### 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.

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 | |

State | 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 |

### Fingerprint

### Cite this

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

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*Numerical Mathematics and Advanced Applications ENUMATH 2017.*Lecture Notes in Computational Science and Engineering, vol. 126, Springer, Cham, pp. 301-309, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017, Voss, Norway, 25/09/17. DOI: 10.1007/978-3-319-96415-7_26

**A least-squares method for a Monge-Ampère equation with non-quadratic cost function applied to optical design.** / Yadav, N.K.; ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - A least-squares method for a Monge-Ampère equation with non-quadratic cost function applied to optical design

AU - Yadav,N.K.

AU - ten Thije Boonkkamp,J.H.M.

AU - IJzerman,W.L.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85060038051&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-96415-7_26

DO - 10.1007/978-3-319-96415-7_26

M3 - Conference contribution

SN - 978-3-319-96414-0

T3 - Lecture Notes in Computational Science and Engineering

SP - 301

EP - 309

BT - Numerical Mathematics and Advanced Applications ENUMATH 2017

PB - Springer

CY - Cham

ER -