标题： 点对点双反射器逆向非球面设计的数学模型 显示英文标题

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

摘要： 在本文中，我们讨论了一个数学模型，用于具有两个反射器的光学系统的逆向非球面设计，其中光线从点光源传输到点目标。 在这个模型中，从点光源发出的光强分布和到达点目标的照度分布是通过分布来指定的。 为了确定光学映射和反射器的形状，我们使用光程长度并考虑能量守恒，从而得到一个生成的雅可比方程。 我们将系统分别表示为球坐标和立体投影坐标，并使用一种复杂的最小二乘算法进行求解。 几个示例说明了该算法处理复杂光分布的能力。 显示英文摘要

摘要： 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.