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讨论了应用于光纤分布式布里渊传感散射谱最优化拟合的Levenberg-Marquardt(L-M)非线性最小二乘算法。分析并推导了一种可较好地反映入纤脉冲宽度越来越窄所引起的光纤分布式布里渊传感散射谱形状变化的Pseu-do-Voigt分析拟合模型。由调制脉冲光和调制器泄漏连续光共同作用所产生的光纤分布式布里渊传感散射谱应为Lorentzian型谱和Gaussian型谱的线性权重组合。Gaussian型函数部分可视为Lorentzian型函数谱的近似修正处理。基于L-M算法对光纤布里渊传感散射谱采样数据进行了曲线拟合和最优化参数估计,所得到的结果与理论分析情况吻合。
The Levenberg-Marquardt (L-M) nonlinear least squares algorithm applied to the optimal fitting of fiber distributed Brillouin scattering spectra is discussed. A Pseu-do-Voigt analysis fitting model that can better reflect the shape change of distributed fiber Brillouin scattering spectrum caused by narrower fiber width is analyzed and deduced. The fiber distributed Brillouin scattering scattering spectrum generated by the combination of modulated pulsed light and continuous light leakage from the modulator should be a linear weight combination of Lorentzian spectrum and Gaussian spectrum. Gaussian-type function part can be regarded as Lorentzian-type function spectrum approximate correction. Based on the L-M algorithm, the curve fitting and the optimal parameter estimation of the fiber Brillouin scattering scattering spectral sampling data were carried out. The obtained results are in good agreement with the theoretical analysis.