{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T11:44:45Z","timestamp":1770464685136,"version":"3.49.0"},"reference-count":34,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,2,18]],"date-time":"2023-02-18T00:00:00Z","timestamp":1676678400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100016775","name":"Lublin University of Technology","doi-asserted-by":"publisher","award":["FD-20\/EE-2\/301"],"award-info":[{"award-number":["FD-20\/EE-2\/301"]}],"id":[{"id":"10.13039\/100016775","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/s23042295","type":"journal-article","created":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T02:29:08Z","timestamp":1676860148000},"page":"2295","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Wavelet Derivative Spectrum Length Method of TFBG Sensor Demodulation"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3986-2690","authenticated-orcid":false,"given":"S\u0142awomir","family":"Ci\u0119szczyk","sequence":"first","affiliation":[{"name":"Institute of Electronics and Information Technology, Lublin University of Technology, Nadbystrzycka 38A, 20-618 Lublin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Krzysztof","family":"Skorupski","sequence":"additional","affiliation":[{"name":"Institute of Electronics and Information Technology, Lublin University of Technology, Nadbystrzycka 38A, 20-618 Lublin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martyna","family":"Wawrzyk","sequence":"additional","affiliation":[{"name":"Doctoral School, Lublin University of Technology, Nadbystrzycka 38D\/406, 20-618 Lublin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patryk","family":"Panas","sequence":"additional","affiliation":[{"name":"Institute of Electronics and Information Technology, Lublin University of Technology, Nadbystrzycka 38A, 20-618 Lublin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"108421","DOI":"10.1016\/j.measurement.2020.108421","article-title":"Study on the performance of polarization maintaining fiber temperature sensor based on tilted fiber grating","volume":"168","author":"Zhao","year":"2021","journal-title":"Measurement"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3905","DOI":"10.1016\/j.optcom.2009.06.058","article-title":"Temperature-independent bending sensor with tilted fiber Bragg grating interacting with multimode fiber","volume":"282","author":"Jin","year":"2009","journal-title":"Opt. Commun."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1393","DOI":"10.1109\/LPT.2008.927875","article-title":"Dynamic temperature compensating interrogation technique for strain sensors with tilted fiber Bragg gratings","volume":"20","author":"Miao","year":"2008","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/j.yofte.2014.05.011","article-title":"Highly sensitive twist sensor based on tilted fiber Bragg grating of polarization-dependent properties","volume":"20","author":"Lu","year":"2014","journal-title":"Opt. Fiber Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"113346","DOI":"10.1016\/j.sna.2021.113346","article-title":"Simultaneous measurement of strain and temperature using a tilted fiber Bragg grating","volume":"335","author":"Takeda","year":"2022","journal-title":"Sens. Actuators A Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6085","DOI":"10.1364\/AO.49.006085","article-title":"Three-parameter optical fiber sensor based on a tilted fiber Bragg grating","volume":"49","author":"Alberto","year":"2010","journal-title":"Appl. Opt."},{"key":"ref_7","first-page":"33","article-title":"A single three-parameter tilted fibre Bragg grating sensor to monitor the thermosetting composite curing process","volume":"8","author":"Fazzi","year":"2022","journal-title":"Adv. Manuf. Polym. Compos. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"085108","DOI":"10.1088\/1361-6501\/ac6d45","article-title":"Monitoring of silicone adhesive in space solar cells with an embedded multi-parameter TFBG sensor in a simulated space environment","volume":"33","author":"Fazzi","year":"2022","journal-title":"Meas. Sci. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1088\/0957-0233\/12\/7\/302","article-title":"Tilted short-period fibre-Bragg-grating-induced coupling to cladding modes for accurate refractometry","volume":"12","author":"Laffont","year":"2001","journal-title":"Meas. Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1002\/mop.24057","article-title":"Temperature-insensitive refractive index sensor based on tilted fiber Bragg grating","volume":"51","author":"Miao","year":"2009","journal-title":"Microw. Opt. Technol. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"108197","DOI":"10.1016\/j.measurement.2020.108197","article-title":"Demodulation of a tilted fibre Bragg grating transmission signal using \u0151\u012a-shape modified Delaunay triangulation","volume":"166","author":"Fazzi","year":"2020","journal-title":"Measurement"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3027","DOI":"10.1109\/JLT.2019.2909644","article-title":"Wide range refractive index measurement based on off-axis tilted fibre Bragg gratings fabricated using femtosecond laser","volume":"37","author":"Pham","year":"2019","journal-title":"J. Light. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"7403","DOI":"10.1109\/JLT.2022.3200999","article-title":"Improved Spectral Interrogation of Tilted Fiber Bragg Grating Refractometer Using Residual Convolutional Neural Networks","volume":"40","author":"Cao","year":"2022","journal-title":"J. Light. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1364\/JOSAA.13.000296","article-title":"Tilted fiber phase gratings","volume":"13","author":"Erdogan","year":"1996","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_15","first-page":"1","article-title":"Improving accuracy and sensitivity of a tilted fiber Bragg grating refractometer using cladding mode envelope derivative","volume":"20","author":"Huang","year":"2022","journal-title":"J. Light. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1109\/LPT.2021.3090314","article-title":"The Structure and Preparation Method of Spectrally Shifted Double-Comb Tilted Fibre Bragg Gratings","volume":"33","author":"Skorupski","year":"2021","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ci\u0119szczyk, S., Skorupski, K., and Panas, P. (2022). Single-and Double-Comb Tilted Fibre Bragg Grating Refractive Index Demodulation Methods with Fourier Transform Pre-Processing. Sensors, 22.","DOI":"10.3390\/s22062344"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Manuylovich, E., Tomyshev, K., and Butov, O.V. (2019). Method for determining the plasmon resonance wavelength in fiber sensors based on tilted fiber Bragg gratings. Sensors, 19.","DOI":"10.3390\/s19194245"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Lin, W., Huang, W., Liu, Y., Chen, X., Qu, H., and Hu, X. (2022). Cladding Mode Fitting-Assisted Automatic Refractive Index Demodulation Optical Fiber Sensor Probe Based on Tilted Fiber Bragg Grating and SPR. Sensors, 22.","DOI":"10.3390\/s22083032"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"164970","DOI":"10.1016\/j.ijleo.2020.164970","article-title":"Spatial frequency spectrum of SPR-TFBG: A simple spectral analysis for in-situ refractometry","volume":"219","author":"Udos","year":"2020","journal-title":"Optik"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"10473","DOI":"10.1364\/OE.18.010473","article-title":"Hybrid fiber grating cavity for multi-parametric sensing","volume":"18","author":"Paladino","year":"2010","journal-title":"Opt. Express"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1752","DOI":"10.1177\/0003702818789695","article-title":"A novel pre-processing algorithm based on the wavelet transform for Raman spectrum","volume":"72","author":"Xi","year":"2018","journal-title":"Appl. Spectrosc."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1998","DOI":"10.1002\/jssc.202000013","article-title":"Wavelet transforms in separation science for denoising and peak overlap detection","volume":"43","author":"Wahab","year":"2020","journal-title":"J. Sep. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/j.infrared.2018.12.036","article-title":"Detection of oil yield from oil shale based on near-infrared spectroscopy combined with wavelet transform and least squares support vector machines","volume":"97","author":"Zhang","year":"2019","journal-title":"Infrared Phys. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.saa.2017.08.039","article-title":"Application of wavelet and Fuorier transforms as powerful alternatives for derivative spectrophotometry in analysis of binary mixtures: A comparative study","volume":"191","author":"Hassan","year":"2018","journal-title":"Spectrochim. Acta Part A Mol. Biomol. Spectrosc."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1016\/j.saa.2015.06.100","article-title":"Continuous Wavelet Transform, a powerful alternative to Derivative Spectrophotometry in analysis of binary and ternary mixtures: A comparative study","volume":"151","author":"Elzanfaly","year":"2015","journal-title":"Spectrochim. Acta Part A Mol. Biomol. Spectrosc."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.saa.2019.01.059","article-title":"High order derivative to investigate the complexity of the near infrared spectra of aqueous solutions","volume":"213","author":"Shao","year":"2019","journal-title":"Spectrochim. Acta Part A Mol. Biomol. Spectrosc."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1021\/ci010333v","article-title":"Approximate derivative calculated by using continuous wavelet transform","volume":"42","author":"Nie","year":"2002","journal-title":"J. Chem. Inf. Comput. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2264","DOI":"10.1109\/LPT.2017.2768601","article-title":"A novel simple TFBG spectrum demodulation method for RI quantification","volume":"29","author":"Harasim","year":"2017","journal-title":"IEEE Photon. Tech. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/j.jsv.2003.03.009","article-title":"Detecting damage in beams through digital differentiator filters and continuous wavelet transforms","volume":"272","author":"Messina","year":"2004","journal-title":"J. Sound Vib."},{"key":"ref_31","first-page":"1514","article-title":"Wavelet derivative: Application in multicomponent analysis of electrochemical signals","volume":"16","author":"Zhang","year":"2004","journal-title":"Electroanal. Int. J. Devoted Fundam. Pract. Asp. Electroanal."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1366\/0003702011952208","article-title":"Retrieving CO concentrations from FT-IR spectra with nonmodeled interferences and fluctuating baselines using PCR model parameters","volume":"55","author":"Bak","year":"2001","journal-title":"Appl. Spectrosc."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"918","DOI":"10.1366\/11-06281","article-title":"Method of spectral subtraction of gas-phase fourier transform infrared (FT-IR) spectra by minimizing the spectrum length","volume":"65","author":"Kozlov","year":"2011","journal-title":"Appl. Spectrosc."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"942","DOI":"10.1080\/10020070612330093","article-title":"Application of the wavelet transforms on axial strain calculation in ultrasound elastography","volume":"16","author":"Luo","year":"2006","journal-title":"Prog. Nat. Sci."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/4\/2295\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:36:02Z","timestamp":1760121362000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/4\/2295"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,18]]},"references-count":34,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["s23042295"],"URL":"https:\/\/doi.org\/10.3390\/s23042295","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,18]]}}}