The Dndc and L distributions
can be found if the FBG parameters are reconstructed for different temperature
or strain states. We consider here the case of two reconstructions q1
and q2 of the same grating at two different temperatures T1
and T2, respectively. The temperature effect on the grating modify
the physical grating period L and the effective refractive index neff
|
(3-27) |
where DT = T2-T1, aL is
the thermal expansion coefficient for the fiber material (approximately 0.55×10-6 for silica) and an represents the thermo-optic
coefficient (8.6×10-6 for germania-doped, silica-core fiber). The changes in the Dnac
and Dndc are neglected as the refractive index changes due to
the temperature mainly modify the effective refractive index (Dn << neff).
The reconstructed coupling coefficients are performed using neff(T1)
and neff(T2). The coupling coefficient phases f1 and f2 are given by equation (3-17)
and their difference Df is reduced to
|
(3-28) |
The grating period L is given by
|
(3-29) |
where Ld is the design period used in the layer-peeling reconstruction
process. Combining equations (3-27) to (3-29), the grating period
for temperature T1 is then found to be
|
(3-30) |
From the grating period, the
distribution Dndc can be obtained from equation (3-17b)
|
(3-31) |
|
