Freeform surface topology prediction for prescribed illumination via semi-supervised learning

TL;DR

This paper introduces a semi-supervised deep learning framework that rapidly predicts smooth freeform surface topologies to generate prescribed illumination patterns, addressing complex inverse design problems in optics.

Contribution

It presents a novel semi-supervised neural network approach for freeform optical surface design, outperforming supervised methods by accounting for multiple solutions.

Findings

Semi-supervised learning outperforms supervised training in freeform topology prediction.

The framework can generate arbitrary irradiance patterns quickly.

Predicted topologies are smooth and suitable for practical optical applications.

Abstract

Despite significant advances in the field of freeform optical design, there still remain various unsolved problems. One of these is the design of smooth, shallow freeform topologies, consisting of multiple convex, concave and saddle shaped regions, in order to generate a prescribed illumination pattern. Such freeform topologies are relevant in the context of glare-free illumination and thin, refractive beam shaping elements. Machine learning techniques already proved to be extremely valuable in solving complex inverse problems in optics and photonics, but their application to freeform optical design is mostly limited to imaging optics. This paper presents a rapid, standalone framework for the prediction of freeform surface topologies that generate a prescribed irradiance distribution, from a predefined light source. The framework employs a 2D convolutional neural network to model the relationship between the prescribed target irradiance and required freeform topology. This network is trained on the loss between the obtained irradiance and input irradiance, using a second network that replaces Monte-Carlo raytracing from source to target. This semi-supervised learning approach proves to be superior compared to a supervised learning approach using ground truth freeform topology/irradiance pairs; a fact that is connected to the observation that multiple freeform topologies can yield similar irradiance patterns. The resulting network is able to rapidly predict smooth freeform topologies that generate arbitrary irradiance patterns, and could serve as an inspiration for applying machine learning to other open problems in freeform illumination design.