摘要
本文以多元复合函数的微分法则为基础，从光线追迹公式中对象面上光线坐标对结构参数的一阶解析偏导数进行了推导，并首次提出了光线坐标对结构参数二阶偏导数解析求导的算法。以此为基础可以进一步得到光学自动设计中各种象差及目标函数对设计变量的所有解析一阶、二阶偏导数。本文同时给出了相应的推导过程和计算实例。通过与差分法求导对比计算表明：解析偏导数不仅无原理误差，而且大大地减少了计算量，可直接应用于光学系统优化设计。
With its simplifies,the difference method to obtain derivatives of the merit function with respect to variables is used by almost every program in lens optimization design. However,calculation of the derivatives by this method is the most time-consuming aspect of the problem. In addition,if the difference increment is not suitable,the computing errors produced by the method are much greater,which usually makes the alternating course of optimization end unexpectedly. Here,a novel algorithm to calculate first and second analytical derivatives is first described in this paper. Based on the differential law of complex function,the first and second analytical derivatives of ray coordinates in the image plane with respect to construct parameters such as radius, thickness etc. can be obtained from only one raytracing. On the basis of this,the first and second derivatives of the merit function with respect to design variables can be easily obtained. The relevant deduction process and examples of computation are also given. The results of practical computations show that it takes much less time (especially for the second derivatives )to obtain the derivatives by the analytical method than by a difference method under the condition that the analytical derivatives have no errors in principle. The analytical derivatives can be used in lens optimization design to improve the quality and to shorten the period of the design.
出处
《仪器仪表学报》
EI
CAS
CSCD
北大核心
1996年第3期278-284,共7页
Chinese Journal of Scientific Instrument
关键词
解析偏导数
光学优化设计
光线追迹
Analytical derivatives,Lens optimization design,Ray tracing.
