Estimation of wave fields of incident beams in a transmission electron microscope by using a small selected-area aperture

The direction of an electron beam in a nanometer-sized area is measured directly by utilizing a selected-area aperture. By the measurements at several areas in a beam, the wavefront curvature and thus the defocus value of the beam are detected. From the defocus value, the wave field at the specimen plane is also reproduced in consideration of the influences of the condenser aperture and spherical aberration of the illumination lens. The result shows that phase deviation of 2π is caused only at about 10 nm apart from the beam center in a beam with a typical diameter for high-resolution transmission electron microscopy. Based on the defocus value, the convergence angle of the beam is also estimated to be about 6 mrad without being influenced by the partial coherence, that is, independently of the type of the electron gun. Measuring the defocus values for only two beam diameters enables us to determine geometrical parameters peculiar to the illumination system, based on which wave fields of any beam diameters by any condenser aperture sizes can be estimated. The technique proposed in this paper is effective in evaluating the influence of wavefront curvature of incident beams on various kinds of precise measurements conducted in transmission electron microscopes.