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10.3. Distributed Fiber-Optic Sensors      593
                                                      sensors coils

                                                     Tl   T2  T3
                                                    OOP














                             output T(z)
           Fig. 10.15. Principle of optical time -domain reflectometry based on Raman scattering.



       where R r is the ratio of anti-Stokes to Stokes intensity in the backscattered
       light, h is the Planck's constant, v is the wave number separation from the
       pump wavelength, k is the Boltzmann's constant, and T is the absolute
       temperature. For example, for glass fiber, if the pump wavelength is at 514 nm,
       R r has a value about 0.15 at room temperature with temperature dependent
       about 0.8%/°C in the range 0°C to 100°C.
          Figure 10.15 illustrates OTDR temperature sensing based on Raman
       scattering. The basic configuration is similar to the Rayleigh scattering case,
       except that a spectrometer is added in front of the photodetector so that the
       Stokes and anti-Stokes spectral lines can be separately detected. Both the
       spectral line locations and intensities are recorded as a function of time. Then,
       the ratio between anti-Stokes to Stokes lines is calculated based on the
       measured data for different times. By substituting this R r(t) and wavelengths
       of Stokes and anti-Stokes lines into Eq. (10.13), the temperature as a function
       time, T(t) can be obtained. Similar to the Rayleigh scattering case, there is also
       a one-to-one relationship between the spatial location, z, and the recording
       time, t, as given by t = 2nz/c. Thus, the temperature profile of the sensing fiber
       can be obtained.
         The major difficulty of Raman OTDR is the low Raman scattering coeffi-
       cient that is about three orders of magnitude weaker than that of the Rayleigh.
       Thus, high input power is needed to implement Raman-OTDR.


         10.3.1.3. Optical Time-Domain Reflectometry Based on Brillouin Scattering
         When an optical pulse launched into an optical fiber, stimulated Brilliouin
       scattering occurs from acoustic vibrations stimulated in the optical fiber [28],
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