Static and dynamic imaging electron optics and spatial–temporal aberrations in a bi-electrode spherical concentric system with electrostatic focusing

In imaging electron optics, for a concentric spherical system composed of two spherical electrodes with electrostatic focusing, the electrostatic potential distribution and the spatial–temporal trajectory of electron motion can be expressed by analytical forms. It is naturally to take such system as an ideal model to investigate the imaging properties, as well as the spatial–temporal aberrations, to analyze its particularity and to find the clue of universalities and regularities. Research on this problem has important significance, which can afford theoretical foundation not only in studying static electron optics for the night vision devices, but also in studying dynamic electron optics for high-speed image converter tubes.In the present paper, based on the practical electron ray equation and electron motion equation for a bi-electrode concentric spherical system with electrostatic focusing, the spatial–temporal trajectories of moving electrons emitted from the photocathode have been solved, the exact and approximate formulae for image position and flight time of electrons, have been deduced. Start from solutions of spatial–temporal trajectories, the electron optical spatial–temporal properties of this system are then discussed. According to the definitions of spatial–temporal aberrations, the paraxial and geometrical lateral aberrations, as well as the paraxial and geometrical temporal aberrations, have been deduced, that are classified by the order of εz/ϕac and εr/ϕac.