基于Buchadhl象差系数和解析偏导数的光学优化设计

本文以基于 Buchadhl 象差系数得到的点列图为目标函数,只需追迹少许光线就可得到近似点列图,大大减少了计算量;同时采用了目标函数对结构参数偏导数解析求导原理并应用于光学自动设计,这样得到的解析偏导数不仅不存在原理误差,同时极大地减少了求得所需的时间;最后给出了使用 DFP-BFGS 优化方法设计一个双高斯物镜的实例.

LENS OPTIMIZATION DESIGN BASED ON BUCHADHL′S ABERRATION COEFFICIENTS AND ANALYTICAL DERIVATIVES

Many of the lens design computer programs use RMS spot size,which is direct measures of the image quality of the design and is commonly obtained by tracing grids of rays through the lens,as a merit function and optimize a design by reducing the spot size to zero or to some target value.The method,while very convenient,can be an expensive way to optimize a lens because of the number of rays that must be traced to get a real spot diagram.Here,we have developed another approach.Based on the Buchdahl’s optical aberration coefficients,we replace the summations in an ordinary spot diagram calculation with integrals over the aperture and thereby obtain the spot diagrams,thus decreasing by the time of computing spot diagrams.With its simplifications,the difference method to obtain derivatives of the merit function with respect fo the 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.Based on the differential law of complex functions,an analytical method to compute the derivatives is described in this paper.The analytical derivatives obtained by this method have the advantages that ist spends much less computing time and has no error in principle.Most lens design calculations today are carried out on large computer programs with an optimization algorithm based on the damped-least-squares method or a variation.Here we use a DFP- BFGS optimization method,which is commonly used by other optimization design programs such as machinery desing program.An example of designing a Gauss objective by this optimization method is given out.