光学优化设计中一阶和二阶偏导数的解析求法

计算物理 ›› 1996, Vol. 13 ›› Issue (1): 92-100.

光学优化设计中一阶和二阶偏导数的解析求法

冯其波

北方交通大学物理系北京 100034

收稿日期:1994-08-28 修回日期:1995-10-04 出版日期:1996-03-25 发布日期:1996-03-25

AN ALGORITHM TO CALCULATE FIRST AND SECOND ANALYTICAL DERIVATIVES IN LENS OPTIMIZATION DESIGN

Feng Qibo

Department of Physics, Northern Jiaotong University, Beijing 100044

Received:1994-08-28 Revised:1995-10-04 Online:1996-03-25 Published:1996-03-25

摘要/Abstract

摘要： 以复合函数的微分法则为基础,提出了光学设计中目标函数对结构参数一阶和二阶偏导数解析求导的方法,给出了相应的推导过程和计算实例。

关键词: 一阶偏导数, 二阶偏导数, 光学优化设计, 光线追迹

Abstract: A novel algorithm to calculate first and second derivatives in lens optimization design is described.Based on the differential law of complex function,the first and second analytical derivatives of ray coordinates in the image plane with respect to 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 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 the difference method.

Key words: First and Second Derivatives, Lens Optimization Design, Ray Tracing

中图分类号:

TB133

冯其波. 光学优化设计中一阶和二阶偏导数的解析求法[J]. 计算物理, 1996, 13(1): 92-100.

Feng Qibo. AN ALGORITHM TO CALCULATE FIRST AND SECOND ANALYTICAL DERIVATIVES IN LENS OPTIMIZATION DESIGN[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1996, 13(1): 92-100.