光学多层薄膜反向工程中局部优化算法的性能分析

Performance Analysis of Local Optimization Algorithm in Reverse Engineering of Multilayer Optical Coatings

以锗基红外宽带增透膜(AR)为例,基于Matlab最优化工具箱,研究了多种局部优化算法在多层膜设计中的性能和反向工程算法开发中的可行性,并就数值实验中出现多解性问题的成因、分析及解决方案进行了探讨。结果表明,Matlab最优化工具箱中的导数算法在多层膜局部优化设计上具有更好的局部极值搜索性能和收敛速度;非导数算法性能较差且收敛时间较长,但具有更多的搜索路径,较适用于设计初期开拓搜索方向。在多层膜反演中,导数算法中的非线性最小二乘估计指令lsqnonlin和非线性方程求解指令fsolve的性能出色,建议作为多层膜反向工程问题的主要算法。无约束优化指令fminunc性能次之,约束优化指令fmincon再次之,可作为备用反演算法。而多目标优化指令fminimax和其余非导数算法由于算法的性能不足和自身内在多解性的原因,不利于多层膜的反演,容易得到错误的结果,不建议作为反演算法使用,仅可作为可选算法以供对比参考。

An infrared antireflection （AR） coating for germanium is taken as an example to numerically analyze the performance of the local optimization algorithm which is based on Matlab optimization toolbox in the local optimal design of multilayer optical coatings and their application feasibility in the algorithm development of reverse engineering of multilayer optical coatings. The reasons and the solutions of the mutiple solutions in numerical experiments are discussed. The numerical optimization results show that the derivative algorithms of Matlab optimization toolbox have better local optimum point search ability and converging speed than reference methods, While the performance of non-derivative algorithms is poor but might be applicable in the initial local design stage to explore more search directions. In the reverse engineering of multilayer optical coatings, the algorithm lsqnonlin and fsolve are excellent in inversion which determines the quality of optical structural parameters. They are recommended to be the main reverse engineering algorithms. The fminunc and fmincon algorithms can be chosen as supplementary reverse engineering algorithms for their acceptable reverse determination effectiveness. The fminimax and other non-derivative algorithms are poor in effectiveness and stochastic in final solutions, which can easily converge to wrong structural parameters and could not be used as reverse engineering algorithms.