Fig. 4

Residual aberration correction applied to a focal series reconstruction of a \(\beta\)-Si\(_3\)N\(_4\) sample. a Reference region of the exit wave with atomic sites shown on half of image. b Complex atomic shape functions \(\mathbf {s}_1\) and \(\mathbf {s}_2\) for Si and N respectively. c Mean absolute difference of exit wave between each iteration. d Progression of the aberration correction algorithm, showing amplitude and phase of current corrected exit wave and symmetrized exit waves, phase difference of the Fourier transforms, and the fitted aberration function \(\chi (q_x,q_y)\) with an outer radius of 15 nm\(^{-1}\)