Limits of realizing irradiance distributions  with shift-invariant illumination systems and finite étendue sources

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.

show abstract

Optimizing freeform lenses for extended sources with algorithmic differentiable ray tracing and truncated hierarchical B-splines

Heemels,

de Koning,

Möller

et al. 2024

Opt. Express

View full text Add to dashboard Cite

We propose a method for optimizing the geometry of a freeform lens to redirect the light emitted from an extended source into a desired irradiance distribution. We utilize a gradient-based optimization approach with MITSUBA 3, an algorithmic differentiable non-sequential ray tracer that allows us to obtain the gradients of the freeform surface parameters with respect to the produced irradiance distribution. To prevent the optimizer from getting trapped in local minima, we gradually increase the number of degrees of freedom of the surface by using Truncated Hierarchical B-splines (THB-splines) during optimization. The refinement locations are determined by analyzing the gradients of the surface vertices. We first design a freeform using a collimated beam (zero-etendue source) for a complex target distribution to demonstrate the method’s effectiveness. Then, we demonstrate the ability of this approach to create a freeform that can project the light of an extended Lambertian source into a prescribed target distribution.

show abstract

Limits of realizing irradiance distributions with shift-invariant illumination systems and finite étendue sources

Cited by 4 publications

References 29 publications

Spherical-freeform lens design for uniform illumination based on differentiable ray tracing with uv polynomials

Spherical-freeform lens design for uniform illumination based on differentiable ray tracing with uv polynomials

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

Optimizing freeform lenses for extended sources with algorithmic differentiable ray tracing and truncated hierarchical B-splines

Contact Info

Product

Resources

About