An electron optical system can be optimized using the "simplex method" or "complex method". By these methods, the final structure of an electron optical system, for example, an extended field lens (EFL), can be searched with a criterion of minimum objective parameter (in the present case, the coefficient of spherical aberration). Because there is no constraint in the simplex method, the constrained optimization method (the complex method) described in this paper is better than the simplex method in the design of electron optical systems. In the simplex method as well as the complex method, it is not necessary to know the explicit functional relation between the objective function and the searching parameters; and the variations of aberration coefficient with respect to some machining tolerance can be easily obtained. Therefore, comparing with other optimization methods, the simplex method and complex method have significant advantage in the optimization design of electron optical systems.
Gu, Chang-xin and Shan, Li-ying
"Constrained Optimization Design of an Electron Optical System,"
Scanning Electron Microscopy: Vol. 3
, Article 9.
Available at: https://digitalcommons.usu.edu/electron/vol3/iss1/9