Synthesis of Electron Lenses

This paper is a review of different approaches to one of the most ambitious goals of Electron and Ion Optics: to produce elements and systems with prescribed first-order properties and minimal aberrations. Synthesis of such elements is usually done in two steps: the first is a search for a field distribution with the given properties and the second is the reconstruction of electrodes (pole pieces) that would produce this field distribution. The first problem can be solved by the use of different techniques: Calculus of Variations, Dynamic Programming or Function Minimization. The second one is more complicated and requires a lot of ingenuity. Our novel approach takes a different course of action. It combines the two steps into one. Low-aberration field distributions are sought by dynamic programming or function minimization procedures in the form of continuous curves constructed of cubic splines. A very simple algorithm is used for the reconstruction of the electrodes or pole pieces. This approach combines the widely recognized advantages of our optimization techniques with a built-in accurate and effective reconstruction procedure. The final design is simplified on the basis of the requirements of manufacturability. High-quality electrostatic lenses have been designed by the use of this technique. Thus, electron and ion optical synthesis has been transformed from a dream to reality