{"paper":{"title":"Designing Illumination Lenses and Mirrors by the Numerical Solution of Monge-Amp\\`ere Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"physics.optics","authors_text":"Andreas Platen, Kolja Brix, Yasemin Hafizogullari","submitted_at":"2015-06-25T09:06:53Z","abstract_excerpt":"We consider the inverse refractor and the inverse reflector problem. The task is to design a free-form lens or a free-form mirror that, when illuminated by a point light source, produces a given illumination pattern on a target. Both problems can be modeled by strongly nonlinear second-order partial differential equations of Monge-Amp\\`ere type. In [Math. Models Methods Appl. Sci. 25 (2015), pp. 803--837, DOI: 10.1142/S0218202515500190] the authors have proposed a B-spline collocation method which has been applied to the inverse reflector problem. Now this approach is extended to the inverse r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07670","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}