Optical fiber sensing is an essential aspect of sensing technology. An optical fiber can be used as a medium through corresponding technical approaches to detect changes in the wavelength and frequency of optical signals, indirectly monitoring changes in the external environment. Because of its significant anti-electromagnetic interference ability, optical fiber sensing technology can work satisfactorily in strong magnetic environments, and it exhibits high-temperature resistance and good corrosion resistance in diverse areas such as aerospace, medical testing, civil engineering, power monitoring, and military applications. This method has received increasing attention and applications. Distributed fiber-optic sensing utilizes the nonlinear scattering properties of light as it travels through the fiber to monitor changes in the external environment, such as the temperature and pressure along the fiber. The Brillouin optical time-domain reflectometer can detect changes in the external environment by measuring the shift in the center frequency of the spontaneous Brillouin scattering spectrum of the pulsed light in the fiber. Brillouin-distributed fiber-optic sensing enables long-distance temperature and stress measurements. This technology has higher measurement accuracy and spatial resolution, and it can be applied to longer measurement distances than other sensing technologies. This technology plays a critical role in various industrial applications. Currently, extraction of the center frequency of the Brillouin scattering spectrum is typically performed according to the Lorentzian function. The frequency-sampled values ??of the Brillouin scattering spectra were measured using equally spaced frequency sweeps and fitted using a Lorentzian function. The frequency value corresponding to the center point of the Lorentz curve obtained by fitting is the center frequency of the Brillouin scattering spectrum, and the Brillouin frequency shift is obtained by subtracting the value from the frequency of the light source. The Brillouin scattering spectrum of single-frequency continuous light satisfies the Lorentz function distribution, but the Brillouin scattering spectrum of pulsed light does not satisfy the Lorentz function distribution. In other words, the spectrum of the incident signal is broadened when pulse modulation is performed, and the Brillouin scattering spectrum is also broadened. Hence, more accurate model fitting results cannot be obtained by fitting a general Lorentzian parameter model. In this study, the expression of the optical fiber Brillouin scattering spectrum function of the pulsed light signal, which significantly improves the fitting accuracy of the Brillouin scattering spectrum, was derived.

In this study, a significant fitting error was observed when the pulsed light Brillouin scattering spectrum was fitted using the traditional Lorentzian curve. Stokes light and anti-Stokes light were used as examples, and the functional expression of the fiber Brillouin scattering spectrum of pulsed light was derived via theoretical analysis. The fitting accuracy was improved using this functional expression. A Brillouin optical time-domain reflectometer was used for measurements. When the light source signal flows through the optical coupler, it is divided into two paths: one is used as the sensing branch, and the other is used as the local reference optical path. The optical signal of the sensing branch was modulated into an optical pulse with a specific repetition frequency after passing through the modulator. The optical signal reflected by the sensing branch after passing through the sensing optical fiber was differentially detected with the local reference optical path, and the signal was collected. The Lorentz fitting and pulsed light function derived in this study were used to fit the measurement results, and the fitting accuracy values were compared.

First, the sampling value of the Brillouin power spectrum of 500 m sensing fiber was selected. The fitting results show a significant error in the fitting of the Lorentz function, which can be significantly reduced using the pulsed light function (Fig. 3). The Brillouin scattering spectrum data were collected every 50 m of the sensing fiber to make the experimental results universal, and the scattering data of the 1000 m constant-temperature zero-strain sensing fiber were collected. The Lorentzian function and pulsed light function derived in this study were used to fit. The functions were compared based on four aspects: the sum of squares of differences, root-mean-square error, mean square error, and goodness of fit (Figs. 4?7). The experimental results show that using the pulsed light function for fitting, the difference sum of squares, root-mean-square error, and mean square error are significantly smaller than those of the Lorentzian function fitting, and the degree of fitting of the pulsed light function is significantly higher than that of the Lorentzian function. Therefore, the fitting performance of the pulse light scattering power spectral density function is higher than that of the Lorentzian function.

The fitting error of the Brillouin scattering spectrum using the Lorentz function is significant, and the central frequency cannot be extracted with high precision, which leads to inaccurate monitoring of external environmental changes. Through theoretical research, the Brillouin scattering power spectral density function of pulsed light was obtained, which improved the fitting accuracy. Through the Brillouin optical time-domain reflectometer sensing experiment, the measured Brillouin scattering spectrum data were fitted using different methods, and the fitting was obtained using the pulsed-light Brillouin scattering power spectral density function. The higher the fitting accuracy, the more accurate would be the parameter estimation and the smaller would be the error. This study can provide valuable information for applying and developing distributed optical fiber sensing.