Sub-Ångstrom 3D Resolution,
Large-Volume Imaging
and Automation Advances
in Electron Ptychography

Prof. Dr. Philipp Pelz

FAU Erlangen-Nürnberg

Institute of Micro- and Nanostructure Research

Outline

Motivation: “We can compute what we cannot yet see”

The gap between atomistic simulations and 3D atomic resolution imaging

• ML potentials are now probing 10⁸ atoms at picosecond–nanosecond time‑steps
  
• 2024: [1] polycrystalline Cu, 100M atoms
• 2023: [2] SARS-CoV-2 Spike glycoprotein in water, 100M atoms

[1]

• 3D atomic resolution imaging has been limited to max. volumes of ~(15nm)³, 10⁴ - 10⁵ atoms
  Adapted from [3]

Note

Ptychographic electron tomography can be developed into an experimental counterpart that can shorten this gap by combining ML-enhanced reconstructions, automation & dose‑efficient scanning.

[1] Shang et al. 10.1109/SC41406.2024.0001 (2024) [2] Musaelian et al. arXiv:2304.10061v (2023) [3] Zhou, J. MRS Bulletin 45, 290–297 (2020).

4D-STEM ptychographic tomography

• Multi-slice ptychography has been limited to ~2nm depth resolution (in some cases sub-nm)
• Introduce tilt-series to reach higher depth resolution

Note

Atomic 3D resolution achievable with 4D-STEM tilt series

Successive approximations in STEM ptychography

Weak-phase appoximation e.g. [1]

Single-slice approximation e.g. [2]

Multi-slice approximation e.g. [3]

\(\psi_{out} = (1+i\phi)\psi_{in}\)

\(\psi_{out} = A(\vec{r}) \cdot e^{i\sigma V(\vec{r})} \cdot \psi_{in}\)

\(\psi_{out} = \mathcal{M}_V(\psi_{in})\)

✅ Real-time results & calibration

✅ Fast reconstruction for thin samples

✅ 2.5D reconstruction for thick samples

✅ highest x-y resolution

Note

Each approximations has its use in ptychographic tomography

[1] Peng et al. (2022), [2] Pelz et al. (2023), [3] Romanov et al. (2024)

Our protagonists today: nanoscale particles and quantum materials

1️⃣ Transition metal chalcogenides in the few-chain limit

Pham, T. et al. PRL (2020)

Stonemeyer, S. et al. JACS(2020)

2️⃣ Strain-engineered Core-Shell Oxide particles

Oh et al. Nature (2020)

3️⃣ Strain-engineered chiral nanoparticles

Liu et al. JACS(2020)

Note

Quantum materials and nanoparticles are ideal test cases for our atomic resolution 3D imaging as we develop scalable algorithms

First unknown 3D atomic structure solved with 4D-STEM tomography

Approach:

1. 4D-STEM tilt series
2. mixed-state ptychography of all tilt angles

3. Joint linear tomography and alignment
4. Sub-pixel atomic peak tracing
5. 3D atomic structure determination

Volume size: (6 nm)³

Note

Elliptic double-wall CNT and complex inner structure resolved in 3D

Pelz et al. (2023)

Ptychographic Tomography Solves Nanostructures

Note

First 3D atomic structure solved with phase-contrast tomography.
Novel ZrTe₂ phase, confirmed stable with DFT simulations.

Pelz et al. (2023)

Depth Resolution Progress Over Time

2022: 2.2 Å in 6nm thick volume using SSPT [1]

2023: 2.0 Å in 18nm thick volume using MSPT [2]

2024: 0.8 Å in 11nm thick volume using E2E-MSPT [3]

Note

Algorithm development drives resolution records and depth of focus enhancements

Pelz et al. (2023), Romanov et al. (2024), You, Romanov, and Pelz (2024)

Next step: Multi-Slice Ptychographic Tomography

Perform MSP reconstruction
for each tilt angle
and project the potential along z







✅ Advantages:
- Decouple tomographic alignment from ptychographic reconstruction
- Can use positions and alignment as input to E2E-MSPT

Multi-slice Ptychographic Tomography forward model

❌ Disadvantage:
- Loses some 3D info from MSP

Romanov et al. (2024)

Joint Tomography and Rigid Alignment enables atomic resolution of beyond-DOF volumes

Multi-scale subpixel alignment
Outer loop: rigid alignment
Inner loop: fixed-alignment reconstruction

Note

Enabled by reaching sub-pixel alignment at each scale

Romanov et al. (2024)

3x DOF volumes display atomic resolution

Note

Volume size: (18.2 nm)³ Voxel size: 0.3 Å

Romanov et al. (2024)

Orthoslices reveal lattice in all 3 dimensions

scale: 1 nm

Note

Lattice resolved, but Co atom contrast overpower O contrast
=> Around 1 Å z resolution required to resolve O atoms

Romanov et al. (2024)

End-to-end reconstruction - putting all pieces together

Fully E2E-MSPT reconstruction includes

1. affine resampling of potential volume
   
2. z-resampling of potential volume (save compute)
   
3. batch-croppping and mixed-state multi-slice model
   
4. far-field propagation
   
5. gradient backpropagation through full model

Note

The most accurate approximation for 4D-STEM tomography to-date.

Difficulty: initialization of the model parameters

You, Romanov, and Pelz (2024)

Successive approximations help initialize “nuisance parameters”

Note

Successive initialization reduces compute
overhead of the most accurate models

You, Romanov, and Pelz (2024)

Sub-Ångstrom alignment accuracy demonstrated in simulations

4D-STEM simulation of
Pt-Al₂O₃ core-shell nanoparticle

Phase projections at different tilt angles

Alignment accuracy

Note

Mean alignment error < voxel size (0.4 Å)

You, Romanov, and Pelz (2024)

Limited-Angle Tomography is an option now

Note

Light and heavy atoms recovered in 3D with 90-degree tilt range.

You, Romanov, and Pelz (2024)

Volume displays clear atomic contrast in 3D

scale box: 1nm

Power spectrum

Contrast adjusted for high frequencies

Note

Recovery of missing wedge with only physical priors.
Reached Nyquist resolution of 0.82 Å

You, Romanov, and Pelz (2024)

Slicing through the volume reveals 3D atomic resolution

2

1

Note

All directions recovered well

Dose reduction by sub-sampling

Note

2.8 Å resolution with 2.2*10⁴ e^-/Ų - virtual sub-sampling
0.82 Å resolution with 12x sub-sampling

You, Romanov, and Pelz (2024)

Atomic resolution tomography has been a postdoc-intensive business

Sanchez-Santolino et al. Nano Letters (2025): “This approach, first suggested by Li and Maiden and recently demonstrated in some particularly challenging systems by Pelz et al. allows one to gain the full three-dimensional knowledge via a tomographic approach […]”

So far:

• highly trained microscopists required for ADF-STEM/4D-STEM tilt series data acquisition

• manual collection & long algorithm chain hinder widespread adoption

• How can we make it more accessible and less challenging?

Note

Automated 4D-STEM tomography
and end-to-end reconstruction are
key to democratizing atomic resolution tomography

Acknowledgements

UCB & NCEM

Mary Scott

Peter Ercius

Alex Zettl

Scott Stonemeyer

Min Gee Cho

Sinead Griffin

Colin Ophus (now Stanford)

Monash University

Scott Findlay

DECTRIS

Daniel Stroppa Matthias Meffert

Indiana University

Xingchen Ye

Baixu Zhu

FAU

Mingjian Wu

Tadahiro Yokosawa

Shengbo You

Andrey Romanov

Nikita Palatkin

Erdmann Spiecker

Summary

• Demonstrated atomic structure determination by ptychographic electron tomography with 1.6Å resolution
• Multi-slice ptychographic tomography results show:
  • Scaling to volumes beyond 3x the depth of field limit
  • Signal of single oxygen atoms sufficient
• End-to-end learning alleviates the missing wedge problem and enables near-isotropic 3D resolution
• Automation should democratize the method in the near future

References 📚

Pelz, Philipp M., Sinéad M. Griffin, Scott Stonemeyer, Derek Popple, Hannah DeVyldere, Peter Ercius, Alex Zettl, Mary C. Scott, and Colin Ophus. 2023. “Solving Complex Nanostructures with Ptychographic Atomic Electron Tomography.” Nature Communications 14 (11): 7906. https://doi.org/10.1038/s41467-023-43634-z.

Romanov, Andrey, Min Gee Cho, Mary Cooper Scott, and Philipp Pelz. 2024. “Multi-Slice Electron Ptychographic Tomography for Three-Dimensional Phase-Contrast Microscopy Beyond the Depth of Focus Limits.” Journal of Physics: Materials 8 (1): 015005. https://doi.org/10.1088/2515-7639/ad9ad2.

You, Shengbo, Andrey Romanov, and Philipp M Pelz. 2024. “Near-Isotropic Sub-Ångstrom 3d Resolution Phase Contrast Imaging Achieved by End-to-End Ptychographic Electron Tomography.” Physica Scripta 100 (1): 015404. https://doi.org/10.1088/1402-4896/ad9a1a.

Open positions at FAU

• 13 open Ph.D. positions in the new Graduate School “Correlative Microscopy”
• Develop Sensor Fusion of 4D-STEM + APT, 4D-STEM + EELS, 4D-STEM + Raman Microscopy