Speckle-based X-ray microtomography via preconditioned Wirtinger flow

KyeoReh Lee; Herve Hugonnet; Jae-Hong Lim; YongKeun Park

doi:10.1038/s41377-025-02118-z

Your Location：

Home >

Browse articles >

Speckle-based X-ray microtomography via preconditioned Wirtinger flow

Original Articles

- Speckle-based X-ray microtomography via preconditioned Wirtinger flow
- Light: Science & Applications Vol. 15, Issue 4, Pages: 1377-1388(2026)
- Affiliations：
  
  1.Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
  2.KAIST Institute for Health Science and Technology, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
  3.Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang 37637, Republic of Korea
  4.Present address: Department of Applied Physics, Yale University, New Haven 06520 Connecticut, USA
- Author bio：
  
  KyeoReh Lee (lee.kyeo@gmail.com)
  YongKeun Park (yk.park@kaist.ac.kr)
- Funds：
- DOI：10.1038/s41377-025-02118-z
  CLC：
- Received：21 May 2025，
  
  Revised：2025-11-03，
  
  Accepted：04 November 2025，
  
  Online First：24 February 2026，
  
  Published：30 April 2026
- Accepted：
Scan QR Code
Lee, K. R. et al. Speckle-based X-ray microtomography via preconditioned Wirtinger flow. Light: Science & Applications, 15, 1377-1388 (2026).
DOI：

Lee, K. R. et al. Speckle-based X-ray microtomography via preconditioned Wirtinger flow. Light: Science & Applications, 15, 1377-1388 (2026). DOI： 10.1038/s41377-025-02118-z.

摘要

Abstract

Three-dimensional quantitative phase imaging has been extensively studied in X-ray microtomography to improve the sensitivity and specificity of measurements

especially for low atomic number materials. However

obtaining quantitative phase images typically requires additional measurements or assumptions

which significantly limit the practical applicability. Here

we present preconditioned Wirtinger flow (PWF) to realize an assumption-free

single-shot

quantitative X-ray microtomography. Accurate phase retrieval is demonstrated using a specialized gradient-based algorithm with an accurate physical model. Partial coherence of the source is taken into account

extending the potential applications to bench-top sources. Improved accuracy and spatial resolution over conventional speckle tracking methods are experimentally demonstrated. The various samples are explored to demonstrate the robustness and versatility of PWF.

关键词

Keywords

references

Momose, A. Recent advances in x-ray phase imaging. Jpn. J. Appl. Phys. 44 , 6355–6367 (2005)..

Snigirev, A. et al. On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation. Rev. Sci. Instrum. 66 , 5486–5492 (1995)..

Cloetens, P. et al. Phase objects in synchrotron radiation hard x-ray imaging. J. Phys. D: Appl. Phys. 29 , 133–146 (1996)..

Pogany, A., Gao, D. & Wilkins, S. W. Contrast and resolution in imaging with a microfocus x-ray source. Rev. Sci. Instrum. 68 , 2774–2782 (1997)..

Burvall, A. et al. Phase retrieval in x-ray phase-contrast imaging suitable for tomography. Opt. Express 19 , 10359–10376 (2011)..

Nugent, K. A. et al. Quantitative phase imaging using hard X rays. Phys. Rev. Lett. 77 , 2961–2964 (1996)..

Cloetens, P. et al. Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays. Appl. Phys. Lett. 75 , 2912–2914 (1999)..

Zanette, I. et al. Holotomography versus x-ray grating interferometry: a comparative study. Appl. Phys. Lett. 103 , 244105 (2013)..

Mercère, P. et al. Hartmann wave-front measurement at 13.4 nm with λ EUV /120 accuracy. Opt. Lett. 28 , 1534–1536 (2003)..

Salas-Peimbert, D. P. et al. Wave-front retrieval from Hartmann test data. Appl. Opt. 44 , 4228–4238 (2005)..

Keitel, B. et al. Hartmann wavefront sensors and their application at flash. J. Synchrotron Radiat. 23 , 43–49 (2016)..

David, C. et al. Differential x-ray phase contrast imaging using a shearing interferometer. Appl. Phys. Lett. 81 , 3287–3289 (2002)..

Weitkamp, T. et al. X-ray phase imaging with a grating interferometer. Opt. Express 13 , 6296–6304 (2005)..

Bon, P. et al. Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells. Opt. Express 17 , 13080–13094 (2009)..

Kottler, C. et al. A two-directional approach for grating based differential phase contrast imaging using hard x-rays. Opt. Express 15 , 1175–1181 (2007)..

Zanette, I. et al. Two-dimensional x-ray grating interferometer. Phys. Rev. Lett. 105 , 248102 (2010)..

Morgan, K. S., Paganin, D. M. & Siu, K. K. W. X-ray phase imaging with a paper analyzer. Appl. Phys. Lett. 100 , 124102 (2012)..

Bérujon, S. et al. Two-dimensional x-ray beam phase sensing. Phys. Rev. Lett. 108 , 158102 (2012)..

Berujon, S., Wang, H. C. & Sawhney, K. X-ray multimodal imaging using a random-phase object. Phys. Rev. A 86 , 063813 (2012)..

Wu, T. F. et al. Multiplexed wavefront sensing with a thin diffuser. Optica 11 , 297–304 (2024)..

Goodman, J. W. Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2007).

Zanette, I. et al. Speckle-based x-ray phase-contrast and dark-field imaging with a laboratory source. Phys. Rev. Lett. 112 , 253903 (2014)..

Berujon, S. & Ziegler, E. Near-field speckle-scanning-based x-ray imaging. Phys. Rev. A 92 , 013837 (2015)..

Zdora, M. C. et al. X-ray phase-contrast imaging and metrology through unified modulated pattern analysis. Phys. Rev. Lett. 118 , 203903 (2017)..

Paganin, D. M. et al. Single-image geometric-flow x-ray speckle tracking. Phys. Rev. A 98 , 053813 (2018)..

Pavlov, K. M. et al. X-ray multi-modal intrinsic-speckle-tracking. J. Opt. 22 , 125604 (2020)..

Quénot, L. et al. Implicit tracking approach for x-ray phase-contrast imaging with a random maskand a conventional system. Optica 8 , 1412–1415 (2021)..

Alloo, S. J. et al. Multimodal intrinsic speckle-tracking (MIST) to extract images of rapidly-varying diffuse X-ray dark-field. Sci. Rep. 13 , 5424 (2023)..

Zdora, M. C. et al. X-ray phase tomography with near-field speckles for three-dimensional virtual histology. Optica 7 , 1221–1227 (2020)..

Savatović, S. et al. Multi-resolution x-ray phase-contrast and dark-field tomography of human cerebellum with near-field speckles. Biomed. Opt. Express 15 , 142–161 (2024)..

Magnin, C. et al. Dark-field and directional dark-field on low-coherence x ray sources with random mask modulations: validation with SAXS anisotropy measurements. Opt. Lett. 48 , 5839–5842 (2023)..

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

Lee, K. & Park, Y. Exploiting the speckle-correlation scattering matrix for a compact reference-free holographic image sensor. Nat. Commun. 7 , 13359 (2016)..

Zhang, F. C. et al. Phase retrieval by coherent modulation imaging. Nat. Commun. 7 , 13367 (2016)..

McDermott, S. & Maiden, A. Near-field ptychographic microscope for quantitative phase imaging. Opt. Express 26 , 25471–25480 (2018)..

Levitan, A. L. et al. Single-frame far-field diffractive imaging with randomized illumination. Opt. Express 28 , 37103–37117 (2020)..

Oh, J., Lee, K. & Park, Y. Single-shot reference-free holographic imaging using a liquid crystal geometric phase diffuser. Laser Photonics Rev. 16 , 2100559 (2022)..

Labeyrie, A. Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images. Astron. Astrophys. 6 , 85 (1970)..

Bertolotti, J. et al. Non-invasive imaging through opaque scattering layers. Nature 491 , 232–234 (2012)..

Katz, O. et al. Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations. Nat. Photonics 8 , 784–790 (2014)..

Antipa, N. et al. Diffusercam: lensless single-exposure 3D imaging. Optica 5 , 1–9 (2018)..

Candès, E. J., Strohmer, T. & Voroninski, V. PhaseLift: exact and stable signal recovery from magnitude measurements via convex programming. Commun. Pure Appl. Math. 66 , 1241–1274 (2013)..

Candès, E. J., Li, X. D. & Soltanolkotabi, M. Phase retrieval via wirtinger flow: theory and algorithms. IEEE Trans. Inf. Theory 61 , 1985–2007 (2015)..

Wang, G., Giannakis, G. B. & Eldar, Y. C. Solving systems of random quadratic equations via truncated amplitude flow. IEEE Trans. Inf. Theory 64 , 773–794 (2018)..

Goldstein, T. & Studer, C. PhaseMax: convex phase retrieval via basis pursuit. IEEE Trans. Inf. Theory 64 , 2675–2689 (2018)..

Wittwer, F. et al. Phase retrieval framework for direct reconstruction of the projected refractive index applied to ptychography and holography. Optica 9 , 295–302 (2022)..

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

Maiden, A. M. & Rodenburg, J. M. An improved ptychographical phase retrieval algorithm for diffractive imaging. Ultramicroscopy 109 , 1256–1262 (2009)..

Saad, Y. Iterative Methods for Sparse Linear Systems 2nd edn (SIAM, 2003).

Lee, K. et al. Direct high-resolution x-ray imaging exploiting pseudorandomness. Light Sci. Appl. 12 , 88 (2023)..

Nesterov, Y. A method for unconstrained convex minimization problem with the rate of convergence O (1/k 2 ). Dokl. SSSR 269 , 543–547 (1983)..

Pavlov, K. M. et al. Single-shot x-ray speckle-based imaging of a single-material object. Phys. Rev. Appl. 13 , 054023 (2020)..

Maiden, A., Johnson, D. & Li, P. Further improvements to the ptychographical iterative engine. Optica 4 , 736–745 (2017)..

Choi, I., Lee, K. & Park, Y. Compensation of aberration in quantitative phase imaging using lateral shifting and spiral phase integration. Opt. Express 25 , 30771–30779 (2017)..

Pfeiffer, F. et al. Hard x-ray phase tomography with low-brilliance sources. Phys. Rev. Lett. 98 , 108105 (2007)..

Pfeiffer, F. et al. Hard-x-ray dark-field imaging using a grating interferometer. Nat. Mater. 7 , 134–137 (2008)..

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

Kak, A. C. & Slaney, M. Principles of Computerized Tomographic Imagin g (Society for Industrial and Applied Mathematics, 2001)..

Zhang, J. et al. Depth-dependent valence stratification driven by oxygen redox in lithium-rich layered oxide. Nat. Commun. 11 , 6342 (2020)..

Bravin, A., Coan, P. & Suortti, P. X-ray phase-contrast imaging: from pre-clinical applications towards clinics. Phys. Med. Biol. 58 , R1–R35 (2013)..

Goodman, J. W. Role of coherence concepts in the study of speckle. In: Proceedings of SPIE 0194, Applications of Optical Coherence 86–97 (SPIE, 1979)

Mandel, L. & Wolf, E. The measures of bandwidth and coherence time in optics. Proc. Phys. Soc. 80 , 894–897 (1962)..

Stockmar, M. et al. X-ray near-field ptychography for optically thick specimens. Phys. Rev. Appl. 3 , 014005 (2015)..

Stockmar, M. et al. X-ray nanotomography using near-field ptychography. Opt. Express 23 , 12720–12731 (2015)..

Rosenthal, P. B. & Henderson, R. Optimal determination of particle orientation, absolute hand, and contrast loss in single-particle electron cryomicroscopy. J. Mol. Biol. 333 , 721–745 (2003)..

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

⁰