{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T17:10:14Z","timestamp":1785431414755,"version":"3.56.0"},"reference-count":16,"publisher":"Optica Publishing Group","issue":"8","license":[{"start":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T00:00:00Z","timestamp":1783468800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T00:00:00Z","timestamp":1783468800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/501100007034","name":"Thales","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100007034","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["J. Opt. Soc. Am. A"],"published-print":{"date-parts":[[2026,8,1]]},"abstract":"<jats:p>\n                    This paper introduces, to our knowledge, novel methods to reduce chromatic aberrations in compound lens systems. We derive an analytical solution, the pentachromat, which corrects five distinct colors and can be extended to an arbitrary number\n                    <jats:italic>N<\/jats:italic>\n                    of lenses. To avoid overconstraining the system when correcting specific spectral lines, we propose a variational formulation that reduces the residual spectrum by orders of magnitude compared to conventional designs like the superachromat while providing theoretical optimality guarantees. This framework enables new design possibilities, including multi-focal-length achromatic systems with custom optical powers and bandwidths. Finally, a combinatorial search identifies optimal glass types and geometries from available catalogs.\n                  <\/jats:p>","DOI":"10.1364\/josaa.600383","type":"journal-article","created":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T13:00:08Z","timestamp":1781614808000},"page":"1152","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Variational framework for optimal broadband chromatic aberration correction in\n                    <i>N<\/i>\n                    -lens systems"],"prefix":"10.1364","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2933-8171","authenticated-orcid":true,"given":"Bastien","family":"Laville","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05gz77z03","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benjamin","family":"Aymard","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05gz77z03","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,7,8]]},"reference":[{"key":"josaa-43-8-1152-R1","doi-asserted-by":"publisher","first-page":"1642","DOI":"10.1126\/science.1127344","type":"journal-article","volume":"313","author":"Betzig","year":"2006","journal-title":"Science"},{"key":"josaa-43-8-1152-R2","doi-asserted-by":"publisher","first-page":"658","DOI":"10.1117\/12.389057","type":"journal-article","volume":"4000","author":"Kroyan","year":"2000","journal-title":"Proc. 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All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}