Estimation of Error in Brillouin Frequency Shift in Distributed Fiber Sensor

Abstract

Brillouin frequency shift (BFS) is the most frequently used quantity in the distributed fiber temperature and strain sensor. To estimate the error in the measured temperature and strain, the influences of signal-to-noise ratio, linewidth (Δ v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> ), number of sweeps, and frequency sweep span (coefficient) on the BFS error are systematically investigated based on a large number of numerically generated Brillouin spectra and the Lorentzian profile-based fitting algorithm. The results reveal that they have a considerable impact on the BFS error. If the other factors remain unchanged, the influence of single factor on the BFS error is as follows: The BFS error varies as a power of the number of sweeps, the exponent is about -0.5. A threefold rise in average time or number of sweeps results in halving BFS error. If the frequency sweep span varies from 0.6Δ v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> to 2Δ v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> , it has no big influence on the error. The BFS error is proportional to linewidth. The BFS error reduces exponentially with increasing signal-to-noise ratio (in dB). Avery large number of Brillouin spectra with the frequency sweep span from v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> - Δ v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> to v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> + Δ v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> , signal-to-noise ratio from 2 to 52 dB, Δ v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> from 0.03 to 0.15 GHz, number of sweeps from 11 to 601 are numerically generated and BFS is calculated. A formula for BFS error estimation is proposed according to the above results. The formula is fully validated through measured Brillouin spectra with different values of signal-to-noise ratio, linewidth, number of sweeps and frequency sweep span.