A mathematical model for inverse freeform design of a point-to-point two-reflector system

TL;DR

This paper develops a mathematical model for designing two-reflector optical systems that precisely control light transfer from a point source to a point target, using advanced coordinate systems and numerical algorithms.

Contribution

It introduces a novel inverse design model for two-reflector systems incorporating energy conservation and optical path length, solved via a least-squares algorithm.

Findings

Successfully models complex light distributions

Demonstrates effectiveness of the numerical algorithm

Provides a versatile framework for freeform reflector design

Abstract

In this paper, we discuss a mathematical model for inverse freeform design of an optical system with two reflectors in which light transfers from a point source to a point target. In this model, the angular light intensity emitted from the point source and illuminance arriving at the point target are specified by distributions. To determine the optical mapping and the shape of the reflectors, we use the optical path length and take energy conservation into account, through which we obtain a generated Jacobian equation. We express the system in both spherical and stereographic coordinates, and solve it using a sophisticated least-squares algorithm. Several examples illustrate the algorithm's capabilities to tackle complicated light distributions.