Optimizing Structure Factors From Four-dimensional Scanning Transmission Electron Microscopy via the Scattering Matrix
Source abstract
Abstract
Abstract Quantitative potential retrieval in scanning transmission electron microscopy (STEM) is of much importance for detailed material characterization but is often hindered by substantial multiple scattering effects in thicker samples. Here, we propose a gradient-descent-based optimization algorithm to obtain the quantitative potential from thick samples from a four-dimensional (4D) STEM dataset using the scattering matrix (S-matrix), which is an operator to calculate the exit-surface wavefunction in the presence of multiple scattering. This optimization uses optimum bright-field STEM data as an initial guess of potential and a loss function based on measured and estimated 4D STEM datasets without the regularization terms commonly used in iterative potential retrieval techniques in STEM. We show the capabilities of our approach through systematic simulations across a range of sample thicknesses, doses, and degrees of spatial incoherence and by applying it to experimental data. The extension of our algorithm from pixelated to segmented detectors is also investigated.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Advanced Electron Microscopy Techniques and Applications · Electron and X-Ray Spectroscopy Techniques · Chemical and Physical Properties of Materials
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
School of Physics and Astronomy, Monash University , Wellington Rd, Clayton, Victoria 3800 ,
Nanostructures Research Laboratory, Japan Fine Ceramics Center , 2-4-1 Mutsuno, Atsuta, Nagoya, Aichi 456-8587 ,
Funding
JSPS KAKENHI · Discovery Projects funding scheme of the Australian Research Council · NCRIS · Australian Research Council
References (54)
Show source-provided references
1. Modelling the inelastic scattering of fast electrons10.1016/j.ultramic.2014.10.011 ↗
2. Dr. Probe: A software for high-resolution STEM image simulation10.1016/j.ultramic.2018.06.003 ↗
3. Structure retrieval at atomic resolution in the presence of multiple scattering of the electron probe10.1103/PhysRevLett.121.266102 ↗
4. Large angle illumination enabling accurate structure reconstruction from thick samples in scanning transmission electron microscopy10.1016/j.ultramic.2018.12.010 ↗
5. Automatic parameter selection for electron ptychography via Bayesian optimization10.1038/s41598-022-16041-5 ↗
6. Electron ptychography achieves atomic-resolution limits set by lattice vibrations10.1126/science.abg2533 ↗
7. Multislice method for large beam tilt with application to HOLZ effects in triclinic and monoclinic crystals10.1107/S0108767397005539 ↗
8. Prismatic 2.0—Simulation software for scanning and high resolution transmission electron microscopy (STEM and HRTEM)10.1016/j.micron.2021.103141 ↗
9. Exact inversion of partially coherent dynamical electron scattering for picometric structure retrieval10.1038/s41467-023-44268-x ↗
10. Complementary ADF-STEM: A flexible approach to quantitative 4D-STEM10.1016/j.ultramic.2022.113627 ↗
11. Computed electron microscope images of atomic defects in f.c.c. Metals10.1107/S0567739478000182 ↗
12. Quantitative structure retrieval using scanning transmission electron microscopy10.1107/S0108767305011293 ↗
13. Dynamics of annular bright field imaging in scanning transmission electron microscopy10.1016/j.ultramic.2010.04.004 ↗
14. Robust atomic resolution imaging of light elements using scanning transmission electron microscopy10.1063/1.3265946 ↗
15. Electron ptychographic microscopy for three-dimensional imaging10.1038/s41467-017-00150-1 ↗
16. A methodology for robust multislice ptychography10.1093/mam/ozae055 ↗
17. Automatic differentiation in machine learning: A survey10.48550/arXiv.1502.05767 ↗
18. The scattering of fast electrons by crystals10.1088/0034-4885/42/11/002 ↗
19. Inverse dynamical photon scattering (IDPS): An artificial neural network based algorithm for three-dimensional quantitative imaging in optical microscopy10.1364/OE.24.007006 ↗
20. Anharmonicity and disorder in simple and complex perovskites: A high energy synchrotron and hot neutron diffraction study10.1088/0953-8984/12/39/305 ↗
21. Kingma · 201510.48550/arXiv.1412.6980 ↗
22. Kirkland · 201010.1007/978-1-4419-6533-2 ↗
23. Real-space visualization of intrinsic magnetic fields of an antiferromagnet10.1038/s41586-021-04254-z ↗
24. Towards sub-Å electron beams10.1016/S0304-3991(99)00013-3 ↗
25. Phase contrast STEM for thin samples: Integrated differential phase contrast10.1016/j.ultramic.2015.10.011 ↗
26. Advances and applications of atomic-resolution scanning transmission electron microscopy10.1017/S1431927621012125 ↗
27. MULTEM: A new multislice program to perform accurate and fast electron diffraction and imaging simulations using graphics processing units with CUDA10.1016/j.ultramic.2015.04.016 ↗
28. The abTEM code: Transmission electron microscopy from first principles10.12688/openreseurope.13015.1 ↗
29. Ptychographic transmission microscopy in three dimensions using a multi-slice approach10.1364/JOSAA.29.001606 ↗
30. An improved ptychographical phase retrieval algorithm for diffractive imaging10.1016/j.ultramic.2009.05.012 ↗
31. Computational microscopy with coherent diffractive imaging and ptychography10.1038/s41586-024-08278-z ↗
32. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later10.1137/S00361445024180 ↗
33. Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction10.1038/ncomms6653 ↗
34. The spatial coherence function in scanning transmission electron microscopy and spectroscopy10.1016/j.ultramic.2014.04.008 ↗
35. Advanced characterization techniques for sulfide-based solid-state lithium batteries10.1002/aenm.202203883 ↗
36. Ultra-high contrast STEM imaging for segmented/pixelated detectors by maximizing the signal-to-noise ratio10.1016/j.ultramic.2020.113133 ↗
37. Dose-efficient phase-contrast imaging of thick weak phase objects via OBF STEM using a pixelated detector10.1093/jmicro/dfae051 ↗
38. Direct imaging of local atomic structures in zeolite using optimum bright-field scanning transmission electron microscopy10.1126/sciadv.adf6865 ↗
39. A fast image simulation algorithm for scanning transmission electron microscopy10.1186/s40679-017-0046-1 ↗
40. Four-dimensional scanning transmission electron microscopy (4D-STEM): From scanning nanodiffraction to ptychography and beyond10.1017/S1431927619000497 ↗
41. Pytorch. An imperative style, high-performance deep learning library10.48550/arXiv.1912.01703 ↗
42. Stacked-Bloch-wave electron diffraction simulations using GPU acceleration10.1016/j.ultramic.2014.03.003 ↗
43. High-resolution Z-contrast imaging of crystals10.1016/0304-3991(91)90004-P ↗
44. Determining the projected crystal structure from four-dimensional scanning transmission electron microscopy via the scattering matrix10.1093/micmic/ozad018 ↗
45. Overcoming information reduced data and experimentally uncertain parameters in ptychography with regularized optimization10.1364/OE.396925 ↗
46. Quantitative electric field mapping in thin specimens using a segmented detector: Revisiting the transfer function for differential phase contrast10.1016/j.ultramic.2017.07.013 ↗
47. Electric field imaging of single atoms10.1038/ncomms15631 ↗
48. The calculation of electron diffraction intensities10.1088/0370-1328/80/2/301 ↗
49. High-resolution multislice X-ray ptychography of extended thick objects10.1103/PhysRevLett.112.053903 ↗
50. Terzoudis-Lumsden · 202510.48550/arXiv.2506.21004 ↗
51. A holographic method to measure the source size broadening in STEM10.1016/j.ultramic.2012.05.007 ↗
52. Quantitative annular dark-field imaging of single-layer graphene—II: Atomic-resolution image contrast10.1093/jmicro/dfv053 ↗
53. Electron ptychographic phase imaging of light elements in crystalline materials using Wigner distribution deconvolution10.1016/j.ultramic.2017.02.006 ↗
54. Uncovering polar vortex structures by inversion of multiple scattering with a stacked Bloch wave model10.1016/j.ultramic.2023.113732 ↗