Nonlinear programming and scientific computing visualization in the optimization design of electron optical system

In part I of this paper, five different nonlinear programming methods, improved Powell method, axis directional search method with fixed step, Hook–Jeeves method, axis directional search method with variable step and Rosenbrock method, are discussed for the optimization design of electron optical systems. Major aspects of these techniques in their applications are systematically studied, which include convergence rate, optimal objective function value and global convergence. The calculation results indicate that Rosenbrock method should be recommended in electron optical system optimization. In part II of this paper, an efficient method, reverse-match interpolation method, is presented for the visualized optimization design of electron optical systems, which is a new development of CAD in electron optics. This method can produce the density distribution of electron beam from electron trajectories worked out in the optimization search process. It makes real-time control system possible.