Measurement of crystal thickness and crystal tilt from HRTEM images and a way to correct for their effects.

The effects of thickness and tilt angle are studied numerically on experimental high-resolution transmission electron microscope (HRTEM) images of a wedge-shaped metal oxide crystal. For sufficiently thin and well-aligned crystals, the amplitudes and phases of the Fourier transforms of the HRTEM images are essentially the same as the crystallographic structure factors. For tilted crystals, the changes of amplitudes and phases as a function of increased thickness and tilt angle can be described by a simple model. A method is presented by which the local thickness can be determined from one HRTEM image and one convergent-beam electron diffraction pattern from the same crystal. It is also shown how the projected potential can be reconstructed from HRTEM images of tilted crystals, disclosing the crystal structure, even from quite thick (>20 nm) samples.