Gap-free Information Transfer in 4D-STEM via Fusion of Complementary Scattering Channels

TL;DR

FF-STEM proposes a gap-free 4D-STEM reconstruction by fusing bright-field ptychography with tilt-corrected dark-field data in Fourier space using Wiener-type, SSNR-based weights. The method derives an analytic SSNR for direct ptychography and a half-data SSNR estimate for tcDF, then combines them so that the total SSNR is additive: $SSNR_{\mathrm{FF-STEM}}(\mathbf{q}) = SSNR_{\mathrm{ptycho}}(\mathbf{q}) + SSNR_{\mathrm{tcDF}}(\mathbf{q})$, with weights $w_{\mathrm{ptycho}}(\mathbf{q})$ and $w_{\mathrm{tcDF}}(\mathbf{q})$. It preserves upsampling and depth-sectioning, delivers high-contrast, dose-efficient imaging across diverse materials, and achieves near-real-time reconstruction on GPUs, enabling live feedback during experiments. The framework is supported by theoretical fusion guarantees and experimental validation across oxide nanostructures, carbon nanotubes, and thick biological specimens. Overall, FF-STEM unites high-frequency phase information with robust low-frequency contrast to overcome traditional transfer gaps in 4D-STEM.

Abstract

Linear phase-contrast scanning transmission electron microscopy (STEM) techniques compatible with high-throughput 4D-STEM acquisition are widely used to enhance phase contrast in weakly scattering and beam-sensitive materials. In these modalities, contrast transfer is often suppressed at low spatial frequencies, resulting in a characteristic contrast gap that limits quantitative imaging. Approaches that retain low-frequency phase contrast exist but typically require substantially increased experimental complexity, restricting routine use. Dark-field STEM imaging captures this missing low-frequency information through electrons scattered outside the bright-field disk, but discards a large fraction of the scattered signal and is therefore dose-inefficient. Fused Full-field STEM (FF-STEM) is introduced as a 4D-STEM imaging modality that overcomes this limitation by combining ptychographic phase reconstruction with tilt-corrected dark-field imaging within a single acquisition. Bright-field data are used to estimate probe aberrations and reconstruct a high-resolution phase image, while dark-field data provide complementary low-frequency contrast. The two channels are optimally fused in Fourier space using minimum-variance weighting based on the spectral signal-to-noise ratio, yielding transfer-gap-free images with high contrast and quantitative fidelity. FF-STEM preserves the upsampling and depth-sectioning capabilities of ptychography, adds robust low-frequency contrast characteristic of dark-field imaging, and enables dose-efficient, near-real-time reconstruction.

Figures (6)

• Figure 1: Schematic illustration of the FF-STEM reconstruction workflow (a) Simplified 4D-STEM acquisition scheme in which a convergent electron probe raster scans through the specimen while a two-dimensional diffraction pattern is recorded at each scan position, the sample is a $\mathrm{Gd_2O_3}$ nanohelix. (b) Example diffraction pattern showing the bright-field (white) and dark-field (gray) regions. The arrows represent the calculated shifts. (c) Aberration-compensated direct ptychography image (d) tcDF image reconstructed by correcting image shifts of the dark field segments indicated by color-coded arrows in (b). Next, the spectral signal-to-noise ratio of both channels is calculated (e) and Wiener-type minimum variance spectral weight for each channel is derived from both SSNRs. (f) and (g) show the spectral weights of ptychography and tcDF respectively. The Fourier spectra of both channels (h,i) are filtered with the optimal weights and are then summed in the Fourier domain and inverse-transformed to yield the final (j) FF-STEM image that utilizes all detected electrons. Scale bars in real space images are 5nm.
• Figure 2: Comparison of direct ptychography, tcDF, FF-STEM, and parallax/tcBF reconstructions. (a–d) Atomic-resolution reconstructions of a $\mathrm{Co_3O_4}$ nanocrystal. In (a), the projected unit cell is indicated. Panels (a) direct ptychography and (b) tcDF reconstruction. Left half without and the right half with Wiener-type filters applied. (c) FF-STEM reconstruction. (d) Parallax/tcBF reconstruction. (e–h) Reconstructions of a 7.2nm-thick amorphous carbon wedge. Real-space scale bars correspond to 5Å, and reciprocal-space scale bars correspond to 1Å^-1
• Figure 3: Demonstration of depth-sectioning capability using FF-STEM reconstruction. Reconstructed images of Ta-Te core-shell carbon nanotubes with different defocus values. Each column shows results from (a, e) direct ptychography, (b, f) tcDF, (c, g) FF-STEM, and (d, h) parallax reconstruction. The top row corresponds to a defocus condition in which the reconstruction focuses on the nanotube bundle at the back of the sample, while the bottom row focuses on the front bundle. The parallax reconstruction provides a comparable focal selectivity but lower overall image clarity. Scale bars: 2nm
• Figure 4: Experimental demonstration of FF-STEM on various 4D-STEM datasets. Each row represents a distinct experimental dataset obtained from different materials and detectors. The FF-STEM results are compared with parallax reconstruction, showing the contrast improvement of the nanoparticle with line profiles overlaid on the images. (a) Reconstructed images of the diffraction grating. All reconstructions, including parallax, are upsampled by a factor of 4. (b) $\mathrm{Gd_2O_3}$ nanohelices acquired with the Timepix4 detector under low dose conditions, all reconstructions are upsampled by 2. (c) carbon nanotubes with Ta-Te core-shell structure. The red dashed line in the fused FF and parallax images mark the region used to extract the line profiles (blue curve). The scale bars in real space correspond to 2nm. Insets on the top right show the power spectrum of the corresponding images with reciprocal-space scale bars of 0.2Å^-1 for diffraction grating, and 0.5Å^-1 for $\mathrm{Gd_2O_3}$, Ta-Te.
• Figure 5: Dose-efficient cryogenic imaging of thick specimens using FF-STEM. (a) EFTEM image reproduced from yu2025dose, acquired at $14 \mathrm{e/\text{\normalfont\AA}^2}$. (b) Direct ptychography reconstruction from the 4D-STEM dataset (c) tcDF reconstruction, (d) tcBF image reproduced from yu2025dose, (e) FF-STEM reconstruction. Red rectangles indicate regions of interest used for quantitative analysis. (f) Image contrast, (g) signal-to-noise ratio (SNR), and (h) fraction of detected electrons remaining, all extracted from identical regions of interest marked in panel (e). Error bars represent the root-mean-square variation of the measured line profiles. The scale bar is 100nm.