An important topic of research about
FBGs concerns the retrieval of the local grating parameters along the fiber
axis, namely the refractive index distribution in the fiber core. Currently,
two main directions are followed to spatially characterize a grating : side
measurement techniques and mathematical reconstruction methods.
In the side measurement techniques, the
refractive index modulation amplitude, average refractive index or grating
period can directly be extracted from the diffraction measurement of a laser
beam that crosses the grating in a direction orthogonal to the fiber axis [1-7
to 1-9]. Refractive index modulation amplitude as low as 10-5 can be
detected with a spatial resolution of 10 mm [1-8].
In the mathematical
reconstructions methods, the distributed grating parameters are
reconstructed from the spectral or impulse responses. The methods that are
limited to amplitude or phase information solely are not interesting in
arbitrary FBG characterization as they have strong requirements, for example
monotonic varying chirp functions [1-10 to 1-12]. For week
gratings, the complex coupling coefficient of the grating is proportional to
the complex impulse response that can be directly measured or obtained by the
Fourier transform of the complex spectral response [1-10, 1-13].
For stronger gratings, a backscattering technique is necessary [1-14, 1-15].
Some methods use an iterative process where at each step a theoretical grating
profile and his reflection or phase spectrum are generated and compared with a
measured spectrum [1-16 to 1-18].
The side measurement techniques are not
suitable for sensing applications where the FBG is embedded in other materials,
for example composite devices. For this reason, we have focused on the
mathematical reconstruction methods. The most performing mathematical methods,
based on back-scattering techniques, require a complex spectral or impulse
response of the grating.
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