# Recent Progress in Fast Distributed Brillouin Optical Fiber Sensing
## 4 Developments of the Fast BOTDA Schemes
### Optical Frequency-Agile Based Fast BOTDA  
As the development of electrical devices, an OFA-based fast BOTDA [34] is proposed to compress the frequency-sweeping process in the time-domain. As shown in Figure 4, for example, an optical wave in the left path is intensity-modulated into a series of pulses with a fixed central frequency used as the pump pulse while an optical wave in the right path is frequency-modulated into the OFA-probe wave by employing an arbitrary waveform generator (AWG) whose output waveform can be user-defined. After the user-defined microwave for the frequency-sweeping process is tailored into the microwave segments with equal duration beyond the round-trip time \(T_{round\_trip}\) and equal frequency interval, all waveforms of the microwave segments are recorded into the memory of the AWG on a head-to-end link mode in a time-domain so that the \(T_{switch}\) is dropped to \(\sim\)ns. Ultimately, the continuous probe wave is single-sideband modulated by the output user-defined microwave (i.e., frequency-agile microwave) generating the OFA-probe wave. Each probe wave segment can be amplified by the corresponding pump pulse and its amplitude obeys the BGS curve. Based on Equation (6), the sampling rate of this scheme can be effectively increased because the frequency-switching time \(T_{switch}\) can be neglected. However, the bandwidth of the AWG is required to be around \(\sim\)11 GHz corresponding to the BFS of the FUT, which has increased the cost of the system. To cut down the bandwidth requirement for the AWG and to increase the spatial resolution, a combination scheme of the second-order sideband modulation (SOSM) [32] and DPP technique [23; 28; 30; 32; 37] is proposed, which is shown in Figure 5. By appropriately selecting the maximum working point of an intensity modulator, the even-order optical sidebands are excited by loading the frequency-agile microwave while the optical carrier and odd-order sidebands are perfectly suppressed (see the black line in Figure 5a). Subsequently, the lower second order optical sideband is selected as the probe wave by an optical filter so that the frequency requirement of the frequency-agile microwave output from the AWG can be decreased to around 5.5 GHz [32]. At the same time, two optical pulses with a narrow width difference are encoded as a pump pulse pair (i.e., \(N_{code}=2\)), which is the black line in Figure 5b. This results in two high SNR Brillouin signals. Then, a reconstructed Brillouin signal with a high SNR can be obtained by subtracting the two Brillouin signals. Its spatial resolution is also equal to the subtraction of the spatial resolutions for these two Brillouin signals. However, the sampling rate of this scheme is also cut by half because it needs two times the duration for the OFA-probe wave to avoid the overlap of the two Brillouin signals. In the experiment, a dynamic strain measurement with a 20-cm spatial resolution [32] is obtained by subtracting two Brillouin signals generated by two pump pulses of 52 ns and 50 ns, respectively. Then, two time-evolutions of the BGSs at the end of the 50-m FUT, corresponding to two different mechanical vibrations, are measured with a 2-kHz sampling rate, as shown in Figure 6a,b. The vibration waveforms are calculated by curve-fitting the BGSs, which is shown in Figure 6c. Figure 4: The OFA-based fast BOTDA scheme [34]. To further decrease the bandwidth requirement for AWG, a dual-modulation scheme [38] is proposed by employing a single-frequency modulation for a pump wave and an OFA modulation for the probe wave, which is shown in Figure 7a. The optical carrier of the right branch is first  
Figure 5: The improved OFA-based fast BOTDA scheme with the SOSM and DPP techniques [32]. **(a)** The frequency relationship of the SOSM and **(b)** the time sequence of the DPP pump wave and the OFA-probe wave. Figure 6: The time-evolutions of the BGS at the vibration section with the frequencies of **(a)** 33.3 Hz and **(b)** 50 Hz. **(c)** The vibration waveforms for the two vibration frequencies [32].