辛卜森积分在非球面光学系统自动设计中的应用  

Application of Simpson numerical integral to the optical automatic design of aspherical optical systems

作　　者：王永仲[1] 王晓[1] 戴建宁[1] 

机构地区：[1]国防科技大学204光电对抗研究组

出　　处：《光学技术》1997年第4期1-4,共4页Optical Technique

摘　　要：为了克服非球面（特别是高次非球面）光学系统自动设计中的严重困难，我们运用辛卜森数值积分及若干数学处理建造了一种全新的优化指标——辛卜森指标。为减少实际追迹光线的计算量并同时满足辛卜森积分对等距节点上函数值的要求，采用拉格郎日插值方法计算若干非常规抽样光线对应的垂轴像差近似值。事实证明，辛卜森指标的引用可以迅速改善很差的初始结构，大大减少优化过程中的慢收敛、发散、震荡或“无解”，实现快速而稳定的优化；将它用于预优化过程，可以为后续自动设计提供优异的“雏型”结构，还可从纯球面系统入手，自动设计出理想的非球面系统；We calculate the approximate values of lateral aberrations of the extraordinary sampled rays with the aid of Lagrange’s interpolation formula, and apply Simpson numerical integral to calculating the areas of lateral aberration curves in order to construct the new type quality functions of image. Weighting the areas, summing the weighted areas and normalizing the sums, we get a kind of special optimization indexes that are extremely useful to the optical automatic design of aspherical optical systems and called Simpson indexes by us. They can be used for improving swiftly the bad original structures, avoiding slow convergence or divergence in the automatic optimization. We have applied them to pre optimization in order to supply the follow up automatic optimization with desired structure parameters. They can be also applied to determining automatically the reasonable increments of the aspherical coefficients for setting up the most effective difference matrixes that decide the solutions in automatic optimization. Starting with spherical structures, we can easily get expected aspherical systems with the aid of automatic optimization of the Simpson indexes. There is an example in the paper.

关 键 词：非球面 光学系统 辛卜森积分 光学自动设计 

分 类 号：TH740.2[机械工程—光学工程]