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arxiv: 2606.07204 · v1 · pith:VXJRYHZUnew · submitted 2026-06-05 · ❄️ cond-mat.mtrl-sci · physics.ins-det

Ptychographic Algorithms for Phase Recovery in 4D Scanning Transmission Electron Microscopy

Amel Shamseldeen Ali Alhassan This is my paper

Pith reviewed 2026-06-27 21:36 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.ins-det
keywords ptychography4D STEMphase recoveryMoS2electron microscopyWigner distribution deconvolutionsingle side-band reconstruction
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The pith

Ptychography recovers the electron probe wavefunction and specimen transmission function from 4D STEM diffraction patterns.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper surveys ptychographic reconstruction methods for phase recovery in momentum-resolved scanning transmission electron microscopy. It describes how a raster-scanned convergent beam produces overlapping 2D diffraction patterns that together encode both the probe shape and the specimen's multiplicative transmission function. Direct and iterative algorithms are presented, including the extended Ptychographic Iterative Engine, Wigner Distribution Deconvolution, and its simplified Single Side-Band variant. An original SSB script is demonstrated on simulated MoS2 monolayer data, and experimental 4D STEM datasets are recorded as a practical step. The work frames these techniques as a route to high-resolution real-space imaging from the full 4D dataset.

Core claim

Ptychography is a reconstruction algorithm that allows the extraction of the probe wavefunction and the multiplicative object transmission function of the specimen. It is implemented through direct and iterative schemes such as ePIE, WDD, and SSB. An SSB reconstruction was performed with an original script on simulated MoS2 monolayer data, and four-dimensional datasets were acquired on a STEM instrument.

What carries the argument

The Single Side-Band (SSB) reconstruction, a simplified form of Wigner distribution deconvolution that isolates phase information from the interference cross-terms in the 4D diffraction data.

If this is right

  • The SSB method demonstrated on simulated data can be applied directly to the recorded experimental 4D STEM datasets for phase imaging.
  • Implementation of the full WDD algorithm would recover additional information beyond the SSB approximation.
  • The mathematical framework allows systematic comparison of iterative (ePIE) and direct (WDD/SSB) schemes on the same dataset.
  • Atomic-resolution transmission functions become available for materials such as monolayer MoS2 without requiring conventional phase-contrast optics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The recorded experimental 4D data sets could serve as a benchmark for testing noise robustness of other ptychographic variants not covered in the thesis.
  • Extending the SSB script to thicker or defective specimens would test how well the multiplicative transmission model holds beyond the monolayer case.
  • Combining the probe recovery from ptychography with conventional STEM imaging modes could reduce dose while maintaining resolution.

Load-bearing premise

The simulated MoS2 monolayer diffraction patterns used for the SSB test accurately reproduce the noise levels and experimental conditions of real 4D STEM measurements.

What would settle it

Applying the same SSB script to actual experimental 4D STEM data of MoS2 and obtaining a reconstructed object function that fails to show the expected atomic lattice positions would show the simulation does not capture real conditions.

Figures

Figures reproduced from arXiv: 2606.07204 by Amel Shamseldeen Ali Alhassan.

Figure 1
Figure 1. Figure 1: STEM anatomy [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 1.1
Figure 1.1. Figure 1.1: The overlapping between the transmitted beam A and the scattered beams B and C contains [PITH_FULL_IMAGE:figures/full_fig_p006_1_1.png] view at source ↗
Figure 1.2
Figure 1.2. Figure 1.2: In the conventional imaging modes of STEM the intensity of the diffraction pattern is [PITH_FULL_IMAGE:figures/full_fig_p007_1_2.png] view at source ↗
Figure 1.3
Figure 1.3. Figure 1.3: Electron waves passing through a specimen will suffer modification in both phase and [PITH_FULL_IMAGE:figures/full_fig_p008_1_3.png] view at source ↗
Figure 1.4
Figure 1.4. Figure 1.4: A subset of the 4D dataset. At each position in real space a diffraction pattern is recorded. [PITH_FULL_IMAGE:figures/full_fig_p009_1_4.png] view at source ↗
Figure 1.5
Figure 1.5. Figure 1.5: The interference diffracted orders’ fringes has the same periodicity of the featured cast in [PITH_FULL_IMAGE:figures/full_fig_p012_1_5.png] view at source ↗
Figure 1.6
Figure 1.6. Figure 1.6: The momentum resolved data recorded for the ptychographic reconstruction is shown. At [PITH_FULL_IMAGE:figures/full_fig_p013_1_6.png] view at source ↗
Figure 1.7
Figure 1.7. Figure 1.7: The ptycographic reconstruction of the amplitudes (b) and (e) and the phases (c) and [PITH_FULL_IMAGE:figures/full_fig_p014_1_7.png] view at source ↗
Figure 1.8
Figure 1.8. Figure 1.8: The hybrid 1% image correspond to the case in which there are missing parts of the 4D [PITH_FULL_IMAGE:figures/full_fig_p015_1_8.png] view at source ↗
Figure 1.9
Figure 1.9. Figure 1.9: (a) shows a schematic of the setup and the reconstruction method. To reduce the dose [PITH_FULL_IMAGE:figures/full_fig_p015_1_9.png] view at source ↗
Figure 1.10
Figure 1.10. Figure 1.10: Phase contrast imaging of simulated data of an adenosine triphosphate (ATP) molecule at [PITH_FULL_IMAGE:figures/full_fig_p016_1_10.png] view at source ↗
Figure 1.11
Figure 1.11. Figure 1.11: Characterization of Double-wall complex carbon nanotube (CNT) peapod. (a) Z-contrast [PITH_FULL_IMAGE:figures/full_fig_p017_1_11.png] view at source ↗
Figure 1.12
Figure 1.12. Figure 1.12: Ptychographic phase-images of a SrTiO3 wedge: (a) original, (b) 25% detector sub [PITH_FULL_IMAGE:figures/full_fig_p018_1_12.png] view at source ↗
Figure 2.1
Figure 2.1. Figure 2.1: Using an imperfect lens a point object is imaged as a disc. It is called an aberrated image [PITH_FULL_IMAGE:figures/full_fig_p025_2_1.png] view at source ↗
Figure 2.2
Figure 2.2. Figure 2.2: The effect of different aberrations on a free electron beam (a) is visualised in the subsequent [PITH_FULL_IMAGE:figures/full_fig_p026_2_2.png] view at source ↗
Figure 2.3
Figure 2.3. Figure 2.3: Schematic presentation of STEM imaging. The orange comments describe the evolution of [PITH_FULL_IMAGE:figures/full_fig_p028_2_3.png] view at source ↗
Figure 2.4
Figure 2.4. Figure 2.4: For iterative ptychographic algorithms (left) compines the known parameters i.e. the aperture [PITH_FULL_IMAGE:figures/full_fig_p029_2_4.png] view at source ↗
Figure 2.5
Figure 2.5. Figure 2.5: Steps of the WDD ptychographic reconstruction algorthim as it maybe implemented in [PITH_FULL_IMAGE:figures/full_fig_p034_2_5.png] view at source ↗
Figure 2.6
Figure 2.6. Figure 2.6: Single Side-Band: Steps of the simpler version of WDD ptychographic reconstruction [PITH_FULL_IMAGE:figures/full_fig_p035_2_6.png] view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: Structure of MoS2 (Kadantsev and Hawrylak (2012)) A 4D data set was simulated using Multislice Frozen Phonon algorithm by M¨arz (2020). It represents 43 x 25 scan positions and 236 x 236 detector pixels. The illumination angle is 24 mrad, the illumination step size is 12.644pm, while the electron acceleration is 80keV equivalent to an electron wavelength of λ = 4.176pm The dataset was used to produce con… view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: Conventional bright field (BF) and high angle annular darrk field (HAADF) STEM image [PITH_FULL_IMAGE:figures/full_fig_p037_3_2.png] view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3: amplitude and phase images of monolayer MoS2 using single side-band ptychography [PITH_FULL_IMAGE:figures/full_fig_p037_3_3.png] view at source ↗
Figure 3.4
Figure 3.4. Figure 3.4: ADF images of characterizing gold grid usually used for the FEI TITAN 30-800 STEM [PITH_FULL_IMAGE:figures/full_fig_p038_3_4.png] view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: Reconstruction of the aberration-free gold image (a in figure [PITH_FULL_IMAGE:figures/full_fig_p038_3_5.png] view at source ↗
Figure 3.6
Figure 3.6. Figure 3.6: Reconstruction of the aberrated gold image (b in figure [PITH_FULL_IMAGE:figures/full_fig_p039_3_6.png] view at source ↗
read the original abstract

In Momentum-resolved Scanning Transmission Electron Microscopy (4D STEM), a convergent electron beam is raster-scanned across a think specimen in 2D in real space. The corresponding 2D diffraction pattern, in momentum space, to each point is recorded, forming a 4D data set. Information decoding process can follow thereafter to produce an image of the specimen in real space. Ptychography is reconstruction algorithm that allow the extraction of the probe wavefunction and the multiplicative object transmission function of the specimen. Ptychography is implemented through direct and iterative schemes. Some of which are the extended Ptychographic Iterative Engine (ePIE), the Wigner Distribution Deconvolution (WDD) and the simpler version of WDD, the Single Side-Band (SSB). This thesis gives an overview of STEM ptychography giving examples of its experimental and simulated implementations. The different ptychographic reconstruction methods are explored in a mathematical framework when applicable. Finally, an SSB reconstruction was made using an original script for simulated data of MoS2 monolayer. Moreover, four-dimensional data was recorded using a STEM instrument. A natural step following this research would be the implementation of the WDD algorithm.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript provides an overview of ptychography in 4D-STEM, describing direct and iterative methods (ePIE, WDD, SSB) with mathematical frameworks where applicable. It reports an original-script SSB reconstruction performed on simulated MoS2 monolayer data and notes the acquisition of experimental 4D-STEM data, with WDD implementation listed as future work.

Significance. If the mathematical sections are rigorous and the SSB implementation is shown to be correct via validation, the work could function as an accessible introduction to 4D-STEM ptychography. The exclusive reliance on simulation without experimental processing or cross-checks against reference codes, however, restricts its contribution to practical phase recovery.

major comments (2)
  1. [Abstract] Abstract: the claim that an SSB reconstruction was performed supplies no equations, validation metrics, error analysis, or comparison to ground truth, so the correctness of the original script cannot be assessed.
  2. [Experimental data section] Section describing experimental data: experimental 4D-STEM data were recorded but left unprocessed, so the central claim that the method extracts probe and object functions in real 4D-STEM settings rests on the untested premise that the MoS2 simulation reproduces experimental noise, aberrations, and detector response.
minor comments (2)
  1. [Abstract] Abstract: 'think specimen' is a typo for 'thin specimen'.
  2. [Abstract] Abstract: 'Ptychography is reconstruction algorithm that allow' should read 'Ptychography is a reconstruction algorithm that allows'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the review and constructive feedback. We address the major comments point by point below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that an SSB reconstruction was performed supplies no equations, validation metrics, error analysis, or comparison to ground truth, so the correctness of the original script cannot be assessed.

    Authors: The abstract is a concise summary; the mathematical framework for SSB (as a simplified WDD) and the implementation details of the original script are presented in the main text. We agree that quantitative validation would strengthen the work and allow direct assessment of correctness. In revision we will add explicit equations for the SSB reconstruction, validation metrics, error analysis, and comparison to the known ground-truth MoS2 structure in a dedicated results subsection. revision: yes

  2. Referee: [Experimental data section] Section describing experimental data: experimental 4D-STEM data were recorded but left unprocessed, so the central claim that the method extracts probe and object functions in real 4D-STEM settings rests on the untested premise that the MoS2 simulation reproduces experimental noise, aberrations, and detector response.

    Authors: The manuscript does not assert that probe and object functions have been extracted from real experimental data. It reports acquisition of the 4D-STEM dataset and explicitly identifies WDD implementation on that data as future work. The SSB demonstration is performed exclusively on simulated MoS2 data. We will revise the text to state these scope limitations more clearly and to note that the simulation does not claim to reproduce all experimental effects. revision: partial

Circularity Check

0 steps flagged

No significant circularity; paper is overview plus implementation of prior methods on simulated data

full rationale

The manuscript is an overview of established ptychographic algorithms (ePIE, WDD, SSB) with a single original-script SSB reconstruction performed exclusively on simulated MoS2 monolayer data. No derivations, parameter fits presented as predictions, self-citation load-bearing steps, or ansatzes smuggled via citation are present. The central contribution reduces to applying known SSB mathematics to synthetic input; the unprocessed experimental dataset is explicitly noted as future work and does not enter any claimed result. This satisfies the default expectation of a self-contained, non-circular implementation report.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard mathematical descriptions of ptychography algorithms and the assumption that simulated data is representative; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • standard math Standard Fourier optics and multiplicative transmission function model for thin specimens in STEM
    Invoked when describing extraction of probe and object functions via ptychography.

pith-pipeline@v0.9.1-grok · 5745 in / 1194 out tokens · 18198 ms · 2026-06-27T21:36:55.178771+00:00 · methodology

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Reference graph

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