3.4 Evaluation of the BOTDA performance

The BOTDA sensing performance is highly dependent on the estimation accuracy of the local BFS. According to recent investigations [52], system parameters such as the FWHM of the BGS ΔνB, the scanning frequency step δ, and the system noise σ, which is the inverse of the signal to noise ratio (SNR) of the normalized Brillouin gain, contribute significantly to an accurate estimation of a local BFS, as presented by the red curve in Figure 6(b). Provided that νBð Þz is the estimated BFS at distance z after a parabolic fitting of all experimental data above a given fraction η of the peak value (see Figure 6(b) for η ¼ 0:5), the estimated error of the BFS is [52]:

#### Figure 6.

(a) Conventional BOTDA setup. RF, radio frequency; MZM, Mach-Zehnder modulator; EDFA, erbiumdoped fiber amplifier; Pol.S., polarization scrambler; FUT, fiber under test; PD, photodiode; Cir, circulator; FBG, fiber Bragg grating; (b) typical measured local BGS (red) and BPS (black) with system parameters that contribute to an uncertainty of the BFS estimation.

The State-of-the-Art of Brillouin Distributed Fiber Sensing DOI: http://dx.doi.org/10.5772/intechopen.84684

$$\sigma\_V(\mathbf{z}) = \sigma(\mathbf{z}) \sqrt{\frac{3 \cdot \delta \cdot \Delta \nu\_B}{8\sqrt{2}(1-\eta)^{3/2}}} \rightarrow \sigma(\mathbf{z}) \sqrt{\frac{3}{4} \delta \cdot \Delta \nu\_B} = \frac{1}{\text{SNR}(\mathbf{z})} \sqrt{\frac{3}{4} \delta \cdot \Delta \nu\_B} \tag{9}$$

As expected, a denser frequency sampling and a higher SNR value lead to a more accurate BFS estimation. Taking the relation of the SNR and number of averaging NAV into consideration, that is, SNR zð Þ<sup>∝</sup> ffiffiffiffiffiffiffiffiffi NAV <sup>p</sup> , the frequency error will also decrease significantly after thousands of averages due to an enhanced SNR. Owing to the linear dependence of the Brillouin phase response in the vicinity of the BFS, the sensor performance can also be evaluated by the linear fitting of the BPS [53] with a narrow frequency scanning and reduced measurement time (see black curve and yellow line in Figure 6(b)).
