{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:30:01Z","timestamp":1772253001131,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,4,14]],"date-time":"2017-04-14T00:00:00Z","timestamp":1492128000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The application of the sensor optical fibers in the areas of scientific instrumentation and industrial instrumentation is very attractive due to its numerous advantages. In the industry of civil engineering for example, quasi-distributed sensors made with optical fiber are used for reliable strain and temperature measurements. Here, a quasi-distributed sensor in the frequency domain is discussed. The sensor consists of a series of low-finesse Fabry-Perot interferometers where each Fabry-Perot interferometer acts as a local sensor. Fabry-Perot interferometers are formed by pairs of identical low reflective Bragg gratings imprinted in a single mode fiber. All interferometer sensors have different cavity length, provoking frequency-domain multiplexing. The optical signal represents the superposition of all interference patterns which can be decomposed using the Fourier transform. The frequency spectrum was analyzed and sensor\u2019s properties were defined. Following that, a quasi-distributed sensor was numerically simulated. Our sensor simulation considers sensor properties, signal processing, noise system, and instrumentation. The numerical results show the behavior of resolution vs. signal-to-noise ratio. From our results, the Fabry-Perot sensor has high resolution and low resolution. Both resolutions are conceivable because the Fourier Domain Phase Analysis (FDPA) algorithm elaborates two evaluations of Bragg wavelength shift.<\/jats:p>","DOI":"10.3390\/s17040859","type":"journal-article","created":{"date-parts":[[2017,4,18]],"date-time":"2017-04-18T11:22:04Z","timestamp":1492514524000},"page":"859","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Theoretical Study and Numerical Simulation of a Quasi-Distributed Sensor Based on the Low-Finesse Fabry-Perot Interferometer: Frequency-Division Multiplexing"],"prefix":"10.3390","volume":"17","author":[{"given":"Jos\u00e9","family":"Guillen Bonilla","sequence":"first","affiliation":[{"name":"Computing and Electronic Departments, Centro Universitario de Ciencias Exactas e Ingenier\u00edas (CUCEI), University of Guadalajara, Blvd. M. Garc\u00eda Barrag\u00e1n 1421, Guadalajara 44410, Jalisco, Mexico"},{"name":"Mathematic Department, Centro Universitario de Ciencias Exactas e Ingenier\u00edas (CUCEI), University of Guadalajara, Blvd. M. Garc\u00eda Barrag\u00e1n 1421, Guadalajara 44410, Jalisco, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alex","family":"Guillen Bonilla","sequence":"additional","affiliation":[{"name":"Departamento de Ciencias Computacionales, Centro Universitario de los Valles, Universidad de Guadalajara, Ameca Km 45.5, Ameca C.P. 46600, Jalisco, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ver\u00f3nica","family":"Rodr\u00edguez Betancourtt","sequence":"additional","affiliation":[{"name":"Materials Science Graduate School, Centro Universitario de Ciencias Exactas e Ingenier\u00edas (CUCEI), University of Guadalajara, Blvd. M. Garc\u00edaBarrag\u00e1n 1421, Guadalajara 44410, Jalisco, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H\u00e9ctor","family":"Guillen Bonilla","sequence":"additional","affiliation":[{"name":"Materials Science Graduate School, Centro Universitario de Ciencias Exactas e Ingenier\u00edas (CUCEI), University of Guadalajara, Blvd. M. Garc\u00edaBarrag\u00e1n 1421, Guadalajara 44410, Jalisco, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonio","family":"Casillas Zamora","sequence":"additional","affiliation":[{"name":"Computing and Electronic Departments, Centro Universitario de Ciencias Exactas e Ingenier\u00edas (CUCEI), University of Guadalajara, Blvd. M. Garc\u00eda Barrag\u00e1n 1421, Guadalajara 44410, Jalisco, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1006\/ofte.1994.1003","article-title":"Photosensitive Optical Fibers: Device and Applications","volume":"1","author":"Kashyap","year":"1994","journal-title":"Opt. Fiber Technol."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Posada-Roman, J.E., Garcia-Souto, J.A., Poiana, D.A., and Acedo, P. (2016). Fast Interrogation of Fiber Bragg Gratins with Electro-Optical Dual Optical Frequency Combs. Sensors, 16.","DOI":"10.1364\/LAOP.2016.LW2C.6"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"18666","DOI":"10.3390\/s150818666","article-title":"Fibre Optic Sensors for Structural Health Monitoring of Aircraft Composite Structures: Recent Advances and Applications","volume":"15","year":"2015","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Miridonov, S.V., Shlyagin, M.G., and Spirin, V.V. (2003, January 23\u201326). Resolution limits and efficient signal processing for fiber optic Bragg grating sensors with direct spectroscopic detection. Proceedings of the Optical Measurements Systems for Industrial Inspection III, Munich, Germany.","DOI":"10.1117\/12.501160"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ben Zaken, B.B., Zanzury, T., and Maka, D. (2016). An 8-Channel Wavelength MMI Demodultiplexer in Slot Waveguide Structures. Materials, 9.","DOI":"10.3390\/ma9110881"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Huang, J., Zhou, Z., Zhang, L., Chen, J., Ji, C., and Pham, T. (2016). Strain Modal Analysis of Small and Light Pipes Using Distributed Fibre Bragg Grating Sensors. Sensors, 16.","DOI":"10.3390\/s16101583"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Weng, Y., Ip, E., Pan, Z., and Wang, T. (2016). Advances Spatial-Division Multiplex Measurement Systems Propositions-From Telecommunication to Sensing Applications: A Review. Sensors, 16.","DOI":"10.3390\/s16091387"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5243","DOI":"10.1364\/AO.54.005243","article-title":"Design and performance investigation of a highly accurate apodized fiber Bragg grating-based strain sensors in single and quasi-distributed systems","volume":"16","author":"Ali","year":"2015","journal-title":"Appl. Opt."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"8719","DOI":"10.1364\/OE.15.008719","article-title":"In-line short cavity Fabry-Perot strain sensor for quasi distributed measurements utilizing standard OTDR","volume":"15","author":"Cibula","year":"2007","journal-title":"Opt. Express"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4081","DOI":"10.1364\/AO.46.004081","article-title":"Multimode All-fiber quasi-distributed refractometer sensor array and cross-talk mitigation","volume":"46","year":"2007","journal-title":"Appl. Opt."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5270","DOI":"10.1109\/JLT.2016.2614581","article-title":"Quasi-Distributed Fiber Bragg Grating Sensing Using Stepped Incoherent Optical Frequency Domain Reflectometry","volume":"34","author":"Werzinger","year":"2016","journal-title":"J. Lightwave Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1587","DOI":"10.1364\/OE.24.001587","article-title":"Quasi-distributed birefringence dispersion measurement for polarization maintain device with high accuracy based on white light interferometry","volume":"24","author":"Yu","year":"2016","journal-title":"Opt. Express"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4659","DOI":"10.1364\/AO.43.004659","article-title":"Exact analysis of low-finesse multimode fiber extrinsic Fabry-Perot interferometers","volume":"43","author":"Han","year":"2004","journal-title":"Appl. Opt."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1364\/AO.35.000663","article-title":"Extrinsic optical-fiber ultrasound sensor using a thin polymer films as a low-finesse Fabry-Perot interferometer","volume":"35","author":"Beard","year":"1996","journal-title":"Appl. Opt."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1109\/68.363370","article-title":"Wide-Band Fabry-Perot-Like Filters in optical fiber","volume":"7","author":"Town","year":"1995","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1109\/JSEN.2003.810112","article-title":"Micromachined low-finesse Fabry-P\u00e9rot interferometer for the measurement od DC and AC electrical currents","volume":"3","author":"Heredero","year":"2003","journal-title":"IEEE Sens. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1519","DOI":"10.1109\/68.541569","article-title":"Simultaneous measurements of displacement and temperature using a low finesse cavity and fiber Bragg grating","volume":"8","author":"Ferreira","year":"1996","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Yan, L., Gui, Z., Wang, G., An, Y., Gu, J., Zhang, M., Liu, X., Wang, Z., Wang, G., and Jia, P. (2017). A micro bubble structure Based Fabry-Perot optical fiber strain sensor with high sensitivity and low-cost characteristics. Sensors, 17.","DOI":"10.3390\/s17030555"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Hirsch, M., Majchrowicz, D., Wierzba, P., Weber, M., Bechelany, M., and J\u0119drzejewaska-Szczerska, M. (2017). Low-coherence interferometric fiber-optic sensors with potential applications as biosensors. Sensors, 17.","DOI":"10.3390\/s17020261"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1258","DOI":"10.1117\/1.1666871","article-title":"Bragg grating Fabry-Perot interferometer with variable finesse","volume":"43","author":"Betts","year":"2004","journal-title":"Opt. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Liang, W., Huang, Y., Xu, Y., Lee, R.K., and Yariv, A. (2005). Highly sensitive fiber Bragg grating refractive index sensors. Appl. Phys. Lett., 86.","DOI":"10.1063\/1.1904716"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.1109\/68.163773","article-title":"Fiber-optic Bragg-Grating Differential-Temperature sensor","volume":"4","author":"Kersey","year":"1992","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3082","DOI":"10.1016\/j.optcom.2012.02.100","article-title":"A large capacity sensing network with identical weak fiber Bragg gratings multiplexing","volume":"285","author":"Zhang","year":"2012","journal-title":"Opt. Commun."},{"key":"ref_24","first-page":"393","article-title":"Fabry-Perot temperature sensors for quasi-distributed measurement utilizing OTDR","volume":"6","author":"Xu","year":"2008","journal-title":"J. Electron. Sci. Technol. China"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/S0030-4018(01)01391-8","article-title":"Quasi-distributed white light fiber optic strain sensor","volume":"196","author":"Zhao","year":"2001","journal-title":"Opt. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"10240","DOI":"10.1364\/OE.24.004842","article-title":"Multiple vibration measurement using phase-sensitive OTDR merged with Mach-Zehnder interferometer based on frequency division multiplexing","volume":"24","author":"He","year":"2016","journal-title":"Opt. Express"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/S0030-4018(01)01160-9","article-title":"Twin-grating fiber optic sensor demodulation","volume":"191","author":"Miridonov","year":"2001","journal-title":"Opt. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1809","DOI":"10.1117\/1.1489048","article-title":"Static strain measurement with sub-micro-strain resolution and large dynamic range using a twin-Bragg-grating Fabry-Perot sensor","volume":"41","author":"Shlyagin","year":"2002","journal-title":"Opt. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Shlyagin, M.G., Miridonov, S.V., and Tentori, D. (1997, January 24). Frequency multiplexing of in-fiber Bragg grating sensors using tunable laser. Proceedings of the Micro-Optical for Measurement, Sensors, and Microsystems II and Optical Fiber Sensor Technologies and Applications, Munich, Germany.","DOI":"10.1117\/12.281246"},{"key":"ref_30","unstructured":"Shlyagin, M.G., Miridonov, S.V., M\u00e1rquez-Borb\u00f3n, I., Spirin, V.V., Swart, P.L., and Chtcherbakov, A.A. (2002, January 10). Multiplexed twin Bragg grating interferometer sensor. Proceedings of the Optical Fiber Sensors Conference Technical Digest (OFS 2002), Portland, OR, USA."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"24914","DOI":"10.3390\/s151024914","article-title":"Development of Metal-Ceramic Coaxial Cable Fabry-Perot Interferometer Sensors for High Temperature Monitoring","volume":"15","author":"Trontz","year":"2015","journal-title":"Sensors"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"12076","DOI":"10.1364\/OE.20.012076","article-title":"Simultaneous wavelength and frequency encoded microstructure based quasi-distributed temperature sensor","volume":"20","author":"Li","year":"2012","journal-title":"Opt. Express"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"5815","DOI":"10.1364\/AO.45.005815","article-title":"Fiber-optic Fabry-Perot sensors based on a combination of spatial-frequency division multiplexing and wavelength division multiplexing formed by chirped fiber Bragg grating pairs","volume":"45","author":"Tao","year":"2006","journal-title":"Appl. Opt."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2063","DOI":"10.1049\/el:19971409","article-title":"Simultaneous strain, temperature and vibration measurement using a multiplexed in-fibre-Bragg-grating\/fibre-Fabry-Perot sensor system","volume":"33","author":"Rao","year":"1997","journal-title":"Electron. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1109\/JSEN.2011.2119479","article-title":"Vibration Disturbance Localization Using a Serial Array of identical Low-Finesse Fiber Fabry-Perot Interferometers","volume":"12","author":"Shlyagin","year":"2012","journal-title":"IEEE Sens."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1109\/LPT.2011.2109057","article-title":"Three-wave Fiber Fabry-Perot Interferometer for Simultaneous Measurement of Temperature and Water Salinity of Seawater","volume":"23","author":"Vasiliev","year":"2011","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_37","unstructured":"Miridonov, S.V., Shlyaing, M.G., and Tentori, D. (1998, January 1). Digital demodulation of twin-grating fiber-optic sensor. Proceedings of the Conference on Fiber Optic and Laser Sensor and Application, Boston, MA, USA."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Shlyagin, M.G., Miridonov, S.V., Tentori Santa-Cruz, D., Mendieta Jim\u00e9nez, F.J., and Spirin, V.V. (1998, January 1). Multiplexing of grating-based fiber sensors using broadband spectral coding. Proceedings of the Conference on Fiber Optic and Laser Sensors and Applications, Boston, MA, USA.","DOI":"10.1117\/12.339101"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/4\/859\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:32:39Z","timestamp":1760207559000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/4\/859"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,14]]},"references-count":38,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,4]]}},"alternative-id":["s17040859"],"URL":"https:\/\/doi.org\/10.3390\/s17040859","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints201704.0001.v1","asserted-by":"object"}]},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,4,14]]}}}