The depth resolution for optical sectioning in the scanning transmission electron microscope is measured using the results of optical sectioning experiments of laterally extended objects. We show that the depth resolution depends on the numerical aperture of the objective lens as expected. We also find, however, that the depth resolution depends on the lateral extent of the object that is being imaged owing to a missing cone of information in the transfer function. We find that deconvolution methods generally have limited usefulness in this case, but that three-dimensional information can still be obtained with the aid of prior information for specific samples such as those consisting of supported nanoparticles. We go on to review how a confocal geometry may improve the depth resolution for extended objects. Finally, we present a review of recent work exploring the effect of dynamical diffraction in zone-axis-aligned crystals on the optical sectioning process.

We show how an effective nonlocality in imaging can lead to the sampling of a spatial region which is not significantly illuminated by an imaging probe. The nonlocality is embodied in the effective nonlocal potential describing inelastic scattering which occurs when coupled channel Schrödinger equations are reduced to a single integro-differential equation. The context in which this prediction will be illustrated is atomic resolution imaging based on energy-loss spectroscopy in scanning transmission electron microscopy.

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