# High Resolution Brillouin Sensing of Micro-Scale Structures
## 4 Correlation-Based Brillouin Sensing
In this technique, the pump and the probe are coded by a binary pseudo random bit sequence (PRBS) with a symbol duration of \(T\), where the spatial resolution is determined by \(\frac{1}{2v_{g}T}\). Two adjacent correlation peaks are separated by \(\frac{1}{2}Mv_{g}T\), where \(M\) is the length of the PRBS stream, which can be chosen to be considerably long to increase the measurement range [44]. This technique achieved a high spatial resolution of 1 cm, as shown in Figure 4b, with a theoretical measurement range of 1 km and experimental measurement range of 200 m. The SNR in this measurement was relatively weak due to the existence of the off-peak scattering, which scales with the measurement length. By introducing the Golomb-coded pump and probe and comparing it with the PRBS, [PERSON] et al. showed that a higher SNR and lower off-peak reflectivity can be achieved [93]. This technique was later combined with a time gating approach to demonstrate a distributed measurement with a spatial resolution of 2 cm and the measurement range of 400 m [94]. Combining BOCDA with the time gating technique has improved the SNR and the measurement range by eliminating the noise attributed to the locations outside the correlation [94; 95; 96]. A novel adaptation of BOCDA, introduced by [PERSON] et al. [47], is based on the ASE of an erbium-doped fibre. This technique introduced a single correlation peak whose spatial resolution relied on the bandwidth of the ASE source according to: \(\Delta z=\frac{v_{g}}{2\Delta f}\), where \(\Delta f\) represents the ASE bandwidth. Unlike the frequency modulation technique, where specialized lasers capable of large modulation amplitude are required, this approach offers a simple and less expensive solution based on an ASE source to obtain mm-scale spatial resolution in optical fibres. Using this technique, a 4-mm hot spot was detected in an optical fibre [47]. The SNR in this approach is affected by the stochastic nature of the ASE source, which introduces an amplitude fluctuation to the SBS response and can be calculated by [47]:  
\[\text{SNR}=\frac{g_{B}P_{P}}{A_{\text{eff}}}\sqrt{\frac{v_{g}T\Delta z}{2}}, \tag{5}\]  
where \(T\) is the detector integration time and \(\Delta z\) is the spatial resolution. It becomes clear from Equation (5) that a system with a small \(A_{\text{eff}}\) and longer integration time could improve the SNR significantly. This was demonstrate in [48], which reported an 800-\(\upmu\)m spatial resolution BOCDA measurement of an on-chip photonic waveguide with a small \(A_{\text{eff}}\) and large \(g_{B}\) compared to the optical fibre and a phase-sensitive detection technique to increase the integration time, and consequently the SNR. Figure 4c shows the detection of the waveguide facet with an 800-\(\upmu\)m spatial resolution using  
Figure 4: BOCDA techniques based on (**a**) frequency modulation [43] (reprinted with permission from [43], Copyright ©2012 IEICE, Permission No. 18 RA0091), (**b**) phase-coding [44] (reprinted from [44], Copyright ©2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim), and (**c**) ASE [48] (reprinted from [48] under a Creative Commons Attribution 4.0 International Public License. this technique. The practical spatial resolution in this technique is limited due to two main reasons. First, the probe amplification scales exponentially with the effective opto-acoustic interaction length; therefore, reduction in the effective opto-acoustic length as a result of increasing the spatial resolution leads to a lower SNR. Second, to achieve sub-mm spatial resolutions, the ASE bandwidth exceeds the BFS, which results in a spectral overlap between the amplified probe and the back-reflected pump, which cannot be optically filtered. In the case of on-chip waveguides, this back-reflection is much stronger due to the additional reflection from the waveguide facets, which sets a limit on the spatial resolution of the on-chip sensing experiments [48; 49; 97].