Investigation of Brillouin frequency shift Error Estimated by Quadratic Fitting and the Improved Algorithm

Abstract A comparison of the performance of the quadratic fitting and the classical Lorentzian, Gaussian, pseudo-Voigt and Voigt fitting according to numerically generated and measured Brillouin spectra has been done. The results reveal that the computational burden of the quadratic fitting is much less than the least-squares ones. However, the Brillouin frequency shift (BFS) error estimated by the former may larger than the errors estimated by the latter. According to a large amount of measured Brillouin spectra with different frequency sweep spans, number of sweeps, signal-to-noise ratios (SNRs), linewidths, deviation of frequency sweep spans and processed by different filters, the influence of the above factors on the BFS error estimated by the quadratic fitting is systematically investigated. The results reveal that the optimal frequency sweep span is about one and a half linewidths. The BFS error decreases as a power of the number of sweep. The BFS error reduces exponentially with SNR (in dB). If the ratio of frequency sweep span and linewidth, and the number of sweep are fixed, the BFS error is approximately proportional to linewidth. Typical filters can significantly improve the accuracy in the estimated BFS and only slightly increase computational burden. An improved quadratic fitting is proposed. In the algorithm, first, Brillouin spectra noise is reduced by typical filter, then one or two linewidths' Brillouin spectra which is symmetric about the peak value are used to estimate BFS by the quadratic fitting. Its accuracy is similar to the classical least-squares fitting. However, its computation time is only one-hundredth of the pseudo-Voigt model based least-squares fitting.