Light in Power: A General and Parameter-free Algorithm for Caustic Design

TL;DR

This paper introduces a versatile, parameter-free algorithm for designing optical components like mirrors and lenses that meet specific light energy constraints, using a unified framework based on visibility diagrams and Power diagrams.

Contribution

The paper presents a novel, generic algorithm that efficiently solves multiple optical design problems through a unified approach involving intersection of Power diagrams with domains.

Findings

Algorithm successfully designs optical components meeting energy constraints

Effective on both simulated and real-world fabricated examples

Supports various target illumination configurations and design constraints

Abstract

We present in this paper a generic and parameter-free algorithm to efficiently build a wide variety of optical components, such as mirrors or lenses, that satisfy some light energy constraints. In all of our problems, one is given a collimated or point light source and a desired illumination after reflection or refraction and the goal is to design the geometry of a mirror or lens which transports exactly the light emitted by the source onto the target. We first propose a general framework and show that eight different optical component design problems amount to solving a light energy conservation equation that involves the computation of visibility diagrams. We then show that these diagrams all have the same structure and can be obtained by intersecting a 3D Power diagram with a planar or spherical domain. This allows us to propose an efficient and fully generic algorithm capable to solve these eight optical component design problems. The support of the prescribed target illumination can be a set of directions or a set of points located at a finite distance. Our solutions satisfy design constraints such as convexity or concavity. We show the effectiveness of our algorithm on simulated and fabricated examples.