2.4        Experimental results

2.4.3       Bragg wavelength determination

For sensing applications when a homogeneous FBG is placed in a homogeneous temperature or strain field, the important information is the Bragg wavelength shift. We have used two different methods to extract this wavelength shift depending on the spectral resolution.

For small resolution measurements, the Bragg wavelength is defined as the zero crossing point of the linear fit of the reflectivity slope between the maximal and minimal values (corresponding to inflexion points). This can be seen in Fig. 2-15 where the spectral response has been simulated for a homogeneous grating (10 mm long and Dn_ac = 5×10^-5) with 2 % of noise and a resolution of 4 pm. Apart from the maximal reflectivity peak, we identify the inflexion points (slope maximum and minimum). The zero crossing point is indicated with an arrow.

Fig. 2-15 Bragg wavelength measurement for low spectral resolution measurement; top : theoretical reflectivity intensity (solid line) and noisy data (dots); bottom : discrete slope (circles) and linear fit between the maximum and the minimum (solid line)

For a high spectral resolution measurement, this method is no more valid as the discrete slope is dominated by the noise and in this case the second method presented hereafter is recommended (or a re-sampling at smaller resolution needs to be performed).

The second technique used to measure the wavelength shift in an experiment is to use the mass center of the reflectivity curve

where l_m and R are a measured wavelength and reflection intensity, respectively. This method requires a high spectral resolution (at least 200 measured points in the Bragg reflectivity peak). This method is also interesting for gratings subjected to non-homogeneous environmental conditions, for example a non-homogeneous strain field, as the Bragg wavelength at the mass center is related to the average Bragg condition. For FBGs with high spectral bandwidths, the mass center calculation should be performed in the frequency domain where the spectral density is proportional to the energy.