OBSERVATION OF LENS ABERRATIONS FOR VERY HIGH-RESOLUTION ELECTRON-MICROSCOPY .1. THEORY

Least-squares fitting methods are described, currently the most accurate known, for determining the imaging aberrations and other important parameters. The data required are either the image displacement or the image diffractogram shape (or both), as a function of injected beam tilt; the analysis is largely common to the two cases. Explicit solutions are given for some simple cases (e.g. coma-free alignment on the basis of three images only) and some promising developments are considered; the relevant aberration theory is set out in detail. Experimental work reported in a companion paper has confirmed the presence of threefold astigmatism at significant levels, but has not shown any evidence of other higher order aberrations.