## Abstract

Designing freeform optical surfaces that control the redistribution of light from a particular source distribution to a target irradiance poses challenging problems in the field of illumination optics. There exists a wide variety of strategies in academia and industry, and there is an interesting link with optimal transport theory. Many freeform optical design problems can be formulated as a generalized Monge-Ampère equation. In this paper, we consider the design of a single freeform lens that converts the light from an ideal point source into a far-field target. We derive the generalized Monge-Ampère equation and numerically solve it using a generalized least-squares algorithm. The algorithm first computes the optical map and subsequently constructs the optical surface. We show that the numerical algorithm is capable of computing a lens surface that produces a projection of a painting on a screen in the far field.

Original language | English |
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Title of host publication | Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference |

Editors | Fred J. Vermolen, Cornelis Vuik |

Place of Publication | Cham |

Publisher | Springer |

Pages | 833-840 |

Number of pages | 8 |

ISBN (Electronic) | 978-3-030-55874-1 |

ISBN (Print) | 9783030558734 |

DOIs | |

Publication status | Published - 3 May 2021 |

Event | European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 - Egmond aan Zee, Netherlands Duration: 30 Sep 2019 → 4 Oct 2019 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 139 |

ISSN (Print) | 1439-7358 |

ISSN (Electronic) | 2197-7100 |

### Conference

Conference | European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 |
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Country | Netherlands |

City | Egmond aan Zee |

Period | 30/09/19 → 4/10/19 |

### Bibliographical note

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