Synthesis of Electrostatic Electron Optical Systems

Abstract

A theory of synthesizing electrostatic electron optical system in three-dimensional electrostatic fields has been put forward in this paper. The general approach followed is to start with a suitable curvilinear coordinate system (u, ν, w) in which ν = constant and w = constant lines, are desired trajectories. The mathematical conditions, under which principal rays, i.e. ν = constant and w = constant lines, become dynamical trajectories with uniformity in focal properties of narrow pencils focusing on these principal rays, are obtained by writing down dynamical equations in various forms. These mathematical conditions when substituted in Laplaces equation for electrostatic potential distribution lead to the nature of the potential field required and the specific nature of the electron trajectories needed for constructing the curvilinear coordinate system for any electron optical system. The analysis shows that the principal rays of any electron optical system should be of type x = νf(z), where f(z) is a suitable exponential function. The potential field obtained to realize these electron optical systems varies exponentially in a direction perpendicular to the optical axis. It will be possible to realize such electron optical system by applying equipotentials on plane bounding surfaces by printed circuit techniques.