1. Introduction

The Brillouin Optical Time-Domain Analysis (BOTDA) technique is based on the interaction between two frequency-shifted, counter-propagating optical waves. By scanning the frequency shift between the two waves, the Brillouin Gain Spectrum (BGS) is retrieved by recording the amplification of the wave at lower frequency (the probe wave). The peak frequency of the BGS, known as Brillouin frequency shift (BFS), is related to the temperature and strain conditions of the optical fiber. Spatial resolution is achieved by pulsing one of the two waves, so that the arrival time of the backscatter signal is easily associated to a specific position of the fiber.

In the classical BOTDA configuration, the acquisition speed is limited by various factors such as the time of flight of the pulses, the amount of averaging, and the switching speed of the microwave source employed to spectrally shift the two waves [1]. Much higher acquisition rates can be achieved by using the Slope-Assisted BOTDA (SA-BOTDA) method, in which the dynamic changes of the BFS are recorded by a probe wave spectrally tuned on the slope of the (static) BGS. In the standard SA-BOTDA configuration, the probe signal has a fixed frequency, so that it cannot sample the BFS dynamic changes in those positions where the static BFS largely deviates from the average BFS of the fiber [2]. In the more elaborated SA-BOTDA configuration described in [3], a specially synthesized probe wave is employed to interrogate fibers with arbitrary distributions of the BFS. While Slope-Assisted techniques are capable of very fast (tens or even hundreds of kHz) acquisition rates, they are limited by the extent of the linear section of the BGS slope (∼600 με @ a 10ns pump pulse). Furthermore, extracting the BFS only from the slope of the BGS, rather than from the whole spectrum, leads to increased detrimental effects from laser phase noise [4], and prevents from the use of advanced signal processing techniques exploiting the redundancy of position-frequency gain map measurements [5]. Furthermore, the measurand information is obtained from intensity measurements, so it is intrinsically sensitive to pump power variations. For these reasons, a fast, frequency scanning BOTDA configuration is highly desirable for distributed dynamic sensing applications. In [1], Peled et al. reported a fast BOTDA technique based on the use of an arbitrary waveform generator for fast switching the probe frequency. In the fast BOTDA method, the acquisition rate is solely limited by the number of averages, the round trip time of flight and the frequency granularity (i.e. the frequency step between adjacent probe frequencies). Full scans of the BGS on a 100m long fiber at an impressive rate of 8.3kHz have been reported [1]. Using a similar set-up, polarization-independent dynamic measurements have been reported in a 145-m long fiber at an acquisition rate of 9.7 kHz [6]. While being capable of very high acquisition rates, the fast BOTDA method requires a high-bandwidth arbitrary waveform generator and/or microwave signal generator with vector modulation capabilities, in order to achieve fast (∼ns), step-like scanning of the probe frequency. These are quite complex and expensive instruments.

In this manuscript, we report a fast BOTDA technique based on the use of a frequency swept microwave source. The proposed method has distributed sensing capabilities, while potentially keeping the same acquisition rate of previously reported fast BOTDA configurations. In the following, we provide a detailed description of the method and its experimental validation. Comparison with standard SA-BOTDA is also provided, demonstrating the slightly better resolution of the proposed method.

2. Method

In the proposed method, here referred to as sweep-BOTDA, fast scanning of the BGS is achieved by use of a microwave source with linear frequency sweep capabilities. The basic idea of the proposed method is illustrated in Fig. 1. The RF generated by the synthesizer, which modulates the probe wave, is made to vary linearly in a proper range (from $f_{start}$ to $f_{end}$) with a sweep time ($t_{end}- t_{start}$) corresponding to the acquisition time of the full BGS. By making the frequency sweep synchronous to the injection of the first pump pulse, a full measurement of the BGS is achieved with a frequency granularity defined by the sweep time and the pulse repetition rate. In detail, the pulse repetition rate is limited by the time of flight, thus by the fiber length. For a given repetition rate, the frequency granularity of the acquired traces will be determined by the slope of the frequency sweep.

 

Fig. 1 Schematic illustration of the sweep-BOTDA method: the BOTDA waveforms are acquired during the frequency sweep of the microwave source.

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As it is obvious from Fig. 1, increasing the slope of the frequency sweep will result in a shorter acquisition time, at the expense of a coarser granularity in the BGS acquisition. From a practical point of view, some averaging of the acquired waveforms is often required in order to reach a satisfactory signal-to-noise ratio [7]. To this aim, a digital signal processing of the acquired signals can be properly realized, so that N successive acquisitions are averaged and associated to a single trace of the frequency-position Brillouin gain map. In this case, the frequency granularity in the BGS scanning will be also determined by the averaging number. In particular, the relationship between the slope of the frequency sweep and data acquisition parameters is as follows:

3. Experimental results

The experimental scheme used to implement the sweep-BOTDA method is illustrated in Fig. 2. The set-up is a typical BOTDA scheme, except from the use of a microwave source with linear sweep capabilities (Vaunix model LMS-123). For the chosen synthesizer, the frequency sweep is a digitally generated sweep, where the step size is internally calculated based on the start/stop sweep frequencies and the sweep time. The sweep is then further linearized through the effective low-pass filter effect of the phase-locked loop (PLL). The FM microwave signal is applied to the electro-optic modulator EOM1, operated with the carrier suppressed. The lower optical sideband generated by EOM1 acts as the (frequency-modulated) probe wave, while the upper sideband is filtered out before detection through the narrowband optical filter FBG. The minimum duration of the RF frequency ramp is 1 ms, while the covered range is 8 – 12 GHz. The polarization scrambler (PS) operates at a fixed frequency of 700 kHz. To avoid imperfect compensation of polarization fading, the repetition rate of the pump pulses should be lower than the scrambling frequency [4]. Thus, for a fiber length less than ∼140 m, the pulse repetition rate in our set-up is limited by the scrambling frequency, rather than by the time of flight. To avoid this limitation, a scheme based on dual orthogonal pump or probe optical fields [6, 9, 10] may be used, instead.

 

Fig. 2 Experimental setup used for sweep-BOTDA measurements: IM: electro-optic modulator, EDFA: Erbium-doped fiber amplifier, PS: polarization scrambler, PD: photodiode, FBG: fiber Bragg grating.

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As a demonstration of the capabilities of the proposed method, we show in Fig. 3(a) the Brillouin gain map measured for a 100m long fiber and a spatial resolution of 1 m (10-ns pulse duration). The power of pump and probe waves were set to 13 dBm and 0 dBm, respectively. The pulse repetition rate was set to 700 kHz, while the number of averages was 256. The slope of the frequency sweep was set in order to achieve a frequency step $\delta =5 MHz$, thus $S_{sweep}=\delta \times f_{rep}\times \frac{1}{N_{av}}=13.7 MHz/ms$. With a spectral scanning range of 450 MHz (from 10550 MHz to 11000 MHz), that resulted in a sweep time of ∼33 ms (for a total of 91 scanned frequencies). Note that, in Fig. 3 the initial and final portions exhibiting a different BFS correspond to two short pigtails spliced to the fiber under test. It is useful to compare the BFS profile obtained by processing the data shown in Fig. 3(a), with the one obtained by repeating the same measurement with a conventional, frequency stepped probe wave (Fig. 3(b)). It is seen that a good agreement exists between the two measurements. It is worth to underline that, while the acquisition time was only 33 ms for the sweep BOTDA measurement, the conventional BOTDA measurement required an acquisition time of about 0.5 seconds, mainly limited by the settling time of the microwave source (about 5 ms per scanned frequency, including the time required to transfer the command from the PC).

 

Fig. 3 (a) Brillouin gain map acquired by using a microwave source sweeping from 10550 MHz to 11000 MHz, in a sweep time of 33 ms; (b) BFS reconstruction obtained by processing the data shown in (a), or the data acquired using a conventional (frequency stepped) BOTDA.

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In order to analyze the influence of the sweep time on the accuracy of the measurements provided by the sweep-BOTDA method, several acquisitions of the BFS profile along the same 100m-long fiber were taken at various frequency steps $\delta$ (i.e. various sweep times according to Eq. (1)). Let us remind that, for a given pulse repetition frequency and averaging number, the frequency span associated to each acquired trace is univocally related to the slope of the FM microwave signal. Increasing this slope, the Brillouin gain spectra are acquired with a coarser granularity, with an expected decrease in BFS estimate accuracy: In [7], Soto et al. have theoretically and experimentally demonstrated that, in BOTDA measurements the error in the BFS estimate increases with the square root of the frequency step. In the sweep-BOTDA, a coarser granularity also implies a larger frequency span covered by the probe wave during the acquisition of each single trace. We report in Fig. 4 the BFS error at different frequency steps and averaging number, for both sweep-BOTDA and conventional BOTDA measurements. The frequency error was determined, in each case, by taking the standard deviation of the BFS in a generic position of the fiber in 200 consecutive measurements. The data related to each conventional BOTDA measurement set has been fitted by a square root function [7]. It is seen that the sweep-BOTDA offers performance similar to the conventional BOTDA, even for large frequency steps. The deviation of the BFS error from the square root fitting function, in case of conventional BOTDA measurements, is 0.020 MHz, 0.015 MHz, or 0.020 MHz (for 256, 512 and 1024 averages, respectively), while the corresponding values for the sweep BOTDA measurements are 0.020 MHz, 0.014 MHz, and 0.011 MHz. From Fig. 4 we see that the deviation is especially evident for lower frequency steps, mainly due to the difficulty in keeping the temperature of the fiber constant during the acquisition of the whole data set.

 

Fig. 4 BFS error as a function on frequency step and number of averages, as calculated from a set of 200 consecutive measurements using the conventional BOTDA method (circles) or the sweep-BOTDA method (squares). The solid lines are the square root fitting functions.

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Another important issue is the linearity of the frequency sweep generated by the microwave source: any deviation from the linearity in the generated ramp will result in a distortion of the retrieved BGS, with consequent decrease of accuracy in the determination of the BFS. In order to analyze the linearity of the ramp generated by our microwave source, in Fig. 5 we compare the BGS acquired at a generic position of the 100m fiber using the conventional (frequency-stepped) BOTDA, with the one acquired at the same position by the sweep-BOTDA method with 1024 averages and various sweep rates (i.e. various acquisition times). In each case, the pulse repetition rate was adjusted in order to have, in all cases, a frequency step $\delta =5 MHz$. As it is seen, the various spectra appear very similar, so that deviation from linearity of the microwave sweep can be considered negligible in all considered cases. In particular, the normalized cross-correlation between the reference BGS (the one captured using the conventional BOTDA) and the BGS acquired using the sweep-BOTDA, was larger than 0.994 in all considered cases.

 

Fig. 5 BGS acquired at a generic position of the 100-m long fiber, using the conventional BOTDA, or the sweep-BOTDA at various sweep rates. In all cases, sweep-BOTDA measurements were taken with a frequency step $\delta =5 MHz$.

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As a demonstration of the dynamic sensing capabilities of the proposed method, we have used it to capture the vibrating strain along a 1-m long cantilever beam. To this aim, the central portion of a 30-m long fiber was epoxy-glued along the surface of the cantilever. The latter was put in free vibration during the measurements. For each acquired temporal frame, the microwave frequency was swept from 10800 MHz to 11050 MHz in 76 ms, thus providing a frequency step $\delta =10MHz$ with $N_{av}=2048$ (26 scanned frequencies). The spatial resolution was set to 1m as usual. While a sweep duration of 76ms would allow for an acquisition rate as high as 13Hz, the actual rate was only 11.5Hz due to the extra time required to transfer (and store) each acquired Brillouin gain map to the host PC. This extra time, which may become relevant for faster BOTDA measurements, could be avoided by using a high-bandwidth memory directly connected to the FPGA for temporary storage of the acquired data. We report in Fig. 6 the dynamic strain acquired along the cantilever beam, or in a static section of the fiber (i.e. far away from the vibrating cantilever), as obtained applying a conventional Lorentzian fitting to each BGS and using a typical BFS/strain transduction coefficient of 0.05 $MHz/\mu \epsilon .$ The figure clearly shows the damped oscillations of the cantilever while vibrating at its natural frequency (∼1.48Hz). The measurement frequency noise, evaluated by determining the standard deviation of the BFS at the static segment, was found to be as low as 3 με.

 

Fig. 6 Dynamic strain acquired along the vibrating cantilever (blue line) or over a static position (red line), as determined from the peaks of Lorentzian fits to the BGSs of each time slot.

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It is useful to compare the performance of the sweep-BOTDA to those of the standard slope-assisted BOTDA method. To show this, we have repeated the same experiment of Fig. 6, with the microwave frequency fixed to the middle of the BGS slope at the sensing (cantilever) position. The slope-assisted measured strain and the sweep-BOTDA results are compared in Fig. 7 (we show only the first 12 seconds of the acquired traces for clarity). For this comparison, the slope-assisted measurement was multiplied by a factor ensuring that the maximum strain coincides with the one provided by the sweep-BOTDA measurement. As expected, the quality of the sweep-BOTDA measurement is sensibly better than the measurement provided by the slope-assisted method, as also highlighted by the Fast Fourier Transform (FFT) of the acquired strains shown in the inset of the same figure. In particular, by fitting the measured strain values with a damped sinusoidal strain waveform at the cantilever vibrating frequency, we achieve a standard error of 7με for the sweep-BOTDA measurement, against a standard error of 17με of the slope assisted method.

 

Fig. 7 Dynamic strain acquired along the vibrating cantilever using the SA-BOTDA method (blue line) compared to the one acquired using the sweep-BOTDA method (red line). The solid black curve is the fitting curve. The inset shows the FFT of the acquired strain temporal waveforms (blue line = SA-BOTDA, red line = sweep-BOTDA).

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4. Conclusions

We have proposed and demonstrated a new technique for fast BOTDA measurements, making use of a linearly swept microwave generator for the implementation of a fast scanning probe. Compared to the conventional, single-laser BOTDA scheme based on a frequency stepped probe wave, the proposed method is faster because the measurement speed is not limited by the switching speed of the microwave source. Therefore, the technique turns out to be especially useful when a large spectral range must be scanned (e.g. in case of large excursions of the measurand or very wide BGS). Instead, when the measuring time is dominated by the acquisition of the single trace (i.e. in case of very long fiber or large number of averages), the improvement provided by the proposed method in terms of measurement speed is less relevant. Since the proposed technique is based on a classical BOTDA, it can be easily combined with spatial resolution improvement techniques [11–13], so allowing fast, cost-effective and high-resolution dynamic sensing.