逐步逼近法计算LED透镜

Successive Approximation Calculations of LED Lens

提出了一个逐次逼近的计算方法,扩展了对LED自由曲面透镜的计算能力。首先用光通量线方法计算来自LED的n条光线的角度,使它们携带着相同的能量;再由照度分布要求求得像面上n个目标落点的位置。设定一个尝试平面为透镜的最后一面,并任意给定此平面上的n个尝试折射点位置,从而得到n个总的光线偏折角。按给定的透镜各面偏折光线能力的权重把总偏折角分配到各面,得到每个表面前后的光线角度,再用折射定律求得构成各面的n个连续的小面。同时可得到光线的修正方向,用于下一次循环计算。这样逐次逼近计算,直至误差满足预先给定的任意小量的要求。新方法可以用于多种计算,包括像面照度分布事先给定、一个或多个透镜的形状的同步计算、远场或近场照明、照明面是平面或曲面,或者以上这些情况的结合。该方法有很强的计算能力,简单易行,且以一个很快的收敛速度达到相应的精度。

A successive approximation method is proposed in this paper, which greatly extends the computational power of the LED lens shape with free form surface. In this method, the angles of the n rays from the LED are calculated firstly using the LFR (Light Flux Ray) method, so that they carry the same energy. The positions of the target n drop points of LFR on the image surface can be obtained according to the requirements of the illumination distribution. An attempt plane is set as the last surface of the lens and the positions of n attempt refraction points on this plane are given arbitrarily, so as to get the n total deflection angles of each ray. These angles are distributed to each surface according to the weight of the deflection light ability given previously, then the ray angles before and after each surface are obtained. Then, by using the law of refraction, the consecutive n facets are obtained which constitute the lens surface. At the same time, the corrected ray directions can be obtained for next cycle calculation. So the successive approximation is computed until the error satisfies any small amount specified in advance. This new method can be used for a wide variety of calculation, including the illumination distribution was given beforehand, the shape with one or more lens are calculated synchronously, the lighting surface location is near or far field, the shape of the lighting surface is flat or curved etc., or their combination of the above. Therefore it has very strong calculating ability and very wide scope of applications. This method is simple and easy to be achieved, and any high computational accuracy can be achieved with a fast convergence speed.