高精度高次非球面最接近球面计算方法

High accuracy algorithm for calculating best fitting sphere of high-order aspheric surface

分析了高次非球面与其加工用最接近球面之间的几何关系特点,提出了一种基于1维搜索的高精度高次非球面最接近球面计算方法。该算法可以计算二次或高次凹(凸)非球面的加工用最接近球面半径、球心位置及非球面度。通过计算实例与现有计算最接近球面的方法相比,该算法在计算高次非球面时将最大非球面度从500.8μm减小到30.0μm,在计算二次非球面时计算结果与精确公式法得到的结果一致。计算实例表明该方法计算高次非球面时得到的最接近球面更优、计算精度更高,且适用于任意次非球面最接近球面的精确计算。

A high accuracy algorithm based on one dimensional search which is used for calculating the BFS（best fitting sphere） of high-order optical aspheric surface is proposed,according to the geometric property between the aspheric surface and its BFS.This method can be used to calculate the radius and the center location of the BFS and the asphericity for conicoid and high-order aspheric surface（including concave and convex surfaces）.The analysis of calculation examples shows that,this method can reduce the maximum asphericity from 500.8 μm to 30 μm for high-order aspheric surface,and it can get the same asphericity for conicoid compared to other methods.In addition,it can get better BFS than other methods when used for high-order aspheric surface,and its fast speed and high accuracy make it suitable for calculating the BFS for aspheric surface of any order.