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We analytically solved the equations for Brillouin optical time domain reflectometry (BOTDR), which is a distributed strain/temperature sensing system that uses a property where the scattering spectrum shifts in proportion to the change of the strain/temperature. Although the equations include both spontaneous and stimulated Brillouin scattering terms, we show that the largest part of the measured spectrum arises from spontaneous scattering in usual BOTDR conditions. This indicates that the term related to stimulated scattering in the equations for BOTDR can be ignored and we show that the observed spectrum is analytically represented in that case.

Analytical Solution to Equations of Brillouin Optical Time Domain Reflectometry and Its Properties