Lorentz microscopy or electron phase microscopy of magnetic objects

The aim of Lorentz electron microscopy is to render visible and make quantitative measurements on the phase variations associated with magnetic specimens. The theory of image formation in the defocus mode is therefore presented in full, beginning with a discussion of resolution and of image formation in the electron microscope. The interaction of electrons with magnetic fields is analyzed and the semi-classical approximate solutions of Schrödinger's equation are summarized. The magnetic phase object is considered and a short section is a reminder of the Aharanov-Bohm effect, first noticed by Ehrenberg and Siday and even earlier by Franz. The interference fringes seen in images of magnetic domain walls are then described and Fraunhofer fringes are likewise studied. A long critical section is devoted to calculation of the image intensity and the validity of the ‘pseudo-classical approximation’ is assessed. Image transfer theory for this situation is described and a final section returns to domain wall measurements. © 2021 Elsevier Inc.