Computational Caustic Design for Surface Light Source

2025-11-12

AI Summary

Conventional freeform optical design methods assume point or collimated sources, leading to inaccurate caustic control under realistic extended light sources. Method: This paper proposes a differentiable joint optimization framework for extended-source illumination. First, arbitrary extended sources are approximated via a differentiable rendering-based optimization that identifies an optimal set of point sources—without requiring prior knowledge of the source’s intensity distribution. Second, a contraction mapping is introduced to implicitly enforce surface normal integrability and photometric flux conservation, transforming constrained optimization into an unconstrained one. Finally, the source representation and freeform surface geometry are co-optimized in an end-to-end differentiable pipeline. Results: Simulations and physical experiments demonstrate that the method substantially outperforms traditional point-source approximations, generating high-fidelity, target-consistent caustics even with unknown source radiance distributions. It significantly improves both design accuracy and practical applicability of freeform optics in real-world lighting scenarios.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Learning & Optimization for CV
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Responsible Web: Algorithmic accountability and transparency on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Designing freeform surfaces to control light based on real-world illumination patterns is challenging, as existing caustic lens designs often assume oversimplified point or parallel light sources. We propose representing surface light sources using an optimized set of point sources, whose parameters are fitted to the real light source's illumination using a novel differentiable rendering framework. Our physically-based rendering approach simulates light transmission using flux, without requiring prior knowledge of the light source's intensity distribution. To efficiently explore the light source parameter space during optimization, we apply a contraction mapping that converts the constrained problem into an unconstrained one. Using the optimized light source model, we then design the freeform lens shape considering flux consistency and normal integrability. Simulations and physical experiments show our method more accurately represents real surface light sources compared to point-source approximations, yielding caustic lenses that produce images closely matching the target light distributions.

Problem

• Designing freeform surfaces for complex surface light sources
• Optimizing point source representation using differentiable rendering
• Ensuring flux consistency and normal integrability in lens design

Innovation

• Representing surface lights via optimized point source set
• Using differentiable rendering without intensity distribution knowledge
• Applying contraction mapping for unconstrained optimization space