Optimal tilt magnitude determination for aberration-corrected super resolution exit wave function reconstruction

Abstract

Transmission electron microscope (TEM) images recorded under tilted illumination conditions transfer higher spatial frequencies than axial images. This super resolution information transfer is highly directional in a single image, but can be extended in all directions through the use of complementary beam tilts during exit wave function reconstruction. We have determined the optimal experimental tilt magnitude for aperture synthesis in an aberration-corrected TEM. It is shown that electron-optical aberration correction allows the use of larger tilt angles and reduces the constraints that are imposed on experimental data acquisition in an uncorrected microscope. We demonstrate that, in many cases, the resolution improvement achievable is now limited by the sample and not by instrumental parameters. An exit wave function is presented that has been successfully reconstructed from a dataset of aberration-corrected images, including images acquired at a beam tilt of 18 mrad, which clearly demonstrates a resolution improvement from 0.11 nm to better than 0.08 nm at 200 kV.

A proposal for the holographic correction of incoherent aberrations by tilted reference waves

“…The mechanism is in principle very similar to the tilt series imaging in high-resolution TEM [19,20]. In tilt series imaging, the entire entrance wave is tilted causing a shift of certain dark-field regions of the object exit wave onto the centre of coherence [16][17][18].…”

“…This approach suggests the synthesis of an Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ultramic effective aperture with larger bandwidth by means of high-resolution image series with varying incident tilt [19]. Promising results were achieved by restoring spatial frequencies beyond the information limit [20]. However, the problem of the strong dependence of the object exit wave on the incident beam tilt due to dynamic scattering remains.…”

“…E.g., the algorithm in Ref. [20] assumes an object exit wave independent of the incident tilts, which is applicable to the special case of weak objects only.…”

New possibilities with aberration-corrected electron microscopy

“…Pennycook et al (2009) demonstrated the power of aberration-corrected scanning transmission electron microscopy (STEM) for solving materials problems at the atomic level of resolution, while Urban et al (2009) described the value of being able to tune spherical aberration to optimize the information available from aberration-corrected transmission electron microscopy (TEM). Improving resolution and quantification by the combination of a set of images taken at different focus and illumination tilt settings in an aberration-corrected environment was the theme of the contribution presented by Kirkland (Haigh et al 2009). Gabor's dream of electron holography One contribution of 14 to a Discussion Meeting Issue 'New possibilities with aberration-corrected electron microscopy'.…”

Applications of the Oxford-JEOL aberration-corrected electron microscope

“…A particular focus of the activity at Oxford is the coupling of techniques to reconstruct the complex wavefunction at the exit-surface of the sample from either a focal-series imaging geometry [7], or an illumination tilt-series [8] using electron optically corrected image data.…”