Numerical correction of anti-symmetric aberrations in single HRTEM   images of weakly scattering 2D-objects
  Here, we present a numerical post-processing method for removing the effect of anti-symmetric residual aberrations in high-resolution transmission electron microscopy (HRTEM) images of weakly scattering 2D-objects. The method is based on applying the same aberrations with the opposite phase to the Fourier transform of the recorded image intensity and subsequently inverting the Fourier transform. We present the theoretical justification of the method and its verification based on simulated images in the case of low-order anti-symmetric aberrations. Ultimately the method is applied to experimental hardware aberration-corrected HRTEM images of single-layer graphene and MoSe2 resulting in images with strongly reduced residual low-order aberrations, and consequently improved interpretability. Alternatively, this method can be used to estimate by trial and error the residual anti-symmetric aberrations in HRTEM images of weakly scattering objects. 
Ossi Lehtinen, Dorin Geiger, Zhongbo Lee, Michale B. Whitwick,   Ming-Wei Chen, Andras Kis, Ute Kaiser
cond-mat.mtrl-sci physics.ins-det physics.optics