Local versus Global Optimization of Electron Lens System Design

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In electron optics, the design of electron lens systems is still a challenge. To optimize such systems, the objective function which should be calculated, depends on the electric potential distribution in the space created by the lenses. To obtain the electric potential, the existing methods are generally based on some mathematical techniques which need to mesh the space of the lens system and derive the electric potential at all mesh points. Hence, calculation of the objective function for such systems are computationally expensive. Therefore, applying a fully automatic optimization routine has not yet been feasible, especially for lens systems with many free variables. Hence, the study of objective-function landscape of such problems has not yet been performed. One of the questions of interest for optical designers, that has not been studied in the literature, is whether this problem can be solved by a local optimizer or is it necessary to apply a global optimizer. Recently we succeeded in implementing a method (based on a so-called SOEM (Second Order Electrode Method) technique) which calculates the electric potential in a fast and reasonably accurate way. In this paper, that method, is implemented to perform the study of local versus global optimization for electron lens design. The global optimization method here is performed by GA (Genetic Algorithm). The objective function is taken to be the probe size of the electron beams at the image plane. The results of our study show that the objective function of this problem has many local minima and the optimization of such problems cannot be handled by a local optimizer. GA is shown to perform well by overcoming these multiple-local minima to arrive at a global minima.

Original languageEnglish
Title of host publication6th International Conference on Optimization and Applications, ICOA 2020 - Proceedings
EditorsHanaa Hachimi, Mohammed Kaicer, Adnane Addaim, Said Melliani
Place of PublicationPiscataway, NJ, USA
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
ISBN (Electronic)9781728166544
Publication statusPublished - 2020
Event6th International Conference on Optimization and Applications, ICOA 2020 - Beni Mellal, Morocco
Duration: 20 Apr 202021 Apr 2020


Conference6th International Conference on Optimization and Applications, ICOA 2020
CityBeni Mellal
OtherVirtual/online event due to COVID-19

Bibliographical note

Virtual/online event due to COVID-19

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Electron Lens Design
  • Genetic Algorithms
  • Global Optimization
  • Local Optimization
  • SOEM (Second Order Electrode Method)


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