通过数值求解蒙日-安培方程设计照明透镜与反射镜
光学
2015-12-08 v2 数值分析
摘要
我们考虑反折射器与反反射器问题。任务是设计自由曲面透镜或自由曲面反射镜，当被点光源照射时，在目标上产生给定的照明模式。这两个问题均可由蒙日-安培型强非线性二阶偏微分方程建模。在[Math. Models Methods Appl. Sci. 25 (2015), pp. 803--837, DOI: 10.1142/S0218202515500190]中，作者提出了一种B样条配置法并应用于反反射器问题。现在该方法被推广到反折射器问题。我们深入解释了该配置法以及如何处理边界条件与约束。本文以折射与反射光学表面的数值结果及其通过光线追踪的验证作结。
引用
@article{arxiv.1506.07670,
title = {Designing Illumination Lenses and Mirrors by the Numerical Solution of Monge-Amp\`ere Equations},
author = {Kolja Brix and Yasemin Hafizogullari and Andreas Platen},
journal= {arXiv preprint arXiv:1506.07670},
year = {2015}
}
备注
16 pages, 6 figures, 2 tables; Keywords: Inverse refractor problem, inverse reflector problem, elliptic Monge-Amp\`ere equation, B-spline collocation method, Picard-type iteration; OCIS: 000.4430, 080.1753, 080.4225, 080.4228, 080.4298, 100.3190. Minor revision: two typos have been corrected and copyright note has been added