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 & Appl.

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

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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.",

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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.

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