## 5 Experimental Data Analysis  
The experiment was conducted using the standard laboratory equipment shown in Figure 16. Measurements were performed in reflective mode with the following components: an optical spectrum analyser (OSA; AQ6370D, Yokogawa Electric Corporation, Kanagawa, Japan), a superluminescent diode (SLD), an optical circulator, and a fibre Bragg grating (FBG) used as a temperature sensor. The light emitted from the SLD source was transmitted through an optical fibre to the first port of the optical circulator and subsequently directed to the second port, which was connected to the FBG sensor placed inside a temperature chamber. The reflection spectra were measured using the OSA, with a resolution of 0.004 nm, connected to the third port of the circulator. Examples of spectra measured at a fixed temperature are presented in Figure 17.  
Details regarding the first part of the experiment are presented in Appendix A. Measurements were performed for three values of the steady-state temperature and during the heating process. Due to the significant visible fluctuations in the determined wavelength during the heating process, additional experiments were performed. This time, the temperature in the climatic chamber was set to 20 \({}^{\circ}\)C, which was identical to the ambient temperature. Then, a temperature stabilisation system, which included, amongst others, a mechanical fan, was turned off. The course of the changes in the spectrum shift length as a function of the sample number is presented in Figure 18. Individual spectra were measured every 3 s. The shift was determined using the centroid algorithm, where the spectrum values were previously raised to the second power. The standard deviation  
Figure 16: Measuring system diagram. Figure 15: Comparison of RMSE for the analysed algorithms using two FBG shapes shown in Figure 14.  
of measurements without a trend was 0.37 \(\times\) 10\({}^{-4}\) nm. At a sensitivity of 9.87 pm/\({}^{\circ}\)C, this corresponded to a standard deviation of the determined temperature of 0.0038 \({}^{\circ}\)C. Histograms of the error distribution are presented in Figure 19. Similar to the previous measurements, the distributions of values deviating from the trend line were close to the normal distribution. The trend component decreased during the measurements by 1.6 pm, which meant a temperature decrease of 0.16 \({}^{\circ}\)C. The trend line was determined using local regression for 15% of the length of the analysed signal. A linear function was used as the regression function. Table 1 presents a comparison of the standard deviation of the wavelength changes (STD \(\lambda\)) calculated for several demodulation algorithms. In each case, raising the spectrum  
Figure 19: Histograms of the deviation error values from the mean value for measurements at temperature T = 20 \({}^{\circ}\)C, (**a**) wavelength, (**b**) temperature; centroid method based on the spectrum raised to the squared power. Figure 17: Example experimental spectra measured for three temperature values. Figure 18: The change in the Bragg wavelength value was calculated using the centroid method from the square of the spectrum value for a temperature set at 20 \({}^{\circ}\)C.  
to the second power caused a decrease in the standard deviation value. The most favourable change occurred for the centroid algorithm, because the standard deviation decreased more than tenfold. The use of a nonlinear filter with significant smoothing (\(K=40\)) before the FPC algorithm was equivalent to a positive effect on the calculation of cross-correlation. In Table 2, we present the results of the analysis of demodulation methods when changing the spectral resolution of the measured spectra. In each measurement spectrum, every fifth sample was selected, which corresponded to a change in the spectral resolution from 0.004 nm to 0.02 nm. For spectra with a smaller number of points, the STD values were obviously higher. However, the effect of filtering and raising the spectrum to the second power was more significant.