Numerical correction of lens aberrations in phase-retrieval HRTEM

Phase-retrieval methods in high-resolution transmission electron microscopy allow one to determine the wave function at the exit-plane of the object (the exit-plane wave function). Viable methods for the retrieval of the exit-plane wave function are off-axis electron holography and focal-series reconstruction. In the framework of these methods, attention has been directed so far mostly at the correction of the wave function with respect to the “main” contributions to the aberration function, which are caused by the spherical aberration and by the defocusing of the objective lens. We describe a procedure which allows to measure and correct routinely for all relevant residual aberrations which may be present due to possible beam misalignment, 2-fold or 3-fold astigmatism. Using focal-series reconstruction it is demonstrated that a substantial gain in interpretable resolution can be observed in the retrieved wave function by taking into account these additional aberration effects.