Pith. sign in

REVIEW 3 major objections 4 minor 63 references

Near, far, wherever you are: simulations on the dose efficiency of holographic and ptychographic coherent imaging

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This simulation study finds that near-field and far-field coherent imaging methods reach similar image quality at equal specimen fluence, so photon fluence, not geometry, sets the resolution limit.

desk verdict Useful NFH-vs-FFP comparison under matched fluence, but the abstract overclaims three-way equivalence and the NFH support mask is an oracle prior that needs robustness testing. read the letter →

arxiv 1908.06770 v2 pith:HJQTWVX4 submitted 2019-08-16 eess.IV physics.app-phphysics.med-ph

Ming Du , Doga Gursoy , Chris Jacobsen This is my paper · ORCID
classification eess.IVphysics.app-phphysics.med-ph
keywords x-raymicroscopydoseefficiencynear-fieldholographyptychographyfar-fieldfluence-resolutionlimitphaseretrievalFourierringcorrelation
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

This paper asks whether the way an x-ray microscope records coherent scattering—holograms in the near field or diffraction patterns in the far field—changes how many photons are needed to reach a given resolution. Earlier comparisons had suggested near-field holography (NFH) is especially dose-efficient, but those comparisons used single-exposure far-field coherent diffraction imaging (CDI), which is fragile. By simulating NFH, near-field ptychography (NFP), and far-field ptychography (FFP) on the same cell phantom with the same reconstruction optimizer and equal fluence on the specimen, the authors find all three deliver comparable image quality, with FFP slightly ahead in signal-to-noise ratio and error. The conclusion is that photon fluence on the specimen, not near-versus-far-field geometry, is the dominant limit to spatial resolution.

What carries the argument

The comparison runs on a single forward model in which the per-pixel Fresnel number $d = \Delta^2/(\lambda z)$ continuously tunes the propagation distance from near-field holography ($d = 10^{-3}$) to far-field diffraction ($d = 0$). Intensity data are generated with Poisson noise for chosen fluences, and two cost functions—least squares and Poisson likelihood—are minimized with the Adam optimizer using automatic differentiation, so the only differences among methods are the illumination geometry and constraints. The load-bearing device is the finite-support mask for NFH, made by thresholding a low-pass-filtered version of the true object, which suppresses the twin image; ptychographic methods instead rely on probe overlap and, in FFP, the probe's finite extent. Resolution is scored by Fourier ring correlation against the half-bit threshold, with signal-to-noise ratio and within-support mean squared error as supporting metrics.

What would settle it

Repeat the same simulations with the NFH support estimated from the measured data alone—for example by shrinkwrap or autocorrelation thresholding—while keeping FFP and NFP unconstrained; if NFH's SNR and Fourier-ring-correlation resolution fall clearly below FFP at equal fluence, the claim that specimen fluence alone sets the resolution limit would be refuted.

Watch

Extended reading notes

Core claim

The central claim is that when reconstructions are done properly, near-field holography, near-field ptychography, and far-field ptychography reconstruct the same phase object with similar fidelity at the same incident fluence. Under a least-squares or Poisson cost function minimized by automatic differentiation, FFP produced the highest whole-image SNR and lowest within-support mean squared error at low fluence; NFH matched it once a finite support mask (about 9 pixels looser than the true boundary) was imposed to suppress the twin image; NFP lagged because uncorrelated high-frequency artifacts appeared even at high fluence. A Fourier ring correlation analysis with the half-bit criterion shows NFH and FFP both reach essentially full resolution near 350 photons per pixel, the value predicted from the object's mean phase shift. The paper therefore concludes that the sample can be near or far: photon fluence on the specimen sets the fundamental resolution limit.

Load-bearing premise

The comparison assumes near-field holography can be given a mask marking where the true object lies (derived by thresholding a low-pass-filtered version of the object), while the ptychographic methods are not given this aid; if such a mask is unavailable in a real experiment, NFH would likely reconstruct worse and the claimed equivalence would weaken.

Editorial extensions

If this is right

  • When comparing coherent x-ray imaging schemes, equalizing specimen fluence rather than total exposure is the correct basis; otherwise apparent dose advantages may reflect reconstruction fragility rather than physics.
  • The previously reported dose advantage of NFH over far-field CDI does not carry over to a robust far-field method: replacing CDI with FFP removes the gap.
  • At low fluence, FFP's advantage is modest and comes with practical costs—high coherence across the beam and accurate probe positioning—so geometry can be chosen for experimental convenience.
  • The Poisson cost function sharpens edges in FFP at low fluence but can introduce fringe-like artifacts, so cost-function choice is not a free improvement.
  • NFP's low-fluence reconstructions are limited by noise-induced ambiguity; more scan positions or a support constraint should improve it.

Reading between the lines

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

  • Editorial inference: the results imply that any apparent 'holographic amplification' from mixing a strong reference with a weak specimen wave is already accounted for by shot noise; the reference beam cannot beat the per-pixel fluence limit.
  • Editorial inference: a practical test would replace the oracle-derived NFH support with one estimated from the data (shrinkwrap or autocorrelation thresholding); if NFH then falls below FFP, the equivalence claim would need qualification for blind reconstructions.
  • Editorial inference: because FFP and NFH both saturate resolution near the fluence predicted from the object's mean phase shift, the same fluence calculation could serve as a planning rule for choosing exposure times in lensless x-ray microscopy.
  • Editorial inference: varying the number of NFP diffraction patterns (e.g., 4, 16, 64) at fixed fluence would test whether NFP's deficit is an information-redundancy problem rather than a fundamental near-field limit.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. This paper reports numerical simulations comparing the dose efficiency of near-field holography (NFH), near-field ptychography (NFP), and far-field ptychography (FFP) for coherent x-ray imaging. Using the same 512×512 cell phantom as a prior study by Hagemann and Salditt, the authors reconstruct images with a unified automatic-differentiation-based optimization framework, using both least-squares and Poisson cost functions, and evaluate reconstructed-image quality under varying photon fluence via SNR, within-support mean squared error (SMSE), Fourier ring correlation (FRC), and a Gaussian feature-width metric. The authors conclude that NFH and FFP achieve similar resolution at the same fluence, with FFP slightly better, while NFP performs worse; they argue that photon fluence on the specimen sets a fundamental limit to spatial resolution.

Significance. If the central claim holds, the study would help settle conflicting reports in the literature about whether near-field or far-field coherent imaging is more dose efficient, by showing that when reconstruction is made well-posed through ptychographic redundancy or support constraints, fluence rather than detection geometry dominates. The paper's strengths include a unified reconstruction framework for the three methods, direct comparison with a previously used phantom, and the use of multiple quantitative metrics (SNR, SMSE, FRC, feature width) with two noise models. However, the abstract and conclusions overstate the results by including NFP in the 'similar image quality' claim, and the NFH comparison relies on a ground-truth-derived support constraint for one method only, so the headline conclusion is only partially supported.

major comments (3)
  1. [Section 3, Eq. (10)] The NFH reconstruction uses a finite support mask that is 'created by thresholding a low-pass-filtered version of the true object, so that the mask is about 9 pixels looser than the actual object boundary.' This mask is derived from the ground truth and is not estimated from measured data, while FFP and NFP are reconstructed without such a constraint. Because the central result is that NFH and FFP achieve similar resolution at the same fluence, the comparison is valid only under the untested assumption that an oracle-like support is available in practice. The paper should test how NFH performance degrades with realistic support errors in extent, position, or shape, or demonstrate a data-driven way to obtain the support; otherwise the NFH/FFP dose-equivalence claim is not established.
  2. [Abstract and Fig. 3] The abstract states that 'all three methods offer similar image quality when using the same fluence on the specimen,' but the paper's own quantitative results contradict this: Fig. 3(b) shows NFP has a larger SMSE than NFH and FFP at every fluence tested, and Fig. 3(a) shows NFP has the lowest SNR. Fig. 6(a) further shows NFP barely reaches full FRC resolution even at 2×10^4 photons/pixel. The attribution of NFP's poor performance to noise-related reconstruction ambiguity is plausible but not demonstrated. The abstract and conclusion should be revised to restrict the equivalence claim to NFH and FFP, or to state NFP's lower performance as a central, quantitative finding rather than a caveat.
  3. [Sections 2 and 4] The reconstruction protocol applies a finite support constraint to NFH but not to NFP: the manuscript states 'we employed a finite support constraint to suppress the twin image in NFH, but not in NFP (nor did we use a finite support constraint in FFP...)' and also states that 'the use of a finite support constraint helps tremendously with reconstruction fidelity in NFH.' This asymmetry biases the comparison against NFP and weakens the conclusion that scanning-type acquisition does not necessarily provide an advantage. The authors should run NFP with the same finite support constraint, or with the same level of support uncertainty as NFH, to separate the effect of imaging geometry from the effect of prior information.
minor comments (4)
  1. [Introduction] In the first paragraph, 'tendancy' should be 'tendency'.
  2. [Section 2] In the paragraph before Eq. (10), 'a similar constraint redonly to NFH reconstructions' should read 'a similar constraint only to NFH reconstructions'.
  3. [Fig. 5 caption and Fig. 6] Fig. 5 states that only LSQ results are shown, but Fig. 6 reports FRC/half-bit crossings for both LSQ and Poisson results; please clarify how the Poisson FRC curves were obtained or state explicitly that they are not shown in Fig. 5.
  4. [Section 3] Only two independent noise instances are used per condition; given the acknowledged sensitivity of FRC crossings to the particular noise instance, adding error bars or using more instances would strengthen the quantitative resolution-versus-fluence claims.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the simulations compare forward models with stated assumptions; the oracle-supported NFH idealization is a limitation, not a reduction of the conclusion to an input.

full rationale

The paper's derivation chain is a forward simulation comparison, not a derivation from fitted parameters. The central claim that NFH, NFP, and FFP give similar resolution at equal fluence is obtained by simulating noisy intensities, reconstructing with a common optimization framework, and measuring SNR, SMSE, and FRC; none of these outputs are encoded in the inputs by construction. The analytic fluence estimate in Eq. 12 uses the independently fixed phantom mean phase (phi-bar = 0.643 rad) and a published formula from [6], and it is used only to select simulation fluence values, not to force the measured resolution curves. The NFH support mask is indeed obtained from the true object ('The finite support mask is created by thresholding a low-pass-filtered version of the true object'), which is an idealization and a genuine external-validity concern for the dose-equivalence conclusion, but it is not circular: the mask constrains where the object may exist and suppresses the twin image; it does not supply the phase values, and it does not mathematically guarantee that FFP will be comparable or slightly better. Self-citations ([6], [41], [43]) support standard formulas and implementation choices and are not load-bearing for the comparison outcome. The results are also benchmarked against the independent prior study of Hagemann and Salditt, with explicit agreement shown in Fig. 6(b). Therefore no circular step can be exhibited, and the appropriate finding is no significant circularity.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central comparison rests on several chosen simulation parameters and idealizations (known probe, exact support for NFH, Poisson-only noise). The mean phase of the phantom is an input, not a fitted parameter. No new physical entities are introduced.

free parameters (6)
  • FFP probe standard deviation = 6 pixels
    Gaussian probe width chosen for the FFP simulations; affects the effective field of view and resolution limit of the reconstructed FFP images.
  • FFP scan step = 5 pixels
    Chosen for sufficient probe overlap; scan density affects ptychographic reconstruction stability and dose distribution.
  • NFP illumination random phase sigma = 0.3 rad
    Chosen for structured illumination in NFP; the phase map is smoothed with sigma = 5 pixels.
  • NFP scan grid = 4x4 (16 diffraction patterns)
    Chosen to satisfy the degrees-of-freedom condition for joint probe/object reconstruction; affects NFP reconstruction quality.
  • Fresnel number d = 1e-3
    Propagation distance parameter used for NFH and NFP, chosen to match prior work by Hagemann and Salditt; the relative method performance may depend on this value.
  • Number of noise instances = 2
    Two independent Poisson noise realizations per condition; limits precision of SNR, SMSE, and FRC estimates.
assumptions (5)
  • domain assumption Fresnel propagation via Fourier-domain convolution accurately models coherent x-ray imaging in the near and far field.
    Used throughout Section 2 (forward models f(n,k,d) and Eq. 6); standard physical optics but an idealization of real synchrotron beams (fully coherent, scalar wave).
  • domain assumption Detected intensity follows a Poisson distribution and the reconstruction cost functions (LSQ, Poisson) are appropriate for the noise level.
    Section 2 Eqs. 7-9; assumes ideal photon-counting detector with no readout noise, dark current, or dynamic-range limits.
  • domain assumption Adam optimization with the described cost functions converges to reconstructions whose quality reflects the information in the data rather than optimizer artifacts.
    Section 2: 'The Adam optimizer in TensorFlow was used to update the object function'; no convergence guarantees are given; NFP artifacts suggest this assumption is fragile.
  • ad hoc to paper The probe function is known exactly for FFP and NFP reconstructions.
    Section 3 states 'all our FFP results shown above were reconstructed with a known probe function'; in practice probe retrieval is often required, which can change dose efficiency conclusions.
  • ad hoc to paper The finite support S for NFH is known to within a few pixels from the true object.
    Section 3: 'The finite support mask is created by thresholding a low-pass-filtered version of the true object'; this is a strong prior not generally available experimentally.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Near, far, wherever you are: simulations on the dose efficiency of holographic and ptychographic coherent imaging." pith.science (2026). https://pith.science/paper/HJQTWVX4

@misc{pith2026190806770,
  author       = {Pith},
  title        = {Pith review of: Near, far, wherever you are: simulations on the dose efficiency of holographic and ptychographic coherent imaging},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HJQTWVX4}},
  note         = {Machine review of arXiv:1908.06770}
}
read the original abstract

Different studies in x-ray microscopy have arrived at conflicting conclusions about the dose efficiency of imaging modes involving the recording of intensity distributions in the near (Fresnel regime) or far (Fraunhofer regime) field downstream of a specimen. We present here a numerical study on the dose efficiency of near-field holography (NFH), near-field ptychography (NFP), and far-field ptychography (FFP), where ptychography involves multiple overlapping finite-sized illumination positions. Unlike what has been reported for coherent diffraction imaging (CDI), which involves recording a single far-field diffraction pattern, we find that all three methods offer similar image quality when using the same fluence on the specimen, with far-field ptychography offering slightly better spatial resolution and lower mean error. These results support the concept that (if the experiment and image reconstruction are done properly) the sample can be near, or far; wherever you are, photon fluence on the specimen sets one limit to spatial resolution.

Figures

Figures reproduced from arXiv: 1908.06770 by the authors.

Figure 1
Figure 1. (a) The 512 × 512 pixel phantom cell object used for our computational experiments. The object is the same pure-phase cell phantom used in a prior study [22], so that one can compare directly with those results. The only difference is that we used the complex conjugate of the phantom so as to have positive rather than negative phase shifts, since x-ray phase is advanced rather than retarded in materials [44]. (b) Th… view at source ↗
Figure 2
Figure 2. Reconstructed images of the cell phantom shown in Fig. 1(a) obtained for near-field holography [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Whole image metrics of image reconstructed image quality as a function of fluence [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Standard deviation of the fitted Gaussian 2D profile for the small bright-spot-like feature pointed [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Fourier ring correlation (FRC) curves for two images reconstructed from separate instances of [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Values for the crossing between the Fourier ring correlation (FRC) curves of Fig. 5 and the half-bit [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

63 extracted references · 61 canonical work pages

  1. [1]

    Sayre, D., Kirz, J., Feder, R., Kim, D. M. & Spiller, E. Potential operating region for ultrasoft x-ray microscopy of biological specimens. Science 196, 1339–1340 (1977)

    work page 1977

  2. [2]

    & Howells, M

    Kirz, J., Jacobsen, C. & Howells, M. Soft x-ray microscopes and their biological applications. Quarterly Reviews of Biophysics 28, 33–130 (1995). Also available as Lawrence Berkeley Laboratory report LBL- 36371

    work page 1995

  3. [3]

    Sayre, D., Kirz, J., Feder, R., Kim, D. M. & Spiller, E. Transmission microscopy of unmodified biological materials. comparative radiation dosages with electrons and ultrasoft x-ray photons. Ultramicroscopy 2, 337–349 (1977)

    work page 1977

  4. [4]

    Howells, M. et al. An assessment of the resolution limitation due to radiation-damage in x-ray diffraction microscopy. Journal of Electron Spectroscopy and Related Phenomena 170, 4–12 (2009)

    work page 2009

  5. [5]

    L., Gullikson, E

    Henke, B. L., Gullikson, E. M. & Davis, J. C. X-ray interactions: Photoabsorption, scattering, transmis- sion, and reflection at E=50–30,000 eV, Z=1–92. Atomic Data and Nuclear Data Tables 54, 181–342 (1993)

    work page 1993

  6. [6]

    & Jacobsen, C

    Du, M. & Jacobsen, C. Relative merits and limiting factors for x-ray and electron microscopy of thick, hydrated organic materials. Ultramicroscopy 184, 293–309 (2018)

    work page 2018

  7. [7]

    & Rudolph, D

    Schmahl, G. & Rudolph, D. Proposal for a phase contrast x-ray microscope. In Cheng, P. C. & Jan, G. J. (eds.) X-ray Microscopy: Instrumentation and Biological Applications , 231–238 (Springer-Verlag, Berlin, 1987)

    work page 1987

  8. [8]

    & Niemann, B

    Schmahl, G., Rudolph, D., Schneider, G., Guttmann, P. & Niemann, B. Phase contrast x-ray microscopy studies. Optik 97, 181–182 (1994)

    work page 1994

Show all 63 references
  1. [9]

    C., Gureyev, T

    Paganin, D., Mayo, S. C., Gureyev, T. E., Miller, P. R. & Wilkins, S. W. Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object. Journal of Microscopy 206, 33–40 (2002)

    2002

  2. [10]

    Baez, A. V. Resolving power in diffraction microscopy with special reference to x-rays. Nature 169, 963–964 (1952)

    1952

  3. [11]

    Baez, A. V. A study in diffraction microscopy with special reference to x-rays. Journal of the Optical Society of America 42, 756–762 (1952)

    1952

  4. [12]

    Cloetens, P. et al. Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays. Applied Physics Letters 75, 2912–2914 (1999). 15

    1999

  5. [13]

    Stockmar, M. et al. Near-field ptychography: phase retrieval for inline holography using a structured illumination. Scientific Reports 3, 1927 (2013)

    2013

  6. [14]

    Prospects for long-wavelength x-ray microscopy and diffraction

    Sayre, D. Prospects for long-wavelength x-ray microscopy and diffraction. In Schlenker, M. et al. (eds.) Imaging Processes and Coherence in Physics , vol. 112 of Lecture Notes in Physics , 229–235 (Springer- Verlag, 1980)

    1980

  7. [15]

    & Sayre, D

    Miao, J., Charalambous, P., Kirz, J. & Sayre, D. An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens. Nature 400, 342–344 (1999)

    1999

  8. [16]

    Fienup, J. R. Reconstruction of an object from the modulus of its Fourier transform. Optics Letters 3, 27–29 (1978)

    1978

  9. [17]

    Beugung im Inhomogenen Prim¨ arstrahlwellenfeld

    Hoppe, W. Beugung im Inhomogenen Prim¨ arstrahlwellenfeld. I. Prinzip einer Phasenmessung. Acta Crystallographica A 25, 495–501 (1969)

    1969

  10. [18]

    Beugung im inhomogenen Primarstrahlwellenfeld

    Hoppe, W. Beugung im inhomogenen Primarstrahlwellenfeld. III. Amplituden-und Phasenbestimmung bei unperiodischen Objekten. Acta Crystallographica A 25, 508–514 (1969)

    1969

  11. [19]

    Faulkner, H. M. L. & Rodenburg, J. Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm. Physical Review Letters 93, 023903 (2004)

    2004

  12. [20]

    Rodenburg, J. et al. Hard-x-ray lensless imaging of extended objects. Physical Review Letters 98, 034801 (2007)

    2007

  13. [21]

    Bartels, M., Krenkel, M., Haber, J., Wilke, R. N. & Salditt, T. X-ray holographic imaging of hydrated biological cells in solution. Physical Review Letters 114, 048103 (2015)

    2015

  14. [22]

    & Salditt, T

    Hagemann, J. & Salditt, T. The fluence–resolution relationship in holographic and coherent diffractive imaging. Journal of Applied Crystallography 50, 531–538 (2017)

    2017

  15. [23]

    N., Chushkin, Y

    Jahn, T., Wilke, R. N., Chushkin, Y. & Salditt, T. How many photons are needed to reconstruct random objects in coherent x-ray diffractive imaging? Acta Crystallographica A 1–11 (2017)

    2017

  16. [24]

    The potential and limitations of neutrons, electrons and X-rays for atomic resolution microscopy of unstained biological molecules

    Henderson, R. The potential and limitations of neutrons, electrons and X-rays for atomic resolution microscopy of unstained biological molecules. Quarterly Reviews of Biophysics 28, 171–193 (1995)

    1995

  17. [25]

    Image contrast in high-resolution electron microscopy of biological macromolecules: TMV in ice

    Henderson, R. Image contrast in high-resolution electron microscopy of biological macromolecules: TMV in ice. Ultramicroscopy 46, 1–18 (1992)

    1992

  18. [26]

    X-ray Microscopy (Cambridge University Press, Cambridge, 2020)

    Jacobsen, C. X-ray Microscopy (Cambridge University Press, Cambridge, 2020)

    2020

  19. [27]

    & Robinson, I

    Williams, G., Pfeifer, M., Vartanyants, I. & Robinson, I. Effectiveness of iterative algorithms in recov- ering phase in the presence of noise. Acta Crystallographica A 63, 36–42 (2007)

    2007

  20. [28]

    Huang, X. et al. Signal-to-noise and radiation exposure considerations in conventional and diffraction x-ray microscopy. Optics Express 17, 13541–13553 (2009)

    2009

  21. [29]

    & Schroer, C

    Schropp, A. & Schroer, C. G. Dose requirements for resolving a given feature in an object by coherent x-ray diffraction imaging. New Journal of Physics 12, 035016 (2010)

    2010

  22. [30]

    & Rodenburg, J

    Godard, P., Allain, M., Chamard, V. & Rodenburg, J. M. Noise models for low counting rate coherent diffraction imaging. Optics Express 20, 25914–25934 (2012)

    2012

  23. [31]

    Villanueva-Perez, P. et al. Signal-to-noise criterion for free-propagation imaging techniques at free- electron lasers and synchrotrons. Optics Express 24, 3189–3201 (2016)

    2016

  24. [32]

    & Thibault, P

    Shen, Q., Bazarov, I. & Thibault, P. Diffractive imaging of nonperiodic materials with future coherent x-ray sources. Journal of Synchrotron Radiation 11, 432–438 (2004)

    2004

  25. [33]

    Reconstruction of a complex-valued object from the modulus of its Fourier-transform using a support constraint

    Fienup, J. Reconstruction of a complex-valued object from the modulus of its Fourier-transform using a support constraint. Journal of the Optical Society of America A 4, 118–123 (1987). 16

    1987

  26. [34]

    Huang, X. et al. Incorrect support and missing center tolerances of phasing algorithms. Optics Express 18, 26441–26449 (2010)

    2010

  27. [35]

    & Sayre, D

    Thibault, P., Elser, V., Jacobsen, C., Shapiro, D. & Sayre, D. Reconstruction of a yeast cell from x-ray diffraction data. Acta Crystallographica A 62, 248–261 (2006)

    2006

  28. [36]

    Bunk, O. et al. Influence of the overlap parameter on the convergence of the ptychographical iterative engine. Ultramicroscopy 108, 481–487 (2008)

    2008

  29. [37]

    Thibault, P. et al. High-resolution scanning x-ray diffraction microscopy. Science 321, 379–382 (2008)

    2008

  30. [38]

    Luke, D. R. Relaxed averaged alternating reflections for diffraction imaging. Inverse Problems 21, 37–50 (2005)

    2005

  31. [39]

    Rall, L. B. Automatic Differentiation: Techniques and Applications , vol. 120 (Springer Berlin Heidel- berg, Berlin, Heidelberg, 1981)

    1981

  32. [40]

    Jurling, A. S. & Fienup, J. R. Applications of algorithmic differentiation to phase retrieval algorithms. Journal of the Optical Society of America A 31, 1348–12 (2014)

    2014

  33. [41]

    Nashed, Y. S. G., Peterka, T., Deng, J. & Jacobsen, C. Distributed automatic differentiation for ptychography. Procedia Computer Science 108, 404–414 (2017)

    2017

  34. [42]

    Kandel, S. et al. Using automatic differentiation as a general framework for ptychographic reconstruc- tion. Optics Express 27, 18653–18672 (2019)

    2019

  35. [43]

    Du, M., Nashed, Y. S. G., Kandel, S., Gursoy, D. & Jacobsen, C. Three dimensions, two microscopes, one code: automatic differentiation for x-ray nanotomography beyond the depth of focus limit. Science Advances 6, eaay3700 (2020)

    2020

  36. [44]

    & Waller, I

    Larsson, A., Siegbahn, M. & Waller, I. Der experimentelle Nachweis der Brechung von R¨ ontgenstrahlen. Naturwissenschaften 12, 1212–1213 (1924)

    1924

  37. [45]

    Goodman, J. W. Introduction to Fourier Optics (W.H. Freeman, New York, 2017), fourth edn

    2017

  38. [46]

    Cai, A. et al. Optimization-based image reconstruction in computed tomography by alternating direction method with ordered subsets. Journal of X-Ray Science and Technology 25, 429–464 (2017)

    2017

  39. [47]

    & Scott, P

    Liu, G. & Scott, P. D. Phase retrieval and twin-image elimination for in-line Fresnel holograms. Journal of the Optical Society of America A 4, 159–165 (1987)

    1987

  40. [48]

    Abadi, M. et al. Tensorflow: Large-scale machine learning on heterogeneous distributed systems . CoRR cs.DC, arXiv:1603.04467 (2016)

    2016 arXiv

  41. [49]

    Kingma, D. P. & Ba, J. Adam: A method for stochastic optimization. In 3rd International Conference on Learning Representations, 1–15 (San Diego, 2015). URL https://arxiv.org/abs/1412.6980

    2015 arXiv

  42. [50]

    Coherent X-ray Optics (Oxford University Press, Oxford, 2006)

    Paganin, D. Coherent X-ray Optics (Oxford University Press, Oxford, 2006)

    2006

  43. [51]

    Huang, X. et al. Artifact mitigation of ptychography integrated with on-the-fly scanning probe mi- croscopy. Applied Physics Letters 111, 023103 (2017)

    2017

  44. [52]

    & Rockmore, A

    Bershad, N. & Rockmore, A. On estimating signal-to-noise ratio using the sample correlation coefficient. IEEE Transactions on Information Theory 20, 112–113 (1974)

    1974

  45. [53]

    & Al-Ali, L

    Frank, J. & Al-Ali, L. Signal-to-noise ratio of electron micrographs obtained by cross correlation. Nature 256, 376–379 (1975)

    1975

  46. [54]

    Saxton, W. O. & Baumeister, W. The correlation averaging of a regularly arranged bacterial cell envelope protein. Journal of Microscopy 127, 127–138 (1982). 17

    1982

  47. [55]

    Similarity measures between images

    van Heel, M. Similarity measures between images. Ultramicroscopy 21, 95–100 (1987)

    1987

  48. [56]

    & Schatz, M

    van Heel, M. & Schatz, M. Fourier shell correlation threshold criteria. Journal of Structural Biology 151, 250–262 (2005)

    2005

  49. [57]

    Miao, J. et al. Quantitative image reconstruction of GaN quantum dots from oversampled diffraction intensities alone. Physical Review Letters 95, 085503 (2005)

    2005

  50. [58]

    & Fienup, J

    Guizar-Sicairos, M. & Fienup, J. R. Phase retrieval with transverse translation diversity: a nonlinear optimization approach. Optics Express 16, 7264–7278 (2008)

    2008

  51. [59]

    Zhang, F. et al. Translation position determination in ptychographic coherent diffraction imaging. Optics Express 21, 13592 (2013)

    2013

  52. [60]

    & Pfeiffer, F

    Thibault, P., Dierolf, M., Bunk, O., Menzel, A. & Pfeiffer, F. Probe retrieval in ptychographic coherent diffractive imaging. Ultramicroscopy 109, 338–343 (2009)

    2009

  53. [61]

    Eriksson, M., van der Veen, J. F. & Quitmann, C. Diffraction-limited storage rings – a window to the science of tomorrow. Journal of Synchrotron Radiation 21, 837–842 (2014)

    2014

  54. [62]

    Phase zone plates for X rays and the extreme UV

    Kirz, J. Phase zone plates for X rays and the extreme UV. Journal of the Optical Society of America 64, 301–309 (1974)

    1974

  55. [63]

    Glaeser, R. M. Radiation damage and biological electron microscopy. In Siegel, B. M. & Beaman, D. R. (eds.) Physical aspects of electron microscopy and microbeam analysis, 205–227 (Wiley, New York, 1975). 18

    1975

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.