The original Lorentzian profile-based nonlinear least-squares problem for BFS estimation is converted to a linear least-squares one. Then, Brillouin frequency shift (BFS) can be readily calculated. The typical nonlinear least-squares Lorentzian, Gaussian, pseudo-Voigt and Voigt fits using Levenberg-Marquardt algorithm, the correlation-based algorithm and the proposed Lorentzian model-based linear least-squares fitting algorithm are used to estimate BFS of the measured Brillouin spectra with different values of SNR (signal-to-noise ratio) and frequency step. The results reveal that the proposed algorithm has similar accuracy with the nonlinear fits. However, the computation time of the typical nonlinear fits is 187.56–11481.67 times as long as the proposed algorithm. The proposed algorithm can estimate BFS with less computational burden and higher accuracy than the correlation-based algorithm. If SNR is low, the frequency step should be set to a low value.

用于BFS估计的原始基于Lorentzian轮廓的非线性最小二乘问题被转换为线性最小二乘。然后，可以容易地计算布里渊频移（BFS）。使用Levenberg-Marquardt算法，基于相关性的算法和基于Lorentzian模型的线性最小二乘拟合算法来估计典型的非线性最小二乘Lorentz，Gaussian，伪Voigt和Voigt拟合，以估计所测布里渊光谱的BFS具有不同的SNR（信噪比）值和频率阶跃值。结果表明，该算法与非线性拟合具有相似的精度。但是，典型非线性拟合的计算时间是所提算法的187.56–11481.67倍。与基于相关的算法相比，所提出的算法能够以更少的计算量和更高的准确性来估计BFS。如果SNR低，则应将频率步长设置为低值。