The three-dimensional point spread function of aberration-corrected scanning transmission electron microscopy

Aberration correction reduces the depth of field in scanning transmission electron microscopy (STEM) and thus allows three-dimensional (3D) imaging by depth sectioning. This imaging mode offers the potential for sub-Ångstrom lateral resolution and nanometer-scale depth sensitivity. For biological samples, which may be many microns across and where high lateral resolution may not always be needed, optimizing the depth resolution even at the expense of lateral resolution may be desired, aiming to image through thick specimens. Although there has been extensive work examining and optimizing the probe formation in two dimensions, there is less known about the probe shape along the optical axis. Here the probe shape is examined in three dimensions in an attempt to better understand the depth resolution in this mode. Examples are presented of how aberrations change the probe shape in three dimensions, and it is found that off-axial aberrations may need to be considered for focal series of large areas. It is shown that oversized or annular apertures theoretically improve the vertical resolution for 3D imaging of nanoparticles. When imaging nanoparticles of several nanometer size, regular STEM can thereby be optimized such that the vertical full-width at half-maximum approaches that of the aberration-corrected STEM with a standard aperture.