###### Abstract  
This paper demonstrates how the processing of Brillouin gain spectra (BGS) by two-dimensional correlation methods improves the accuracy of Brillouin frequency shift (BFS) extraction in distributed fiber optic sensor systems based on the BOTDA/BOTDR (Brillouin optical time domain analysis/reflectometry) principles. First, the spectra corresponding to different spatial coordinates of the fiber sensor are resampled. Subsequently, the resampled spectra are aligned by the position of the maximum by shifting in frequency relative to each other. The spectra aligned by the position of the maximum are then averaged, which effectively increases the signal-to-noise ratio (SNR). Finally, the Lorentzian curve fitting (LCF) method is applied to the spectrum with improved characteristics, including a reduced scanning step and an increased SNR. Simulations and experiments have demonstrated that the method is particularly efficacious when the signal-to-noise ratio does not exceed 8 dB and the frequency scanning step is coarser than 4 MHz. This is particularly relevant when designing high-speed sensors, as well as when using non-standard laser sources, such as a self-scanning frequency laser, for distributed fiber-optic sensing. distributed fiber optic sensors; Brillouin frequency shift; signal processing; image processing; correlation methods +
Footnote †: journal: _Algorithms_  
**Citation**: [PERSON]; [PERSON]; [PERSON] An Image Processing-Based Correlation Method for Improving the Characteristics of Brillouin Frequency Shift Extraction in Distributed Fiber Optic Sensors. **Electronic Engineering**: 1, 2019  
(BGS), which comprises a set of frequencies that are instrumental in characterizing Brillouin scattering in optical fibers [23]:  
\[g(v)=\sum_{j}\left[\frac{g_{B0}\;v_{B}\;\Delta v_{B}}{A_{ao}^{(j)}\;v_{ac}^{(j)} \;\Delta v_{ac}^{(j)}}.\frac{\left(\Delta v_{ac}^{(j)}/2\right)^{2}}{\left[v- \left(v_{0}-v_{ac}^{(j)}\right)\right]^{2}+\left(\Delta v_{ac}^{(j)}/2\right)^ {2}}\right], \tag{1}\]  
where \(j\) is the indices of longitudinal acoustic modes; \(\Delta v_{ac}^{(j)}\) is the width of the spectral line of the \(j\)-th order, which can be considered approximately the same for all acoustic modes; \(v_{ac}^{(j)}\) is the effective speed of sound; \(A_{ao}^{(j)}\) is the acousto-optic effective area of the \(j\)-th order; \(v_{B}\) is the Brillouin frequency shift; \(g_{B0}\) is the Brillouin gain peak; \(\Delta v_{B}\) is the Brillouin linewidth, and \(v_{0}\) is the base wavelength. \(v_{ac}^{(j)}\) and \(A_{ao}^{(j)}\) are qualitatively different for all acoustic modes. The expression \(g(v)\) is a superposition of the Lorentzian functions, the maximum of which must be detected. Determining a particular physical quantity in this method comes down to establishing the correct value of the central frequency of the spectrum:  
\[v_{B}=v_{ac}^{1}=2n_{eff}\;V_{\pi}\;\lambda_{0}^{-1}=F(T,\;\sigma) \tag{2}\]  
where \(n_{eff}\) is the effective refractive index of the fiber core; \(V_{\pi}\) is the speed of sound in a fiber core; \(\lambda_{0}\) is the wavelength of radiation; \(T\) is the ambient temperature; \(\sigma\) is the mechanical stress in the fiber. The complexity of this task increases when the length of the sensor line is sufficiently long, and the signal-to-noise ratio at the far end of the line becomes extremely low. In some cases, the complexity of the task is compounded by the necessity of increasing the measurement speed through the use of an increased step frequency scanning, which results in a small number of points in the Brillouin gain spectrum (BGS), as exemplified by the use of a laser with frequency self-scanning [24; 25]. This becomes pertinent, for instance, in monitoring the integrity of an aircraft structure in real-time (Figure 1). In this case, the traditional Lorentzian curve fitting (LCF) method for solving this problem [29; 30; 31] does not provide high accuracy of BFS extraction. Consequently, researchers often resort to various new techniques.