Determination and correction of the coherent wave aberration from a single off-axis electron hologram by means of a genetic algorithm

Using off-axis electron holography, the interpretable resolution can be improved up to the information limit of the electron microscope by means of a posteriori correction of the coherent wave aberration. Successful correction depends, however, on accurate determination of the coherent wave aberration effective in the particular hologram. Fortunately, both the wave aberration of the electron microscope as well as the object structure under investigation are saved in a single snapshot, the off-axis electron hologram. After recording and reconstruction of the hologram, the main task is the separation of microscope characteristics and object information on the basis of very general principles. In order to determine the aberration coefficients, an algorithm for determination and correction of the coherent wave aberration has been developed which is based on a combination of genetic algorithm and downhill-simplex algorithm. The basic criterion is the minimization of the amplitude contrast which is a well-established correction guideline for weak phase objects. The possibilities and the limitations of the determination algorithm are discussed and its successful application to holograms of an Si3N4 crystal is demonstrated where a small amorphous edge was sufficient for aberration determination.