Abstract
Tilted fibre Bragg grating (TFBG) are used as sensors to determine many quantities such as refractive index, temperature, stress, rotation and bending. The TFBG spectrum contains a lot of information and various algorithms are used for its analysis. However, most of these algorithms are dedicated to the analysis of spectral changes under the influence of the refractive index. The most popular algorithm used for this purpose is to calculate the area occupied by cladding modes. Among the remaining algorithms, there are those that use the determination of the cut-off wavelength as a surrounding refractive index (SRI) indicator. Projection on the wavelength axis can also be used to calculate the bending radius of the fibre. However, this is a more difficult task than with SRI, because the mode decay in bending is not so easy to catch. In this article, we propose a multi-step algorithm that allows to determine the impact of bending on mode leakage. At the same time, the place on the wavelength from the side of the Bragg mode and the ghost mode is determined, which represents the cladding mode radiated from the cladding under the influence of bending. The developed algorithm consists of the following operations carried out on the transmission spectrum: Fourier filtering, calculation of the cumulative value of the spectral length, low-pass filtering of the cumulative curve or its corresponding polynomial approximation, determination of the first and second derivative of the approximated curve, and projection of the second derivative of the curve on the wavelength axis. The shift of the wavelength determined in this way indirectly indicates the bending radius of the optical fibre. Based on multiple measurements, we prove that the presented algorithm provides better results when determining the bending radius compared to other algorithms adopted for this purpose and proposed for SRI measurements. Additionally, we analyse the method of determining the shift of a fragment of the spectrum using the phase of the discrete Fourier transform.
Highlights
With spectrometric interrogation of tilted fibre Bragg grating (TFBG) grating, we obtain multidimensional spectral information. The use of this information depends on the selection of the appropriate algorithm and the extraction of such parameters that are correlated with the measured quantity
In the article we presented the analysis of TFBG spectrum features extraction methods in terms of their applicability to the determination of bending curvature
We proposed two new methods for determining the changes in TFBG spectrum under the influence of bending
Summary
Other quantities that can be measured with TFBG gratings, such as temperature, stress, rotation, twist, and bending, have not been provided with dedicated algorithms The determination of these quantities on the basis of spectra is based either on the universal algorithm of envelope of cladding modes [9], or on changes in the amplitude and shifts of individual modes [10,11]. Ghost mode is a composite of multiple cladding modes and is affected by bending This influence can be used to determine the curvature through power changes measurement [20]. In order to improve the measurement properties of the system with TFBG grating for determining the bending radius, a dedicated algorithm should be developed, which will consist of several steps.
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