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Fibre optic sensors using tilted fibre Bragg grating (TFBG) have high sensitivity for refractive
index measurements. In order to achieve good metrological parameters of the measurement, an
appropriate method of spectrum demodulation must be used. The method proposed in the article is
an improvement of the spectral length algorithm. The spectral length parameter is treated as the sum
of the derivative filter responses. In the original version, the first difference of spectrum elements was
used, while this article proposes to use the wavelet transform to calculate the numerical derivative
approximation. The advantage of this solution is an easy way to select the level of smoothing
filtration by changing the scale parameter. The derivation is appropriate even for a relatively low
signal-to-noise level. The approximation of the spectral length by the derivative calculated using the
wavelet transform eliminates the high-frequency noise of the optical signal. The absolute value of
determined spectral derivatives after significant smoothing can be used to estimate the wavelength
of the decay of modes. After analyzing experimental data and performing calculations, it turns out
that this is a linear method with better resolution than the contour length algorithm.
