{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T02:53:18Z","timestamp":1787021598824,"version":"build-2736575974"},"reference-count":44,"publisher":"Optica Publishing Group","issue":"2","license":[{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62506243"],"award-info":[{"award-number":["62506243"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012131","name":"Department of Science and Technology of Liaoning Province","doi-asserted-by":"publisher","award":["2025-MS-131"],"award-info":[{"award-number":["2025-MS-131"]}],"id":[{"id":"10.13039\/501100012131","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007620","name":"Department of Education of Liaoning Province","doi-asserted-by":"publisher","award":["LJ222510144004"],"award-info":[{"award-number":["LJ222510144004"]}],"id":[{"id":"10.13039\/501100007620","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["J. Opt. Soc. Am. A"],"published-print":{"date-parts":[[2026,2,1]]},"abstract":"<jats:p>We propose PIRNet, a lightweight, physics-informed deep learning framework for non-interferometric wavefront sensing in optical beam expansion systems. The network simultaneously estimates spherical aberration, coma, and astigmatism from single-shot beam intensity patterns. A large-scale dataset is generated by simulating vortex beam propagation through combined aberrations using the ABCD transfer matrix method. To ensure physical plausibility, we introduce a physics-consistency loss that reconstructs the beam pattern from the predicted coefficients via an optical propagation model and compares it with the input, dynamically balanced with the regression loss through a learnable uncertainty weighting mechanism. A staged training strategy stabilizes convergence by first focusing on regression before introducing the physical constraint. Comparative experiments demonstrate that PIRNet outperforms ResNet18, ResNet34, ResNet50, and Xception across multiple metrics under varying noise levels and cropping ratios. The integration of physical priors enhances both accuracy and generalization, positioning PIRNet as a promising approach for model-driven wavefront characterization in adaptive optics and free-space optical communication.<\/jats:p>","DOI":"10.1364\/josaa.581822","type":"journal-article","created":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T19:00:06Z","timestamp":1766516406000},"page":"346","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Physics-informed deep learning framework for\u00a0wavefront sensing via optical beam pattern\u00a0analysis"],"prefix":"10.1364","volume":"43","author":[{"given":"Tengfei","family":"Chai","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03m20nr07","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0480-3882","authenticated-orcid":true,"given":"Xiaoyun","family":"Liu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03m20nr07","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongwei","family":"Wang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03m20nr07","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yumeihui","family":"Jin","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03m20nr07","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianyu","family":"Huang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03m20nr07","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianyu","family":"Shi","sequence":"additional","affiliation":[{"name":"Shenyang Ligong University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yueqiu","family":"Jiang","sequence":"additional","affiliation":[{"name":"Shenyang Ligong University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,1,14]]},"reference":[{"key":"josaa-43-2-346-R1","doi-asserted-by":"publisher","first-page":"050101","DOI":"10.1117\/1.AP.2.5.050101","type":"journal-article","volume":"2","author":"Yuan","year":"2020","journal-title":"Adv. Photonics"},{"key":"josaa-43-2-346-R2","doi-asserted-by":"publisher","first-page":"17146","DOI":"10.1038\/lsa.2017.146","type":"journal-article","volume":"7","author":"Erhard","year":"2018","journal-title":"Light Sci. Appl."},{"key":"josaa-43-2-346-R3","doi-asserted-by":"publisher","first-page":"163903","DOI":"10.1103\/PhysRevLett.97.163903","type":"journal-article","volume":"97","author":"Tamburini","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"josaa-43-2-346-R4","doi-asserted-by":"publisher","first-page":"20298","DOI":"10.1364\/OE.22.020298","type":"journal-article","volume":"22","author":"Zhou","year":"2014","journal-title":"Opt. Express"},{"key":"josaa-43-2-346-R5","doi-asserted-by":"publisher","first-page":"030901","DOI":"10.1063\/5.0031230","type":"journal-article","volume":"6","author":"Willner","year":"2021","journal-title":"APL Photonics"},{"key":"josaa-43-2-346-R6","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1515\/nanoph-2021-0527","type":"journal-article","volume":"11","author":"Wang","year":"2022","journal-title":"Nanophotonics"},{"key":"josaa-43-2-346-R7","doi-asserted-by":"publisher","first-page":"260502","DOI":"10.1103\/PhysRevLett.120.260502","type":"journal-article","volume":"120","author":"Wang","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"josaa-43-2-346-R8","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1364\/AOP.7.000066","type":"journal-article","volume":"7","author":"Willner","year":"2015","journal-title":"Adv. Opt. Photonics"},{"key":"josaa-43-2-346-R9","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1038\/35085529","type":"journal-article","volume":"412","author":"Mair","year":"2001","journal-title":"Nature"},{"key":"josaa-43-2-346-R10","doi-asserted-by":"publisher","first-page":"107079","DOI":"10.1016\/j.optlastec.2021.107079","type":"journal-article","volume":"141","author":"Kumar","year":"2021","journal-title":"Opt. Laser Technol."},{"key":"josaa-43-2-346-R11","doi-asserted-by":"publisher","first-page":"115302","DOI":"10.1088\/0957-0233\/21\/11\/115302","type":"journal-article","volume":"21","author":"Doloca","year":"2010","journal-title":"Meas. Sci. Technol."},{"key":"josaa-43-2-346-R12","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/s10686-009-9142-0","type":"journal-article","volume":"25","author":"Strano","year":"2009","journal-title":"Exp. Astron."},{"key":"josaa-43-2-346-R13","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1080\/0003379031000080961","type":"journal-article","volume":"60","author":"Malet","year":"2003","journal-title":"Ann. Sci."},{"key":"josaa-43-2-346-R14","doi-asserted-by":"crossref","DOI":"10.1117\/3.43000","volume-title":"Aberration Theory Made Simple","volume":"6","author":"Mahajan","year":"1991"},{"key":"josaa-43-2-346-R15","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1117\/12.55600","type":"journal-article","volume":"29","author":"Klein","year":"1990","journal-title":"Opt. Eng."},{"key":"josaa-43-2-346-R16","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1063\/1.1652612","type":"journal-article","volume":"13","author":"Dabby","year":"1968","journal-title":"Appl. Phys. Lett."},{"key":"josaa-43-2-346-R17","doi-asserted-by":"publisher","first-page":"1405","DOI":"10.1364\/OPTICA.434040","type":"journal-article","volume":"8","author":"Sawant","year":"2021","journal-title":"Optica"},{"key":"josaa-43-2-346-R18","doi-asserted-by":"publisher","first-page":"3009","DOI":"10.1016\/j.visres.2006.03.005","type":"journal-article","volume":"46","author":"McLellan","year":"2006","journal-title":"Vis. Res."},{"key":"josaa-43-2-346-R19","doi-asserted-by":"publisher","first-page":"1872","DOI":"10.1364\/AO.11.1872_1","type":"journal-article","volume":"11","author":"Kocher","year":"1972","journal-title":"Appl. Opt."},{"key":"josaa-43-2-346-R20","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/s10043-004-0337-3","type":"journal-article","volume":"11","author":"Hanayama","year":"2004","journal-title":"Opt. Rev."},{"key":"josaa-43-2-346-R21","doi-asserted-by":"publisher","first-page":"2296","DOI":"10.1364\/AO.54.002296","type":"journal-article","volume":"54","author":"Malacara-Hern\u00e1ndez","year":"2015","journal-title":"Appl. Opt."},{"key":"josaa-43-2-346-R22","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1117\/12.450850","type":"journal-article","volume":"4779","author":"Neal","year":"2002","journal-title":"Proc. SPIE"},{"key":"josaa-43-2-346-R23","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1086\/133367","type":"journal-article","volume":"106","author":"Takato","year":"1994","journal-title":"Publ. Astron. Soc. Pac."},{"key":"josaa-43-2-346-R24","doi-asserted-by":"publisher","first-page":"6456","DOI":"10.1364\/OE.14.006456","type":"journal-article","volume":"14","author":"Guo","year":"2006","journal-title":"Opt. Express"},{"key":"josaa-43-2-346-R25","doi-asserted-by":"publisher","first-page":"33504","DOI":"10.1364\/OE.27.033504","type":"journal-article","volume":"27","author":"Hu","year":"2019","journal-title":"Opt. Express"},{"key":"josaa-43-2-346-R26","doi-asserted-by":"publisher","first-page":"474","DOI":"10.1364\/PRJ.506778","type":"journal-article","volume":"12","author":"Qiao","year":"2024","journal-title":"Photonics Res."},{"key":"josaa-43-2-346-R27","doi-asserted-by":"publisher","first-page":"29044","DOI":"10.1364\/OE.401933","type":"journal-article","volume":"28","author":"Saha","year":"2020","journal-title":"Opt. Express"},{"key":"josaa-43-2-346-R28","doi-asserted-by":"publisher","first-page":"105322","DOI":"10.1063\/5.0167585","type":"journal-article","volume":"13","author":"Jiang","year":"2023","journal-title":"AIP Adv."},{"key":"josaa-43-2-346-R29","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/j.optcom.2018.10.036","type":"journal-article","volume":"433","author":"Ma","year":"2019","journal-title":"Opt. Commun."},{"key":"josaa-43-2-346-R30","doi-asserted-by":"publisher","first-page":"37874","DOI":"10.1364\/OE.470595","type":"journal-article","volume":"30","author":"Yang","year":"2022","journal-title":"Opt. Express"},{"key":"josaa-43-2-346-R31","doi-asserted-by":"publisher","first-page":"2737","DOI":"10.1364\/JOSAA.14.002737","type":"journal-article","volume":"14","author":"Alda","year":"1997","journal-title":"J. Opt. Soc. Am. A"},{"key":"josaa-43-2-346-R32","doi-asserted-by":"publisher","first-page":"1168","DOI":"10.1364\/JOSA.60.001168","type":"journal-article","volume":"60","author":"Collins","year":"1970","journal-title":"J. Opt. Soc. Am."},{"key":"josaa-43-2-346-R33","doi-asserted-by":"publisher","first-page":"5893","DOI":"10.1364\/AO.32.005893","type":"journal-article","volume":"32","author":"Siegman","year":"1993","journal-title":"Appl. Opt."},{"key":"josaa-43-2-346-R34","first-page":"11531","article-title":"ECA-Net: efficient channel attention for deep convolutional neural networks","volume-title":"IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR)","author":"Wang","year":"2020"},{"key":"josaa-43-2-346-R35","doi-asserted-by":"publisher","author":"Hendrycks","year":"2016","DOI":"10.48550\/arXiv.1606.08415","type":"preprint"},{"key":"josaa-43-2-346-R36","doi-asserted-by":"publisher","first-page":"2729","DOI":"10.1016\/j.physleta.2014.07.032","type":"journal-article","volume":"378","author":"Ji","year":"2014","journal-title":"Phys. Lett. A"},{"key":"josaa-43-2-346-R37","doi-asserted-by":"publisher","first-page":"055705","DOI":"10.1088\/2040-8978\/16\/5\/055705","type":"journal-article","volume":"16","author":"Deng","year":"2014","journal-title":"J. Opt."},{"key":"josaa-43-2-346-R38","doi-asserted-by":"publisher","first-page":"014201","DOI":"10.7498\/aps.69.20191254","type":"journal-article","volume":"69","author":"Kang-Le","year":"2020","journal-title":"Acta Opt. Sin."},{"key":"josaa-43-2-346-R39","doi-asserted-by":"publisher","first-page":"735","DOI":"10.3844\/jcssp.2006.735.739","type":"journal-article","volume":"2","author":"Shalabi","year":"2006","journal-title":"J. Comput. Sci."},{"key":"josaa-43-2-346-R40","doi-asserted-by":"publisher","first-page":"1273","DOI":"10.1007\/s00521-015-1933-9","type":"journal-article","volume":"27","author":"Ben Abdallah","year":"2016","journal-title":"Neural Comput. Appl."},{"key":"josaa-43-2-346-R41","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/B978-0-12-374457-9.00007-X","article-title":"Image noise models","volume-title":"The Essential Guide to Image Processing","author":"Boncelet","year":"2009"},{"key":"josaa-43-2-346-R42","doi-asserted-by":"publisher","first-page":"1909","DOI":"10.1109\/TPAMI.2014.2313118","type":"journal-article","volume":"36","author":"Mitra","year":"2014","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"josaa-43-2-346-R43","doi-asserted-by":"publisher","first-page":"1339","DOI":"10.1109\/TPAMI.2007.1151","type":"journal-article","volume":"29","author":"Schechner","year":"2007","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"josaa-43-2-346-R44","doi-asserted-by":"publisher","first-page":"125879","DOI":"10.1016\/j.optcom.2020.125879","type":"journal-article","volume":"472","author":"Yang","year":"2020","journal-title":"Opt. Commun."}],"container-title":["Journal of the Optical Society of America A"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=josaa-43-2-346&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T14:54:06Z","timestamp":1778684046000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=josaa-43-2-346"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,14]]},"references-count":44,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026]]},"published-print":{"date-parts":[[2026]]}},"URL":"https:\/\/doi.org\/10.1364\/josaa.581822","relation":{},"ISSN":["1084-7529","1520-8532"],"issn-type":[{"value":"1084-7529","type":"print"},{"value":"1520-8532","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,14]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/JOSAA.581822","name":"articlelink","label":"Crossref DOI link to publisher maintained version"},{"value":"research-article","name":"content_type","label":"Article type"},{"value":"Screened by Similarity Check","name":"cross_check","label":"Similarity check"},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"14 October 2025","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"22 December 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"14 January 2026","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2026 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}