On Overlap Ratio in Defocused Electron Ptychography

Amirafshar Moshtaghpour; Angus I. Kirkland

REVIEW 3 major objections 5 minor 1 cited by

On Overlap Ratio in Defocused Electron Ptychography

T0 review · 3 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read The paper claims that a 40% overlap ratio is enough for stable, high-quality reconstructions in defocused electron ptychography.

desk verdict Useful geometric redundancy analysis, but the 40% overlap claim is a phase-object best case, not the universal guideline the abstract implies. read the letter →

arxiv 2502.00762 v2 pith:MLP34QM5 submitted 2025-02-02 eess.SP cs.IRphysics.app-phphysics.med-ph

Amirafshar Moshtaghpour , Angus I. Kirkland This is my paper · ORCID

classification eess.SPcs.IRphysics.app-phphysics.med-ph

keywords 4DscanningtransmissionelectronmicroscopydefocusedptychographyoverlapratiophaseretrievalconstrainedPIEobjectapproximationPoissonnoisedataredundancy

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out to establish the minimum overlap ratio between adjacent illuminated probe positions needed for reliable defocused electron ptychography. It introduces two scan-geometry quantities, D(ρ) and C(ρ), that measure data redundancy independently of the specimen and the reconstruction algorithm. Using these quantities and a constrained PIE algorithm on simulated 4D STEM data with Poisson noise, the paper concludes that an overlap ratio of 40% or greater yields stable, high-quality phase reconstructions. This matters because lower overlap means larger fields of view and less beam damage for the same number of probe positions.

What carries the argument

The argument rests on a geometric overlap model plus a modified iterative algorithm. The function $\rho = R(\gamma)$ converts the ratio of scan step to probe diameter into an overlap fraction, and a piecewise Taylor-based inverse $R^{-1}(\rho)$ turns a desired overlap into a scan step. The quantities $D(\rho)$ (number of neighbouring illuminations overlapping a primary illumination) and $C(\rho)$ (number of times each pixel is illuminated) then measure data redundancy purely from scan geometry. On the algorithmic side, Constrained PIE (CPIE) is PIE with an added phase-object constraint that resets the object amplitude toward unity after each update, and it is this constraint that makes low-overlap reconstructions stable in the paper's simulations.

What would settle it

Simulate a 4D STEM dataset with a specimen that has known amplitude modulation (for example, amplitude varying by ±20% around unity) and run CPIE at 40% overlap. If the NRMSE gap versus 60% overlap widens relative to the pure-phase case, the 40% threshold depends critically on the phase-object assumption rather than on overlap alone.

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Extended reading notes

Core claim

For a phase object and a known probe, an overlap ratio of 40% between adjacent illuminated areas is sufficient for stable, high-quality electron ptychography reconstructions. The paper demonstrates this by defining geometry-only redundancy measures and by benchmarking a Constrained PIE (CPIE) algorithm on simulated 4D STEM datasets for two phase images under noiseless and Poisson-noise conditions. In both test images, 40% overlap gave reconstruction quality comparable to 60% overlap; one of the images required 70% overlap to match the quality of 95% overlap. The paper also finds that the unconstrained PIE algorithm needs substantially larger overlaps, showing that the phase-object constraint is central to the 40% result.

Load-bearing premise

Everything rests on treating the specimen as a pure phase object whose transmission amplitude is close to one; if a real sample has strong amplitude contrast, the 40% overlap finding may not hold.

Editorial extensions

If this is right

If the 40% threshold holds, experimentalists can use larger scan steps in defocused-probe ptychography, covering larger fields of view or reducing dose for a given field of view.
The geometry-only quantities D(ρ) and C(ρ) allow users to estimate critical overlap values from the scan grid before running an experiment, without knowing the specimen or choosing a specific reconstruction algorithm.
The phase-object constraint in CPIE is what makes 40% overlap viable; unconstrained PIE needs larger overlaps, so the constraint is a load-bearing part of the recipe.
The 40% threshold is object-dependent in detail: the rice test image needed 70% overlap to match 95%-overlap quality, suggesting users check their specific specimen contrast before fixing an overlap.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the phase-object approximation is relaxed to allow amplitude contrast, the 40% threshold likely shifts; a natural test is to repeat the paper's simulations with mixed amplitude-and-phase objects.
The same D(ρ) and C(ρ) redundancy measures could be applied to non-raster scan patterns, such as Fermat spirals, to predict whether the critical overlap changes with scan trajectory.
Because CPIE enforces unit amplitude, real specimens with absorption or strong scattering may require a modified constraint; the 40% finding should be read as a best-case scenario for weakly scattering phase objects.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: the geometric redundancy quantities are a genuine addition, but the 40% rule in the abstract is a phase-object best case, not the universal statement it reads as.

The paper's real contribution is the recovery-agnostic analysis: D(rho) and C(rho) depend only on scan geometry, and the approximate inverse R^{-1}(rho) is a practical tool for converting desired overlap into scan step. These are cleanly derived, self-contained, and useful for planning defocused 4D STEM acquisitions. The CPIE algorithm, PIE with a unit-amplitude projection, is a small but sensible modification for phase objects, and the simulation framework (known probe, Poisson noise, NRMSE with global phase removal) is careful and reproducible. The observation that 40% overlap performs comparably to 60% for CPIE on these two test images is a concrete, potentially useful refinement of Bunk et al.'s 60% recommendation.

The soft spots are in the packaging. The conclusion properly says 'within the parameter space considered,' but the abstract drops that qualifier. The rice image itself requires 70% overlap to match the 95% quality level, so 'stable, high-quality reconstructions' for all images at 40% is not established. The phase-object assumption is built into the algorithm (line 10 of Algorithm 1) and into all simulated objects; if a real specimen has amplitude contrast, the unit-amplitude constraint is wrong and the threshold could shift or vanish. I'd also like to see error bars or repeated runs with different probe orders, since the algorithm randomizes probe selection. The authors note their detector-plane correction (line 7) is only suitable for noiseless settings, which is a bit awkward for the noisy experiments, though the results still look reasonable.

The citation pattern is fine: Bunk et al. is credited, and the handful of self-citations are to relevant prior work on low-dose ptychography. No circularity problem; the D/C quantities are derived from geometry, not fit to the reconstructions.

Who's this for? Anyone planning defocused 4D STEM experiments who wants a quick way to think about redundancy, and anyone working on phase-object ptychographic algorithms. It deserves serious peer review; the referee should push for amplitude-contrast simulations, error bars, and an abstract that matches the conclusion.

Referee Report

3 major / 5 minor

Summary. The paper studies how the overlap ratio between adjacent illuminated areas affects data redundancy and reconstruction quality in defocused-probe electron ptychography. It proposes a closed-form approximation to the inverse of the overlap-ratio function, defines two geometry-only quantities D(ρ) and C(ρ) that are independent of the object and of the reconstruction algorithm, and introduces a phase-object-constrained variant of PIE (CPIE). The numerical study uses two simulated phase objects (USAF-1951 chart and a rice image), three noise levels (noiseless and Poisson noise at 20 and 26 dB mSNR), and overlap ratios from 0% to 95%. The abstract claims that a 40% or greater overlap ratio yields stable, high-quality reconstructions, while the conclusion adds the qualifier 'within the parameter space considered'.

Significance. The geometric analysis in Sec. III is self-contained and provides a useful, algorithm-independent way to reason about overlap-induced redundancy; the error bound for the approximate inverse, |ρ − R(R^{-1}(ρ))| < 0.008, is a concrete and checkable quantitative claim. The paper also makes a practical algorithmic contribution by adding a phase-object projection to PIE, and it tests this algorithm across several noise levels. If the 40% threshold were robust, it would offer practical dose-saving guidance for 4D STEM acquisition. However, the current evidence is narrower than the central claim: only two pure phase objects are tested, the rice object requires 70% overlap to match the 95% case, and no repeat runs or error bars are provided despite random probe ordering and Poisson noise. The significance of the paper is therefore real but contingent on a careful restatement of the conditions under which the threshold holds.

major comments (3)

[Abstract and §IV (Fig. 4)] The abstract's central sentence, 'a 40% or greater overlap ratio yields stable, high-quality reconstructions,' is not supported by the paper's own numerical results. Section IV states that the rice phase object requires a minimum overlap of 70% to achieve phase retrieval quality comparable to that obtained with 95% overlap, while the USAF object reaches that level at 40%. Thus, for one of the two test objects, 40% overlap does not yield the same quality as the high-overlap reference. The conclusion already limits the claim to 'within the parameter space considered,' but the abstract omits this qualifier. Please revise the abstract to state the object-dependent nature of the threshold, or redefine 'high-quality' operationally (for example, as 'comparable to 60% overlap') and apply that definition consistently.
[§II, Algorithm 1 (line 10), and §III-C] The numerical validation is performed entirely under the phase-object approximation. Section II assumes 'the specimen is a phase object, meaning the amplitude of the object is small and close to one,' and Algorithm 1 line 10 enforces this assumption by replacing the updated object amplitude with unit amplitude. All simulated objects in Sec. IV are constructed as phase-only objects. This makes the 40% threshold a best-case result for pure phase objects. For real specimens with appreciable amplitude contrast, the constraint in line 10 is not valid, and the threshold may shift or disappear. Please either add simulations with amplitude-modulated and mixed amplitude/phase objects, or explicitly restrict the central claim to the phase-object case and state that extension to amplitude contrast is untested.
[§IV (Fig. 4) and Algorithm 1] The reported NRMSE curves are single realizations with no error bars. Algorithm 1 processes probe locations in an order that the text describes as random, and the Poisson noise realizations are random as well, so the exact positions of the 40% and 70% crossover points are not established. The term 'stable' in the central claim therefore lacks statistical support. Please report the mean and standard deviation over multiple independent runs, especially at the threshold overlaps and noise levels, specify the random seed protocol, and state the NRMSE threshold used to classify a reconstruction as 'high-quality.'

minor comments (5)

[§I (Introduction)] The sentence beginning 'The authors in [17–20] have established with applications in ptychography' is incomplete and should be rewritten or removed.
[§III-C (Quality measure)] The statement 'NRMSE(o, co) = ∞' appears to be a sign error. With the given ν minimizing ||o − ν ohat||², the residual for ohat = co is zero, so the dB value is −∞, not +∞. Please correct the notation and define the normalization convention explicitly.
[§III-B (Fig. 2)] The hypothesis that critical overlap ratios correspond to jump discontinuities in D, mC, or MC is stated but not tested. The paper would be strengthened by a direct comparison of the predicted critical ratios {18.2, 39, 45}% with the observed NRMSE transitions in Fig. 4.
[§IV (Fig. 4)] The phrase 'the behaviour of the NRMSE of CPIE correlates with the σC(ρ)/µC(ρ) curve' is qualitative. Since σC/µC is a candidate predictor, please report a numerical correlation measure such as Spearman's ρ over the stated overlap range, or weaken the claim.
[General] There are minor typographical issues, e.g., 'complex objects structures' in the introduction should read 'complex object structures.' A careful proofread would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the overlap-ratio quantities are geometry-only, the 40% threshold is an observed simulation outcome, and the phase-object restriction is a scope limitation, not a fitted input.

full rationale

The claimed derivation chain is self-contained. D(ρ) and C(ρ) in Sec. III-B are computed purely from scan geometry via Eq. (6), with no fitted parameters derived from reconstruction quality. The inverse-overlap approximation R^{-1}(ρ) in Eq. (5) is a Taylor-series numerical approximation to the geometric function R(γ) in Eq. (4); its threshold parameters ρ0 and ρ1 are chosen to control the approximation error (|ρ - R(R^{-1}(ρ))| < 0.008), not to produce a target overlap threshold. The central 40% claim is reported as an observed result of the simulations in Sec. IV (Fig. 4), where CPIE's NRMSE at 40% is compared with the 60% and 95% cases; it is not a parameter fitted to those outcomes and renamed a prediction. The phase-object assumption is an explicit scope condition (Sec. II and Algorithm 1 line 10) and is stated again in the conclusion as 'within the parameter space considered'; it limits generality but does not make the result equivalent to its input. Self-citations [8,9,11,13] concern dose, compressive sensing, and low-dose regularisation, and are not load-bearing for the overlap threshold. No uniqueness theorem is imported, and no known result is renamed. The abstract's unconditional phrasing of the 40% claim is a presentation issue, not circularity.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard ptychography assumptions (multiplicative exit wave, Fraunhofer diffraction) plus the paper-specific assumptions of a known probe and a pure phase object. The 40% threshold is empirical and depends on the chosen test images and algorithm hyperparameters; no new physical entities are introduced.

free parameters (4)

rho_0 = 0.0448
Threshold in piecewise inverse R^{-1} (Eq. 5), chosen by numerical analysis to keep approximation error below 0.008; not related to the 40% result.
rho_1 = 0.5816
Threshold in piecewise inverse R^{-1} (Eq. 5), chosen with rho_0 for accuracy.
alpha_o = 0.1
Object learning rate in CPIE (Algorithm 1), chosen by hand; the 40% threshold could depend on this hyperparameter, but no sensitivity analysis is given.
Nitr = 100
Number of iterations in CPIE, chosen by hand; no convergence or sensitivity analysis is reported.

assumptions (4)

domain assumption Exit wave is the product of probe and object transmission function (Eq. 1)
Standard thin specimen approximation in ptychography; used in the sensing model.
domain assumption Detector wave is the 2D DFT of the exit wave (Eq. 2)
Fraunhofer far-field propagation; standard in 4D STEM.
domain assumption Object amplitude is close to one (phase object)
Stated in Sec. II; used in CPIE constraint (Algorithm 1 line 10) and in simulation objects.
domain assumption Probe is known from aberration parameters
Stated as assumption (i) in Sec. II; removes probe retrieval from the problem.

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Cite this review

Pith. "Pith review of On Overlap Ratio in Defocused Electron Ptychography." pith.science (2026). https://pith.science/paper/MLP34QM5

@misc{pith2026250200762,
  author       = {Pith},
  title        = {Pith review of: On Overlap Ratio in Defocused Electron Ptychography},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MLP34QM5}},
  note         = {Machine review of arXiv:2502.00762}
}

read the original abstract

Four-dimensional Scanning Transmission Electron Microscopy (4D STEM) with data acquired using a defocused electron probe is a promising tool for characterising complex biological specimens and materials through a phase retrieval process known as Electron Ptychography (EP). The efficacy of 4D STEM acquisition and the resulting quality of EP reconstruction depends on the overlap ratio of adjacent illuminated areas. This paper demonstrates how the overlap ratio impacts the data redundancy and the quality of the EP reconstruction. We define two quantities as a function of the overlap ratio that are independent of both the object and the EP algorithm. Subsequently, we evaluate an EP algorithm for varying overlap ratios using simulated 4D STEM datasets. Notably, a 40% or greater overlap ratio yields stable, high-quality reconstructions.

Figures

Figures reproduced from arXiv: 2502.00762 by the authors.

**Figure 1.** Defocused-probe 4D STEM. An electron probe scans a FoV over the object and a diffraction pattern per probe location is collected using a 2-D electron detector. Scanning all probe locations creates the 4-D dataset. Defocus and convergence semiangle parameters are denoted, respectively, by ∆f and α and are discussed in Sec. III. Let o ∈ C No be the discretised and vectorised version of the object wave function over a… view at source ↗

**Figure 2.** Values of the quantities defined in Sec. III-B. These values are independent from the recovery algorithm, illuminated [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Ground truth images used for generating 4D STEM data. USAF-1951 (left) and rice (middle) images used for the object [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Performance of CPIE and PIE reconstructions for phase object approximation. Efficient overlap ratio for stable [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: Recovered object phase images via CPIE algorithm for different overlap ratios and mean SNRs. [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

LoRePIE: $\ell_0$ Regularised Extended Ptychographical Iterative Engine for Low-dose and Fast Electron Ptychography
physics.app-ph 2024-11 conditional novelty 4.0 of 10

LoRePIE, an l0-regularized ePIE with DCT-domain hard thresholding, reconstructs useful electron ptychography images from probe positions with as low as 56% overlap.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

[1] [1]

Resolution beyond the information limit in transmission electron microscopy,

P. Nellist and B. McCallum, “Resolution beyond the information limit in transmission electron microscopy,” nature, vol. 374, no. 6523, pp. 630–632, 1995

work page 1995

[2] [2]

A phase retrieval algorithm for shifting illumination,

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Applied physics letters, vol. 85, no. 20, pp. 4795–4797, 2004

work page 2004

[3] [3]

An improved ptychographical phase retrieval algorithm for diffractive imaging,

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy, vol. 109, no. 10, pp. 1256–1262, 2009

work page 2009

[4] [4]

Probe retrieval in ptychographic coherent diffractive imaging,

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy, vol. 109, no. 4, pp. 338–343, 2009

work page 2009

[5] [5]

Relaxed averaged alternating reflections for diffraction imaging,

D. R. Luke, “Relaxed averaged alternating reflections for diffraction imaging,” Inverse problems, vol. 21, no. 1, p. 37, 2004

2004

[6] [6]

Semi-implicit relaxed Douglas-Rachford algorithm (sdr) for ptychography,

M. Pham, A. Rana, J. Miao, and S. Osher, “Semi-implicit relaxed Douglas-Rachford algorithm (sdr) for ptychography,” Optics Express, vol. 27, no. 22, pp. 31 246–31 260, 2019

work page 2019

[7] [7]

Maximum-likelihood refinement for coherent diffractive imaging,

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New Journal of Physics , vol. 14, no. 6, p. 063004, 2012

work page 2012

[8] [8]

Ex- ploring low-dose and fast electron ptychography using l0 regularisation of extended ptychographical iterative engine,

A. Moshtaghpour, A. Velazco-Torrejon, A. W. Robinson, A. I. Kirkland, and N. D. Browning, “Ex- ploring low-dose and fast electron ptychography using l0 regularisation of extended ptychographical iterative engine,” Microscopy and Microanalysis, vol. 29, no. Supplement 1, pp. 344–345, 2023

work page 2023