To investigate the error in temperature and strain simultaneous measurement based on Brillouin scattering and Brillouin dynamic grating (BDG), the error estimation for birefringence-induced frequency shift in BDG reflected spectra is systematically investigated. In view of the validity of characterization of the BDG reflected spectra by the coupled-wave equations and estimation of birefringence-induced frequency shift by Gaussian model, the BDG reflected spectra with different values of frequency sweep span, signal-to-noise ratio (SNR), linewidth and number of sweeps are numerically generated based on solving of the coupled-wave equations. The birefringence-induced frequency shift is estimated by fitting the Gaussian model to the numerically generated spectra. The relationship between the error in the birefringence-induced frequency shift and the above factors is obtained by the least-squares fit. The results reveal that the birefringence-induced frequency shift error decreases exponentially with increasing SNR. The error is approximately proportional to linewidth. The error decreases as a power of the number of sweeps and the exponent is −0.5. Too narrow or wide frequency sweep span corresponds to a large error. The frequency sweep span is suggested to be set to one linewidth. An estimation formula for birefringence-induced frequency shift error in BDG reflected spectra is proposed based on a large number of generated spectra.

为了研究基于布里渊散射和布里渊动态光栅（BDG）的温度和应变同时测量的误差，系统地研究了双折射引起的BDG反射光谱的频移误差估计。鉴于通过耦合波方程表征BDG反射光谱以及通过高斯模型估计双折射引起的频移的有效性，具有不同扫频范围，信噪比（SNR）值的BDG反射光谱），线宽和扫描次数是根据耦合波方程的求解数值生成的。通过将高斯模型拟合到数字生成的光谱中，可以估计双折射引起的频移。通过最小二乘拟合获得双折射引起的频移的误差与以上因素之间的关系。结果表明，双折射引起的频移误差随SNR的增加呈指数下降。误差大约与线宽成比例。误差随着扫描次数的幂而减小，并且指数为-0.5。太窄或太宽的频率扫描范围对应于较大的误差。建议将扫频范围设置为一个线宽。基于大量产生的光谱，提出了双折射引起的双折射引起的频移误差的估计公式。误差大约与线宽成比例。误差随着扫描次数的幂而减小，并且指数为-0.5。太窄或太宽的频率扫描范围对应于较大的误差。建议将扫频范围设置为一个线宽。针对大量产生的光谱，提出了双折射引起的双折射引起的频移误差的估计公式。误差大约与线宽成比例。误差随着扫描次数的幂而减小，并且指数为-0.5。太窄或太宽的频率扫描范围对应于较大的误差。建议将扫频范围设置为一个线宽。基于大量产生的光谱，提出了双折射引起的双折射引起的频移误差的估计公式。