{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T18:16:19Z","timestamp":1774721779583,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T00:00:00Z","timestamp":1721088000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003787","name":"Hebei Natural Science Foundation","doi-asserted-by":"publisher","award":["F2022203011"],"award-info":[{"award-number":["F2022203011"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003787","name":"Hebei Natural Science Foundation","doi-asserted-by":"publisher","award":["QN2022112"],"award-info":[{"award-number":["QN2022112"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science Research Project of Hebei Education Department","award":["F2022203011"],"award-info":[{"award-number":["F2022203011"]}]},{"name":"Science Research Project of Hebei Education Department","award":["QN2022112"],"award-info":[{"award-number":["QN2022112"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The fast and accurate reconstruction of the turbulence phase is crucial for compensating atmospheric disturbances in free-space coherent optical communication. Traditional methods suffer from slow convergence and inadequate phase reconstruction accuracy. This paper introduces a deep learning-based approach for atmospheric turbulence phase reconstruction, utilizing light intensity images affected by turbulence as the basis for feature extraction. The method employs extensive light intensity-phase samples across varying turbulence intensities for training, enabling phase reconstruction from light intensity images. The trained U-Net model reconstructs phases for strong, medium, and weak turbulence with an average processing time of 0.14 s. Simulation outcomes indicate an average loss function value of 0.00027 post-convergence, with a mean squared error of 0.0003 for individual turbulence reconstructions. Experimental validation yields a mean square error of 0.0007 for single turbulence reconstruction. The proposed method demonstrates rapid convergence, robust performance, and strong generalization, offering a novel solution for atmospheric disturbance correction in free-space coherent optical communication.<\/jats:p>","DOI":"10.3390\/s24144604","type":"journal-article","created":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T15:05:51Z","timestamp":1721142351000},"page":"4604","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Atmospheric Turbulence Phase Reconstruction via Deep Learning Wavefront Sensing"],"prefix":"10.3390","volume":"24","author":[{"given":"Yutao","family":"Liu","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China"},{"name":"The Key Laboratory for Special Fiber and Fiber Sensor of Hebei Province, Qinhuangdao 066004, China"}]},{"given":"Mingwei","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China"}]},{"given":"Xingqi","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1364\/OL.480981","article-title":"Secure turbulence-resistant coherent free-space optical communications via chaotic region-optimized probabilistic constellation shaping","volume":"48","author":"Wu","year":"2023","journal-title":"Opt. 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