Unified mathematical framework for a class of fundamental freeform optical systems

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Abstract

We present a unified mathematical framework for sixteen fundamental optical systems. The systems have a parallel or point source and a parallel, point, near-field or far-field target. These choices give eight configurations if we use reflectors only and take the minimum number of freeform surfaces required. Similarly, we get eight lens systems if we only use lens surfaces. The mathematical model for each system is based on Hamilton’s characteristic functions and conservation of luminous flux. Some configurations lead to standard or generalized Monge-Ampère equations. The remaining systems are described by so-called generated Jacobian equations.

Original languageEnglish
Pages (from-to)31650-31664
Number of pages15
JournalOptics Express
Volume29
Issue number20
DOIs
Publication statusPublished - 27 Sept 2021

Bibliographical note

Publisher Copyright:
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.

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