Romijn L B, Anthonissen M J H, Ten Thije Boonkkamp J H M, IJzerman W L
J Opt Soc Am A Opt Image Sci Vis. 2021 Mar 1;38(3):356-368. doi: 10.1364/JOSAA.411883.
Many LED lighting applications involve the design of multiple optical surfaces. A prime example is a single lens with two refractive surfaces. In this paper, we consider an LED light source approximated as a point and a far-field target intensity. Using Hamilton's characteristic functions, the design problem is converted into two generalized Monge-Ampère equations by deriving a generating function for each optical surface. The generating function is a generalization of the cost function in optimal transport theory. The generalized Monge-Ampère equations are solved using an iterative least-squares algorithm. To compute the first optical surface, we choose an intermediate far-field target intensity. By choosing different intermediate target intensities based on the source and target intensity, we develop a "knob" to distribute the refractive power over both surfaces of the lens. We apply the algorithm on two example problems and show it is capable of producing complicated target distributions.
许多LED照明应用涉及多个光学表面的设计。一个典型的例子是具有两个折射面的单透镜。在本文中，我们将LED光源近似为一个点，并考虑远场目标强度。利用哈密顿特征函数，通过为每个光学表面推导一个生成函数，将设计问题转化为两个广义蒙日-安培方程。生成函数是最优传输理论中成本函数的推广。使用迭代最小二乘算法求解广义蒙日-安培方程。为了计算第一个光学表面，我们选择一个中间远场目标强度。通过根据光源和目标强度选择不同的中间目标强度，我们开发了一个“旋钮”来在透镜的两个表面上分配折射光焦度。我们将该算法应用于两个示例问题，并表明它能够产生复杂的目标分布。
