ISTEM
: A Realisation of Incoherent Imaging for Ultra‐High Resolution
TEM
beyond the Classical Information Limit
Authors: Krause Florian F. , Schowalter Marco , Mehrtens Thorsten , Müller‐Caspary Knut , Béché Armand , van den Bos Karel W. H. , Van Aert Sandra , Verbeeck Johan , Rosenauer Andreas 
Published: December 2016

The ISTEM (Imaging STEM) method [Phys. Rev Lett. 113, 096101(2014)] presented here constitutes a novel way for the realisation of TEM imaging with spatially incoherent illumination. It is well‐known that such incoherent image formation allows for an increased resolution and higher robustness towards chromatic aberrations compared to coherent illumination as used in conventional TEM (CTEM). This has been realised in scanning TEM (STEM) via reciprocity, which however suffers from other resolution‐limiting factors such as scan noise or the finite extent of the electron source.
The ISTEM mode circumvents these problems entirely. It combines STEM illumination with CTEM imaging as illustrated in Fig. 1: A camera is used to acquire images formed by the focused electron probe that is scanning over the specimen while the imaging system is in imaging mode. With an exposure time chosen equal to the STEM scan time, the resulting image corresponds to a sum over the images of all probe positions. Because different specimen positions are illuminated at different times, the corresponding intensities are summed up incoherently. ISTEM is therefore a spatially incoherent imaging mode and benefits from the associated improvement of resolution. Beyond this simple explanation, the equivalence of the ISTEM illumination and CTEM with an extended and incoherent electron source can be furthermore rigorously shown mathematically within the mutual intensity formalism. From this, the gain of resolution can be intuitively understood in the limit of total incoherence, in which case the transfer is given by the autocorrelation of the coherent transfer function. The theoretical considerations also show that neither scan noise nor source size have any influence on ISTEM‐images. Aberrations and defocus of the condenser system cancel out completely as well. ISTEM imaging is therefore independent from probe correction.
In simulative studies the capability of ISTEM to extend the point resolution beyond the diffraction limit, its robustness towards temporal incoherence and the resulting possibility to overcome the information limit are demonstrated. These calculations are confirmed by experimental ISTEM‐micrographs of GaN in [11–20] and [1–100] projection, as presented in Fig. 3, which are found in good agreement with simulations. For the [1–100] direction neighbouring gallium and nitrogen columns at a distance of only 63 pm are resolved despite an information limit of 83 pm of the image‐corrected FEI TITAN 80/300 G1 microscope used for the acquisition. The classical information limit is thereby clearly overcome by 24%.

A further study was conducted that compared the results of strain‐state analysis from simulated ISTEM images of a strained InGaAs‐crystal with annular dark‐field and bright‐field STEM micrographs simulated for a probe‐corrected microscope. The results are displayed in Fig. 2. They promise a significant increase in precision for ISTEM compared to STEM, due to the immunity to both scan noise and source size clearly recognisable by the smaller error bars. This was experimentally confirmed by an ISTEM study of PbTiO
3
in which the heavy Pb and TiO atomic columns as well as the lighter oxygen columns are clearly resolved and the evaluation based on a parametrically fitted model yields a significantly increased precision for position measurement compared to aberration corrected STEM images which were acquired from the same sample area.

With the help of the principle of reciprocity, ISTEM can finally be made equivalent to any STEM mode by appropriate choice of objective and condenser aperture, with the difference that ISTEM images will show no scan noise whatsoever. This will allow for the realisation of e.g. annular bright‐field STEM, holding out the prospect of ultra‐high resolution imaging of even lightest elements.