Brillouin optical time-domain analysis (BOTDA) is a performing tool to monitor physical quantities at each point along a sensing fiber [1,2]. The Brillouin frequency shift (BFS) at any fiber position, depending linearly on the local temperature/strain change, is estimated by postprocessing the local Brillouin gain spectrum (BGS) reconstructed by scanning the pump–probe frequency difference [3,4]. The BGS parameters like the peak gain and the full width at half-maximum (FWHM), determine the BFS accuracy [3]. Since the BGS profile results from the convolution between the pulse power spectrum and the fiber natural Brillouin spectrum [5], the use of a shorter pump pulse leads to a broader FWHM and lower peak gain, drastically impairing superlinearly the sensor performance. A limit for a good BFS accuracy is therefore set for conventional BOTDAs when the pump pulse and natural BGS show a comparable FWHM, corresponding to a pump duration of 12 ns, or about 1 m spatial resolution (SR). This sets a constraint when applying BOTDA to applications requiring sharp (submeter) SRs. A large quantity of advanced time-domain [6–10] and correlation-domain techniques [11,12] has been proposed to overcome this trade-off between SR and BFS accuracy, compromising on other specifications such as measurement time and/or sensing range.

In this Letter, we propose and demonstrate a simple alternative to retrieve a targeted SR by simply postprocessing measurements obtained using a conventional BOTDA with a fixed long pump pulse, substantially longer than the acoustic response time. Such a postprocessing is based on the concept of deconvolution [13], performed via fast Fourier transform (FFT), thus being fast in processing time. The proposed technique circumvents the negative impact of the acoustic inertial response, overcoming the traditional trade-off between SR and BFS accuracy, while keeping the same measurement time and sensing range. The technique is only compromised by the predictable BFS errors appearing prior to hotspots, which may be reduced by using more sophisticated algorithms. To verify the feasibility of the proposed approach, SRs of 2 m, 1 m, and 0.2 m are experimentally demonstrated by postprocessing measurements obtained from standard BOTDA with long pump pulses.

The working principle of the proposed approach is elaborated as follows: in a standard BOTDA, the sensing fiber is interrogated by a CW probe and an isolated pump pulse $p(t)$, where the pulse duration ${T_p}$ determines the SR. In this case, the obtained time-domain trace ${r_{\!p}}(t)$ is represented by the linear convolution between $p(t)$ and the fiber impulse response $h(t)$, merged with an additive noise $e(t)$,

Due to the inertial feature of the acoustic wave in BOTDA, each delta function in $d(t)$ contributes differently, following an envelope (red dashed curve in Fig. 1) that can be analytically expressed as [9]

 

Fig. 1. Illustration of the pulse decomposition concept and the equivalent convolution process.

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Fig. 2. (a) Simulated BGS using the proposed technique and conventional BOTDA. (b) Improvement factors on BFS accuracy (blue) and SNR improvement (red) as a function of spatial resolution, provided by the proposed technique with respect to the classical approach. (c) Envelope function of $d(t)$ at different pump–probe frequency offsets.

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By performing such a postprocessing on each time-domain BOTDA trace, BGS at each fiber location can be reconstructed. Such postprocessed BGS exhibit a Lorentzian profile with a linewidth equal to the Brillouin natural value of ${\sim}{30}\;{\rm MHz}$, and the peak Brillouin gain depends linearly on the target SR, as confirmed by the simulated results shown in Fig. 2(a), for 2 m and 1 m SRs (blue and red solid curves) retrieved from 6 m SR data. This feature is crucially advantageous over the conventional single-pulse BOTDA with the same SR, for which the corresponding BGS [black and green dashed curves in Fig. 2(a)] present a much smaller amplitude and a wider FWHM, globally giving a BGS broadening once convolved with the pump spectrum.

Notably, after performing the postprocessing based on Eq. (4), the noise is actually amplified by a factor of $\sqrt {{\rm mean}({1/D{{(f\,)}^2}})}$ with respect to the original noise level [14]. This noise amplification factor is calculated to be ${\sim}{1.5}$ for any retrieved SR, which represents a minor penalty that only partially impairs the aforementioned advantages provided by the proposed technique. Taking all these aspects into account, the SNR and the BFS accuracy improvements over the conventional single-pulse BOTDA are shown as a function of SR in Fig. 2(b). Larger improvements can be obtained for sharper SRs that are more affected by the acoustic transient effects.

Note that systematic errors on BFS determination may appear in fiber sections ahead of hotspots by a distance equal to the width of the original long pulse, as will be shown in the experimental part of this paper. This is because the envelope function [Eq. (4)] used in this method only describes precisely the situation at the Brillouin resonance frequency, while the functional dependence for detuned frequencies are actually slightly different, as shown in Fig. 2(c). These systematic errors turn out to be empirically up to 3 MHz by repeated tests with different SR over large temperature steps. This may not be of crucial importance for some applications, and such predictable errors may be eliminated by combining one more measurement, as will be shown in the experimental part. Besides, since the error locations can be identified from the locations of hotspots, it is possible to process and reduce those BFS errors using more sophisticated algorithms.

Validation tests using a standard dual-sideband BOTDA are carried out to verify the feasibility of the proposed technique. Results are mainly investigated around a 2-m-long hotspot at 40°C, placed at the end of a 47.52-km-long sensing fiber at room temperature (27°C). First, a classical measurement is performed using a 60 ns long pump pulse, corresponding to an original SR of 6 m. Each temporal trace is averaged 1024 times. The 2D-mapping of the Brillouin gain distribution, as a function of fiber position and scanning frequency, is shown in Fig. 3(a), where the 2 m hotspot cannot be clearly resolved. Then, the sharpening to a 2 m SR is carried out using the proposed postprocessing, resulting in a good retrieval of the hotspot characteristics, as can be observed in Fig. 3(b). The retrieved BGS exhibits a Lorentzian shape with FWHM of 34 MHz, as proved in Fig. 4(a) for two typical fiber positions (i.e., inside and 2 m away from the hotspot), in good agreement with the aforementioned theory. The estimated BFS profile around the hotspot is shown by the blue curve in Fig. 4(b), with the notable exception of BFS errors appearing over a short interval ahead of the hotspot, as explained above. Then, another measurement is performed using a 120 ns pulse, and the estimated BFS is shown by the red line in Fig. 4(b). The distorted region is clearly moved ahead by the distance equal to the width of the original long pulse. The distortion can therefore be eliminated by combining the results obtained using two long pulses of different duration at the expense of doubled measurement time. The resulting BFS profile without distortion is shown as a red line in Fig. 4(c), which matches well with the reference curve (blue) taken by a standard BOTDA with 2 m SR.

 

Fig. 3. Brillouin gain distribution versus frequency and fiber position with (a) original 6 m SR and (b) retrieved 2 m SR.

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Fig. 4. BGS profiles inside and outside the hotspot with (a) 2 m and (e) 1 m SR retrievals. (b) BFS profiles of 2 m retrieval from 60 ns and 120 ns pump pulses. (c) BFS profiles obtained combined 2 m retrieval and 20 ns pump pulse. BFS uncertainties for (d) 2 m and (f) 1 m SRs.

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To further validate the performance improvement, the obtained BFS uncertainty along the fiber in the case of 2 m SR retrieval is shown by the red curve in Fig. 4(d), which outperforms the one using standard BOTDA (black) by a factor 1.56, in good agreement with the theoretical prediction shown in Fig. 2(b). To demonstrate the flexibility of the proposed technique, 1 m SR is retrieved using the same raw data at 6 m SR. Fig. 4(e) shows the retrieved BGS for 1 m SR, the gain being reduced by half compared to the BGS at 2 m SR and the FWHM keeping unchanged. Then, the resulting BFS uncertainty is compared with a conventional BOTDA with 1 m SR, as illustrated in Fig. 4(f), showing a 3.5 times improvement matching again the prediction in Fig. 2(b).

In order to validate the capability of a submetric SR retrieval, the proposed method is compared with a differential pulse-pair (DPP) technique [7], by carrying out another set of experiments, using a 10.22-km-long sensing fiber with a 20-cm-long hotspot (55°C) placed at the fiber far-end. A polarization switch (PSw.) is used to mitigate the polarization fading effect. The long and short pulses for DPP technique are set to 42 ns and 40 ns, respectively, corresponding to a 20 cm SR after the differentiation process. Each temporal trace is averaged 512 times. The same SR is realized by applying the proposed postprocessing on a single dataset measured using a 40 ns pulse, resulting in a halved measurement time compared to the DPP technique. As expected, the BGS retrieved by the proposed technique shows a FWHM of 34 MHz, as shown in Fig. 5(a) for two typical fiber positions (i.e., inside and outside the hotspot). The obtained BFS profiles around the hotspot for both techniques are compared in Fig. 5(b), showing a good agreement except over the interval subject to systematic BFS errors. Such errors do not show up clearly at other fiber positions although the BFS is nonuniform along the fiber (i.e., equivalent to multiple hotspots), as exemplified by the inset in Fig. 5(b).

 

Fig. 5. (a) BGS profiles inside and outside of the hotspot with 20 cm SR retrieval. (b) BFS profiles obtained by 20 m retrieval and DPP. (c) BFS uncertainty for 20 cm SR with PSw.

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The BFS uncertainty at the fiber far-end resulting from the proposed technique is illustrated by the red curve in Fig. 5(c), showing a 1.7-fold improvement over the DPP technique (blue). This difference in BFS accuracy is assigned to the imperfect compensation of polarization fading that varies during long-term measurements, which turns out more detrimental in DPP due to the differentiation operation that enhances this negative impact. On the contrary, the proposed technique actually alleviates this imperfection: the polarization fading is mitigated in the same proportion as the reduction of signal from the coarse SR to the sharper SR. This bonus in polarization fading suppression can be further demonstrated by substituting the polarization switch by a polarization scrambler (PSc.) that causes a larger polarization uncertainty. Keeping the aforementioned experimental parameters, the 2D-mapping of the Brillouin gain distribution obtained from the DPP technique and the proposed technique, both with PSc., are, respectively, shown in Figs. 6(a) and 6(b). A worse measurement quality is clearly observed using DPP. The BFS uncertainty near the fiber far-end obtained by the two techniques is illustrated by the red and blue curves in Fig. 6(c), showing a 3 times difference. Notably, the proposed technique can provide a similar BFS uncertainty using PSw. and PSc., as verified by the similar red curves in Figs. 5(c) and 6(c). This offers a flexibility in the choice of polarization diversity components, and a better robustness when performing long-term measurements.

 

Fig. 6. The Brillouin gain distribution as a function of frequency and fiber position using PSc. obtained by (a) DPP and (b) 20 cm SR retrieval. (c) BFS uncertainty for 20 cm SR with PSc.

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In conclusion, a novel postprocessing method for flexibly retrieving a chosen SR based on standard BOTDA has been proposed and demonstrated by proof-of-concept experiments, offering the following advantages:

All the aforementioned advantages come at the expense of systematic BFS errors up to 3 MHz appearing over short fiber sections ahead of sharp transitions, which may be overcome using more sophisticated postprocessing algorithms.