Computation of optical properties off the Gaussian plane for electron-beam systems

A new method has been developed for computing the electron-optical properties on and off the Gaussian image plane for an electron optical system comprising any combination of magnetic and electrostatic lenses and deflectors. Formulae, with which the electron beam size and profile can be modelled in any image plane, have been derived to compute the general electron trajectories based on the third-order geometrical aberrations and first-order chromatic aberration. The shapes and positions of the crossover in the object plane and of the final aperture are used as the initial conditions to define the electron beam, which enables estimation of the effects of the misalignments of the source and the aperture. The electron distribution at the source has been taken into account to calculate the images. Computer programs using the new formulae have been developed. Some examples and discussions are presented in this paper.