Key Parameter Extraction for Fiber Brillouin Distributed Sensors Based on the Exact Model

Abstract

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.

Robust Vector BOTDA Signal Processing with Probabilistic Machine Learning

“…Curve fitting approaches model the BGS as a smooth parametric function (Lorentzian, Gaussian, and pseudo-Voigt) depending on the parameters of the incident pump light [25,26]. The BGS profile usually has a Lorentzian shape if the pump light pulse width is larger than 10 ns [27], and a Lorentzian fit is often adopted for long-distance BOTDA applications.…”

Effects of Pump-Pulse Width and Temperature on Experimental Brillouin Gain Spectrum Obtained from Brillouin Optical Time-Domain Analysis Sensors

“…Thus, the fitting of measured BGS with an arbitrary chosen profile may provide lower fitting performance depending on the pump-pulse width. However, the convolution operation always provides a shape of the measured BGS to be in between a Lorentzian profile and a Gaussian profile which is referred to as a Voigt profile [11,12]. The fitting of measured BGS with Voigt profile involves convolution operation which is computationally complex and thus relatively slower.…”

“…The fitting of measured BGS with Voigt profile involves convolution operation which is computationally complex and thus relatively slower. To reduce such complexity, the Voigt profile can be well-approximated by pseudo-Voigt profile which is solely the weighted summation of Lorentzian and Gaussian profiles [12,13]. As a result, the fitting of measured BGS obtained using pump-pulses of different widths with a pseudo-Voigt profile should provide reasonably better fitting performance as compared to that with a Lorentzian or a Gaussian profile.…”

Highly Precise Birefringence Demodulation to Overcome the Sensing Limitation From the Free Spectral Range on the Fiber Lyot Filter

“…The least squares curve fitting method [21], as an effective method for accurately evaluating parameters in the model, has been widely used in spectroscopy and sensing applications. Specifically, it is mostly applied to fiber Brillouin distributed sensing parameter extraction [22] and fiber Fabry-Perot cavity length evaluation [23], but rarely used for Lyot filter birefringence demodulation. In our work, we propose a high precision demodulation method for expanding the temperature measurement range of the fiber Lyot filter.…”