Computational Caustic Design for Surface Light Source

TL;DR

Realistic caustic design requires modeling extended LED surface light sources rather than ideal point or parallel sources. The authors introduce a differentiable flux-based rendering framework and represent a planar light source with $N$ point lights $(x_k,y_k,q_k)$ whose parameters are optimized to match ground-truth caustics; this light-source model then guides a separate freeform lens optimization using flux, image, and regularization losses. Key contributions include a practical surface light-source representation, a fully differentiable flux transport renderer, and a caustic-design workflow that yields patterns far closer to targets than point-based designs, demonstrated in simulations and physical prototypes. The work advances high-fidelity caustic design for real-world illumination with potential impact in architectural and industrial optics, while promising extensions to curved light sources and colored caustics and integration with fabrication processes.

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.

Figures (19)

• Figure 1: The rendered results of the optimized freeform surface lens under the illumination of a surface light source according to the target image. The above lenses were obtained through the caustic design based on a point light source and an optimized surface light source model, respectively. The light pattern produced by the caustic lens based on our method closely resembles the target image. Some regions are enlarged for better inspection of details.
• Figure 2: Light source model optimization process: optimizing the surface light source model based on the difference between the rendering result and the reference image.
• Figure 3: The surface light source model. Each point light source in this model contains three attributes: $x$-coordinate, $y$-coordinate, and its illumination intensity $q_k$.
• Figure 4: Our rendering model. It consists of three components: an input light source, a lens, and a receiving plane. The light undergoes two refractions through the front and back surfaces of the lens before forming an image on the receiving plane.
• Figure 5: Schematic diagram of solid angle calculation: $\vec{r_1}$, $\vec{r_2}$ and $\vec{r_3}$ are the unit vectors connecting $l^k$ and the three vertices of $t_i^k$.