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. 2018 Jan 31;18(2):409.
doi: 10.3390/s18020409.

Brillouin Frequency Shift of Fiber Distributed Sensors Extracted from Noisy Signals by Quadratic Fitting

Hanrong Zheng  1   2 , Zujie Fang  3 , Zhaoyong Wang  4 , Bin Lu  5   6 , Yulong Cao  7 , Qing Ye  8 , Ronghui Qu  9 , Haiwen Cai  10
Affiliations

Brillouin Frequency Shift of Fiber Distributed Sensors Extracted from Noisy Signals by Quadratic Fitting

Hanrong Zheng et al. Sensors (Basel). .

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.

Keywords: Brillouin; fiber optics sensors; optical time domain reflectometry; scattering.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
(a) Fitted peak frequency deviation (b) and standard deviation of fitted peak frequencies vs. data range’s center deviation.
Figure 2
Figure 2
(a) Brillouin frequency shift (BFS) variance and its average vs test number, blue dot is BFS of each simulation; (b) BFS variances (blue points) and standard deviations (black points) vs. noise level.
Figure 3
Figure 3
Standard deviation of fitted peak frequencies vs. frequency step.
Figure 4
Figure 4
Calculated linewidth of quadratic fitting vs. data number with FWHM of 40 MHz.
Figure 5
Figure 5
Standard deviation of fitted peak frequencies vs. data number used in fitting.
Figure 6
Figure 6
Standard deviation of fitted peak frequencies vs. averaging number.
Figure 7
Figure 7
Standard deviation of fitted peak frequencies vs. frequency step.
Figure 8
Figure 8
Quadratic fitting linewidths Δx vs. data length.
Figure 9
Figure 9
Standard deviation of fitted peak frequencies with data length used in fitting.
Figure 10
Figure 10
Processing results of experimental data: (a) Deviation of fitted peak frequency from Brillouin peak vs data range’s center deviation; (b) Standard deviation of fitted peak frequencies vs data range’s center deviation.
Figure 11
Figure 11
(a) Fitted peak deviation vs iteration times and (b) standard deviation of fitted peaks vs iteration times; (c) The BFS caused by temperature change is extracted by iterative quadratic fitting.
See this image and copyright information in PMC

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