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The first method for distributed fiber measurements was the optical-domain reflectometry. This method used backward Rayleigh scattering to observe the optical loss along the fiber. Distributed temperature and strain measurements can be realized by using stimulated Brillouin scattering. This effect can be described s three-wave interaction of pump laser wave, a Stokes wave and an acoustic wave of characteristic Brillouin frequency. This frequency depends on temperature and strain. This effect was used for distributed measurements and realized in Brillouin optical time-domain analysis. Brillouin optical frequency-domain analysis is discussed. In the method, the continuous wave light of narrow linewidth pump laser is coupled into one end of the sensor fiber and a sinusoidal modulated intensity of a probe laser is coupled to the other end. If the frequency difference between both lasers equals to characteristic Brillouin frequency, the pump light will interact with the modulated prove light in the fiber. By analyzing the transmitted pump intensity at different frequency difference between probe and pump lasers, the temperature and strai distribution along the fiber can be determined. By analyzing the dependence of transmitted pump intensity on frequency difference the magnitude of temperature and strain is determined. Numerical simulation of a Brillouin optical frequency-domain analysis is represented. In this numerical simulation several fiber lengths with different but spatial constant gain coefficients were placed one after another. For each fiber part the fundamental oscillation of the transmitted pump intensity is calculated by the derived analytical expression with respect to individual Brillouin gain coefficients. The DC components of the input pump and stokes powers of each region are determined by numerical iteration. Alternating part of pump intensity is assumed not to interact with to interact with Stokes power because it is very week. Only the DC component of the pump power produces Brillouin interaction. Considering the phase shift of the transmitted alternating components of the pump powrs of each different located fiber regions, the baseband modulation transfer function is calculated. In the modulation a 944-m- length single-mode fiber was considered. It has two regions (length 20 m and 1.5m) of higher temperature (T=78C) than that of the unheated fiber, which had a temperature of 26 C, and 50-m and 3-m-long regions of higher strain (e=0.1%). The unheated and unstrained parts of the fiber had a characteristic Brillouin frequency of 12.8 Ghz. The characteristic Brillouin frequencies of heated and stained regions were 12.86 GHz and 12.85 Ghz. If the frequency is near 12.8GHz, Brillouin interaction and loss of the pump wave only in the undisturbed regions will be observed. With increasing frequency difference, the Brillouin gain coefficient in the undisturbed fiber will be reduced. The Brillouin gain coefficient in the strained regions will be increased because the frequency difference between the pump and probe lasers approaches the characteristic Brillouin frequency of these regions. At the frequency difference of 12.83GHz Brillouin loss of the pump wave are observed in the heated fiber parts. The maximum interaction in the strained regions will be reached, if the frequency difference amounts to 12.85GHz. Then it will be reduced and when the frequency difference with reach 12.86GHz, maximum interaction will be reached in heated regions.
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