## Abstract

In this article, we present a least-squares method to compute freeform surfaces of a lens with parallel incoming and outgoing light rays, which is a transport problem corresponding to a non-quadratic cost function. The lens can transfer a given emittance of the source into a desired illuminance at the target. The freeform lens design problem can be formulated as a Monge–Ampère type differential equation with transport boundary condition, expressing conservation of energy combined with the law of refraction. Our least-squares algorithm is capable to handle a non-quadratic cost function, and provides two solutions corresponding to either convex or concave lens surfaces.

Original language | English |
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Pages (from-to) | 475-499 |

Number of pages | 25 |

Journal | Journal of Scientific Computing |

Volume | 80 |

Issue number | 1 |

Early online date | 27 Mar 2019 |

DOIs | |

Publication status | Published - 15 Jul 2019 |

## Keywords

- Freeform lens surfaces
- Inverse problem
- Least-squares method
- Monge–Ampère equation
- Non-quadratic cost function
- Optical design
- Transport boundary conditions