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Express"],"published-print":{"date-parts":[[2026,4,6]]},"abstract":"<jats:p>Three-dimensional distributed shape sensing of marine optical cables is critical for marine information acquisition, given that the time-varying of marine optical cables influence affects the accuracy of multi-dimensional localization of marine objects, personnel underwater operations, etc. In this work, a novel distributed hydro-acoustic shape sensing (DHS) method is proposed with distributed acoustic sensing (DAS) and an adaptive constrained inversion method (ACIM). DAS is introduced to detect the acoustic field and time-delay distribution of signals along the sensing fiber, from two sources or two positions of a moving acoustic source. The arrival time difference equations are built and resolved with the proposed adaptive constrained inversion method, and then the cable shape is obtained. Sea trials verify the feasibility of the proposed method with a 93\u2005m acoustic sensitive optical cable (ASOC), where the reconstructed root-mean-square error is 2.41\u2005m, and the maximum error is less than 4.30\u2005m. This method achieves distributed shape sensing with only a few asynchronous acoustic sources. which provides a practical and flexible solution both for ASOC and existing cables based on DAS, potentially improving the application of DAS in complex marine environments.<\/jats:p>","DOI":"10.1364\/oe.590633","type":"journal-article","created":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T11:00:10Z","timestamp":1773658810000},"page":"12365","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Distributed hydro-acoustic shape sensing based on adaptive constrained inversion method"],"prefix":"10.1364","volume":"34","author":[{"given":"Feifei","family":"Song","sequence":"first","affiliation":[{"name":"Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4163-2085","authenticated-orcid":true,"given":"Jinyi","family":"Wu","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"},{"name":"Zhangjiang Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0235-5596","authenticated-orcid":true,"given":"Zhaoyong","family":"Wang","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yichen","family":"Zhao","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-4553-0029","authenticated-orcid":true,"given":"Yifan","family":"Liu","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuan","family":"Li","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haoyang","family":"Pi","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kan","family":"Gao","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haiwen","family":"Cai","sequence":"additional","affiliation":[{"name":"Zhangjiang Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ronghui","family":"Qu","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qing","family":"Ye","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,3,26]]},"reference":[{"key":"oe-34-7-12365-R1","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1007\/s44295-025-00089-w","type":"journal-article","volume":"3","author":"Zhao","year":"2025","journal-title":"Intell. 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