1. Introduction

Due to increasing demand for structural health monitoring of civil infrastructure, a variety of fiber-optic sensors have been extensively studied [1–3]. In particular, distributed optical fiber sensors based on Brillouin scattering [4] have been receiving considerable attention due to their measurement capabilities for strain and temperature change. Hence, many types of Brillouin-based measurement schemes have been developed, including Brillouin optical time-, frequency-, and correlation-domain analysis (BOTDA [5–9], BOFDA [10–12], and BOCDA [13–17]), and Brillouin optical time- and correlation-domain reflectometry (BOTDR [18–22] and BOCDR [23–30]). Each scheme is being extensively studied and has its own advantages and disadvantages; here, we focus on BOCDR, which has a high spatial resolution and operates by single-end light injection.

Since the basic BOCDR system was first proposed in 2008 [23], numerous configurations have been implemented in order to improve its performance [24–34]. For example, the measurement range was elongated using temporal gating [24] and double modulation [25]; millimeter-order spatial resolution was achieved by use of a tellurite glass fiber [26] and by apodization [27]; and the strain dynamic range was extended using polymer optical fibers [28, 29]. In addition, one of the latest breakthroughs is phase-detection-based BOCDR [30], which enables a high sampling rate of >100 kHz per point. We have recently developed another high-speed configuration, motivated by previous implementations in the time domain [31–33], called slope-assisted (SA-) BOCDR [34], in which the spectral power of the Brillouin gain spectrum (BGS) is exploited to deduce the Brillouin frequency shift (BFS). This configuration can potentially allow for higher-speed operation than the phase-detection-based method, and for detection of not only changes in strain and temperature, but also optical losses, if necessary. Although the proof of concept for SA-BOCDR has been demonstrated [34], there is still much room for performance improvement. One fundamental issue that must be solved in order to characterize SA-BOCDR operation is the correspondence between the final system output (i.e., power-change distribution) and the actual BFS distribution. In standard BOCDR systems based on frequency information, these two distributions have been proven to be identical, in principle; however, in an SA-BOCDR system based on power information, no report has been made so far.

In this paper, we theoretically and experimentally show that the final system output of SA-BOCDR is generally different from the actual BFS distribution. When the strained section is sufficiently longer than the nominal spatial resolution, the power-change distribution almost reproduces the actual BFS (or strain) distribution. However, when the strained section is almost equal to or only a few times longer than the nominal resolution, the actual BFS distribution is not directly obtained (further data processing is necessary). We also show that even when the strained section is shorter than the nominal resolution some shift in the power change can be observed. This feature is unique to SA-BOCDR and potentially useful for practical applications.

2. Principle

In general, fiber-optic distributed Brillouin sensors operate based on the dependence of the BFS on strain and temperature [4]. As mentioned above, BOCDR is the only technique with intrinsic single-end accessibility and a relatively high spatial resolution. It resolves the sensing locations using a so-called correlation peak [23], which can be generated in the fiber under test (FUT) via sinusoidal frequency modulation of the laser output. The location of the correlation peak can be scanned for along the FUT by sweeping the modulation frequency f_m; thus, distributed BFS measurement becomes feasible. Sinusoidal frequency modulation results in the periodic generation of multiple correlation peaks along the FUT, and their frequency determines the measurement range d_m by [35]

In conventional BOCDR, the BFS at one sensing position is determined from a peak frequency after the acquisition of the whole BGS [23, 35], while in SA-BOCDR, it is obtained using the spectral power change at a fixed frequency, by exploiting its one-to-one correspondence with the BFS [34]. Consequently, the BFS distribution along the FUT is obtained as a power-change distribution in SA-BOCDR. The measurement range and the spatial resolution are given by the same equations as are used for standard BOCDR (Eqs. (1) and (2)). Note that with this scheme, loss points can also be detected in a distributed manner and the sampling rate can potentially be drastically enhanced (refer to Ref. 18 for the detailed operating principle of SA-BOCDR).

3. Simulation

We simulated the system output of SA-BOCDR. We assumed that one section of the FUT was uniformly strained. The magnitude of the strain was assumed to constantly lie below the upper limit of the linear region (~2000 µε) [34]. The length of the strained section was set to 0.25R, 0.5R, 0.75R, R, 2R, 5R, and 10R, where R indicates the nominal spatial resolution calculated using Eq. (2). First, the simulation results for the strain distributions acquired using standard BOCDR (deduced from the BFS distributions using the linear BFS-to-strain relationship) are shown in Fig. 1(a), which completely reproduce the actual BFS distributions. Next, the simulation results for the strain distributions obtained from SA-BOCDR (also deduced from the final power-change distributions simply based on the linear power-to-strain relationship) are shown in Fig. 1(b) (strained: 0.5R, R, 2R, 5R, and 10R) and Fig. 1(c) (strained: 0.25R, 0.5R, 0.75R, and R). Here, for simplicity, we neglected both the complicated longitudinal shape of the correlation peak and the influence of its sidelobes [36]; that is, the longitudinal shape of the correlation peak was approximated by a rectangular profile with a length of R. At the ends of the strained section (i.e., the boundaries between the strained and non-strained sections), the power change varied linearly with the length of R; consequently, each whole power-change distribution showed a trapezoidal shape (including triangular). Thus, we see that when the strained section is sufficiently longer than R, the power-change distribution almost reproduces the actual BFS distribution. In contrast, when the length of the strained section is approximately R or only a few times longer than R, the correct BFS distribution cannot be directly obtained (under the assumption that the strain is uniformly applied; however, the correct information can be easily derived). What is notable here is that even when the strained section is shorter than R, we can observe a trapezoidal-shaped shift in the power change and thereby obtain the information that some irregularity has occurred at that point. For instance, when the length of the strained section is 0.5R, a trapezoidal shape with a maximal power-change shift corresponding to half the amount seen with a strained section longer than R is observed. This “beyond-nominal-resolution” information, which neither standard BOCDR systems nor SA-BOTDR/BOTDA systems can provide (note that standard BOCDR systems determine the BFS as the frequency at which the highest spectral peak is observed; even when the local Brillouin spectrum includes a low spectral peak corresponding to strain, as long as this peak is lower than the initial spectral peak corresponding to the non-strained sections, it does not contribute to the derived BFS), will be of great use in practical applications. One important benefit is that using this effect, we can effectively elongate the measurement range of BOCDR, which generally suffers from the trade-off relation between the spatial resolution and the measurement range.

 

Fig. 1 Deduced strain distributions directly obtained from the final power outputs of (a) standard BOCDR and (b, c) SA-BOCDR. Note that the traces in (a) give the correct strain distributions.

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4. Experimental setup

The experimental setup for SA-BOCDR used to evaluate the aforementioned simulation results is shown schematically in Fig. 2(a), following the same basic setup as previously reported [34]. The light output from a 1.55 µm laser was divided into pump and reference beams. The pump beam was guided through a polarization scrambler (PSCR) to suppress the polarization-dependent signal fluctuations, then amplified to ~27 dBm using an erbium-doped fiber amplifier (EDFA) and injected into the FUT. The backscattered Stokes light was amplified to ~2 dBm using another EDFA. The reference beam was guided through a ~1-km-long delay line and amplified to ~1 dBm. The Stokes and the reference beams were then mixed (heterodyned), converted into an electrical signal using a photo diode (PD), and guided to an electrical spectrum analyzer (ESA). Using the narrow band-pass filtering function of the ESA (with the video bandwidth and resolution bandwidth set to 10 kHz and 10 MHz, respectively), the change in the spectral power at 10.81 GHz was sequentially output to an oscilloscope (OSC). An electrical amplifier was not used in this measurement.

 

Fig. 2 (a) Experimental setup for SA-BOCDR, which is basically the same as Fig. 3 of Ref. 34. EDFA: erbium-doped fiber amplifier, ESA: electrical spectrum analyzer, FUT: fiber under test, OSC: oscilloscope, PD: photo diode, PSCR: polarization scrambler. The blue curves indicate silica fibers, and the green lines indicate electrical cables. (b) Structure of an FUT with a relatively high spatial resolution (9.5 cm). (c) Structure of an FUT with a relatively low spatial resolution (19.6 cm).

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The FUT was a 13.0-m-long single-mode silica fiber with a BFS of 10.86 GHz at 1.55 µm at room temperature. Measurements were performed using two configurations: one for a relatively high spatial resolution and the other for a relatively low resolution (required to investigate the beyond-nominal-resolution effect). In the first, high-resolution configuration, strains of 750 µε and 1500 µε were applied to 5-cm-, 10-cm-, 20-cm-, 50-cm-, and 100-cm-long sections of the FUT, as depicted in Fig. 2(b). The modulation frequency f_m and amplitude ∆f were set to 7.11–7.31 MHz and 1.3 GHz, respectively, corresponding to the measurement range of 14.5 m and the theoretical spatial resolution of 9.5 cm according to Eqs. (1) and (2). In the second, low-resolution configuration, a strain of 1500 µε was applied to 5-cm-, 10-cm-, 15-cm-, and 20-cm-long sections of the FUT (see Fig. 2(c)). The modulation frequency f_m was swept in the same range (7.11–7.31 MHz), thus giving the same measurement range (14.5 m). The modulation amplitude ∆f was reduced to 0.7 GHz, corresponding to a theoretical spatial resolution of 19.6 cm. In both configurations, the repetition rate was set to 100 Hz, and 64 times averaging was performed on the OSC to improve the signal-to-noise ratio (SNR). The room temperature was 25 °C.

5. Experimental results

First, we present the experimental results with relatively high spatial resolution (9.5 cm). An example of the measured power change distribution (converted into strain) along the whole length of the FUT (with a 1500 µε strain applied to a 20-cm-long section) is shown in Fig. 3(a). At this scale, it appears that the correct amount of strain was detected at the correct location. The strain distributions measured when strains of 750 µε and 1500 µε were applied (magnified views around the strained sections), simply deduced from the power-change distributions based on the linear power-to-strain relationship, are shown in Fig. 3(b) and 3(c), respectively. Each distribution is shifted by 3000 µε, and the simulated data is indicated by dotted lines. The trends in the measured distributions agree well with the simulation results, including the case where the strained section is half the nominal spatial resolution. This indicates that our relatively rough simulation is almost sufficient to predict the experimental results, which is beneficial from the viewpoint of simulation cost. The discrepancy from the simulation results probably originates from signal fluctuations due to an insufficient SNR and the fact that the influence of the correlation peak sidelobes was not considered in the simulation process.

 

Fig. 3 Deduced strain distributions with a spatial resolution of 9.5 cm: (a) example measurement along the whole length of the FUT when a 1500 µε strain was applied to a 20-cm-long section, and magnified views when strains of (b) 750 µε and (c) 1500 µε were applied to 5-cm- to 100-cm-long sections. In (b) and (c), each distribution was shifted by 3000 µε, and the dotted lines indicate the simulated data.

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Subsequently, we performed similar experiments with a relatively low spatial resolution (19.6 cm) to evaluate the beyond-nominal-resolution effect. The magnified views of the strain distributions (simply deduced from the power-change distributions), measured when a strain of 1500 µε was applied, are shown in Fig. 4. As the strained section becomes shorter, the maximal power-change shift becomes smaller. The trend in the measured distributions is basically in good agreement with the simulation results. As the strained section is shortened further, the signal is buried by the noise. The standard deviation of the noise floor (power fluctuations corresponding to the strain of the non-strained sections) was calculated to be approximately 130 με in this measurement. This amount is theoretically obtained as the maximal strain when the strained section is 1.7 cm, which could be regarded as the shortest detectable length. Note that this value is influenced by various experimental parameters such as the amount of the actual strain, the number of averaging, the incident power, etc.

 

Fig. 4 Magnified views of the deduced strain distributions with a spatial resolution of 19.6 cm; a 1500 µε strain was applied to 5-cm- to 20-cm-long sections. Each distribution was shifted by 3000 µε, and the dotted lines indicate the simulated data.

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6. Conclusions

The final system output (i.e., the power-change distribution) of the SA-BOCDR system has been shown, both theoretically and experimentally, not to reproduce the actual BFS (or strain) distribution. When the strained section was sufficiently longer than the nominal spatial resolution, the system output almost corresponded to the actual BFS distribution. In contrast, when the length of the strained section was equal to or only a few times the nominal resolution, the BFS distribution was not reproduced correctly. These findings will be of great importance in improving the performance of SA-BOCDR systems in the future. In addition, we have also demonstrated that a strained section that is even shorter than the nominal resolution can still be detected as a shift in the power change. Beyond-nominal-resolution sensing of temperature change will be also feasible in the same way (cf. the influence of thermal expansion [37] is smaller than the noise floor fluctuations in this measurement). As for loss sensing, as it is point detection, the same effect cannot be observed (not available); in theory, the measured power gradually changes along the length equal to the nominal resolution. We anticipate that this feature, unique to SA-BOCDR, will be an attractive advantage in every application where even slight strain or heat cannot be permitted (regarded as irregular) because of the required high-level constancy, such as nuclear plant monitoring.