{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T15:22:22Z","timestamp":1784128942770,"version":"3.55.0"},"reference-count":20,"publisher":"Optica Publishing Group","issue":"2","license":[{"start":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T00:00:00Z","timestamp":1767052800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T00:00:00Z","timestamp":1767052800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Lett."],"published-print":{"date-parts":[[2026,1,15]]},"abstract":"<jats:p>Refractive error is a global public health challenge, with astigmatism\n\t\t\t\t\tcorrection being one of the key issues. While spherocylindrical lenses\n\t\t\t\t\tcompensate for static astigmatism, they fail to address optical axis\n\t\t\t\t\tshifts during eye movement. To address this problem, we propose a\n\t\t\t\t\tsingle vision lens design method with freeform surfaces based on\n\t\t\t\t\tdifferentiable ray tracing. Our method integrates the rotation model\n\t\t\t\t\tof the human eye into the optical design framework. Besides, it\n\t\t\t\t\tleverages the high design freedom of the freeform surface to realize\n\t\t\t\t\teffective correction of optical focus errors across different fields\n\t\t\t\t\tof view. To verify the effectiveness of the method, we develop\n\t\t\t\t\tspectacle lens designs to correct astigmatism in the human eye through\n\t\t\t\t\tsystematic comparison of traditional spherocylindrical and aspheric\n\t\t\t\t\tlenses with various freeform designs, including deformed XY\n\t\t\t\t\tpolynomials and both single- and double-Zernike surfaces. Results show\n\t\t\t\t\tthat our method achieves superior off-axis aberration correction at\n\t\t\t\t\tequivalent optimization orders, demonstrating its technical advantage\n\t\t\t\t\tfor vision correction.<\/jats:p>","DOI":"10.1364\/ol.583052","type":"journal-article","created":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T15:00:10Z","timestamp":1765378810000},"page":"265","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Differentiable ray tracing optimization of freeform spectacle lens for astigmatism correction"],"prefix":"10.1364","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-0419-0182","authenticated-orcid":true,"given":"Hanni","family":"Qiu","sequence":"first","affiliation":[{"name":"Beijing Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinghua","family":"Pan","sequence":"additional","affiliation":[{"name":"Beijing Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zexin","family":"Feng","sequence":"additional","affiliation":[{"name":"Beijing Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2025,12,30]]},"reference":[{"key":"ol-51-2-265-R1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.joco.2017.08.009","type":"journal-article","volume":"30","author":"Hashemi","year":"2018","journal-title":"J. Curr.\n\t\t\t\t\tOphthalmol."},{"key":"ol-51-2-265-R2","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1111\/j.1444-0938.2007.00112.x","type":"journal-article","volume":"90","author":"Read","year":"2007","journal-title":"Clin. Exp. Optom."},{"key":"ol-51-2-265-R3","doi-asserted-by":"publisher","first-page":"3579","DOI":"10.1364\/AO.31.003579","type":"journal-article","volume":"31","author":"Atchison","year":"1992","journal-title":"Appl. Opt."},{"key":"ol-51-2-265-R4","doi-asserted-by":"publisher","first-page":"1391","DOI":"10.1007\/s11431-012-4762-4","type":"journal-article","volume":"55","author":"Li","year":"2012","journal-title":"Sci. China Technol.\n\t\t\t\t\tSci."},{"key":"ol-51-2-265-R6","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1097\/00055735-200002000-00007","type":"journal-article","volume":"11","author":"Novis","year":"2000","journal-title":"Curr. Opin. 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All rights,\n\t\t\t\t\tincluding for text and data mining (TDM), Artificial Intelligence (AI)\n\t\t\t\t\ttraining, and similar technologies, are\n\t\t\t\t\treserved.","name":"copyright","label":"Copyright"}]}}