Comparison of Time and Frequency Approaches to Simulation of Signals of Optical Rayleigh Reflectometers

The range of applications for distributed fiber-optic sensors is constantly expanding due to both the growing needs of industry and the development of the measurement capabilities of the sensors themselves. In connection with the need to develop methods for interpreting sensor signals, it is extremely important to form sets of test signals for distributed fiber-optic sensors obtained under known conditions and effects on the fiber. In the presence of reliable analytical models of signals from distributed fiber-optic sensors, it is extremely convenient to obtain test signals in the course of numerical experiments. The paper will consider the processes of formation of backscattering signals in Rayleigh reflectometric systems and describe physical and mathematical models that allow calculations of signals under different operating conditions. Two approaches for calculating the resulting backscatter signal are proposed: (1) based on the temporal representation of the probing signal and the impulse response of the sensitive fiber and (2) an alternative approach based on the spectral representation of the probing signal and the transfer function of the fiber. The presented results can be used both for direct simulation of the operation of reflectometric systems using Rayleigh scattering and for the analysis of existing limitations and the specifics of their operation.