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arxiv: 2606.28056 · v1 · pith:Y7NXPUS6new · submitted 2026-06-26 · ❄️ cond-mat.mes-hall · physics.atm-clus

Determining Electron Beam Lateral Coherence in a Scanning Electron Microscope Using Electron Diffraction

Evelijn Akerboom , Fatemeh Kiani , Giulia Tagliabue , Wiebke Albrecht , Joanne Etheridge , F. Javier Garc\'ia de Abajo , Albert Polman This is my paper

Pith reviewed 2026-06-29 02:46 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall physics.atm-clus
keywords electron beam coherencescanning electron microscopeselected area electron diffractionconvergent beam electron diffractionlateral coherenceSTEM in SEM30 keV electronsquantum coherent interactions
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The pith

Electron diffraction in an SEM sets a 60% lower limit on beam lateral coherence over 5% of its diameter at 30 keV.

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

The paper develops scanning transmission electron microscopy capabilities inside a scanning electron microscope to measure the lateral coherence of the electron beam in the specimen plane. High-quality selected-area electron diffraction maps and convergent-beam electron diffraction patterns are recorded from single-crystalline gold flakes and a graphene monolayer. Interference between electrons whose wave vectors differ by 0.031 per angstrom is then analyzed to extract a lower limit of approximately 60% coherence across 5% of the beam diameter. A sympathetic reader would care because the result indicates that the beam coherence already reaches levels needed for quantum-coherent electron-light-matter interaction experiments inside a standard SEM rather than only in specialized transmission instruments.

Core claim

We develop and characterize STEM capabilities within an SEM at 30 keV. Using single-crystalline Au flakes and a monolayer of graphene we obtain high-quality SAED maps and CBED patterns. Adapting an interference analysis from TEM techniques, we measure the degree of lateral coherence by examining electrons with two different wave vectors separated by 0.031 per angstrom and extract a lower limit of approximately 60% over 5% of the e-beam diameter. These coherence values are sufficient to enable quantum-coherent electron-light-matter interaction experiments in the SEM.

What carries the argument

Interference analysis between electrons with wave vectors separated by 0.031 per angstrom in SAED and CBED patterns, adapted from TEM, to quantify lateral coherence in the specimen plane.

If this is right

  • The SEM can produce high-quality SAED maps and CBED patterns at 30 keV on crystalline samples.
  • Lateral coherence reaches at least 60% over 5% of the beam diameter, enabling quantum-coherent electron-light-matter experiments.
  • The adapted interference method provides a direct probe of beam coherence in the specimen plane.
  • Crystallographic information can be obtained in the SEM using these diffraction techniques.

Where Pith is reading between the lines

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

  • Routine coherence checks could become feasible in many SEM facilities without dedicated TEM access.
  • The same diffraction-based approach might be used to track how coherence changes with beam energy or lens settings.
  • Hybrid instruments could combine SEM scanning with coherent diffraction for new classes of experiments.

Load-bearing premise

The TEM-derived interference analysis remains valid in the SEM geometry without major changes from aberrations, sample charging, or beam instabilities at 30 keV.

What would settle it

Repeating the diffraction measurements on the same samples and finding interference contrast much lower than predicted for 60% coherence, or obtaining substantially different values with an independent coherence method on the identical SEM setup, would falsify the extracted lower limit.

read the original abstract

We develop and characterize scanning transmission electron microscopy (STEM) capabilities within a scanning electron microscope (SEM) to investigate the effective lateral coherence of the electron beam (e-beam) in the specimen plane. Using single-crystalline Au flakes and a sample composed of a monolayer of graphene, we obtain high-quality selected-area electron diffraction (SAED) maps and convergent-beam electron diffraction (CBED) patterns, validating the systems ability to probe crystallographic information at an acceleration voltage of 30 keV. Building on these capabilities, we implement a method, which is adapted from techniques traditionally used in transmission electron microscopy, to measure the degree of lateral coherence of the e-beam in the specimen plane of the SEM. By analyzing interference between electrons with two different wave vectors separated by 0.031 per angstrom, we extract a lower limit for the degree of lateral coherence over 5% of the e-beam diameter of approximately 60%. These coherence values are sufficient to enable quantum-coherent electron-light-matter interaction experiments in the SEM.

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 / 1 minor

Summary. The manuscript develops and validates STEM capabilities in an SEM at 30 keV using SAED maps and CBED patterns on single-crystalline Au flakes and monolayer graphene. It then adapts a TEM interference-visibility technique to extract a lower limit of ~60% lateral coherence over 5% of the e-beam diameter from interference between wave-vector components separated by 0.031 Å^{-1}, concluding that the values suffice for quantum-coherent electron-light-matter experiments in the SEM.

Significance. If the coherence extraction is robust and the TEM-adapted analysis is shown to be free of significant SEM-specific dephasing, the result would enable quantum experiments on a more accessible platform than TEMs. The diffraction validation at 30 keV is a useful technical step, but the absence of raw data, fitting details, and error analysis prevents a full assessment of the central numerical claim.

major comments (2)
  1. [Abstract] Abstract: the central claim of a 60% lower limit on lateral coherence is stated without raw diffraction patterns, the visibility fitting procedure, error analysis, or cross-validation against known TEM results, so the numerical extraction cannot be verified.
  2. [Coherence measurement] Coherence measurement (adapted from TEM): no quantitative bound is supplied on residual dephasing from SEM-specific factors (sample charging on graphene/Au, 30 keV lens aberrations, or scan instabilities) that could reduce the observed contrast below the true coherence value.
minor comments (1)
  1. [Abstract] The wave-vector separation is given as '0.031 per angstrom'; standardize to 0.031 Å^{-1} for clarity and consistency with crystallography notation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting points that will improve the clarity and robustness of our claims. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim of a 60% lower limit on lateral coherence is stated without raw diffraction patterns, the visibility fitting procedure, error analysis, or cross-validation against known TEM results, so the numerical extraction cannot be verified.

    Authors: The abstract is necessarily brief, but the supporting elements are present in the main text: raw SAED maps and CBED patterns appear in Figures 2 and 3, the visibility fitting procedure (including the two-beam interference model and extraction of the 0.031 Å^{-1} separation) is given in Section 4, and the resulting lower-limit value with its stated uncertainty is derived there. Cross-validation against TEM literature values is not performed because the experiment is conducted at 30 keV in an SEM; we will add a short comparative paragraph in the revised manuscript. To improve verifiability from the abstract alone we will insert a clause referencing the relevant sections and figures. We will also make the fitting scripts and example raw patterns available as supplementary material. revision: partial

  2. Referee: [Coherence measurement] Coherence measurement (adapted from TEM): no quantitative bound is supplied on residual dephasing from SEM-specific factors (sample charging on graphene/Au, 30 keV lens aberrations, or scan instabilities) that could reduce the observed contrast below the true coherence value.

    Authors: We agree that an explicit bound on possible SEM-specific dephasing would strengthen the interpretation. The current manuscript does not supply such quantitative estimates. In the revision we will add a dedicated paragraph that (i) notes the high conductivity and grounding of both the Au flakes and graphene, (ii) states that the SEM condenser and objective lenses were operated under calibrated conditions at 30 keV, and (iii) reports that acquisition times were kept short to limit scan drift. Order-of-magnitude estimates for residual contrast loss from each source will be included; where a rigorous bound cannot be derived without additional measurements we will state the limitation explicitly. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental coherence lower limit derived from direct interference visibility data

full rationale

The paper's chain consists of experimental validation via SAED/CBED patterns at 30 keV followed by an interference contrast measurement between wave-vector components separated by 0.031 Å^{-1}. The reported ~60% lower limit on lateral coherence is obtained directly from observed visibility in the adapted TEM-style analysis; no equations, fitted parameters, or self-citations are shown that reduce this value to an input by construction. The adaptation is presented as a methodological transfer without load-bearing self-citation or ansatz smuggling. This is the standard experimental definition of partial coherence via fringe visibility and remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the transferability of TEM coherence extraction formulas to the SEM without additional calibration or correction terms.

axioms (1)
  • domain assumption The interference visibility between two wave-vector components separated by 0.031 Å⁻¹ directly quantifies lateral coherence fraction in the specimen plane.
    This is the standard TEM relation invoked without re-derivation or SEM-specific validation in the abstract.

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discussion (0)

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