Off-axis electron holography combining summation of hologram series with double-exposure phase-shifting: Theory and application

In this paper we discuss developments for Lorentz mode or “medium resolution” off-axis electron holography such that it is now routinely possible obtain very high sensitivity phase maps with high spatial resolution whilst maintaining a large field of view. Modifications of the usual Fourier reconstruction procedure have been used to combine series of holograms for sensitivity improvement with a phase-shifting method for doubling the spatial resolution. In the frame of these developments, specific attention is given to the phase standard deviation description and its interaction with the spatial resolution as well as the processing of reference holograms. An experimental study based on Dark-Field Electron Holography (DFEH), using a SiGe/Si multilayer epitaxy sample is compared with theory. The method's efficiency of removing the autocorrelation term during hologram reconstruction is discussed. Software has been written in DigitalMicrograph that can be used to routinely perform these tasks. To illustrate the real improvements made using these methods we show that a strain measurement sensitivity of  ±  0.025 % can be achieved with a spatial resolution of 2 nm and  ±  0.13 % with a spatial resolution of 1 nm whilst maintaining a useful field of view of 300 nm. In the frame of these measurements a model of strain noise for DFEH has also been developed.