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Local-orbital ptychography for ultrahigh-resolution imaging


Technical advances paired with developments in methodology have enabled electron microscopy to reach atomic resolution. Further improving the information limit in microscopic imaging requires further improvements in methodology. Here we report a ptychographic method that describes the object as the sum of discrete atomic-orbital-like functions (for example, Gaussian functions) and the probe in terms of aberration functions. Using this method, we realize an improved information limit of microscopic imaging, reaching down to 14 pm. High-quality probes and objects contribute to superior signal-to-noise ratios at low electron doses, allowing for relaxation of the sample thickness restriction to 50 nm for dense materials. Additionally, our method has the capability to decompose the total phase into element components, revealing that the information limit is element dependent. With enhanced spatial resolution, signal-to-noise ratio and thickness threshold compared with conventional ptychography methods, our local-orbital ptychography may find applications in atomic-resolution imaging of metals, ceramics, electronic devices or beam-sensitive material.

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Fig. 1: Schematic of LOP.
Fig. 2: Dose dependence of the LOP and CPP reconstructions.
Fig. 3: Ptychography reconstructions on experimental datasets.
Fig. 4: Phase and diffractograms obtained by separating different elements.

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Data availability

All data that support the findings of this study have been deposited in Zenodo52.

Code availability

The code needed to evaluate the conclusions in this article are available on request from the corresponding author.


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R.Y. was supported by the National Natural Science Foundation of China (52388201, 51525102). For this work we used the resources of the Physical Sciences Center and Center of High-Performance Computing of Tsinghua University.

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Authors and Affiliations



R.Y. supervised the project, conceived the idea and designed the research. W.Y. wrote the codes with the help of H.S. and L.M. W.Y. and H.S. performed experiments. J.C. performed simulations. W.Y. and R.Y. co-wrote the paper. All authors discussed the results and commented on the paper.

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Correspondence to Rong Yu.

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Nature Nanotechnology thanks William Bowman, Yu Han and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Reconstruction via the LOP method on simulation datasets of SrTiO3.

a and b, The probe amplitude and the object potential used to generate the simulation 4D-dataset; c and d, The probe amplitude and the object phase reconstructed via the LOP method; Scale bars in a-d, 2 Å.

Extended Data Fig. 2 Experimental diffraction patterns.

a and b, The PACBED and a single CBED for the dataset of SrTiO3; c and d, The PACBED and a single CBED for the dataset of DyScO3.

Extended Data Fig. 3 The diffraction patterns of simulation datasets.

a, The position-averaged convergent beam electron diffraction (PACBED) with respect to different electron dose; b, The single CBED with respect to different electron dose.

Extended Data Fig. 4 Amplitude of initialized probe function in LOP for the dataset of DyScO3.

All aberrations are at zero, except for a defocus value of 20 nm. Scale bar, 5 Å.

Extended Data Fig. 5

Phase of initialized object function in LOP for the dataset of DyScO3.

Extended Data Fig. 6 Ptychography reconstruction results on an experimental dataset of a thick (50 nm) sample of SrTiO3.

a and b, Probe amplitude; c and d, object phase. The LOP reconstruction converged well, but the CPP reconstruction did not. The first probe mode is shown; Scale bars in a-d, 4 Å.

Extended Data Fig. 7 Reconstructed probe on experimental datasets.

a and b, Probe reconstructed via the LOP and CPP methods for the dataset of DyScO3; c and d, Probe reconstructed via the LOP and CPP methods for the dataset of SrTiO3.

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Yang, W., Sha, H., Cui, J. et al. Local-orbital ptychography for ultrahigh-resolution imaging. Nat. Nanotechnol. 19, 612–617 (2024).

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