Prospects for quantitative and time-resolved double and continuous exposure off-axis electron holography

The technique of double exposure electron holography, which is based on the superposition of two off-axis electron holograms, was originally introduced before the availability of digital image processing to allow differences between electron-optical phases encoded in two electron holograms to be visualised directly without the need for holographic reconstruction. Here, we review the original method and show how it can now be extended to permit quantitative studies of phase shifts that oscillate in time. We begin with a description of the theory of off-axis electron hologram formation for a time-dependent electron wave that results from the excitation of a specimen using an external stimulus with a square, sinusoidal, triangular or other temporal dependence. We refer to the more general method as continuous exposure electron holography, present preliminary experimental measurements and discuss how the technique can be used to image electrostatic potentials and magnetic fields during high frequency switching experiments.