### Abstract

We aim to solve inverse problems in illumination optics by means of optimal control theory. This is done by first formulating geometric optics in terms of Liouville’s equation, which governs the evolution of light distributions on phase space. Choosing a metric that measures how close one distribution is to another, the formal Lagrange method can be applied. We show that this approach has great potential by a simple numerical example of an ideal lens.

Original language | English |
---|---|

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 | 311-319 |

Number of pages | 9 |

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

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

DOIs | |

Publication status | Published - 2019 |

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

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
---|---|

Volume | 126 |

ISSN (Print) | 1439-7358 |

### Conference

Conference | European Conference on Numerical Mathematics and Advanced Applications 2017 |
---|---|

Abbreviated title | ENUMATH 2017 |

Period | 25/09/17 → 29/09/17 |

## Fingerprint Dive into the research topics of 'Solving inverse illumination problems with Liouville's equation'. Together they form a unique fingerprint.

## Cite this

van Lith, B. S., ten Thije Boonkkamp, J. H. M., & IJzerman, W. L. (2019). Solving inverse illumination problems with Liouville's equation. In F. A. Radu, K. Kumar, I. Berre, J. M. Nordbotten, & I. S. Pop (Eds.),

*Numerical Mathematics and Advanced Applications ENUMATH 2017*(pp. 311-319). (Lecture Notes in Computational Science and Engineering; Vol. 126). Springer. https://doi.org/10.1007/978-3-319-96415-7_27