Practical optimization of electrostatic lenses

A method for the optimization of electrostatic lenses is presented. It is applied to optimize several three‐electrode lens designs for particular applications. The free parameters of the optimization are the physical quantities describing the shape of the lens: the electrode thicknesses, the gaps between the electrodes, and the electrode radii at a number of axial points for each electrode. With these parameters a cubic spline approximation to the axial potential is found by solving a system of linear equations. The method has been named the second‐order electrode method. Constraints for the optimization are the working distance on object and image side, a breakdown limit on off‐axis field strength, a limit to electrode potentials and minimum and maximum values for all parameters. No constraints are used to keep the object and image at their specified position. Before each merit function evaluation the middle electrode excitation is adjusted in order to satisfy the specified first‐order optical properties, so this construction keeps the first‐order properties out of the optimization. The figure of merit is application dependent and is a function of the chromatic and spherical aberration coefficients. The optimization method is based on a nonlinear optimization algorithm.