Imaging electron-optics and spatial-temporal aberrations for a bi-electrode spherical concentric system with electrostatic focusing

In the present paper, based on the practical electron ray equation and the electron motion equation,for a bi-electrode concentric spherical system with electrostatic focusing, the spatial-temporal trajectories of moving electrons emitted from the photocathode are obtained, the exact and the approximate formulae for image position and flight time of electrons are deduced. Starting from the solutions of spatial-temporal trajectories, the electron optical spatial-temporal properties of this system are then discussed. A unified definition of spatial-temporal aberrations is given, in which the lateral aberration can be regarded as a combination of paraxial lateral aberration and geometrical lateral aberration; and the temporal aberration can be regarded as a comibination of paraxial temporal aberration and geometrical temporal aberration. All expressions of these corresponding aberrations are deduced.