Reconstruction of electrodes and pole pieces from randomly generated axial potential distributions of electron and ion optical systems

摘要

The purpose of this investigation is to examine synthesis for reconstruction of electrostatic lenses having an axial potential distribution four times continuously differentiable. The solution of the electrode and pole piece reconstruction is given. Spline functions are used to approximate a continuous function to fit a curve. The present method of synthesis is based on cubic spline functions, which have only two simultaneous continuous derivatives, and all the other higher derivatives are ignored. The fifth-order or quintic spline is introduced simply because it has four simultaneous continuous derivatives. So the reconstruction program would have three terms appearing in the series expansion of the off-axis potential distribution, with regard to two terms when using cubic functions.