The importance of temporal and spatial incoherence in quantitative interpretation of 4D-STEM.

Recent developments in pixelated detectors, when combined with aberration correction of probe forming optics have greatly enhanced the field of scanning electron diffraction. Differential phase contrast is now routine and deep learning has been proposed as a method to extract maximum information from diffraction patterns. This work examines the effects of temporal and spatial incoherence on convergent beam electron diffraction patterns and demonstrates that simple center of mass measurements cannot be naively interpreted. The inclusion of incoherence in deep learning data sets is also discussed.

[1]  B. C. McCallum,et al.  Resolution beyond the 'information limit' in transmission electron microscopy , 1995, Nature.

[2]  Veit Elser,et al.  Electron ptychography of 2D materials to deep sub-ångström resolution , 2018, Nature.

[3]  J. Rodenburg,et al.  The theory of super-resolution electron microscopy via Wigner-distribution deconvolution , 1992, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[4]  M. Weyland,et al.  Structure Retrieval at Atomic Resolution in the Presence of Multiple Scattering of the Electron Probe. , 2018, Physical review letters.

[5]  Leland McInnes,et al.  Manifold learning of four-dimensional scanning transmission electron microscopy , 2018, npj Computational Materials.

[6]  A. J. D’Alfonso,et al.  Practical aspects of diffractive imaging using an atomic-scale coherent electron probe. , 2016, Ultramicroscopy.

[7]  W. Hoppe,et al.  Beugung im inhomogenen Primärstrahlwellenfeld. III. Amplituden- und Phasenbestimmung bei unperiodischen Objekten , 1969 .

[8]  A. Kirkland,et al.  Atomic electrostatic maps of 1D channels in 2D semiconductors using 4D scanning transmission electron microscopy , 2019, Nature Communications.

[9]  M. Chi,et al.  Sub-Ångstrom electric field measurements on a universal detector in a scanning transmission electron microscope , 2018, Advanced Structural and Chemical Imaging.

[10]  S D Findlay,et al.  Towards quantitative, atomic-resolution reconstruction of the electrostatic potential via differential phase contrast using electrons. , 2015, Ultramicroscopy.

[11]  Josef Zweck,et al.  Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction , 2014, Nature Communications.

[12]  Malcolm L. H. Green,et al.  Simultaneous atomic-resolution electron ptychography and Z-contrast imaging of light and heavy elements in complex nanostructures , 2016, Nature Communications.

[13]  S D Findlay,et al.  Modelling the inelastic scattering of fast electrons. , 2015, Ultramicroscopy.

[14]  Ondrej Dyck,et al.  Mapping mesoscopic phase evolution during E-beam induced transformations via deep learning of atomically resolved images , 2018, npj Computational Materials.

[15]  R. Holmestad,et al.  The evolution of precipitate crystal structures in an Al-Mg-Si(-Cu) alloy studied by a combined HAADF-STEM and SPED approach , 2018, Materials Characterization.

[16]  Ondrej Dyck,et al.  Mitigating e-beam-induced hydrocarbon deposition on graphene for atomic-scale scanning transmission electron microscopy studies , 2018 .

[17]  H. De,et al.  Differential Phase Contrast in a STEM , 2022 .

[18]  John M. Rodenburg,et al.  Experimental tests on double-resolution coherent imaging via STEM , 1993 .

[19]  Colin Ophus,et al.  Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM): From Scanning Nanodiffraction to Ptychography and Beyond , 2019, Microscopy and Microanalysis.

[20]  Naoya Shibata,et al.  Differential phase-contrast microscopy at atomic resolution , 2012, Nature Physics.

[21]  W. Hoppe,et al.  Dynamische Theorie der Kristallstrukturanalyse durch Elektronenbeugung im inhomogenen Primärstrahlwellenfeld , 1970 .

[22]  I. M. Andersen,et al.  Crystal Phase Mapping by Scanning Precession Electron Diffraction and Machine Learning Decomposition , 2018, Microscopy and Microanalysis.