Measurement of Peak Frequency in Mandelstam-Brillouin Scattering Spectrum

The paper presents a mathematical model for operation of optic fiber sensors based on Brillouin scattering principle. Matrix relations are given which make it possible to calculate the strain and temperature in the optic fiber using the shift of the center frequency and the intensity of the backscattering signal spectrum. Lorenz, Gauss, Pseudo-Voigt and Voigt models are analyzed. The analysis of noise sources in sensors is performed. Special attention is given to the problem of experimental spectrum approximation by the method of least squares using quadratic function. The formulas are derived for mean-square estimate of the center spectrum frequency measurement. The simulation results are shown.