{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:43:14Z","timestamp":1760179394828,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2020,9,8]],"date-time":"2020-09-08T00:00:00Z","timestamp":1599523200000},"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":["61875203"],"award-info":[{"award-number":["61875203"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In adaptive optics (AO), multiple different incident wavefronts correspond to a same far-field intensity distribution, which leads to a many-to-one mapping. To solve this problem, a single far-field deep learning adaptive optics system based on four-quadrant discrete phase modulation (FQDPM) is proposed. Our method performs FQDPM on an incident wavefront to overcome this many-to-one mapping, then convolutional neural network (CNN) is used to directly predict the wavefront. Numerical simulations indicate that the proposed method can achieve precise high-speed wavefront correction with a single far-field intensity distribution: it takes nearly 0.6ms to complete wavefront correction while the mean root mean square (RMS) of residual wavefronts is 6.3% of that of incident wavefronts, and the Strehl ratio of the far-field intensity distribution increases by 5.7 times after correction. In addition, the experiment results show that mean RMS of residual wavefronts is 6.5% of that of incident wavefronts and it takes nearly 0.5 ms to finish wavefront reconstruction, which verifies the correctness of our proposed method.<\/jats:p>","DOI":"10.3390\/s20185106","type":"journal-article","created":{"date-parts":[[2020,9,8]],"date-time":"2020-09-08T09:03:48Z","timestamp":1599555828000},"page":"5106","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Single Far-Field Deep Learning Adaptive Optics System Based on Four-Quadrant Discrete Phase Modulation"],"prefix":"10.3390","volume":"20","author":[{"given":"Xuejing","family":"Qiu","sequence":"first","affiliation":[{"name":"Key Laboratory of Adaptive Optics, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, Sichuan, China"},{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, Sichuan, China"},{"name":"University of Chinese Academy of Science, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Cheng","sequence":"additional","affiliation":[{"name":"Key Laboratory of Adaptive Optics, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, Sichuan, China"},{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, Sichuan, China"},{"name":"University of Chinese Academy of Science, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lingxi","family":"Kong","sequence":"additional","affiliation":[{"name":"Key Laboratory of Adaptive Optics, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, Sichuan, China"},{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, Sichuan, China"},{"name":"University of Chinese Academy of Science, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuai","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Adaptive Optics, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, Sichuan, China"},{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, Sichuan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing","family":"Xu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Adaptive Optics, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, Sichuan, China"},{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, Sichuan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"16871","DOI":"10.1364\/OE.27.016871","article-title":"Machine learning based adaptive optics for doughnut-shaped beam","volume":"27","author":"Zhang","year":"2019","journal-title":"Opt. 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Express"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2200","DOI":"10.1088\/0022-3727\/6\/18\/305","article-title":"An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations","volume":"6","author":"Misell","year":"1973","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1117\/12.7972989","article-title":"Phase retrieval and diversity in adaptive optics","volume":"21","author":"Gonsalves","year":"1982","journal-title":"Opt. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4575","DOI":"10.1364\/OE.22.004575","article-title":"Laser beam complex amplitude measurement by phase diversity","volume":"22","author":"Nicolas","year":"2014","journal-title":"Opt. Express"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1364\/OL.43.001235","article-title":"Machine learning for improved image-based wavefront sensing","volume":"43","author":"Paine","year":"2018","journal-title":"Opt. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1364\/OE.27.000240","article-title":"Deep learning wavefront sensing","volume":"27","author":"Nishizaki","year":"2019","journal-title":"Opt. Express"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"10765","DOI":"10.1364\/OE.27.010765","article-title":"DNN-based aberration correction in a wavefront sensorless adaptive optics system","volume":"27","author":"Tian","year":"2019","journal-title":"Opt. Express"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"31767","DOI":"10.1364\/OE.26.031767","article-title":"Feature-based phase retrieval wavefront sensing approach using machine learning","volume":"26","author":"Ju","year":"2018","journal-title":"Opt. Express"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Guo, H.Y., Xu, Y.J., Li, Q., Du, S.P., He, D., Wang, Q., and Huang, Y.M. (2019). Improved machine learning approach for wavefront sensing. 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