### Abstract

Freeform optical surfaces can transfer a given light distribution of the source into a desired distribution at the target. Freeform optical design problems can be formulated as a Monge-Ampère type differential equation with transport boundary condition, using properties of geometrical optics, conservation of energy, and the theory of optimal mass transport. We present a least-squares method to compute freeform lens surfaces corresponding to a non-quadratic cost function. The numerical algorithm is capable to compute both convex and concave surfaces.

Original language | English |
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Title of host publication | Numerical Mathematics and Advanced Applications ENUMATH 2017 |

Editors | Florin Adrian Radu, Kundan Kumar, Inga Berre, Jan Martin Nordbotten, Iuliu Sorin Pop |

Place of Publication | Cham |

Publisher | Springer |

Pages | 301-309 |

Number of pages | 9 |

ISBN (Electronic) | 978-3-319-96415-7 |

ISBN (Print) | 978-3-319-96414-0 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

Event | European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017 - Voss, Norway Duration: 25 Sep 2017 → 29 Sep 2017 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 126 |

ISSN (Print) | 1439-7358 |

### Conference

Conference | European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017 |
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Country | Norway |

City | Voss |

Period | 25/09/17 → 29/09/17 |

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## Cite this

Yadav, N. K., ten Thije Boonkkamp, J. H. M., & IJzerman, W. L. (2019). A least-squares method for a Monge-Ampère equation with non-quadratic cost function applied to optical design. In F. A. Radu, K. Kumar, I. Berre, J. M. Nordbotten, & I. S. Pop (Eds.),

*Numerical Mathematics and Advanced Applications ENUMATH 2017*(pp. 301-309). (Lecture Notes in Computational Science and Engineering; Vol. 126). Cham: Springer. https://doi.org/10.1007/978-3-319-96415-7_26