Double freeform illumination design for prescribed wavefronts and irradiances

TL;DR

This paper introduces a PDE-based mathematical model and numerical method for designing double freeform optical surfaces that control irradiance and wavefronts without restrictions to paraxiality or planar wavefronts.

Contribution

It extends existing models to nonparaxial, nonplanar wavefronts and provides a numerical solution approach for double freeform lens and mirror design.

Findings

Effective numerical algorithm demonstrated on mirror and lens systems.

Model overcomes limitations of previous PDE models for freeform optics.

Designs achieve prescribed wavefronts and irradiance distributions.

Abstract

A mathematical model in terms of partial differential equations (PDE) for the calculation of double freeform surfaces for irradiance and phase control with predefined input and output wavefronts is presented. It extends the results of B\"osel and Gross [J. Opt. Soc. Am. A 34, 1490 (2017)] for the illumination design of single freeform surfaces for zero-\'etendue light sources to double freeform lenses and mirrors. The PDE model thereby overcomes the restriction to paraxiality or the requirement of at least one planar wavefront of the current design models in the literature. In contrast with the single freeform illumination design, the PDE system does not reduce to a Monge-Amp\`ere type equation for the unknown freeform surfaces, if nonplanar input and output wavefronts are assumed. Additionally, a numerical solving strategy for the PDE model is presented. To show its efficiency, the algorithm is applied to the design of a double freeform mirror system and double freeform lens system.