# Polarization Influence on Algorithms of TFBG Sensors Data Analysis for Bending Application
## 3 Analysis of Measurement Data  
### Quantitative Analysis of Spectra  
Quantitative analysis of spectra requires the definition of an appropriate model of the relationship between the determined quantity and the parameters of the measured spectrum. The structure of the data was initially determined because each grid differs slightly in spectral parameters. In particular, if the refractive index inclination angle and the refractive index modulation depth of the grating are changed, the parameters extracted from the spectrum will change. In principle, separate calibration is required for each such sensor. The simplest and most popular algorithms use the amplitude changes of individual cladding mode resonances.  
Determining a single parameter based on the optical spectrum basically serves two functions in the data analysis process. This is the extraction of features and at the same time reduction of the dimensionality of data.  
The spectra change overall and locally. The determined parameters can use intensities from all points of a given range. The selection of this range may give the algorithm a local or global character. Global methods are characterized by a larger measurement range.  
The first and most popular algorithm is the algorithm of the area occupied between the upper and lower envelope of the cladding modes. However, this algorithm most often uses the search for individual peaks in the spectrum. It does not use all the available information. Additionally, it is sensitive to noise contained in the spectrum, coming from the radiation source and the spectrum analyzer itself. To use all the information contained in the spectrum, all available points in the spectrum should be used for calculations, not just one point related to the peak of a given cladding mode. The general rule is to use all points of the spectrum carrying information in a given range. It is the spectral range of the analyzed spectrum that we match with the measurement range we are interested in. A narrow spectral range limits the measurement range, and a too wide one causes deterioration of its metrological parameters.  
Figure 2: The whole transmission spectra of 2\({}^{\circ}\) TFBG for two values of bending radii (**a**); spectrum range with the strongest bending sensitivity (**b**).  
The second type of method is those of projecting changes in spectrum parameters onto the wavelength axis. In general, such methods are less sensitive to changes in the radiation intensity of the source. For methods that determine parameters on the wavelength axis, the fundamental problem is the discrete nature of cladding modes. For local methods, it limits the measurement range when a single mode is used. For global methods, there are problems related to jumping the determined characteristic wavelength between modes. In global methods a parameter is basically determined, which is an estimate of the cut-off wavelength. For SRI measurements, these methods are characterized by very good linearity, significantly better than all the methods based on parameters reflecting changes in spectral intensity. The initial location of the cut-off wave can be made by selecting a mode whose intensity has decreased significantly compared to longer wavelength modes. In order to determine the cut-off wavelength more precisely, a method was proposed to determine the maximum of the derivative for the upper and lower envelope of the cladding modes [21]. The effect of this solution is a smoother relationship between the determined wavelength parameter and the SRI coefficient.