RESUMO
In this work, the problems in the existing Brillouin frequency shift (BFS) error estimation formulas for distributed optical fiber sensing technology based on Brillouin scattering are discussed. Based on the analysis, a new, to the best of our knowledge, BFS error estimation formula is proposed. To validate the proposed formula, a large number of Brillouin spectra with different frequency sweep spans, signal-to-noise ratios, linewidths, and frequency steps are numerically generated, and at the same time, Brillouin spectra with different values of incident light pulse widths and frequency sweep spans are measured with a Brillouin optical time domain reflectometer. Based on those Brillouin spectra, the errors of the proposed formula and existing formulas are systematically compared. The results reveal that the proposed formula generally has a higher accuracy than the existing typical formulas, especially when the frequency sweep span or incident light pulse width is large. Therefore, it has a much wider application range.
RESUMO
The cross-correlation method has a low computational burden and is less sensitive to noise, but the method may have a long spectra measurement time, especially for Brillouin spectra with an asymmetric frequency sweep span. To improve the real-time performance of spectra measurement, the influence of the frequency sweep span, sweep span deviation, and frequency step on the error in the estimated Brillouin frequency shift (BFS) is systematically investigated. Based on the results, the optimal sweep span and its influencing factors are investigated. The results reveal that when the frequency sweep span is not wide enough and there is a sweep span deviation, the BFS error will not decrease with a decreasing frequency step. The error decreases rapidly with an increasing frequency sweep span, and then it tends to a stable value. The linewidth and sweep span deviation have an important effect on the optimal sweep span. An estimation formula for the optimal sweep span is presented, and an improved cross-correlation method is proposed based on it. The proposed method is compared with existing classic cross-correlation methods. The results reveal that the proposed method can ensure high BFS accuracy and decrease measurement time.
RESUMO
Errors in the extracted key parameters directly influence the errors in the temperature and strain measured by fiber Brillouin distributed sensors. Existing key parameter extraction algorithms for Brillouin gain spectra are mainly based on simplified models, therefore, the extracted parameters may have significant errors. To ensure high accuracy in the extracted key parameters in different cases, and consequently to measure temperature and strain with high accuracy, a key parameter extraction algorithm based on the exact Voigt profile is proposed. The objective function is proposed using the least-squares method. The Levenberg-Marquardt algorithm is used to minimize the objective function and consequently extract the key parameters. The optimization process is presented in detail, at the same time the initial values obtainment method and the convergence criterion are given. The influences of the number of sample points in Gauss-Hermite quadrature on the accuracy and the computation time of the algorithm are investigated and a suggestion about the selection of the number of sample points is given. The direct algorithm, the random algorithm and the proposed algorithm are implemented in Matlab and are used to extract key parameters for abundant numerically generated and measured Brillouin gain spectral signals. The results reveal that the direct algorithm requires less computation time, but its errors are considerably larger than that of the proposed algorithm. The convergence rate of the random algorithm is about 80~90%. The proposed algorithm can converge in all cases. Even for the convergence cases, the computation time and the fitting error of the random algorithm are 1~2 times larger than those of the proposed algorithm.
