Minimum-dose phase-contrast tomography by successive numerical optical sectioning employing the aberration-corrected STEM and a pixelated detector.

Aberration correction combined with a pixelated detector enable atomic-resolution phase-contrast imaging in the scanning transmission electron microscope (STEM) using all elastically scattered electrons within the illumination cone. The review describes this possibility in detail revisiting the image formation in the STEM on a fundamental quantum-mechanical treatment of electron scattering within the object and the effect of the lenses on the electron wave. Describing electron scattering by means of scattering amplitudes enables a straightforward derivation of a) the reciprocity theorem, b) the optical theorem of electron scattering, and c) the precise formulation of the image intensity distribution in the STEM for different modes of operation. The second part of the review describes in detail a novel method for obtaining pure phase-contrast images in the STEM using the integrated differential phase-contrast (IDPC) procedure. The incorporation of a chromatic (Cc) and spherically (Cs) corrected objective lens and a pixelated detector in the STEM combined with numerical through-focusing enables optical sectioning with atomic 3D resolution of thick objects with about the same dose as that for a 2D object, at least in principle. Numerical simulations of the IDPC transfer function and the point spread function for the focal plane and several reconstructed defocused planes demonstrate the feasibility of the method.