采样点分布对基于面形斜率径向基模型的自由曲面拟合精度的影响

Influence of sampling point distribution in freeform surfaces fitting with radial based function model

鉴于自由曲面模型的面形拟合精度在自由曲面表征以及面形初始结构选取等研究中的重要性,本文针对基于面形斜率的高斯径向基表征模型,研究了不同的采样点分布类型对该模型面形拟合精度的影响。采用不同采样点分布拟合离轴二次曲面和带凸起的抛物面,结果表明采用均匀随机分布的采样点有利于实现高精度的面形拟合,且达到一定的拟合精度后,采样点的数目对拟合精度的影响有限。以离轴三反系统为设计实例,对比了由不同采样方式生成初始面形后系统的像质优化结果。结果显示,采用均匀随机型采样方式得到的初始面形进行系统优化,最终全视场平均调制传递函数(MTF)可以达到0.72以上,远高于由边缘集中采样方式生成初始面形后系统像质的优化结果,从而印证了理论研究结果。

In view of the importance of surface shape fitting precision of free-form surface model in researches such as free-form surface representation and selection of initiating structure of surface shape,the influence of different sampling point distribution patterns on surface shape fitting precisionof the Gaussian Radial Basis Function Based on Slope（Gaussian RBF-BS）model was investigated.An off-axis quadric surface and an bumpy paraboloid were fitted with different sampling point distributions which were uniformly random points and edged-clustered points.The results show that the uniformly random grid is better for surface shape fitting due to the high precision.The influence of sampling point quantity on fitting precision remains constant when certain fitting precision is reached.The off-axis Three Mirror Anastigmat（TMA）system was optimized experimentally by using initial surface shapes generated with different sampling methods.The results show that,by using initial surface shape generated from uniformly random sampling method for the system optimization,the average Modulation Transfer Function（MTF）of whole field of view is more than 0.72,which is much higher than that by using surface shape generated by edge cluster sampling points.Thus the theoretical research results were verified.