### 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.

Language | English |
---|---|

Pages | 475-499 |

Number of pages | 25 |

Journal | Journal of Scientific Computing |

Volume | 80 |

Issue number | 1 |

Early online date | 27 Mar 2019 |

DOIs | |

State | Published - Jul 2019 |

### Fingerprint

### Keywords

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

### Cite this

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*Journal of Scientific Computing*, vol. 80, no. 1, pp. 475-499. DOI: 10.1007/s10915-019-00948-9

**A Monge–Ampère problem with non-quadratic cost function to compute freeform lens surfaces.** / Yadav, N.K. (Corresponding author); ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - A Monge–Ampère problem with non-quadratic cost function to compute freeform lens surfaces

AU - Yadav,N.K.

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

AU - IJzerman,W.L.

PY - 2019/7

Y1 - 2019/7

N2 - 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.

AB - 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.

KW - Freeform lens surfaces

KW - Inverse problem

KW - Least-squares method

KW - Monge–Ampère equation

KW - Non-quadratic cost function

KW - Optical design

KW - Transport boundary conditions

UR - http://www.scopus.com/inward/record.url?scp=85064340947&partnerID=8YFLogxK

U2 - 10.1007/s10915-019-00948-9

DO - 10.1007/s10915-019-00948-9

M3 - Article

VL - 80

SP - 475

EP - 499

JO - Journal of Scientific Computing

T2 - Journal of Scientific Computing

JF - Journal of Scientific Computing

SN - 0885-7474

IS - 1

ER -