{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T03:29:40Z","timestamp":1776742180433,"version":"3.51.2"},"reference-count":26,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T00:00:00Z","timestamp":1565654400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural National Science Foundation of China (NSFC)","award":["V1738204"],"award-info":[{"award-number":["V1738204"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In the adaptive optics (AO) system, to improve the effectiveness and accuracy of wavefront sensing-less technology, a phase-based sensing approach using machine learning is proposed. In contrast to the traditional gradient-based optimization methods, the model we designed is based on an improved convolutional neural network. Specifically, the deconvolution layer, which reconstructs unknown input by measuring output, is introduced to represent the phase maps of the point spread functions at the in focus and defocus planes. The improved convolutional neural network is utilized to establish the nonlinear mapping between the input point spread functions and the corresponding phase maps of the optical system. Once well trained, the model can directly output the aberration map of the optical system with good precision. Adequate simulations and experiments are introduced to demonstrate the accuracy and real-time performance of the proposed method. The simulations show that even when atmospheric conditions D\/r0 = 20, the detection root-mean-square of wavefront error of the proposed method is 0.1307 \u03bb, which has a better accuracy than existing neural networks. When D\/r0 = 15 and 10, the root-mean-square error is respectively 0.0909 \u03bb and 0.0718 \u03bb. It has certain applicative value in the case of medium and weak turbulence. The root-mean-square error of experiment results with D\/r0 = 20 is 0.1304 \u03bb, proving the correctness of simulations. Moreover, this method only needs 12 ms to accomplish the calculation and it has broad prospects for real-time wavefront sensing.<\/jats:p>","DOI":"10.3390\/s19163533","type":"journal-article","created":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T04:31:21Z","timestamp":1565670681000},"page":"3533","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":59,"title":["Improved Machine Learning Approach for Wavefront Sensing"],"prefix":"10.3390","volume":"19","author":[{"given":"Hongyang","family":"Guo","sequence":"first","affiliation":[{"name":"The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"Key Laboratory of Optical Engineering, Chinese Academy of Sciences, No.1 Guangdian Road, Chengdu 610209, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Yangjie","family":"Xu","sequence":"additional","affiliation":[{"name":"The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"Key Laboratory of Optical Engineering, Chinese Academy of Sciences, No.1 Guangdian Road, 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":"The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"Key Laboratory of Optical Engineering, Chinese Academy of Sciences, No.1 Guangdian Road, Chengdu 610209, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"School of Optoelectronic Science and Engineering, University of Electronic Science and Technology of China, No. 4 Section 2 North Jianshe Road, Chengdu 610054, China"}]},{"given":"Shengping","family":"Du","sequence":"additional","affiliation":[{"name":"The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"Key Laboratory of Optical Engineering, Chinese Academy of Sciences, No.1 Guangdian Road, Chengdu 610209, China"}]},{"given":"Dong","family":"He","sequence":"additional","affiliation":[{"name":"The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"Key Laboratory of Optical Engineering, Chinese Academy of Sciences, No.1 Guangdian Road, Chengdu 610209, China"}]},{"given":"Qiang","family":"Wang","sequence":"additional","affiliation":[{"name":"The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"Key Laboratory of Optical Engineering, Chinese Academy of Sciences, No.1 Guangdian Road, Chengdu 610209, China"}]},{"given":"Yongmei","family":"Huang","sequence":"additional","affiliation":[{"name":"The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"Key Laboratory of Optical Engineering, Chinese Academy of Sciences, No.1 Guangdian Road, Chengdu 610209, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2884","DOI":"10.1364\/JOSAA.14.002884","article-title":"Supernormal vision and high-resolution retinal imaging through adaptive optics","volume":"14","author":"Liang","year":"1997","journal-title":"J. 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