基于子曲面分割和迭代的自由曲面光线追迹方法

Ray tracing method of optic free-form surface based on segmentation and iteration of sub-surface

根据光学自由曲面数学描述复杂,但面形较为平滑的特点,提出一种新的基于子曲面分割和迭代的自由曲面光线追迹方法。通过离散点分割形成子曲面阵列,根据三角形内角和定理确定目标子曲面,对目标子曲面进行切平面迭代完成光线追迹。通过数值仿真,采用所提方法分别对偶次非球面、双圆锥曲面、扩展多项式面和单透镜无像散系统进行光线追迹,并与ZEM-AX追迹结果进行比对。结果表明:该方法在离散点采样密度很低的情况下(降低了计算机的内存消耗和运算时间)仍然可以保证光线追迹的精确性,与ZEMAX中光线和自由曲面交点的偏差达到10-3(nm)量级,出射光线角度的偏差达到10-3(")量级。

A novel method based on segmentation and iteration of sub-surface is presented as the description of optic free-form surface, aiming at the complex and relatively smooth character of its figure. Three steps are executed in the whole process of ray tracing of free-form surface. Firstly the free-form surface is divided into some sub-surfaces by discrete points. Then the tar- get sub-surface is determined based on the angle sum of a triangle theorem. And finally the it- erative algorithm is utilized on the target sub-surface. Even asphere, biconic surface, extended polynomial surface and a single lens system with a free-form surface are set into simulation. The comparison between the result of the method presented and the result of ZEMAX shows that the method presented is of high precision, good versatility and high speed.