自由曲面配光中的鳞甲子面光通量计算

Flux calculation of a quadric reptile sub-surface in freeform optical design

二次支撑曲面设计方法是一种将多个二次子面拼接形成一个鳞甲光学面来获得目标面上离散光分布的自由曲面光学设计方法,而如何高精度求解子曲面上的光通量是一个难题。现有的解决方案是光线仿真统计,存在效率低和精度低的缺陷。提出一套解析与数值方法相结合的求解思路,先解析求出相邻二次曲面的交线,再利用二分法确定交线作为子面边界的两个端点以确定边界区间,重复以上过程确定出所有边界,进而求得子面相对于光源的角空间,最终通过数值积分确定子面光通量。与现有统计方法相比,所提方法将子面光通量的计算精度由10-4提高到10-7,时间节省了近7倍。光学仿真和实验均验证了这种方法的有效性,对实现任意光分布的自由曲面配光设计具有实际的应用价值。

Supporting quadric method（SQM）is a nonimaging optical design method to obtain a reptile optical surface blending of some quadric surfaces,which can cast a discrete illuminance distribution on the target screen.It is difficult to calculate the flux through each sub-surface on the reptile surface due to the complicity of sub-area boundaries.The existing solution is the light statistics method,which has the shortcomings of low efficiency and low accuracy.A new solution combined with analytical and numerical methods is proposed.First,the intersection curve of two adjacent surfaces is solved.Then the intersection curve is used to determine the two endpoints of the subsurface edge,and all edges can be determined by repeating above process,then the angle space of the subsurface to the light source is obtained.A numerical integration method is adopted to calculate the illuminance flux through the subsurface.Compared with the existing method,the flux accuracy of the subsurface with our method is increased from 10-4 to 10-7 and the time saved by nearly 7 times.Both the results of optical simulation and experiment can show that this method is effective,and it is of practical value for the freeform optical design to generate an arbitrary light distribution.