Abstract
It is a basic task in Brillouin distributed fiber sensors to extract the peak frequency of the scattering spectrum, since the peak frequency shift gives information on the fiber temperature and strain changes. Because of high-level noise, quadratic fitting is often used in the data processing. Formulas of the dependence of the minimum detectable Brillouin frequency shift (BFS) on the signal-to-noise ratio (SNR) and frequency step have been presented in publications, but in different expressions. A detailed deduction of new formulas of BFS variance and its average is given in this paper, showing especially their dependences on the data range used in fitting, including its length and its center respective to the real spectral peak. The theoretical analyses are experimentally verified. It is shown that the center of the data range has a direct impact on the accuracy of the extracted BFS. We propose and demonstrate an iterative fitting method to mitigate such effects and improve the accuracy of BFS measurement. The different expressions of BFS variances presented in previous papers are explained and discussed.
Highlights
The Brillouin optical fiber distributed sensor is attractive for the measurement of strain and temperature change in fiber under test (FUT), based on the Brillouin frequency shift (BFS), which is a function of strain and temperature
A narrow linewidth laser with frequency shifted by acousto-optic modulator (AOM) was used as the probe in the experiment; and frequency shifted by acousto-optic modulator (AOM) was used as the probe in the experiment; a Brillouin fiber laser was used as the local oscillator for heterodyne detection, as described in [7,8,9]
We proposed a new formula for the minimum detectable peak frequency change
Summary
The Brillouin optical fiber distributed sensor is attractive for the measurement of strain and temperature change in fiber under test (FUT), based on the Brillouin frequency shift (BFS), which is a function of strain and temperature. Where d is the frequency step of the spectrum, SNRA is the signal-to-noise ratio of the optical signal amplitude, and η is the fraction of peak level, over which a quadratic least-square fitting is carried out. The expression of BFS uncertainty due to Gaussian noise is deduced strictly in detail based on quadratic fitting with the least-square algorithm, giving new formulas for fitted BFS variance and linewidth varying with data length and the data range’s center, noise levels, frequency step, and others. It is shown that the data length and data range’s center deviation relative to the Brillouin peak have a direct impact on the accuracy of the extracted BFS To mitigate this impact, a method of iterative quadratic fitting is proposed and demonstrated in this paper. By way of practical applications to the experimental data, that the method is effective with negligible increase of calculation time
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