{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T18:35:41Z","timestamp":1778870141012,"version":"3.51.4"},"reference-count":29,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,3,18]],"date-time":"2022-03-18T00:00:00Z","timestamp":1647561600000},"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>The development of fibre optic sensors for measuring the refractive index is related to the creation of new periodic structures and demodulation algorithms for the measured spectrum. Recently, we proposed a double-comb Tilted fibre Bragg grating (DCTFBG) structure. In this article, we analyse such a structure for measuring the refractive index in comparison to a single classical structure. Increasing the number of modes causes a significant change in the Fourier spectrum of optical spectra. For the purpose of data pre-processing, we propose the Fourier Transform as a filtering method in the frequency domain. Then, we analyse separately the band-filtered optical spectra for several frequency ranges. For quantitative analysis, we use algorithms that use quantitative changes in the transmission, i.e., the method of the envelope and the length of the spectrum contour. We propose the use of the Hilbert transform as the envelope method. The second type of algorithms used are methods determining the shift of spectrum features along the wavelength axis. The method of determining the centre of gravity of the area bounded by the envelope and the maximum of the second derivative of the smoothed cumulative spectrum contour length is proposed here. Using the developed methods, the measurement resolution was achieved at the level of 2 \u00d7 10\u22125 refractive index unit.<\/jats:p>","DOI":"10.3390\/s22062344","type":"journal-article","created":{"date-parts":[[2022,3,20]],"date-time":"2022-03-20T21:37:17Z","timestamp":1647812237000},"page":"2344","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Single- and Double-Comb Tilted Fibre Bragg Grating Refractive Index Demodulation Methods with Fourier Transform Pre-Processing"],"prefix":"10.3390","volume":"22","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, 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, 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, 20-618 Lublin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,18]]},"reference":[{"key":"ref_1","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 fibre Bragg grating","volume":"335","author":"Takeda","year":"2022","journal-title":"Sens. Actuators A Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1007\/s11082-020-02609-w","article-title":"Tilted fibre Bragg grating design for a simultaneous measurement of temperature and strain","volume":"53","author":"Kipriksiz","year":"2021","journal-title":"Opt. Quantum Electron."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ci\u0119szczyk, S., Harasim, D., Ormanbekova, A., Skorupski, K., and Wawrzyk, M. (2021). Methods of Projecting Mode Amplitude Changes on the Wavelength Axis in Order to Determine the Bending Radius on the Basis of TFBG Grating Spectra. Sensors, 21.","DOI":"10.3390\/s21227526"},{"key":"ref_4","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. Lightwave Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TIM.2021.3125104","article-title":"Signal Demodulation for Surface Plasmon Resonance Tilted Fibre Bragg Grating Based on Root Sum Squared Method","volume":"70","author":"Ooi","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"114220","DOI":"10.1088\/1674-1056\/27\/11\/114220","article-title":"Cascaded tilted fibre Bragg grating for enhanced refractive index sensing","volume":"27","author":"Jiang","year":"2018","journal-title":"Chin. Phys. B"},{"key":"ref_7","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_8","doi-asserted-by":"crossref","first-page":"1574","DOI":"10.1109\/LPT.2010.2072955","article-title":"Simultaneous Two-Parameter Sensing Using a Single Tilted Moir\u00e9 Fibre Bragg Grating with Discrete Wavelet Transform Technique","volume":"22","author":"Wong","year":"2010","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1109\/LPT.2017.2682183","article-title":"Wide Range Refractive Index Measurement Using a Multi-Angle Tilted Fibre Bragg Grating","volume":"29","author":"Chen","year":"2017","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Li, H., Zhao, X., Rao, B., Wang, M., Wu, B., and Wang, Z. (2021). Fabrication and Characterization of Line-by-Line Inscribed Tilted Fibre Bragg Gratings Using Femtosecond Laser. Sensors, 21.","DOI":"10.3390\/s21186237"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"106615","DOI":"10.1016\/j.optlastec.2020.106615","article-title":"The manufacturing process and spectral features of tilted fibre Bragg gratings","volume":"134","author":"Wen","year":"2021","journal-title":"Opt. Laser Technol."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Jiang, B., Hao, Z., Feng, D., Zhou, K., Zhang, L., and Zhao, J. (2019). Hybrid grating in reduced-diameter fibre for temperature-calibrated high-sensitivity refractive index sensing. Appl. Sci., 9.","DOI":"10.3390\/app9091923"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1713","DOI":"10.1364\/OL.40.001713","article-title":"Absolute near-infrared refractometry with a calibrated tilted fibre Bragg grating","volume":"40","author":"Zhou","year":"2015","journal-title":"Opt. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1600157","DOI":"10.1002\/lpor.201600157","article-title":"A true fibre optic refractometer","volume":"11","author":"Zhou","year":"2017","journal-title":"Laser Photonics Rev."},{"key":"ref_15","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_16","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 \u03b1-shape modified Delaunay triangulation","volume":"166","author":"Fazzi","year":"2020","journal-title":"Measurement"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"113","DOI":"10.3390\/opt2020012","article-title":"Refractometric Properties of a TFBG Sensor Demodulated Using \u03b1-Shape Modified Delaunay Triangulation","volume":"2","author":"Fazzi","year":"2021","journal-title":"Optics"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4531","DOI":"10.1109\/JLT.2019.2909162","article-title":"Integrated Differential Area Method for Variable Sensitivity Interrogation of Tilted Fibre Bragg Grating Sensors","volume":"37","author":"Gang","year":"2019","journal-title":"J. Lightwave Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.snb.2018.04.083","article-title":"Signal processing in SPR fibre sensors: Some remarks and a new method","volume":"268","author":"Navarrete","year":"2018","journal-title":"Sens. Actuators B Chem."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2703","DOI":"10.1109\/LPT.2005.859411","article-title":"Demodulation technique for weakly tilted fibre Bragg grating refractometer","volume":"17","author":"Caucheteur","year":"2005","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1016\/j.yofte.2014.05.002","article-title":"Concentration sensor based on a tilted fibre Bragg grating for anions monitoring","volume":"20","author":"Melo","year":"2014","journal-title":"Opt. Fibre Technol."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Ci\u0119szczyk, S., Kisa\u0142a, P., and Mroczka, J. (2019). New parameters extracted from tilted fibre Bragg grating spectra for the determination of the refractive index and cut-off wavelength. Sensors, 19.","DOI":"10.3390\/s19091964"},{"key":"ref_23","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 Photonics Technol. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1002\/mop.24057","article-title":"Temperature-insensitive refractive index sensor based on tilted fibre Bragg grating","volume":"51","author":"Miao","year":"2009","journal-title":"Microw. Opt. Technol. Let."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1016\/j.bios.2013.12.054","article-title":"In-situ detection of density alteration in non-physiological cells with polarimetric tilted fibre grating sensors","volume":"55","author":"Guo","year":"2014","journal-title":"Biosens. Bioelectron."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"112016","DOI":"10.1016\/j.sna.2020.112016","article-title":"High-precision data analysis for TFBG-assisted refractometer","volume":"308","author":"Tomyshev","year":"2020","journal-title":"Sens. Actuators A Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"174501","DOI":"10.1063\/1.5025645","article-title":"Demodulation method for tilted fibre Bragg grating refractometer with high sensitivity","volume":"123","author":"Pham","year":"2018","journal-title":"J. Appl. Phys."},{"key":"ref_28","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_29","doi-asserted-by":"crossref","unstructured":"Manuylovich, E., Tomyshev, K., and Butov, O.V. (2019). Method for determining the plasmon resonance wavelength in fibre sensors based on tilted fibre Bragg gratings. 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