Accurate Estimation of Brillouin Frequency Shift in Brillouin Optical Correlation Domain Analysis

Estimation of the accurate value of Brillouin frequency shift (BFS) in a Brillouin optical correlation domain analysis (BOCDA) is challenging due to the contributions to the Brillouin gain spectrum (BGS) from the locations other than corresponding to the correlation between the pump and the probe. In this scenario, we demonstrate optimal post-processing algorithms to retrieve the BFS accurately. We first demonstrate a linear approximation based approach to estimate the BFS with an accuracy of <; 1 MHz. This approach needs to be modified for situations where simultaneous sensing is carried out from two or more locations, or with lock-in detection methods. A gradient descent method is proposed and demonstrated in such cases where the component corresponding to the second harmonic of the modulation frequency is used to optimally recover BFS. The method is tested for its performance at different locations of correlation peaks and for perturbation frequency range of >500 MHz, under different SNR conditions. The error in estimation is found to be less than 1.7 MHz across the entire frequency range for an SNR as low as 5 dB. The algorithm is also validated by comparison with experimental data. The proposed algorithm effectively increases the range and sensitivity of measurement for BFS estimation even when multiple locations are monitored simultaneously.