一种LED光源矩形斑照明的优化算法及其仿真

微分方程求解法是设计自由曲面最常用的一种方法之一,此方法是通过建立照明源与被照明面之间的几何关系,来实现自由曲面的数值求解。通常会基于照明光源的光分布与被照明面的照明要求,建立一组偏微分方程,方程组的未知数为自由曲面的每一个节点的坐标和曲率值。通过能量守恒原理,解出所需要的自由曲面每个节点的具体坐标值。在现有微分方程理论的基础上,通过分割自由曲面和变步长的龙格-库塔算法,大幅改善了矩形照明斑的形状、能量利用率及均匀性等,对矩形照明斑质量实现了优化。

Optimization algorithm and simulation of rectangle lighting using an LED source

The differential equation solution is the most commonly used method in the design of free form surfaces. This method is achieved by establishing the geometric relationship between the illumination source and the illumination surface to calculate the values of the free form surface. Usually, a set of partial differential equations is created based on the distribution of illumination light source and the illuminated surface lighting requirements, and unknowns to be solved by the equations are set to be the coordinates and curvature values of the free-form surfaces of each node, and then by the principle of conservation of energy, the solution of the free curved specific coordinate values of each node is obtained. On the basis of the existing theory of differential equations, by dividing the free-form surface and variable step size Runge Kutta algorithm, the parameters of the shape of the illumination spot, energy efficiency and uniformity are improved. In this way, an optimization of rectangular spot lighting quality is realized.