A simple model of holography and some enhanced resolution methods in electron microscopy

A simple pictorial model of electron interference effects based on an extended representation of the autocorrelation function is described and developed. Unlike Abbe's theory of transmission imaging, the model incorporates fully the effect of the loss of phase that occurs in the detector plane. The aperture transfer function and information limit (envelope function) are also incorporated with reference to the simplest scattering geometry of Young's slits. The model is then applied to holography, the diffraction phase problem, ptychography, Wigner distribution deconvolution, conventional bright-field imaging, single side-band imaging and tilt-series reconstruction. Some of these methods require an understanding of four-dimensional integral functions, but the model reduces the problem into a projection of a two-dimensional space. It is hoped that the model will help material scientists who are not specialists in imaging and diffraction theory to understand some recent developments in advanced super-resolution imaging methods.