Beyond Contrast Transfer: Spectral SNR as a Dose-Aware Metric for STEM Phase Retrieval

Colin Ophus; Georgios Varnavides; Julie Marie Bekkevold; Lewys Jones; Mary C Scott; Stephanie M Ribet

REVIEW 5 major objections 5 minor 4 references

Beyond Contrast Transfer: Spectral SNR as a Dose-Aware Metric for STEM Phase Retrieval

T0 review · 5 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper argues that the standard contrast-transfer metric overestimates STEM phase retrieval performance and shows, via spectral signal-to-noise ratio, that iterative ptychography's signal saturates at $\sqrt{2}/2$, a detective quantum…

desk verdict Useful dose-aware metric and a solid comparison of direct methods, but the headline result on iterative ptychography's dose dependence is not yet separated from the fixed-step SGD artifact. read the letter →

arxiv 2507.19476 v2 pith:J4DMSC6X submitted 2025-07-25 physics.optics cond-mat.mtrl-sci

Georgios Varnavides , Julie Marie Bekkevold , Stephanie M Ribet , Mary C Scott , Lewys Jones , Colin Ophus This is my paper · ORCID

classification physics.opticscond-mat.mtrl-sci

keywords scanningtransmissionelectronmicroscopyphaseretrievalspectralsignal-to-noiseratiocontrasttransferfunctioniterativeptychographydetectivequantumefficiencydosePoissonnoise

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

Electron microscopists usually grade STEM phase retrieval techniques by their contrast transfer function, which describes the maximum signal an ideal linear system can pass. This paper argues that the CTF is the wrong yardstick because it ignores Poisson shot noise and total electron fluence, and it puts forward the spectral signal-to-noise ratio as a dose-aware alternative. On numerical white-noise reconstructions, the authors derive closed-form, dose-independent SSNR expressions for center-of-mass imaging, parallax imaging, and direct ptychography, and show that iterative ptychography is the exception: at low fluence it behaves like direct ptychography, while at high fluence its SSNR saturates at $\sqrt{2}/2$, implying a detective quantum efficiency of $1/2$ compared with ideal Zernike phase contrast. This makes CTF-based rankings misleading, especially for dose-sensitive samples, and suggests that cheap direct methods may be as effective as iterative ptychography at low dose.

What carries the argument

The central object is the spectral signal-to-noise ratio (SSNR), defined from $M$ independent reconstructions of the same object as the magnitude of the mean Fourier amplitude divided by the sample standard deviation at each spatial frequency, with the reference SSNR for a white-noise object taken as $\sqrt{N_e}$. The paper couples this to the complex-valued contrast transfer function $\mathcal{L}_j(\mathbf{q})$, written as a cross-correlation of probe and detector functions, so that the numerator signal in the SSNR is $|\mathcal{L}(\mathbf{q})|$ and the denominator is a per-technique noise term: $1/q$ for center-of-mass imaging, constant for parallax imaging, and $\sqrt{\mathcal{L}_{\mathrm{ptycho}}(\mathbf{q})/2}$ for direct ptychography. Iterative ptychography is handled numerically, and its observed SSNR dose dependence carries the argument that the unit CTF is misleading.

What would settle it

Reconstruct the same simulated white-noise objects with an adaptive step size or a much larger iteration count at low fluence and measure the SSNR; if the low-fluence SSNR rises to the high-fluence $\sqrt{2}/2$ plateau, the dose dependence is an optimizer artifact and the paper's central claim collapses.

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Extended reading notes

Core claim

The central claim is that the spectral signal-to-noise ratio (SSNR), rather than the contrast transfer function, is the correct measure of how much object information a STEM phase retrieval method actually recovers at a given electron dose. Using numerical reconstructions of white-noise objects, the authors show that center-of-mass imaging, parallax imaging, and direct ptychography have dose-independent SSNRs with closed-form analytical expressions. Iterative ptychography is different: at low electron fluence its SSNR converges to that of direct ptychography, while at high fluence it saturates at $\sqrt{2}/2$, corresponding to a detective quantum efficiency of $1/2$ relative to an ideal Zernike phase-contrast reference. This saturation is consistent with recent quantum Fisher information bounds, and the authors conclude that the unit CTF attributed to iterative ptychography substantially overstates its practical low-dose performance.

Load-bearing premise

The argument assumes that iterative ptychography's SSNR dose dependence reflects the algorithm's fundamental information limits rather than an artifact of the fixed step size used in the stochastic gradient descent implementation, a caveat the authors themselves raise.

Editorial extensions

If this is right

The contrast transfer function overestimates achievable signal for iterative ptychography at finite dose, so dose-aware metrics are needed for fair comparison of phase retrieval methods.
Center-of-mass imaging should be performed in focus, since its SSNR vanishes near zero spatial frequency and at twice the probe aperture, with noise growing as $1/q$.
Parallax imaging has an SSNR equal to its CTF with constant noise, requiring defocus for contrast and phase-flipping across zero crossings.
Direct ptychography has a dose-independent SSNR, and low-dose iterative ptychography converges to this direct-ptychography limit.
Even at high fluence, iterative ptychography still recovers low spatial frequencies inefficiently, so its advantages over direct methods appear mainly at high frequencies and high dose.

Reading between the lines

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

If the $\sqrt{2}/2$ saturation is fundamental, further algorithmic work on iterative ptychography should target low spatial frequencies and the optimization itself, since the high-frequency ceiling already reaches the quantum Fisher information limit.
The white-noise SSNR curves could be used as calibration curves to predict real-sample performance by convolution with a sample's power spectrum, turning SSNR into an acquisition-planning tool that assigns the fluence needed per spatial frequency.
A direct experimental extension would be to acquire many repeated low-dose scans of the same field of view and compute SSNR empirically; observing the predicted convergence to direct ptychography would confirm that the dose-aware ranking transfers from simulations to real instruments.
The dose-independence of direct methods suggests their performance can be extrapolated from one electron dose to another, simplifying detector and acquisition optimization without rerunning reconstructions at every dose.

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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: this paper gives the STEM phase retrieval community a better metric than CTF for thinking about low-dose performance, and the numerical comparison of four methods is useful. The headline result—iterative ptychography's SSNR is dose-dependent, approaching direct ptychography at low fluence and saturating at sqrt(2)/2 at high fluence—is genuinely interesting but not yet established, because the authors themselves note it might be an artifact of the fixed step size in their SGD implementation, and they don't report a step-size sweep, an optimizer comparison, or convergence checks. Code and data are also not yet available, so the numerical result can't be separated from the optimizer schedule.

What's new: using SSNR as a dose-aware metric for comparing STEM phase retrieval methods is a legitimate and overdue application. The observation that CTF-based assessments overestimate realizable performance, especially at low dose, is well motivated, and the experimental power spectra in Figure 1 support the point. For COM, parallax, and direct ptychography, the paper shows that SSNR is dose-independent and provides simple closed-form expressions. That part is solid and useful, even though the noise terms in Eq. 12 are 'fitted from Figure 4' rather than derived from first principles. The fitted forms are simple enough that they could be verified independently, but as presented they reduce the analytical claim to a curve fit.

The soft spot is the iterative ptychography result. The paper's central claim is that the dose dependence is a property of iterative phase retrieval, and the low-dose limit matching direct ptychography would be a practical insight for radiation-sensitive samples. But the paper's own caveat—'this might be a limitation of the fixed step-size used in the stochastic gradient descent implementation'—is exactly the kind of thing that determines whether the result is about the algorithm or about the optimizer. Without a convergence sweep or alternative optimizer, the evidence doesn't separate those possibilities. The agreement with the quantum Fisher information bound at high fluence is suggestive, but it's a consistency statement, not a derivation.

Who it's for: anyone comparing phase retrieval methods for low-dose STEM, especially in cryo-EM of biological samples. The SSNR framework and the direct-method comparisons are worth having; the iterative ptychography claim needs more work before it can be taken as a guide to experimental practice.

Recommendation: send it to peer review. The metric is useful and the direct-method analysis is defensible, but the central novel claim needs an optimizer and convergence sweep, and the analytical noise terms need independent derivation or validation. A serious referee could push the authors to fix these and the paper would be stronger for it.

Referee Report

5 major / 5 minor

Summary. The paper proposes the spectral signal-to-noise ratio (SSNR) as a dose-aware alternative to the contrast transfer function (CTF) for evaluating STEM phase retrieval methods. Using 100 numerical reconstructions of white-noise objects, the authors report dose-independent SSNRs for center-of-mass imaging, parallax imaging, and direct ptychography, with claimed closed-form expressions. For iterative ptychography, they report a dose-dependent SSNR: at low fluence it approaches direct ptychography, while at high fluence it saturates at sqrt(2)/2, implying a detective quantum efficiency limit of 1/2 relative to ideal Zernike phase contrast. The authors conclude that SSNR/DQE should complement or replace CTF analysis and that direct imaging techniques may be comparably effective for dose-sensitive samples.

Significance. If the central claim holds, the paper would provide a useful and practically relevant correction to CTF-based evaluation in STEM phase retrieval, especially for low-dose biological and soft-matter imaging. The paper's demonstration that the CTF overestimates iterative ptychography performance is well motivated by the experimental power spectra in Figure 1, and the SSNR framework is a sensible extension of prior noise analyses. However, the significance is currently conditional: the closed-form expressions are not independent derivations because the noise terms are fitted from the same numerical curves, and the dose dependence of iterative ptychography may be an artifact of the fixed-step SGD implementation, as the authors themselves note. The quantitative connection to quantum Fisher information bounds is also stated rather than derived. With additional numerical tests and a clearer separation of fitted versus derived results, the paper could become an influential reference for low-dose STEM evaluation.

major comments (5)

[Spectral Signal-to-Noise Ratio, Eq. (10)] The SSNR definition as printed is dimensionally incorrect: the denominator is written as sqrt(sum_i |Phi_i(q) - overline{Phi}(q)| / (M-1)), which lacks the square on the deviations and therefore does not define a standard deviation. The standard definition requires sqrt((1/(M-1)) sum_i |Phi_i(q) - overline{Phi}(q)|^2). If the numerical results used the correct formula, the text should be corrected; if the text is literal, all reported SSNR values are not computed according to the stated metric. Since every quantitative claim in the paper depends on this definition, this issue must be resolved.
[Derived Analytical Expressions, Eq. (12)] The 'closed-form analytical expressions' for center-of-mass, parallax, and direct ptychography are not independent of the numerical results: Eq. (12) states that the noise terms were 'fitted from Figure 4'. Consequently, the agreement between the dotted analytical curves and the solid numerical curves in Figure 4 is partly circular and cannot serve as validation of the expressions. The authors should either derive the noise expressions from a statistical model of the reconstructions or explicitly present them as empirical fits, and then adjust the claims made in the abstract and conclusions accordingly.
[Spectral Signal-to-Noise Ratio, iterative ptychography paragraph] The central novel claim—that iterative ptychography exhibits a dose-dependent SSNR that converges to direct ptychography at low fluence and saturates at sqrt(2)/2 at high fluence—is not separated from the optimization schedule. The text notes that 'this might be a limitation of the fixed step-size used in the stochastic gradient descent implementation', but no step-size sweep, no comparison with alternative optimizers, and no convergence criterion or iteration count are reported. Without such tests, the observed dose dependence could be an artifact of the specific algorithm settings rather than an intrinsic property of iterative phase retrieval. The authors should provide an optimizer and convergence study, or substantially soften the claim that this is a fundamental information-transfer limit.
[Spectral Signal-to-Noise Ratio and Conclusions, quantum Fisher information comparison] The statement that the high-fluence saturation at sqrt(2)/2 is 'in agreement with' or 'consistent with' recent quantum Fisher information bounds is not quantitatively established in the manuscript. No derivation is given showing that the cited bounds imply DQE = 1/2 or SSNR saturation at sqrt(2)/2. The agreement is therefore a qualitative consistency claim, not a supporting derivation. The authors should either provide the explicit connection or label the sqrt(2)/2 result as an empirical observation that remains to be explained theoretically.
[Availability of Data and Materials] The manuscript states that 'All other processed datasets/notebooks are available at [Add Zenodo link]', but the link is a placeholder. Because the main conclusions depend on numerical reconstructions whose simulation parameters (object size, dose values, probe model, reconstruction algorithm details) are not fully specified in the text, the absence of code and data currently prevents independent verification of the key results. The repository should be provided and cited before publication.

minor comments (5)

[Abstract] The abstract contains the typo 'close-form analytic expressions'; this should be 'closed-form'.
[CTF Comparison & Limitations] The phrase 'in-fact' should be 'in fact'.
[Center of Mass Imaging, Eq. (6)] The denominator 'i |q|^2' appears to be a typographical or rendering error; it should presumably be 'i |q|^2' as a complex factor, but the notation should be clarified so that the reader can verify the reduction to Eq. (7).
[Spectral Signal-to-Noise Ratio] The paper does not report the electron fluence values used in Figure 4 or the number of iterations for iterative ptychography at each dose. Adding these simulation details would improve reproducibility, even independent of the optimizer sweep recommended above.
[Figure 1] The caption says the top-left and top-right panels are parallax and iterative ptychography, but the text in the Introduction refers to 'Figure 1, right half' when discussing iterative ptychography oscillations. The correspondence between the text and the figure panels should be made explicit.

Circularity Check

1 steps flagged · score 6.0 of 10

Analytical SSNR expressions for COM/parallax/direct ptychography are fitted to the curves they then reproduce; iterative-ptychography dose dependence remains an independent numerical observation.

fitted input called prediction [Section 'Derived Analytical Expressions', Eq. 12]
"The dashed lines in the top panels of Figure 4 are analytical closed-form SSNR expressions for center-of-mass imaging, parallax imaging, and direct ptychography. The signal in the SSNR numerator is given by |ℒ(𝒒)|, while the denominator noise has been fitted from Figure 4 to be: NoiseiCOM(𝒒) = 1/𝒒, Noiseparallax(𝒒) = 1, Noiseptycho(𝒒) = √ℒptycho(𝒒)/2 (12)"

The noise terms in Eq. 12 are fit parameters, adjusted to reproduce the numerical solid curves in Figure 4; the dashed 'analytical' curves are then plotted using those same fitted noise terms and presented as closed-form analytical SSNR expressions. Their agreement with the numerical data is therefore guaranteed by construction rather than being a predictive validation. The fitted expressions are subsequently used in the text to draw conclusions (e.g., COM noise is 1/q, direct ptychography noise motivates OBF normalization), so those conclusions inherit the fit. This does not invalidate the numerical SSNR curves themselves, nor the iterative-ptychography dose-dependence observation, but it makes the claimed derivation of the closed-form expressions circular.

full rationale

The paper's central novel claim is the dose-dependence of iterative ptychography SSNR (low-fluence limit approaching direct ptychography, high-fluence plateau at sqrt(2)/2). This is supported by M=100 numerical reconstructions and is not itself a fitted analytical expression; the fixed-step SGD caveat is an explicit validity limitation, not a circularity. The CTF derivations follow Hammel and Rose and prior work, and self-citations to Varnavides et al. and Bekkevold et al. are background or interpretive, not load-bearing reductions. However, the paper also claims as a main result closed-form analytical SSNR expressions for COM, parallax, and direct ptychography; Eq. 12 openly states that the noise denominators were 'fitted from Figure 4,' the same numerical curves the dashed 'analytical' lines are compared against. That is a fitted-input-called-prediction step: the agreement is by construction. The claimed agreement with quantum Fisher information bounds is a consistency statement, not a derivation, but it is not circular because the saturation value is read from independent numerics and the DQE conversion is definitional. Overall, the partial circularity in the analytical expressions warrants a score of 6, while noting the iterative-ptychography dose-dependence result has independent numerical content.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a set of domain assumptions about weak-phase imaging, Poisson statistics, and white-noise objects. The most fragile additions are the fitted noise terms in Eq. 12 and the unstated SGD hyperparameters, which together determine the analytical SSNR curves and the iterative ptychography dose dependence.

free parameters (4)

noise_iCOM(q) = 1/q = 1/q
Fitted from the numerical SSNR curves in Figure 4, top panel, and used as the denominator in the analytical SSNR expression for center-of-mass imaging.
noise_parallax(q) = 1 = 1
Fitted constant noise term for parallax imaging; used in Eq. 12.
noise_ptycho(q) = sqrt(L_ptycho(q)/2) = sqrt(L_ptycho/2)
Fitted noise term for direct ptychography, proportional to the square root of its CTF, used in Eq. 12.
SGD fixed step size = not stated
The iterative ptychography results depend on this hyperparameter; the paper notes the dose dependence might be caused by it, but no value or scheduling is given.

assumptions (5)

domain assumption Weak-phase linear imaging model: reconstructed image Fourier transform is 2*phi(q)*L(q) (Eq. 1)
All CTF and SSNR expressions assume a linear relationship between sample phase and reconstructed image, valid only for weak phase objects.
domain assumption White-noise object assumption
Numerical reconstructions use white-noise objects to isolate imaging system performance; real samples have colored spectra, so SSNR values may differ.
domain assumption Poisson-limited electron detection
The paper's motivation is that detection is Poisson-limited, but the dose-independence claim for direct methods is not derived from this statistical model.
ad hoc to paper Noise expressions in Eq. 12 are correct
These forms are fitted from Figure 4, not derived, and the paper uses them to construct analytical SSNR predictions.
domain assumption Iterative ptychography CTF is unity
The paper relies on prior numerical studies that iterative ptychography can recover all spatial frequencies, despite the low-dose experimental power spectra showing Thon-like oscillations.

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Cite this review

Pith. "Pith review of Beyond Contrast Transfer: Spectral SNR as a Dose-Aware Metric for STEM Phase Retrieval." pith.science (2026). https://pith.science/paper/J4DMSC6X

@misc{pith2026250719476,
  author       = {Pith},
  title        = {Pith review of: Beyond Contrast Transfer: Spectral SNR as a Dose-Aware Metric for STEM Phase Retrieval},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J4DMSC6X}},
  note         = {Machine review of arXiv:2507.19476}
}

read the original abstract

The contrast transfer function (CTF) is widely used to evaluate phase retrieval methods in scanning transmission electron microscopy (STEM), including center-of-mass imaging, parallax imaging, direct ptychography, and iterative ptychography. However, the CTF reflects only the maximum usable signal, neglecting the effects of finite electron fluence and the Poisson-limited nature of detection. As a result, it can significantly overestimate practical performance, especially in low-dose regimes. Here, we employ the spectral signal-to-noise ratio (SSNR), as a dose-aware statistical framework to evaluate the recoverable signal as a function of spatial frequency. Using numerical reconstructions of white-noise objects, we show that center-of-mass, parallax, and direct ptychography exhibit dose-independent SSNRs, with close-form analytic expressions. In contrast, iterative ptychography exhibits a surprising dose dependence: at low fluence, its SSNR converges to that of direct ptychography; at high fluence, it saturates at a value consistent with the maximum detective quantum efficiency predicted by recent quantum Fisher information bounds. The results highlight the limitations of CTF-based evaluation and motivate SSNR as a more accurate, dose-aware metric for assessing STEM phase retrieval methods.

Figures

Figures reproduced from arXiv: 2507.19476 by the authors.

**Figure 2.** Geometric and mathematical interpretation of the probe autocorrelation functions limiting STEM-based phase retrieval. For an ideal probe, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Center-of-mass imaging, parallax imaging, direct ptychography, and iterative ptychography CTFs for acquisitions in-focus and 200 Å defocus, [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Numerical (solid lines) spectral signal-to-noise ratios for STEM phase retrieval techniques for in-focus and defocused acquisitions. For center [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: Summary figure convolving relatively low-fluence SSNRs of various STEM phase retrieval techniques for three different imaging conditions [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

4 extracted references · 2 canonical work pages

[2017]

Iterative Phase Retrieval Algorithms for Scanning Transmission Electron Microscopy

Dose-Efficient Cryo-STEM Imaging of Whole Cells Using the Electron Microscope Pixel Array De- tector. Microscopy and Microanalysis 23, 804–805.. https://doi.org/10.1017/s1431927617004688 Unser, M., Trus, B.L., Steven, A.C., 1987. A new resolu- tion criterion based on spectral signal-to-noise ratios. 9 Ultramicroscopy 23, 39–51.. https://doi.org/10.1016/ 0...

work page Pith review arXiv doi:10.48550/arxiv.2309.05250
[2019]

Ultramicroscopy 196, 131– 135

High dose efficiency atomic resolution imaging via electron ptychography. Ultramicroscopy 196, 131– 135.. https://doi.org/10.1016/j.ultramic.2018.10.005 Rodenburg, J., Maiden, A., 2019. Ptychography, in: Springer Handbook of Microscopy. Springer Interna- tional Publishing, pp. 819–904.. https://doi.org/ 10. 1007/978-3-030-00069-1_17 Seki, T., Ikuhara, Y.,...

doi:10.1016/j.ultramic.2018.10.005 2018
[2024]

Microscopy 74, 98–106

Dose-efficient phase-contrast imaging of thick weak phase objects via OBF STEM using a pixelated detector. Microscopy 74, 98–106.. https://doi.org/10. 1093/jmicro/dfae051 O’Leary, C.M., Martinez, G.T., Liberti, E., Humphry, M.J., Kirkland, A.I., Nellist, P .D., 2021. Contrast transfer and noise considerations in focused-probe electron ptychography. Ultram...

work page arXiv
[2025]

Journal of Microscopy

Accelerating iterative ptychography with an integrated neural network. Journal of Microscopy.. https://doi.org/10.1111/jmi.13407 Ooe, K., Seki, T., Ikuhara, Y., Shibata, N., 2021. Ultra- high contrast STEM imaging for segmented/pixelated detectors by maximizing the signal-to-noise ratio. Ul- tramicroscopy 220, 113133.. https://doi.org/ 10.1016/j. ultramic...

arXiv 2021

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [2017]

Iterative Phase Retrieval Algorithms for Scanning Transmission Electron Microscopy

Dose-Efficient Cryo-STEM Imaging of Whole Cells Using the Electron Microscope Pixel Array De- tector. Microscopy and Microanalysis 23, 804–805.. https://doi.org/10.1017/s1431927617004688 Unser, M., Trus, B.L., Steven, A.C., 1987. A new resolu- tion criterion based on spectral signal-to-noise ratios. 9 Ultramicroscopy 23, 39–51.. https://doi.org/10.1016/ 0...

work page Pith review arXiv doi:10.48550/arxiv.2309.05250

[2] [2019]

Ultramicroscopy 196, 131– 135

High dose efficiency atomic resolution imaging via electron ptychography. Ultramicroscopy 196, 131– 135.. https://doi.org/10.1016/j.ultramic.2018.10.005 Rodenburg, J., Maiden, A., 2019. Ptychography, in: Springer Handbook of Microscopy. Springer Interna- tional Publishing, pp. 819–904.. https://doi.org/ 10. 1007/978-3-030-00069-1_17 Seki, T., Ikuhara, Y.,...

doi:10.1016/j.ultramic.2018.10.005 2018

[3] [2024]

Microscopy 74, 98–106

Dose-efficient phase-contrast imaging of thick weak phase objects via OBF STEM using a pixelated detector. Microscopy 74, 98–106.. https://doi.org/10. 1093/jmicro/dfae051 O’Leary, C.M., Martinez, G.T., Liberti, E., Humphry, M.J., Kirkland, A.I., Nellist, P .D., 2021. Contrast transfer and noise considerations in focused-probe electron ptychography. Ultram...

work page arXiv

[4] [2025]

Journal of Microscopy

Accelerating iterative ptychography with an integrated neural network. Journal of Microscopy.. https://doi.org/10.1111/jmi.13407 Ooe, K., Seki, T., Ikuhara, Y., Shibata, N., 2021. Ultra- high contrast STEM imaging for segmented/pixelated detectors by maximizing the signal-to-noise ratio. Ul- tramicroscopy 220, 113133.. https://doi.org/ 10.1016/j. ultramic...

arXiv 2021