Fresnel reflections in inverse freeform lens design

TL;DR

This paper introduces a novel method for designing freeform lenses that accounts for Fresnel reflections, combining optical mapping and energy balance to improve transmitted intensity predictions.

Contribution

It develops a new approach integrating Fresnel reflection effects into freeform lens design using a generalized Monge-Ampère equation and a numerical solver.

Findings

Successfully applied to theoretical and practical road lighting cases.

Enhanced accuracy in predicting transmitted light intensity.

Provides a framework for incorporating reflection losses in lens design.

Abstract

In this paper we propose a method to design a freeform lens including the effect of Fresnel reflections on the transmitted intensity. This method is elaborated for a lens with one freeform surface shaping a far-field target from a point source or collimated input beam. It combines the optical mapping with the energy balance incorporating the loss due to Fresnel reflections, which leads to a generalized Monge-Amp\`ere equation. We adapt a least-squares solver from previous research to solve the model numerically. This is then tested with a theoretical example and a test case related to road lighting.