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arxiv: 2509.16503 · v2 · submitted 2025-09-20 · ⚛️ physics.optics · physics.med-ph

Moir\'e Artifact Reduction in Grating Interferometry Using Multiple Harmonics and Total Variation Regularization

Hunter C. Meyer , Joyoni Dey , Conner B. Dooley , Murtuza S. Taqi , Varun R. Gala , Christopher D. Morrison , Victoria L. Fontenot , Kyungmin Ham
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Leslie G. Butler Alexandra Noel
This is my paper

Pith reviewed 2026-05-18 16:07 UTC · model grok-4.3

classification ⚛️ physics.optics physics.med-ph
keywords Moiré artifactsgrating interferometrytotal variation regularizationphase stepping positionsX-ray imagingdifferential phase contrastdark-field imagingTalbot-Lau interferometer
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The pith

An algorithm estimates true phase stepping positions with multiple harmonics and total variation regularization to remove Moiré artifacts from X-ray grating interferometry images.

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

The paper develops an image recovery method for grating-based X-ray interferometry that corrects for errors in phase stepping positions caused by grating inaccuracies and multi-harmonic effects. These errors create Moiré artifacts that degrade the attenuation, differential-phase, and dark-field images. The method models the fringe pattern with several harmonics and uses total variation regularization to recover smooth variations in amplitudes and phases. A reader would care because this enables higher quality images for potential clinical uses such as lung imaging without requiring perfect hardware alignment.

Core claim

The central claim is that inaccuracies in grating position and multi-harmonic fringes produce Moiré artifacts when assuming a perfectly sinusoidal pattern with evenly spaced steps, and that an algorithm estimating the true phase stepping positions via multiple harmonics and total variation regularization removes these artifacts in the three image types. The authors demonstrate this for Talbot-Lau and Modulated Phase Grating Interferometers on samples like PMMA microspheres and a euthanized mouse.

What carries the argument

The image recovery algorithm that estimates true phase stepping positions from a sum of multiple harmonics with total variation regularization on their amplitudes and phases.

If this is right

  • Removes Moiré artifacts from attenuation images.
  • Removes Moiré artifacts from differential-phase images.
  • Removes Moiré artifacts from dark-field images.
  • Applies to both Talbot-Lau and Modulated Phase Grating Interferometers.
  • Demonstrated effective on imaging of PMMA microspheres and a euthanized mouse.

Where Pith is reading between the lines

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

  • The method could allow experimental setups to tolerate small mechanical positioning errors without sacrificing image quality.
  • Higher fidelity images might support more reliable quantitative measurements in clinical applications such as lung imaging.
  • The same regularization approach could be tested in other phase-sensitive X-ray or optical interferometry systems facing similar fringe distortions.
  • Direct comparison against independent measurements of stepping positions would quantify how much artifact reduction comes from the multi-harmonic model versus the regularization alone.

Load-bearing premise

The observed fringe pattern can be accurately represented by a sum of a small number of harmonics whose amplitudes and phases vary smoothly enough for total variation regularization to recover the true stepping positions without introducing new bias.

What would settle it

A controlled test with precisely known even phase steps and purely sinusoidal fringes where the algorithm either leaves visible Moiré artifacts or distorts the recovered images would show the central claim is not correct.

Figures

Figures reproduced from arXiv: 2509.16503 by Alexandra Noel, Christopher D. Morrison, Conner B. Dooley, Hunter C. Meyer, Joyoni Dey, Kyungmin Ham, Leslie G. Butler, Murtuza S. Taqi, Varun R. Gala, Victoria L. Fontenot.

Figure 1
Figure 1. Figure 1: Schematics of the (a) Talbot-Lau and (b) Modulated Phase Grating Interferometers. In this study, the Talbot-Lau Interferometer used curved gratings. For the MPGI, a RectMPG was used and no G0 grating was used. imaging the grating at several phase stepping positions, where the grating is laterally shifted over at least one period. The phase stepping curves are analyzed on a pixel-by-pixel basis by fitting t… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Attenuation, (b) differential-phase, and (c) dark-field images taken with a TLI with no object (comparing two reference scans), calculated using the nominal phase steps. The variance in the region of interest is σ 2 = 1.77 × 10−5 . grating are used. Images were acquired at 55 µA. Phase stepping was performed by stepping the MPG using a Newport AG-LS25-27P motorized linear stage with 12 µm phase steps, … view at source ↗
Figure 3
Figure 3. Figure 3: (a) Attenuation, (b) differential-phase, and (c) dark-field images taken with a TLI with no object (comparing two reference scans), calculated using the iterative method with 1 harmonic. The variance in the region of interest is σ 2 = 1.60 × 10−5 . When compared with the variance from Figure 2a using a two-sample F-test for equal variances, the variance is significantly (α = 0.05) lower in the corrected im… view at source ↗
Figure 4
Figure 4. Figure 4: (a) Attenuation, (b) differential-phase, and (c) dark-field images taken with a TLI of a euthanized mouse, calculated using the nominal phase steps. The variance was calculated in the region of interest for each image and compared between the images calculated with the nominal phase steps and corrected phase steps. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Attenuation, (b) differential-phase, and (c) dark-field images taken with a TLI of a euthanized mouse, calculated using the iterative method with 1 harmonic. The variance was calculated in the region of interest for each image and compared between the images calculated with the nominal phase steps and corrected phase steps. It was found that the variance was significantly (α = 0.05) lower for the corre… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the average value, a r 0 (x, y), for the MPGI calculated with the (a) nominal phase steps, (b) phase steps estimated using the proposed method with 1 harmonic, and (c) phase steps using the proposed method with 3 harmonics. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of the visibility, V r (x, y), for the MPGI calculated with (a) the linear method, (b) the iterative method with 1 harmonic, and (c) the iterative method with 3 harmonics. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of the attenuation image, Γ(x, y), for the MPGI calculated with (a) the linear method, (b) the iterative method with 1 harmonic, and (c) the iterative method with 3 harmonics. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of the differential-phase image, ∆ϕ(x, y), for the MPGI calculated with (a) the linear method, (b) the iterative method with 1 harmonic, and (c) the iterative method with 3 harmonics. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of the dark-field image, Σ(x, y), for the MPGI calculated with (a) the linear method, (b) the iterative method with 1 harmonic, and (c) the iterative method with 3 harmonics. 4. Discussion We presented an iterative method for removing Moir´e artifacts present in attenuation, differential￾phase, and dark-field images by correcting phase step positions by modeling higher order harmonics in our ph… view at source ↗
read the original abstract

X-ray interferometry is an emerging imaging modality with a wide variety of potential clinical applications, including lung imaging. A grating interferometer uses a diffraction grating to produce a periodic interference pattern and measures how a patient or sample perturbs the pattern, producing three unique images that highlight X-ray absorption, refraction, and small angle scattering, known as the attenuation, differential-phase, and dark-field images, respectively. Inaccuracies in grating position and multi-harmonic fringes produce Moir\'e artifacts when assuming the fringe pattern is perfectly sinusoidal and the phase steps are evenly spaced. We have developed an image recovery algorithm that estimates the true phase stepping positions using multiple harmonics and total variation regularization, removing the Moir\'e artifacts present in the attenuation, differential-phase, and dark-field images. We demonstrate the algorithm's utility for the Talbot-Lau and Modulated Phase Grating Interferometers by imaging multiple samples, including PMMA microspheres and a euthanized mouse.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript proposes an image recovery algorithm for X-ray grating interferometry that estimates true phase-stepping positions by modeling the fringe pattern as a sum of multiple harmonics whose amplitudes and phases are recovered under total-variation regularization. The method is applied to both Talbot-Lau and Modulated Phase Grating Interferometers and is demonstrated on samples including PMMA microspheres and a euthanized mouse, with the claim that it removes Moiré artifacts from the attenuation, differential-phase, and dark-field images.

Significance. If the recovered stepping positions are shown to be quantitatively accurate rather than merely cosmetic, the approach would be useful for practical X-ray interferometry, particularly for clinical applications such as lung imaging where artifact-free images are needed. The combination of a multi-harmonic model with TV regularization is a plausible way to handle grating-position inaccuracies and non-sinusoidal fringes.

major comments (2)
  1. [Results] Results section: the manuscript provides no quantitative metrics (e.g., RMSE or SSIM against ground-truth phase steps or reference images), error bars, or direct comparison to standard single-harmonic least-squares fitting. Without these, the central claim that artifacts are removed rather than smoothed cannot be verified.
  2. [Methods] Methods section: the assumption that a small number of harmonics plus TV regularization recovers unbiased stepping positions is load-bearing. Any mismatch from unmodeled higher harmonics, sample-induced spatial variations, or grating diffraction effects would cause the regularized solution to converge to incorrect positions; the paper should include residual analysis or synthetic-data validation with known ground truth.
minor comments (2)
  1. [Abstract] Abstract: the number of harmonics employed is not stated; this parameter should be given explicitly along with the chosen regularization strength.
  2. [Figures] Figure captions: several figures lack scale bars or quantitative labels on the artifact reduction (e.g., before/after line profiles).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important aspects for strengthening the validation of our method. We agree that additional quantitative metrics and robustness checks will improve the manuscript and plan to incorporate them in the revision.

read point-by-point responses

  1. Referee: [Results] Results section: the manuscript provides no quantitative metrics (e.g., RMSE or SSIM against ground-truth phase steps or reference images), error bars, or direct comparison to standard single-harmonic least-squares fitting. Without these, the central claim that artifacts are removed rather than smoothed cannot be verified.

    Authors: We acknowledge the value of quantitative validation. In the revised manuscript we will add RMSE and SSIM metrics comparing our recovered images to reference images (where high-precision stepping data or phantom references are available), include error bars on these metrics, and provide a side-by-side comparison against conventional single-harmonic least-squares fitting. These additions will allow readers to assess whether artifacts are suppressed rather than smoothed. revision: yes

  2. Referee: [Methods] Methods section: the assumption that a small number of harmonics plus TV regularization recovers unbiased stepping positions is load-bearing. Any mismatch from unmodeled higher harmonics, sample-induced spatial variations, or grating diffraction effects would cause the regularized solution to converge to incorrect positions; the paper should include residual analysis or synthetic-data validation with known ground truth.

    Authors: We agree that demonstrating unbiased recovery under realistic mismatches is important. The revised version will include synthetic-data experiments with known ground-truth phase steps, incorporating controlled higher harmonics, spatial sample variations, and grating diffraction effects. We will also add residual analysis on both synthetic and experimental datasets to quantify model fit and confirm that the multi-harmonic TV approach recovers stepping positions without systematic bias. revision: yes

Circularity Check

0 steps flagged

No circularity: algorithmic recovery method with independent empirical demonstration

full rationale

The paper presents a practical image-recovery algorithm that models fringes as a sum of harmonics and applies total-variation regularization to recover phase-step positions. No derivation chain, closed-form prediction, or fitted parameter is shown to reduce to its own inputs by construction. The abstract and method description treat the harmonic count and regularization strength as design choices whose performance is then demonstrated on separate samples (PMMA microspheres, euthanized mouse). Because the central claim is an algorithmic procedure whose success is evaluated externally rather than forced by self-definition or self-citation, the work is self-contained against the listed circularity patterns.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the modeling assumption that the fringe can be decomposed into a small number of harmonics whose spatial variation is piecewise smooth, plus the practical assumption that TV regularization will recover the true stepping positions from real data without overfitting noise.

free parameters (2)
  • number of harmonics
    Chosen to capture multi-harmonic fringes; value not stated in abstract but required for the fit.
  • TV regularization strength
    Controls smoothness of estimated phase steps; must be tuned and directly affects artifact removal.
axioms (1)
  • domain assumption The observed intensity pattern is a linear combination of a small number of harmonic components whose amplitudes and phases vary smoothly across the detector.
    Invoked when the method replaces the single-sinusoid model with multiple harmonics.

pith-pipeline@v0.9.0 · 5742 in / 1373 out tokens · 26888 ms · 2026-05-18T16:07:51.686943+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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

  1. X-ray dark-field imaging from intensity flow: A Fokker-Planck approach to grating interferometry

    physics.med-ph 2026-05 unverdicted novelty 7.0

    A Fokker-Planck-derived algorithm retrieves transmission and dark-field X-ray images from grating interferometry data, matching conventional results while suppressing artifacts from perturbations and noise.

Reference graph

Works this paper leans on

32 extracted references · 32 canonical work pages · cited by 1 Pith paper

  1. [1]

    Dark-field chest radiography signal characteristics in inspiration and expiration in healthy and emphysematous subjects

    Theresa Urban, Florian T. Gassert, Manuela Frank, et al. “Dark-field chest radiography signal characteristics in inspiration and expiration in healthy and emphysematous subjects”. In:European Radiology Experimental9.1 (Mar. 2025), p. 40.issn: 2509-9280.doi:10.1186/s41747-025-00578- x.url:https://doi.org/10.1186/s41747-025-00578-x

    work page doi:10.1186/s41747-025-00578- 2025

  2. [2]

    X-ray dark-field radiography facilitates the diagnosis of pulmonary fibrosis in a mouse model

    Katharina Hellbach, Andre Yaroshenko, Konstantin Willer, et al. “X-ray dark-field radiography facilitates the diagnosis of pulmonary fibrosis in a mouse model”. In:Scientific Reports7.1 (Mar. 2017), p. 340.issn: 2045-2322.doi:10.1038/s41598-017-00475-3.url:https://doi.org/10. 1038/s41598-017-00475-3

    work page doi:10.1038/s41598-017-00475-3.url:https://doi.org/10 2017

  3. [3]

    Comparison of dark-field chest radio- graphy and CT for the assessment of COVID-19 pneumonia

    Florian T. Gassert, Henriette Bast, Theresa Urban, et al. “Comparison of dark-field chest radio- graphy and CT for the assessment of COVID-19 pneumonia”. In:Frontiers in RadiologyVolume 4 - 2024 (2025).issn: 2673-8740.doi:10 . 3389 / fradi . 2024 . 1487895.url:https : / / www . frontiersin.org/journals/radiology/articles/10.3389/fradi.2024.1487895

    work page doi:10.3389/fradi.2024.1487895 2024

  4. [4]

    X-ray Dark-field Radiography - In-Vivo Diagnosis of Lung Cancer in Mice

    Kai Scherer, Andre Yaroshenko, Deniz Ali B¨ ol¨ ukbas, et al. “X-ray Dark-field Radiography - In-Vivo Diagnosis of Lung Cancer in Mice”. In:Scientific Reports7.1 (Mar. 2017), p. 402.issn: 2045-2322. doi:10.1038/s41598-017-00489-x.url:https://doi.org/10.1038/s41598-017-00489-x

    work page doi:10.1038/s41598-017-00489-x.url:https://doi.org/10.1038/s41598-017-00489-x 2017

  5. [5]

    Non-invasive classification of microcalcifications with phase-contrast X-ray mammography

    Zhentian Wang, Nik Hauser, Gad Singer, et al. “Non-invasive classification of microcalcifications with phase-contrast X-ray mammography”. In:Nature Communications5.1 (May 2014), p. 3797. issn: 2041-1723.doi:10.1038/ncomms4797.url:https://doi.org/10.1038/ncomms4797

    work page doi:10.1038/ncomms4797.url:https://doi.org/10.1038/ncomms4797 2014

  6. [6]

    Bi-Directional X-Ray Phase-Contrast Mammography

    Kai Scherer, Lorenz Birnbacher, Michael Chabior, et al. “Bi-Directional X-Ray Phase-Contrast Mammography”. In:PLOS ONE9.5 (May 2014), pp. 1–7.doi:10.1371/journal.pone.0093502. url:https://doi.org/10.1371/journal.pone.0093502

    work page doi:10.1371/journal.pone.0093502 2014

  7. [7]

    Slit-scanning differential x-ray phase- contrast mammography: proof-of-concept experimental studies

    Thomas Koehler, Heiner Daerr, Gerhard Martens, et al. “Slit-scanning differential x-ray phase- contrast mammography: proof-of-concept experimental studies”. en. In:Med Phys42.4 (Apr. 2015), pp. 1959–1965

    work page 2015

  8. [8]

    Experimental results from a preclinical X-ray phase-contrast CT scanner

    Arne Tapfer, Martin Bech, Astrid Velroyen, et al. “Experimental results from a preclinical X-ray phase-contrast CT scanner”. en. In:Proc Natl Acad Sci U S A109.39 (Sept. 2012), pp. 15691– 15696

    work page 2012

  9. [9]

    Sub-pixel porosity revealed by x-ray scatter dark field imaging

    V. Revol, I. Jerjen, C. Kottler, et al. “Sub-pixel porosity revealed by x-ray scatter dark field imaging”. In:Journal of Applied Physics110.4 (Aug. 2011), p. 044912.issn: 0021-8979.doi: 10.1063/1.3624592. eprint:https://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/1. 3624592/13589811/044912\_1\_online.pdf.url:https://doi.org/10.1063/1.3624592

    work page doi:10.1063/1.3624592 2011

  10. [10]

    Theoretical and experimental analysis of the modulated phase grating X-ray interferometer

    Hunter Meyer, Joyoni Dey, Sydney Carr, et al. “Theoretical and experimental analysis of the modulated phase grating X-ray interferometer”. In:Scientific Reports14.1 (Nov. 2024), p. 26780

    work page 2024

  11. [11]

    Real-time interferometric monitoring and measuring of pho- topolymerization based stereolithographic additive manufacturing process: sensor model and algo- rithm

    Xiayun Zhao and David W. Rosen. “Real-time interferometric monitoring and measuring of pho- topolymerization based stereolithographic additive manufacturing process: sensor model and algo- rithm”. In:Measurement Science and Technology28 (2016).url:https://api.semanticscholar. org/CorpusID:125660749

    work page 2016

  12. [12]

    Early detection of fracture failure in SLM AM tension testing with Talbot-Lau neutron interferometry

    Adam J. Brooks, Hong Yao, Jumao Yuan, et al. “Early detection of fracture failure in SLM AM tension testing with Talbot-Lau neutron interferometry”. In:Additive Manufacturing22 (2018), pp. 658–664.issn: 2214-8604.doi:https://doi.org/10.1016/j.addma.2018.06.012.url: https://www.sciencedirect.com/science/article/pii/S221486041730324X

    work page doi:10.1016/j.addma.2018.06.012.url: 2018

  13. [13]

    Recent Advances in X-ray Phase Imaging

    Atsushi Momose. “Recent Advances in X-ray Phase Imaging”. In:Japanese Journal of Applied Physics44.9R (Sept. 2005), p. 6355.doi:10.1143/JJAP.44.6355.url:https://dx.doi.org/ 10.1143/JJAP.44.6355

    work page doi:10.1143/jjap.44.6355.url:https://dx.doi.org/ 2005

  14. [14]

    X-ray dark-field and phase-contrast imaging using a grating interferometer

    F. Pfeiffer, M. Bech, O. Bunk, et al. “X-ray dark-field and phase-contrast imaging using a grating interferometer”. In:Journal of Applied Physics105.10 (May 2009), p. 102006.issn: 0021-8979. doi:10.1063/1.3115639. eprint:https://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/ 1.3115639/15038269/102006\_1\_online.pdf.url:https://doi.org/10.1063/1.3115639

    work page doi:10.1063/1.3115639 2009

  15. [15]

    On the origin of visibility contrast in x-ray Talbot interferometry

    W. Yashiro, Y. Terui, K. Kawabata, et al. “On the origin of visibility contrast in x-ray Talbot interferometry”. In:Opt. Express18.16 (Aug. 2010), pp. 16890–16901.doi:10 . 1364 / OE . 18 . 016890.url:https://opg.optica.org/oe/abstract.cfm?URI=oe-18-16-16890. 11

    work page 2010

  16. [16]

    General solution for quantitative dark-field contrast imaging with grating interferom- eters

    M. Strobl. “General solution for quantitative dark-field contrast imaging with grating interferom- eters”. In:Scientific Reports4.1 (Nov. 2014), p. 7243.issn: 2045-2322.doi:10.1038/srep07243. url:https://doi.org/10.1038/srep07243

    work page doi:10.1038/srep07243 2014

  17. [17]

    A generalized quantitative interpretation of dark-field contrast for highly concentrated microsphere suspensions

    Spyridon Gkoumas, Pablo Villanueva-Perez, Zhentian Wang, et al. “A generalized quantitative interpretation of dark-field contrast for highly concentrated microsphere suspensions”. In:Scientific Reports6.1 (Oct. 2016), p. 35259.issn: 2045-2322.doi:10.1038/srep35259.url:https://doi. org/10.1038/srep35259

    work page doi:10.1038/srep35259.url:https://doi 2016

  18. [18]

    Inverse geometry for grating-based x- ray phase-contrast imaging

    Tilman Donath, Michael Chabior, Franz Pfeiffer, et al. “Inverse geometry for grating-based x- ray phase-contrast imaging”. In:Journal of Applied Physics106.5 (Sept. 2009), p. 054703.issn: 0021-8979.doi:10 . 1063 / 1 . 3208052. eprint:https : / / pubs . aip . org / aip / jap / article - pdf/doi/10.1063/1.3208052/14797839/054703\_1\_online.pdf.url:https://d...

    work page doi:10.1063/1.3208052/14797839/054703 2009

  19. [19]

    Improved reconstruction of phase-stepping data for Talbot–Lau x-ray imaging

    Sebastian Kaeppler, Jens Rieger, Georg Pelzer, et al. “Improved reconstruction of phase-stepping data for Talbot–Lau x-ray imaging”. In:Journal of Medical Imaging4.3 (2017), p. 034005.doi: 10.1117/1.JMI.4.3.034005.url:https://doi.org/10.1117/1.JMI.4.3.034005

    work page doi:10.1117/1.jmi.4.3.034005.url:https://doi.org/10.1117/1.jmi.4.3.034005 2017

  20. [20]

    Analytical and simulative investigations of moiré artefacts in Talbot-Lau X-ray imaging

    Christian Hauke, Martino Leghissa, Georg Pelzer, et al. “Analytical and simulative investigations of moiré artefacts in Talbot-Lau X-ray imaging”. In:Opt. Express25.26 (Dec. 2017), pp. 32897–32909.doi:10.1364/OE.25.032897.url:https://opg.optica.org/oe/abstract. cfm?URI=oe-25-26-32897

    work page doi:10.1364/oe.25.032897.url:https://opg.optica.org/oe/abstract 2017

  21. [21]

    Improved reconstruction method for phase stepping data with stepping errors and dose fluctuations

    Koh Hashimoto, Hidekazu Takano, and Atsuhi Momose. “Improved reconstruction method for phase stepping data with stepping errors and dose fluctuations”. In:Opt. Express28.11 (May 2020), pp. 16363–16384.doi:10.1364/OE.385236.url:https://opg.optica.org/oe/abstract.cfm? URI=oe-28-11-16363

    work page doi:10.1364/oe.385236.url:https://opg.optica.org/oe/abstract.cfm 2020

  22. [22]

    Moir´ e artifacts reduction in Talbot-Lau X-ray phase con- trast imaging using a three-step iterative approach

    Siwei Tao, Yueshu Xu, Ling Bai, et al. “Moir´ e artifacts reduction in Talbot-Lau X-ray phase con- trast imaging using a three-step iterative approach”. In:Opt. Express30.20 (Sept. 2022), pp. 35096– 35111.doi:10.1364/OE.466277.url:https://opg.optica.org/oe/abstract.cfm?URI=oe- 30-20-35096

    work page doi:10.1364/oe.466277.url:https://opg.optica.org/oe/abstract.cfm 2022

  23. [23]

    De- sign and operation of FACT-the first G-APD Cherenkov telescope

    Ohsung Oh, Daeseung Kim, Ho Kyung Kim, et al. “Image reconstruction method in grating inter- ferometer with phase stepping using grating position and dose fluctuation correction”. In:Journal of Instrumentation18.07 (July 2023), P07006.doi:10.1088/1748- 0221/18/07/P07006.url: https://dx.doi.org/10.1088/1748-0221/18/07/P07006

    work page doi:10.1088/1748- 2023

  24. [24]

    An iterative algorithm for interferograms with random phase shifts and high-order harmonics

    Jiancheng Xu, Qiao Xu, and Liqun Chai. “An iterative algorithm for interferograms with random phase shifts and high-order harmonics”. In:Journal of Optics A: Pure and Applied Optics10.9 (Aug. 2008), p. 095004.doi:10.1088/1464-4258/10/9/095004.url:https://dx.doi.org/10. 1088/1464-4258/10/9/095004

    work page doi:10.1088/1464-4258/10/9/095004.url:https://dx.doi.org/10 2008

  25. [25]

    Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources

    Franz Pfeiffer, Timm Weitkamp, Oliver Bunk, et al. “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources”. In:Nature Physics2.4 (Apr. 2006), pp. 258–261.issn: 1745-2481.doi:10.1038/nphys265.url:https://doi.org/10.1038/nphys265

    work page doi:10.1038/nphys265.url:https://doi.org/10.1038/nphys265 2006

  26. [26]

    J. Dey, N. Bhusal, L. Butler, et al.Phase Contrast X-ray Interferometry. US Patent 10,872,708, Dec 22, 2020

    work page 2020

  27. [27]

    J. Dey, N. Bhusal, L. Butler, et al.Phase Contrast X-ray Interferometry. US Patent 11,488,740 B2, Nov 1, 2022

    work page 2022

  28. [28]

    X-ray interferometry without analyzer for breast CT application: a simulation study

    Jingzhu Xu, Kyungmin Ham, and Joyoni Dey. “X-ray interferometry without analyzer for breast CT application: a simulation study”. In:Journal of Medical Imaging7.2 (2020), p. 023503.doi: 10.1117/1.JMI.7.2.023503.url:https://doi.org/10.1117/1.JMI.7.2.023503

    work page doi:10.1117/1.jmi.7.2.023503.url:https://doi.org/10.1117/1.jmi.7.2.023503 2020

  29. [29]

    Neutron interferometry using a single modulated phase grat- ing

    I. Hidrovo, J. Dey, H. Meyer, et al. “Neutron interferometry using a single modulated phase grat- ing”. In:Review of Scientific Instruments94.4 (Apr. 2023), p. 045110

    work page 2023

  30. [30]

    Improved algorithm for processing grating-based phase contrast interferometry image sets

    S. Marathe, L. Assoufid, X. Xiao, et al. “Improved algorithm for processing grating-based phase contrast interferometry image sets”. In:Rev Sci Instrum85.1 (Jan. 2014), p. 013704

    work page 2014

  31. [31]

    Natick, Massachusetts, United States, 2025.url:https://www.mathworks.com

    The MathWorks Inc.Optimization Toolbox version: 25.1 (R2025a). Natick, Massachusetts, United States, 2025.url:https://www.mathworks.com. 12

    work page 2025

  32. [32]

    Clarification on generalized Lau condition for X-ray interferometers based on dual phase gratings

    Aimin Yan, Xizeng Wu, and Hong Liu. “Clarification on generalized Lau condition for X-ray interferometers based on dual phase gratings”. In:Opt. Express27.16 (Aug. 2019), pp. 22727– 22736.doi:10.1364/OE.27.022727.url:https://opg.optica.org/oe/abstract.cfm?URI=oe- 27-16-22727. 13

    work page doi:10.1364/oe.27.022727.url:https://opg.optica.org/oe/abstract.cfm 2019