{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T15:33:44Z","timestamp":1772206424151,"version":"3.50.1"},"reference-count":12,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,1,31]],"date-time":"2018-01-31T00:00:00Z","timestamp":1517356800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61377062"],"award-info":[{"award-number":["61377062"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61475165"],"award-info":[{"award-number":["61475165"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61405227"],"award-info":[{"award-number":["61405227"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61675216"],"award-info":[{"award-number":["61675216"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003399","name":"Science and Technology Commission of Shanghai Municipality","doi-asserted-by":"publisher","award":["15XD1524500"],"award-info":[{"award-number":["15XD1524500"]}],"id":[{"id":"10.13039\/501100003399","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>It is a basic task in Brillouin distributed fiber sensors to extract the peak frequency of the scattering spectrum, since the peak frequency shift gives information on the fiber temperature and strain changes. Because of high-level noise, quadratic fitting is often used in the data processing. Formulas of the dependence of the minimum detectable Brillouin frequency shift (BFS) on the signal-to-noise ratio (SNR) and frequency step have been presented in publications, but in different expressions. A detailed deduction of new formulas of BFS variance and its average is given in this paper, showing especially their dependences on the data range used in fitting, including its length and its center respective to the real spectral peak. The theoretical analyses are experimentally verified. It is shown that the center of the data range has a direct impact on the accuracy of the extracted BFS. We propose and demonstrate an iterative fitting method to mitigate such effects and improve the accuracy of BFS measurement. The different expressions of BFS variances presented in previous papers are explained and discussed.<\/jats:p>","DOI":"10.3390\/s18020409","type":"journal-article","created":{"date-parts":[[2018,1,31]],"date-time":"2018-01-31T05:51:17Z","timestamp":1517377877000},"page":"409","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Brillouin Frequency Shift of Fiber Distributed Sensors Extracted from Noisy Signals by Quadratic Fitting"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8562-1292","authenticated-orcid":false,"given":"Hanrong","family":"Zheng","sequence":"first","affiliation":[{"name":"Shanghai Key Laboratory of All Solid-State Laser and Applied Techniques, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Zujie","family":"Fang","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of All Solid-State Laser and Applied Techniques, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China"}]},{"given":"Zhaoyong","family":"Wang","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of All Solid-State Laser and Applied Techniques, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China"}]},{"given":"Bin","family":"Lu","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of All Solid-State Laser and Applied Techniques, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Yulong","family":"Cao","sequence":"additional","affiliation":[{"name":"Nanjing Pioneer Lasersensing, Nanjing 210019, China"}]},{"given":"Qing","family":"Ye","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of All Solid-State Laser and Applied Techniques, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China"}]},{"given":"Ronghui","family":"Qu","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of All Solid-State Laser and Applied Techniques, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China"}]},{"given":"Haiwen","family":"Cai","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of All Solid-State Laser and Applied Techniques, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1364\/OL.22.000787","article-title":"Temperature and strain dependence of the power level and frequency of spontaneous Brillouin scattering in optical fibers","volume":"22","author":"Parker","year":"1997","journal-title":"Opt. 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Opt."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/2\/409\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:53:13Z","timestamp":1760194393000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/2\/409"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,31]]},"references-count":12,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,2]]}},"alternative-id":["s18020409"],"URL":"https:\/\/doi.org\/10.3390\/s18020409","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1,31]]}}}