{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T20:51:11Z","timestamp":1773953471135,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2019,8,23]],"date-time":"2019-08-23T00:00:00Z","timestamp":1566518400000},"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":["V1738204"],"award-info":[{"award-number":["V1738204"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011454","name":"State Key Laboratory of Pulsed Power Laser Technology","doi-asserted-by":"publisher","award":["SKL2018KF05"],"award-info":[{"award-number":["SKL2018KF05"]}],"id":[{"id":"10.13039\/501100011454","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, an improved method of measuring wavefront aberration based on image with machine learning is proposed. This method had better real-time performance and higher estimation accuracy in free space optical communication in cases of strong atmospheric turbulence. We demonstrated that the network we optimized could use the point spread functions (PSFs) at a defocused plane to calculate the corresponding Zernike coefficients accurately. The computation time of the network was about 6\u20137 ms and the root-mean-square (RMS) wavefront error (WFE) between reconstruction and input was, on average, within 0.1263 waves in the situation of D\/r0 = 20 in simulation, where D was the telescope diameter and r0 was the atmospheric coherent length. Adequate simulations and experiments were carried out to indicate the effectiveness and accuracy of the proposed method.<\/jats:p>","DOI":"10.3390\/s19173665","type":"journal-article","created":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T04:38:23Z","timestamp":1566794303000},"page":"3665","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["An Improved Method of Measuring Wavefront Aberration Based on Image with Machine Learning in Free Space Optical Communication"],"prefix":"10.3390","volume":"19","author":[{"given":"Yangjie","family":"Xu","sequence":"first","affiliation":[{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, No.1 Guangdian Road, Chengdu 610209, China"},{"name":"Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Dong","family":"He","sequence":"additional","affiliation":[{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, No.1 Guangdian Road, Chengdu 610209, China"},{"name":"Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Qiang","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, No.1 Guangdian Road, Chengdu 610209, China"},{"name":"Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Hongyang","family":"Guo","sequence":"additional","affiliation":[{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, No.1 Guangdian Road, Chengdu 610209, China"},{"name":"Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4364-1257","authenticated-orcid":false,"given":"Qing","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, No.1 Guangdian Road, Chengdu 610209, China"},{"name":"Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, No.2006 Xiyuan Ave, West Hi-Tech Zone, Chengdu 611731, China"}]},{"given":"Zongliang","family":"Xie","sequence":"additional","affiliation":[{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, No.1 Guangdian Road, Chengdu 610209, China"},{"name":"Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Yongmei","family":"Huang","sequence":"additional","affiliation":[{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, No.1 Guangdian Road, Chengdu 610209, China"},{"name":"Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,23]]},"reference":[{"key":"ref_1","first-page":"573","article-title":"History and principles of Shack-Hartmann wavefront sensing","volume":"17","author":"Platt","year":"1995","journal-title":"J. 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