Fig. 2

a Electron probe intensity and b phase distribution obtained by correcting all the aberrations (up to the fifth order) of the electron optics (corrected probe). The distortion observed in the probe intensity from an ideal Airy-Gaussian-like shape, and in the probe phase from an ideal zero phase, is due to the residual third order (C₃₂) aberrations. c Electron probe intensity and d phase distribution obtained by correcting all the aberrations (up to the fifth order) with the exception of fourfold astigmatism, C₃₄, which was explicitly set to 15 μm. The aberrated electron probe still has an atomic size, but it also shows tails with relative large intensities when compared with the corrected probe. The phase distribution of the tails has a fourfold symmetry that varies from π/2 to −π/2 between each adjacent tail. e, f Z-contrast STEM images of a LaMnAsO grain oriented along the c-axis and obtained with the corrected probe [shown in (a)] and with the C₃₄ aberrated probe [shown in (c)], respectively. Insets in (e, f) schematically illustrate the position of the La/As, Mn↑/O and Mn↓/O atomic columns