of raw Brillouin phase-to-gain ratio [33,34], the BFSs along the whole sensing fiber for the MPI without using the DnCNN are estimated. The average number in acquiring each raw Brillouin gain and phase trace is 2048. The estimated BFSs in 10 consecutive measurements are shown as the blue curves in Fig. 6(c). They fluctuate dramatically due to the low SNR, in contrast to the BFSs retrieved using the DnCNN [red curves in Fig. 6(c)]. These red curves also indicate that the BFS distribution along the sensing fiber is not uniform, which is caused by the pre-stressing force induced by fiber coiling. Figure 6(d) shows the zoom-in of Fig. 6(c) near the distal fiber end, where a hot spot with a temperature of 40°C is created by placing a 6-m fiber into a water bath. Owing to the use of the DnCNN, the temperature-induced BFS transitions are observed much more clearly with a spatial resolution of 2 m, which is estimated from the distance needed for BFS transition building up from its 10 to 90% in the rising and falling edges.

Fig. 6. Measurement uncertainty reduction via the DnCNN. (a) Measured Brillouin phase-gain ratio versus pump-probe frequency difference. (b) Measured Brillouin linewidth versus distance. Estimated BFS (c) along the whole sensing fiber and (d) near the distal fiber end in 10 consecutive measurements for the MPI with and without image denoising. Estimated BFS (e) along the whole sensing fiber and (f) near the distal fiber end in 10 consecutive measurements for the two sensing schemes based on the balanced direct detection (BDD) and the MPI. The combination of the BDD and distributed Raman amplification achieves the state-of-the-art single-pulse Brillouin fiber sensing performance and serves as a benchmark. (g) BFS measurement uncertainty versus distance. (h) BFS measurement uncertainty versus scanning frequency at 90 km. A BFS measurement uncertainty of <2MHz over a BFS offset measurement range of 80 MHz is realized for a single frequency scanning. This indicates a sensing speed acceleration of >20 times compared to the BDD-based scheme.

To assess the performance of our sensing strategy over the state-of-the art, the BDD is then performed as its combination with the Raman amplification represents the state-of-the art performance for a current single-pulse BOTDA as mentioned earlier (the experimental setup is detailed in Supplement 1 Section 1.3). In this condition, the BFS is estimated by a conventional spectrum fitting approach. We vary the pump-probe frequency difference from 10.76–10.96 GHz in a step of 4 MHz to measure the Brillouin gain spectrum. The average number is also set to 2048 as in the previous cases. In Fig. 6(e), the estimated BFSs in 10 consecutive measurements by the BDD-based scheme (blue curve) and MPI-based approach (red curve) are illustrated. Their zoom-ins near the distal fiber ends are shown in Fig. 6(f). As seen in Figs. 6(e) and 6(f), the average values obtained by the two techniques are comparable, indicating that our MPI-based sensing scheme does not cause extra measurement errors.

The BFS measurement uncertainty versus distance for the BDD and MPI schemes, with and without image denoising, is further shown in Fig. 6(g). The uncertainty at a fiber position corresponds to the standard deviation of the BFSs at that fiber position in the 10 consecutive measurements shown in Fig. 6(e). Such a BFS uncertainty evaluation approach is the same as the so-called sequential-domain approach in [32] and has proven reliable. For the MPI-based scheme, the BFS measurement uncertainty at 90 km is reduced from 8.5 MHz to 0.8 MHz (or by ∼10.6 times) owning to the DnCNN. It indicates that the 11.2-dB (or 13 times) SNR enhancements, as shown in Fig. 5, fully translates into the measurement uncertainty reduction [15]. Moreover, Fig. 6(h) shows the BFS measurement uncertainty at 90 km versus pump-probe frequency difference for the MPI-based approach using the DnCNN. A measurement uncertainty of less than 2 MHz over a BFS measurement range of 80 MHz is achieved for a single frequency scanning. This means that the MPI-based scheme with a frequency scanning step of 80 MHz provides a smaller measurement uncertainty compared to the BDD-based scheme with a frequency scanning step of 4 MHz. In other words, the sensing speed of the sensor is accelerated by more than 20 times over the state-of-the-art. In addition, extended experimental results for the BDD-based scheme are shown in Supplement 1 Fig. S14, which clearly show that the reduction of the BFS measurement uncertainty owing to the DnCNN is marginal when conventional signal processing is performed. In Fig. 7, we additionally show that the PNI-CD-based, DnCNN-enhanced, and slope-assisted sensing scheme cannot outperform the state-of-the-art because of the low quality of the raw data. The reason behind the experimental results can be explained from the standpoint of SNR. The SNR of raw Brillouin gain measured by the MPI is ∼5.8 times that measured by the PNI-CD. This means that the PNI-CD needs ∼34(5.8×5.8) times averaging to realize the same SNR of raw Brillouin gain. As a result, the sensing speed of the PNI-CD scheme is only ∼1/34 that of the MPI scheme and thus ∼20/34 that of the BDD scheme, indicating that it cannot outperform the state-of-the-art.

D. Dynamic Sensing Scenario

Since the sensing speed is significantly increased by our scheme, we further use it to track fast temperature change. In order to create dynamic temperature change, the same 6-m fiber segment in the static sensing case is heated from 25°C to 55°C through a water bath in the first stage. Then, it is put into the 20°C water in the second stage. At last, the fiber is put back in the water bath and heated from 25°C to 55°C in the third stage. 100 consecutive data acquisitions with 2048 averages are implemented in each stage (?S=8.41GHz and ?LO=2.45GHz) and thus we collect 300 raw Brillouin gain and phase spatial-domain traces to measure the temperature changes. The time needed for each data acquisition is 5 s; thereby the total time is 1500 s. The sizes of the raw gain and phase images are both 300×150000 and the sizes of the denoised images are both 276×150000 as the sliding temporal window is 25. Figures 8(a) and 8(b) show the raw and denoised gain images, while Figs. 8(c) and 8(d) show the raw and denoised phase images. To better observe the hot spot, only the results in the distance range of 117.31–117.39 km are shown. Figure 8(e) shows the estimated BFS changes of the hot spot through the raw Brillouin gain and phase. These traces fluctuate and overlap with each other due to the low measurement certainty. Figure 8(f) shows the BFS changes estimated through denoised Brillouin gain and phase. The temperature changes can now be visualized more clearly due to the considerably reduced measurement uncertainty. The BFS versus time profiles at the middle of the hot spot (i.e., 117.385 km) before and after the use of the DnCNN is further shown as the blue and red curves in Fig. 8(g). For comparison, we also use a low-pass 1D moving average filter with a window size of 25 to denoise the raw Brillouin gain and phase versus time profiles at 117.385 km. The estimated BFS change using the denoised data provided by the moving average filter is shown as the green curve in Fig. 8(g). Such a linear filter inevitably introduces time delay and edge blurring. In contrast, the DnCNN avoids these issues, as shown as the red curve in Fig. 8(g). This is essential for Brillouin fiber sensors, ensuring that image denoising does not compromise the real-time sensing capabilities or introduce measurement errors, thereby enabling a robust sensing speed acceleration.

Fig. 7. Impact of raw data quality on BFS estimation. Estimated BFSs along the whole sensing fiber with an average number of 2048 for the MPI scheme and average numbers of (a) 2048 and (b) 2048×20 for the PNI-CD scheme. (c) Zoom-in results of (b) in the distance range of 89–91 km (worst SNR regions). The reference shown as the black curves is the average trace of the 10 BFSs versus distance traces for the BDD scheme shown as the blue curves in Fig. 6(e). The PNI-CD scheme cannot outperform the MPI scheme even if the average number increases to 2048×20 in acquiring raw data. Thus, the sensing speed cannot be accelerated compared to the state-of-the-art BDD scheme.

Fig. 8. Dynamic sensing performance. (a) Raw and (b) denoised Brillouin gain as well as (c) raw and (d) denoised Brillouin phase images. For the sake of clarity, only the results in the distance range of 117.31–117.39 km are shown. Estimated BFS changes in the vicinity of the hot spot through (e) raw and (f) denoised Brillouin gain and phase. (g) Estimated BFS versus time profile at the middle of the hot spot with and without image denoising. For comparison, the low-pass 1D moving average filter with a window size of 25 is also performed. This result shows that the DnCNN does not cause time delay and edge blurring.

3. DISCUSSION AND CONCLUSION

The MPI uses the destructive interference between two replicas of a microwave signal sent through a microwave-photonic link to eliminate amplitude and phase noises. For the Raman-assisted BOTDA, noises induced by fiber GD jitter and GVD, Raman pump RIN transfer, and local oscillator phase noise transfer are all converted into common-mode noises, and thus all of them have been successfully eliminated by the MPI. This enables the most precise simultaneous raw differential Brillouin gain and phase extraction to date. Additionally, we further show the potential of the MPI in eliminating other noise sources, as summarized in Table S1.

In order to further improve the precision of Brillouin gain and phase, the DnCNN is used for digital denoising of raw data. It learns the all-frequency-band features of the noises via a training process, and then it exhibits attractive and desirable denoising advantages, including high SNR enhancement of >10dB, no time delay, no edge blurring, capability of removing white probe-ASE beating noise and non-white probe-DRS beating noise, and negligible signal processing time of 0.55 s because of GPU acceleration. This is quite needed for a slope-assisted method since the BFS is directly mapped from the denoised data, which means that any signal distortion or time-delay would impair sensing performance including measurement error, measurement uncertainty, and real-time capabilities. Except for the DnCNN used here, numerous powerful image denoising methods have been proposed owning to the rapid development of computer vision and artificial intelligence, such as graph neural networks [53] and generative adversarial networks [54]. These advanced denoising methods can be readily used in Brillouin fiber sensors to enhance the sensing performance.

The high immunity of the MPI to environmental perturbations makes its real deployments in numerous practical applications possible. In addition, since the sensing speed can be considerably enhanced, it would be a suitable choice for the monitoring of dynamic deformations of large infrastructures, such as bridges, railway tracks, freeways, and high-voltage lines. Both human activities (such as the passages of truck and train) and natural phenomena (such as rain and wind) apply dynamic deformations to them. The successful measurements of those deformation dynamics can provide valuable information for their structural health monitoring. The sensing speed is ultimately determined by residual noises, such as polarization noises and probe-ASE beating noises. Some current Brillouin scattering optimizing methods provide the potential of reducing those noises, such as polarization diversity [13,55,56], lumped amplification [48], and pulse coding [57]. Their combination with the MPI may further enhance the sensing speed.

Besides the Brillouin fiber sensors we studied here, SBS in optical waveguides resulting from coherent light-sound coupling also enables a wide range of other applications, such as lasers, filters, and microwave synthesizers [58]. The material platforms of SBS have also been extended from the commonly used silica optical fiber to chalcogenide, silicon, and dilute nitride [58]. To reveal interesting Brillouin properties and develop useful technical applications, it is crucial to precisely measure waveguide Brillouin responses in terms of gain, phase, or sometimes both. Given that MPI is insensitive to noises from laser and microwave sources owing to destructive interference, we envision it could precisely measure Brillouin properties of integrated optical waveguides, particularly those with very low backward Brillouin gain coefficients [59,60].

In conclusion, we proposed the MPI for precise raw Brillouin response detection insensitive to a multitude of amplitude and phase noises via destructive interference. It extracted ultra-precise differential raw Brillouin gain and phase data in a Raman-assisted BOTDA. Accurate BFS estimation through the slope-assisted analysis of the Brillouin phase-gain ratio based on the image-denoised data was then achieved. The noise reduction via image denoising clearly leads to measurement uncertainty reduction. Our approach truly makes Brillouin fiber sensing benefit from image denoising, and thus links Brillouin fiber sensing with any other advanced image denoising method. In addition, the MPI method minimizes the variance of the raw data, which is quite important in making an image-denoising-enhanced, slope-assisted Brillouin fiber sensor outperform the state-of-the-art. The MPI may also be adapted to precisely measure backward Brillouin properties of many other optical waveguides, and contribute to the development of new Brillouin fiber optics and integrated photonic platforms.