Abstract
The purpose of this paper is to present a method for the design of two-reflector optical systems that transfer a given energy density of the source to a desired energy density at the target. It is known that the two-reflector design problem gives rise to a Monge-Amp`\{e}re equation with transport boundary condition. We solve this boundary value problem using a recently developed least-squares algorithm [1]. It is one of the few numerical algorithms capable to solve these type of problems efficiently. The least-squares algorithm can provide two solutions of the Monge-Amp`\{e}re problem, one is concave and the other one is convex. The reflectors are validated for several numerical examples by a ray-tracer based on Monte-Carlo simulation.
| Original language | English |
|---|---|
| Article number | 034001 |
| Number of pages | 16 |
| Journal | JPhys Photonics |
| Volume | 1 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 16 Jul 2019 |
Keywords
- least-squares method, Monge-Amp\`{e}re equation, inverse problem, transport boundary conditions, optical design, freeform optics, ray tracing
- Inverse reflector problem
- Least-squares method
- Monge–Ampère equation
- Freeform optics