Numerically solving generated Jacobian equations in freeform optical design

Lotte B. Romijn

doi:10.1051/epjconf/202023802001

Numerically solving generated Jacobian equations in freeform optical design

Lotte B. Romijn

Center for Analysis, Scientific Computing and Applications

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

Abstract

We present an efficient numerical algorithm that can be used to solve the generalized Monge-Ampère equations for a single freeform reflector and lens surface. These equations are instances of so-called ‘generated Jacobian equations’ which are characterized by associated generating functions. The algorithm has a wide applicability to any optical system that can be described by a smooth generating function.

Original language	English
Title of host publication	EPJ Web of Conferences
Chapter	Topical Meeting (TOM) 2- Computational, Adaptive and Freeform Optics
Number of pages	2
Volume	238
DOIs	https://doi.org/10.1051/epjconf/202023802001
Publication status	Published - 20 Aug 2020

Access to Document

10.1051/epjconf/202023802001Licence: CC BY

Cite this

@inproceedings{dc11271b7cda42738cf415202f4a4c88,

title = "Numerically solving generated Jacobian equations in freeform optical design",

abstract = "We present an efficient numerical algorithm that can be used to solve the generalized Monge-Amp{\`e}re equations for a single freeform reflector and lens surface. These equations are instances of so-called {\textquoteleft}generated Jacobian equations{\textquoteright} which are characterized by associated generating functions. The algorithm has a wide applicability to any optical system that can be described by a smooth generating function.",

author = "Romijn, {Lotte B.}",

year = "2020",

month = aug,

day = "20",

doi = "10.1051/epjconf/202023802001",

language = "English",

volume = "238",

booktitle = "EPJ Web of Conferences",

}

TY - GEN

T1 - Numerically solving generated Jacobian equations in freeform optical design

AU - Romijn, Lotte B.

PY - 2020/8/20

Y1 - 2020/8/20

N2 - We present an efficient numerical algorithm that can be used to solve the generalized Monge-Ampère equations for a single freeform reflector and lens surface. These equations are instances of so-called ‘generated Jacobian equations’ which are characterized by associated generating functions. The algorithm has a wide applicability to any optical system that can be described by a smooth generating function.

AB - We present an efficient numerical algorithm that can be used to solve the generalized Monge-Ampère equations for a single freeform reflector and lens surface. These equations are instances of so-called ‘generated Jacobian equations’ which are characterized by associated generating functions. The algorithm has a wide applicability to any optical system that can be described by a smooth generating function.

U2 - 10.1051/epjconf/202023802001

DO - 10.1051/epjconf/202023802001

M3 - Conference contribution

VL - 238

BT - EPJ Web of Conferences

ER -

Numerically solving generated Jacobian equations in freeform optical design

Abstract

Access to Document

Fingerprint

Cite this