Towards Quantitative Structure Determination Through Electron Holographic Methods

The problem of quantitative interpretation of high-resolution electron microscopy is studied in the framework of parameter estimation. Ideally, quantitative interpretation means that unknown structural parameters of an object such as atom types and coordinates are determined from fitting with the experimental dataset. However, in the imaging process, the influence of these parameters is completely scrambled over a large area of the image. As a consequence, the fitting becomes a search process in the higher dimensional space of all coupled parameters. The real importance of holographic methods such as off-axis holography and focus variation is that they restore (deblur) to some extent the imaging process so as to unscramble the influence of the different model parameters. In this way the dimension of the search space becomes manageable. In this framework the concept of resolution in the sense of Rayleigh is not valid anymore, but it has to be replaced by the notice of parameter precision. In case two atoms are very close, the parameter space may become degenerate so that the atoms cannot be discriminated. The probability of this degeneracy is a function of the distance between the atoms and the dose of the imaging particles.