# Polarization Influence on Algorithms of TFBG Sensors Data Analysis for Bending Application
## 3 Analysis of Measurement Data
### Analysis of the Influence of Polarization on Demodulation Accuracy  
In order to assess the influence of the polarization state on demodulation algorithms and bending radius determination, a series of numerical experiments were performed on previously collected measurement data. The characteristics of the normalized parameters determined on the basis of the spectrum were established depending on the curvature and bending radius. Then, the bending radii were determined using the characteristics for the zero polarization state. The results were presented in the form of graphs of the estimated radius value against the actual bending radius value and the difference between the estimated and actual value as a function of the radius.  
To determine the radius, a curve depending on the curvature was used as a calibration characteristic. For the envelope region, it is shown in Figure 7a. It was better conditioned numerically than the dependence of the envelope area on the radius (Figure 7b). However, ray analysis was easier and simpler to understand. When analyzing Figure 7b, one immediately notices an increase in the spread of characteristics as the radius of curvature increases. Therefore, for longer radii, its determined values will differ more significantly from the real values when polarization changes (Figure 7c). The error value increases significantly for radii longer than 30 mm (Figure 7d).  
Similar conclusions as those obtained for the analysis of the influence of polarization on the envelope area method can be drawn for the contour length method (Figure 8a-d). The dispersion of the curves in Figure 8b for radii larger than 30 mm is particularly noticeable, which also results in a significant error in determining the radius.  
Figure 6: Characteristics of normalized wavelength method: (**a**) curvature versus normalized wavelength parameter; (**b**) resolution and accuracy calculated for maximum wavelength of filtered contour length.  
Figure 8: Polarization influence on normalized contour length method: (**a**) normalized contour versus curvature; (**b**) normalized contour versus radius; (**c**) estimated radii versus real radii; (**d**) error of radii estimation.  
Figure 7: Polarization influence on normalized envelope method: (**a**) normalized envelope versus curvature; (**b**) normalized envelope versus radius; (**c**) estimated radii versus real radii; (**d**) error of radii estimation.  
The dependency curves characteristic of the mean deviation from the local mean method are located closer to each other (Figure 9a). The spread of the dependence of the mean deviation on the radius increases for larger radius values less than for the two previous methods (Figure 9b). However, the radius values determined on the basis of the spectrum also differ significantly from the real values (Figure 9c,d).  
The above analysis of the three amplitude methods indicates that they are significantly dependent on the introduced radiation polarization. Wavelength determination methods are generally less sensitive to additional influencing factors. Figure 10a,b shows a very uniform distribution of characteristics for the entire analyzed range of radii. The estimated radius values shown in Figure 10c,d are less dependent on polarization than for the amplitude methods. For radii above 40 mm, the increase in error for extreme polarizations is twice as large but is significantly smaller than for the amplitude methods.  
Figure 9: Polarization influence on normalized mean deviation from local average method: (**a**) normalized mean deviation versus radius; (**b**) normalized mean deviation versus curvature; (**c**) estimated radii versus real radii; (**d**) error of radii estimation.