Comparison of Different Optimization Techniques in Electron Lens Design

Abstract

To design electron lens systems, applying a fully automated optimization routine has not yet been feasible, especially for the case where the optimization has many free variables of the lens system, such as all parameters that define the geometry of the lens electrodes and the voltage of each electrode. Hence, the study of the implementation of different optimization procedures has not yet been possible either. In one of our previous studies, we have proposed to use the so-called Second Order Electrode Method (SOEM) which performs the electrostatic field calculations in a very short time by the approximations of the field near the optical axis. There, using SOEM in field calculation, a Genetic Algorithm (GA) was successfully implemented to optimize the electron lens systems. One of the questions that has not been studied and answered in the literature yet, is whether the GA is the most suitable option among different optimization techniques for the design/optimization of electron lens systems. In this paper, by implementing the SOEM technique as the field calculation method, different optimization procedures are implemented and their performances are compared. For this study, a typical six electrode lens system is employed. The implemented optimization techniques include calculus-based local optimization (‘Fmin’) and metaheuristic methods such as GA, Particle Swarm Optimization (PSO), and Simulated Annealing (SA). The results demonstrate that the population-based global optimization techniques like GA and PSO significantly outperform single-based local optimization methods such as ‘Fmin’ and SA. Additionally, PSO shows slightly better performance than GA, although it cannot be concluded that PSO will always outperform GA for every electron lens design problem. Furthermore, in the comparison between the two single-based optimization techniques, the metaheuristic approach (SA) outperforms the calculus-based one (‘Fmin’). Hence, we recommend implementing metaheuristic, global, population-based optimization techniques like GA and PSO for the optimization electron lens systems.