## 3 Selection of Gabor Filters for the Analysis of TFBG Spectra
Therefore, it is necessary to eliminate the low-frequency components while strengthening the frequencies associated with the first and second harmonics of the cladding modes. Such properties are characteristic of algorithms that determine the derivative of a signal. For discrete signals, the derivative can be approximated by first difference. Taking the derivative causes significant amplification of the higher frequencies above the second harmonic, which can be identified as noise. However, a Gabor filter will significantly reduce these frequencies. In the frequency  
Figure 2:7 Adaptive matching of centre frequency of the log-Gabor filter. Figure 2:8 Envelope derivatives of optical spectra processed by the adaptive log-Gabor filter. domain, the first and second harmonics of the modes lie in the frequency range up to 3 nm\({}^{-1}\). Higher frequencies can be relatively easily removed by using, for example, a smoothing filter. Figure 21 shows the envelopes determined by the log-Gabor filter based on the derivative of the optical spectrum. It is noticeable that a clear shape of the envelope derivative has been achieved, which can be defined as the edge on the side of smaller wavelengths (edge on the left). In most cases, these edges for individual SRI values are parallel to each other. The second feature of these edges is their uniform growth. As a result, the envelope shaped in this way will, as a result of the differentiation operation, be transformed into the curves shown in Figure 2:9 In the entire SRI range, the derivatives of the envelopes are close to the Gaussian shape and can be assigned a high value of quality factor (Q-factor). The slope of the calibration curve in Figure 23 is greater than that in Figure 4.0  
Figure 4.1 Frequency response of the adaptive log-Gabor filter matched to frequency spectra of the optical spectra. Figure 4.2 Envelope derivatives for an adaptive log-Gabor filter fitted to the second harmonic of the optical spectra. In subsequent calculations, the envelopes for the second harmonic derivatives of the optical spectra were determined. The derivatives of the envelopes are shown in Figure 4.3  
Figure 4.4 Dependence of the cut-off wavelength shift on the SRI coefficient value for optical spectra processed by an adaptive log-Gabor filter. Figure 4.5 Envelopes determined with a log-Gabor filter based on the first derivative of the TFBG transmission spectra. Figure 4.6 Envelope derivatives for an adaptive log-Gabor filter fitted to the first harmonic based on the first derivative of the TFBG spectra. The shapes of the peaks in the entire range of the measured SRI differ significantly from the background level. Additionally, the half width of these shapes can be determined over the entire range. Thus, methods such as centroid can be used here to determine the cut-off wavelength shift. The curves in Figure 24 are largely symmetrical. Symmetry deformations occur only in the lower part of individual curves. Based on 20 repetitions for each of the 15 SRI values, the measurement resolution was determined to be 2.3 \(\times\) 10\({}^{-5}\) RIU. The SRI value versus cut-off shift curve was approximated by a linear function. The maximum error in determining the SRI value was 1.4 \(\times\) 10\({}^{-4}\) RIU. For comparison, calculations were made for the method of area between envelopes determined on the basis of peaks. When calculated directly, the resolution (standard deviation from the mean value for 20 repeated measurements of a single SRI value) was 10\({}^{-4}\) RIU. Using additional smoothing filters and interpolating the envelope between peaks using spline functions, the best resolution was 5 \(\times\) 10\({}^{-5}\). Moreover, the function between the value of the envelope area and SRI was non-linear, and its approximation using a 5 th degree polynomial turned out to be optimal. The maximum error in determining the SRI was 3.3 \(\times\) 10\({}^{-4}\) RIU. It seems that the proposed methods using Gabor filters are characterized by better quality of metrological parameters.