{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T16:15:02Z","timestamp":1785428102747,"version":"3.56.0"},"reference-count":26,"publisher":"Optica Publishing Group","issue":"14","license":[{"start":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T00:00:00Z","timestamp":1777939200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T00:00:00Z","timestamp":1777939200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"name":"The National Key Research and Development\n\t\t\t\t\t\tProgram of China","award":["2021YFF0700400"],"award-info":[{"award-number":["2021YFF0700400"]}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Appl. Opt."],"published-print":{"date-parts":[[2026,5,10]]},"abstract":"<jats:p>Freeform optical elements are increasingly used in practical optical\n\t\t\t\t\tsystems, enabled by advances in fabrication and metrology. The\n\t\t\t\t\tautomated design of off-axis freeform reflective systems under\n\t\t\t\t\tmulti-field constraints remains difficult because aberrations are\n\t\t\t\t\tstrongly coupled, and the design space is high-dimensional. We present\n\t\t\t\t\tan automated design workflow that combines multi-field seed-curve\n\t\t\t\t\textension with constrained nonlinear least-squares refinement. The\n\t\t\t\t\tinitial freeform geometry is constructed under global field\n\t\t\t\t\tconstraints to embed the desired ray mapping. The freeform\n\t\t\t\t\tcoefficients are then optimized using the Levenberg\u2013Marquardt\n\t\t\t\t\talgorithm to improve image quality while controlling distortion. We\n\t\t\t\t\tdemonstrate the method by designing a vehicle head-up display (HUD)\n\t\t\t\t\tsystem and validating it in Zemax OpticStudio. The optimized design\n\t\t\t\t\tachieves a maximum distortion below 3% and an MTF above 0.3 at\n\t\t\t\t\t6\u00a0lp\/mm across the full eye box. The results demonstrate that\n\t\t\t\t\tthe proposed workflow is effective for the HUD design example studied\n\t\t\t\t\tin this work and is promising for similar off-axis reflective imaging\n\t\t\t\t\tsystems.<\/jats:p>","DOI":"10.1364\/ao.591683","type":"journal-article","created":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T16:00:10Z","timestamp":1776700810000},"page":"4732","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Automatic design of off-axis reflective HUD systems based on multi-field SCE and the LM\u00a0algorithm"],"prefix":"10.1364","volume":"65","author":[{"given":"PengShuo","family":"Fu","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00ay9v204","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ChengXiang","family":"Fan","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00ay9v204","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"WenJun","family":"Lu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00ay9v204","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5288-2258","authenticated-orcid":true,"given":"XiaoXiao","family":"Wei","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00ay9v204","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,5,5]]},"reference":[{"key":"ao-65-14-4732-R1","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1117\/12.280356","type":"journal-article","volume":"3061","author":"Johnson","year":"1997","journal-title":"Proc. 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All rights, including\n\t\t\t\t\tfor text and data mining (TDM), Artificial Intelligence (AI) training,\n\t\t\t\t\tand similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}