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Multislice hollow ptychography for simultaneous atomic-layer-resolved three-dimensional structural imaging and spectroscopy

Yu Lei1 and Peng Wang1,2,*

  • *Contact author: peng.wang.3@warwick.ac.uk

Phys. Rev. Applied 26, 034066 – Published 28 September, 2026

DOI: https://doi.org/10.1103/by27-b9mc

Abstract

Electron-matter interactions produce elastic and inelastic scattering, forming the basis for imaging and spectroscopy in electron microscopy. However, integrating electron energy-loss spectroscopy (EELS) with 4D-STEM and ptychography remains challenging due to detector geometry conflicts. Hollow ptychography introduced by Song et al., which uses a central aperture to allow low-angle electrons into the EELS spectrometer, suffers from multiple scattering in thicker samples. We propose multislice hollow ptychography (MHP), which incorporates a multislice model to address dynamical scattering and enables robust high-resolution imaging from hollow diffraction patterns while supporting simultaneous EELS acquisition. MHP achieves sub-ångström lateral resolution at intermediate doses (104–108  e−/Å2) and enables full three-dimensional (3D) atomic-layer reconstruction at ultrahigh doses (≥108  e−/Å2), limited only by lattice vibrations. Of note, up to 70% of electrons remain available for spectroscopy. This flexible and dose-efficient framework supports correlative 3D imaging and chemical mapping, opening new possibilities for analyzing complex energy and quantum materials.

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References (84)

  1. D. B. Williams and C. B. Carter, Transmission Electron Microscopy: A Textbook for Materials Science, 2nd ed. (Springer US, New York, NY, 2009).
  2. M. Varela, J. Gazquez, T. J. Pennycook, C. Magen, M. P. Oxley, and S. J. Pennycook, in Scanning Transmission Electron Microscopy: Imaging and Analysis, edited by S. J. Pennycook and P. D. Nellist (Springer New York, New York, NY, 2011), p. 429.
  3. K. Kimoto, T. Asaka, T. Nagai, M. Saito, Y. Matsui, and K. Ishizuka, Element-selective imaging of atomic columns in a crystal using STEM and EELS, Nature (London) 450, 702 (2007).
  4. D. A. Muller, L. F. Kourkoutis, M. Murfitt, J. H. Song, H. Y. Hwang, J. Silcox, N. Dellby, and O. L. Krivanek, Atomic-scale chemical imaging of composition and bonding by aberration-corrected microscopy, Science 319, 1073 (2008).
  5. D. A. Muller, Structure and bonding at the atomic scale by scanning transmission electron microscopy, Nat. Mater. 8, 263 (2009).
  6. S. J. Pennycook and P. D. Nellist, Scanning transmission electron microscopy (2011).
  7. P. D. Nellist, M. F. Chisholm, N. Dellby, O. L. Krivanek, M. F. Murfitt, Z. S. Szilagyi, A. R. Lupini, A. Borisevich, W. H. Sides Jr., and S. J. Pennycook, Direct sub-angstrom imaging of a crystal lattice, Science 305, 1741 (2004).
  8. R. F. Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope, 3rd ed. (Springer, New York, 2011).
  9. Y.-G. Lee, S. Fujiki, C. Jung, N. Suzuki, N. Yashiro, R. Omoda, D.-S. Ko, T. Shiratsuchi, T. Sugimoto, S. Ryu et al., High-energy long-cycling all-solid-state lithium metal batteries enabled by silver–carbon composite anodes, Nat. Energy 5, 299 (2020).
  10. X. Liu, R. Garcia-Mendez, A. R. Lupini, Y. Cheng, Z. D. Hood, F. Han, A. Sharafi, J. C. Idrobo, N. J. Dudney, C. Wang et al., Local electronic structure variation resulting in Li ‘filament’ formation within solid electrolytes, Nat. Mater. 20, 1485 (2021).
  11. A. Y. Borisevich, A. R. Lupini, and S. J. Pennycook, Depth sectioning with the aberration-corrected scanning transmission electron microscope, Proc. Natl. Acad. Sci. U.S.A. 103, 3044 (2006).
  12. H. L. Xin and D. A. Muller, Aberration-corrected ADF-STEM depth sectioning and prospects for reliable 3D imaging in S/TEM, J. Electron Microsc. 58, 157 (2009).
  13. J. Miao, P. Ercius, and S. J. L. Billinge, Atomic electron tomography: 3D structures without crystals, Science 353, aaf2157 (2016).
  14. R. Ballabriga, J. Alozy, G. Blaj, M. Campbell, M. Fiederle, E. Frojdh, E. H. M. Heijne, X. Llopart, M. Pichotka, and S. Procz, The Medipix3RX: A high resolution, zero dead-time pixel detector readout chip allowing spectroscopic imaging, J. Instrum. 8, C02016 (2013).
  15. M. W. Tate, P. Purohit, D. Chamberlain, K. X. Nguyen, R. Hovden, C. S. Chang, P. Deb, E. Turgut, J. T. Heron, D. G. Schlom et al., High dynamic range pixel array detector for scanning transmission electron microscopy, Microsc. Microanal. 22, 237 (2016).
  16. C. Ophus, Four-dimensional scanning transmission electron microscopy (4D-STEM): From scanning nanodiffraction to ptychography and beyond, Microsc. Microanal. 25, 563 (2019).
  17. N. Shibata, S. D. Findlay, Y. Kohno, H. Sawada, Y. Kondo, and Y. Ikuhara, Differential phase-contrast microscopy at atomic resolution, Nat. Phys. 8, 611 (2012).
  18. W. Hoppe, Diffraction in inhomogeneous primary wave fields. 1. Principle of phase determination from electron diffraction interference, Acta Crystallogr., Sect. A 25, 495 (1969).
  19. W. Mao, L. Zhou, S. Gao, and P. Wang, in Encyclopedia of Condensed Matter Physics, edited by T. Chakraborty, 2nd ed. (Academic Press, Oxford, 2024), p. 71.
  20. J. M. Rodenburg and R. H. T. Bates, The theory of super-resolution electron microscopy via Wigner-distribution deconvolution, Philos. Trans. R. Soc., A 339, 521 (1992).
  21. P. D. Nellist, B. C. McCallum, and J. M. Rodenburg, Resolution beyond the ‘information limit’ in transmission electron microscopy, Nature (London) 374, 630 (1995).
  22. Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner et al., Electron ptychography of 2D materials to deep sub-angstrom resolution, Nature (London) 559, 343 (2018).
  23. P. Wang, F. Zhang, S. Gao, M. Zhang, and A. I. Kirkland, Electron ptychographic diffractive imaging of boron atoms in LaB6 crystals, Sci. Rep. 7, 2857 (2017).
  24. H. Yang, I. MacLaren, L. Jones, G. T. Martinez, M. Simson, M. Huth, H. Ryll, H. Soltau, R. Sagawa, Y. Kondo et al., Electron ptychographic phase imaging of light elements in crystalline materials using Wigner distribution deconvolution, Ultramicroscopy 180, 173 (2017).
  25. H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M. L. Green, H. Soltau et al., Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures, Nat. Commun. 7, 12532 (2016).
  26. Z. Ding, S. Gao, W. Fang, C. Huang, L. Zhou, X. Pei, X. Liu, X. Pan, C. Fan, A. I. Kirkland et al., Three-dimensional electron ptychography of organic-inorganic hybrid nanostructures, Nat. Commun. 13, 4787 (2022).
  27. J. Song, C. S. Allen, S. Gao, C. Huang, H. Sawada, X. Pan, J. Warner, P. Wang, and A. I. Kirkland, Atomic resolution defocused electron ptychography at low dose with a fast, direct electron detector, Sci. Rep. 9, 3919 (2019).
  28. L. Zhou, J. Song, J. S. Kim, X. Pei, C. Huang, M. Boyce, L. Mendonça, D. Clare, A. Siebert, C. S. Allen et al., Low-dose phase retrieval of biological specimens using cryo-electron ptychography, Nat. Commun. 11, 2773 (2020).
  29. Z. Chen, M. Odstrcil, Y. Jiang, Y. Han, M.-H. Chiu, L.-J. Li, and D. A. Muller, Mixed-state electron ptychography enables sub-angstrom resolution imaging with picometer precision at low dose, Nat. Commun. 11, 2994 (2020).
  30. N. Schnitzer, M. Palos, G. Topore, N. Agarwal, M. Gates, Y. Li, R. Hovden, I. E. Baggari, S. H. Sung, and M. S. Conroy, Helium-cooled cryogenic STEM imaging and ptychography for atomic-scale study of low-temperature phases, arXiv:2603.10892.
  31. Z. Wang, X. Hu, Y. Zhang, X. Wu, H. Shi, W. Liu, and Y. Yu, Ptychographic observation of lithium atoms in the irradiation-sensitive garnet-type solid electrolyte at sub-angstrom resolution, J. Am. Chem. Soc. 147, 18025 (2025).
  32. J. G. Lozano, G. T. Martinez, L. Jin, P. D. Nellist, and P. G. Bruce, Low-dose aberration-free imaging of Li-rich cathode materials at various states of charge using electron ptychography, Nano Lett. 18, 6850 (2018).
  33. X. Pei, L. Zhou, C. Huang, M. Boyce, J. S. Kim, E. Liberti, Y. Hu, T. Sasaki, P. D. Nellist, P. Zhang et al., Cryogenic electron ptychographic single particle analysis with wide bandwidth information transfer, Nat. Commun. 14, 3027 (2023).
  34. A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, Ptychographic transmission microscopy in three dimensions using a multi-slice approach, J. Opt. Soc. Am. A 29, 1606 (2012).
  35. S. Gao, P. Wang, F. Zhang, G. T. Martinez, P. D. Nellist, X. Pan, and A. I. Kirkland, Electron ptychographic microscopy for three-dimensional imaging, Nat. Commun. 8, 163 (2017).
  36. A. M. Maiden and J. M. Rodenburg, An improved ptychographical phase retrieval algorithm for diffractive imaging, Ultramicroscopy 109, 1256 (2009).
  37. Z. Chen, Y. Jiang, Y.-T. Shao, M. E. Holtz, M. Odstrčil, M. Guizar-Sicairos, I. Hanke, S. Ganschow, D. G. Schlom, and D. A. Muller, Electron ptychography achieves atomic-resolution limits set by lattice vibrations, Science 372, 826 (2021).
  38. H. Kp, R. Xu, K. Patel, K. J. Crust, A. Khandelwal, C. Zhang, S. Prosandeev, H. Zhou, Y.-T. Shao, L. Bellaiche et al., Electron ptychography reveals a ferroelectricity dominated by anion displacements, Nat. Mater. 24, 1433 (2025).
  39. H. Sha, Y. Ma, G. Cao, J. Cui, W. Yang, Q. Li, and R. Yu, Sub-nanometer-scale mapping of crystal orientation and depth-dependent structure of dislocation cores in SrTiO3, Nat. Commun. 14, 162 (2023).
  40. M. Zhu, M. Xu, Y. Yun, L. Wu, O. Shafir, C. Gilgenbach, L. W. Martin, I. Grinberg, J. E. Spanier, and J. M. LeBeau, Insights into chemical and structural order at planar defects in Pb2MgWO6 using multislice electron ptychography, ACS Nano 19, 5568 (2025).
  41. H. Zhang, G. Li, J. Zhang, D. Zhang, Z. Chen, X. Liu, P. Guo, Y. Zhu, C. Chen, L. Liu et al., Three-dimensional inhomogeneity of zeolite structure and composition revealed by electron ptychography, Science 380, 633 (2023).
  42. Z. Dong, Y. Zhang, C.-C. Chiu, S. Lu, J. Zhang, Y.-C. Liu, S. Liu, J.-C. Yang, P. Yu, Y. Wang et al., Sub-nanometer depth resolution and single dopant visualization achieved by tilt-coupled multislice electron ptychography, Nat. Commun. 16, 1219 (2025).
  43. C. M. O’Leary, H. Sha, J. Zhang, C. Su, S. Kahn, H. Jiang, A. Zettl, J. Ciston, and J. Miao, Three-dimensional structure of buried heterointerfaces revealed by multislice ptychography, Phys. Rev. Appl. 22, 014016 (2024).
  44. B. Song, Z. Ding, C. S. Allen, H. Sawada, F. Zhang, X. Pan, J. Warner, A. I. Kirkland, and P. Wang, Hollow electron ptychographic diffractive imaging, Phys. Rev. Lett. 121, 146101 (2018).
  45. N. Y. Kim, S. Cao, K. L. More, A. R. Lupini, J. Miao, and M. Chi, Hollow ptychography: Toward simultaneous 4D scanning transmission electron microscopy and electron energy loss spectroscopy, Small 19, e2208162 (2023).
  46. K. Wakonig, H.-C. Stadler, M. Odstrčil, E. H. R. Tsai, A. Diaz, M. Holler, I. Usov, J. Raabe, A. Menzel, and M. Guizar-Sicairos, PtychoShelves, a versatile high-level framework for high-performance analysis of ptychographic data, J. Appl. Crystallogr. 53, 574 (2020).
  47. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, High-resolution scanning X-ray diffraction microscopy, Science 321, 379 (2008).
  48. P. Thibault and M. Guizar-Sicairos, Maximum-likelihood refinement for coherent diffractive imaging, New J. Phys. 14, 063004 (2012).
  49. P. Thibault and A. Menzel, Reconstructing state mixtures from diffraction measurements, Nature (London) 494, 68 (2013).
  50. E. H. R. Tsai, I. Usov, A. Diaz, A. Menzel, and M. Guizar-Sicairos, X-ray ptychography with extended depth of field, Opt. Express 24, 29089 (2016).
  51. See Supplemental Material at http://link.aps.org/supplemental/10.1103/by27-b9mc for additional experimental and simulation details, 3D optical-sectioning analyses, reference-free atomic localization, and temporal-coherence effects, which includes Refs. [52–57].
  52. T. M. Gesing, R. Uecker, and J.-C. Buhl, Refinement of the crystal structure of praseodymium orthoscandate, PrScO3, Zeitschrift für Kristallographie—New Crystal Structures 224, 365 (2009).
  53. G. Behan, E. C. Cosgriff, A. I. Kirkland, and P. D. Nellist, Three-dimensional imaging by optical sectioning in the aberration-corrected scanning transmission electron microscope, Philos. Trans. R. Soc., A 367, 3825 (2009).
  54. E. J. Kirkland, in Advanced Computing in Electron Microscopy (Springer International Publishing, Cham, 2020), p. 143.
  55. P. B. Allen and B. Mitrović, Solid State Physics, edited by H. Ehrenreich, F. Seitz, and D. Turnbull (Academic Press, New York, NY, 1983), p. 1.
  56. L.-M. Peng, G. Ren, S. L. Dudarev, and M. J. Whelan, Debye–Waller factors and absorptive scattering factors of elemental crystals, Acta Crystallogr., Sect. A 52, 456 (1996).
  57. K. N. Trueblood, H. B. Bürgi, H. Burzlaff, J. D. Dunitz, C. M. Gramaccioli, H. H. Schulz, U. Shmueli, and S. C. Abrahams, Atomic displacement parameter nomenclature. Report of a subcommittee on atomic displacement parameter nomenclature, Acta Crystallogr., Sect. A 52, 770 (1996).
  58. J. Gázquez, G. Sánchez-Santolino, N. Biškup, M. A. Roldán, M. Cabero, S. J. Pennycook, and M. Varela, Applications of STEM-EELS to complex oxides, Mater. Sci. Semicond. Process. 65, 49 (2017).
  59. J. Madsen and T. Susi, The abTEM code: Transmission electron microscopy from first principles, Open Res. Eur. 1, 24 (2021).
  60. C. Zhang, Y. Feng, Z. Han, S. Gao, M. Wang, and P. Wang, Electrochemical and structural analysis in all-solid-state lithium batteries by analytical electron microscopy: Progress and perspectives, Adv. Mater. 32, 1903747 (2020).
  61. Z. Zhan, Y. Liu, W. Wang, G. Du, S. Cai, and P. Wang, Atomic-level imaging of beam-sensitive COFs and MOFs by low-dose electron microscopy, Nanoscale Horiz. 9, 900 (2024).
  62. J. M. Zuo and J. C. H. Spence, in Advanced Transmission Electron Microscopy: Imaging and Diffraction in Nanoscience (Springer New York, New York, NY, 2017), p. 403.
  63. R. F. Egerton, in Electron Energy-Loss Spectroscopy in the Electron Microscope (Springer US, Boston, MA, 2011), p. 111.
  64. J. Miao, Computational microscopy with coherent diffractive imaging and ptychography, Nature (London) 637, 281 (2025).
  65. D. J. Chang, D. S. Kim, A. Rana, X. Tian, J. Zhou, P. Ercius, and J. Miao, Ptychographic atomic electron tomography: Towards three-dimensional imaging of individual light atoms in materials, Phys. Rev. B 102, 174101 (2020).
  66. S. Lazar, P. Tiemeijer, C. S. Schnohr, M. Meledina, C. Patzig, T. Höche, P. Longo, and B. Freitag, Enabling electron-energy-loss spectroscopy at very high energy losses: An opportunity to obtain X-ray absorption spectroscopy-like information using an electron microscope, Phys. Rev. Appl. 23, 054095 (2025).
  67. J. L. Hart, A. C. Lang, Y. Li, S. Shahrezaei, D. D. Alix-Williams, M. L. Falk, S. N. Mathaudhu, A. I. Frenkel, and M. L. Taheri, Revealing local order via high energy EELS, Mater. Today Nano 21, 100298 (2023).
  68. I. El Baggari, B. H. Savitzky, A. S. Admasu, J. Kim, S.-W. Cheong, R. Hovden, and L. F. Kourkoutis, Nature and evolution of incommensurate charge order in manganites visualized with cryogenic scanning transmission electron microscopy, Proc. Natl. Acad. Sci. U.S.A. 115, 1445 (2018).
  69. M.-W. Chu, G. Y. Guo, W. T. Chen, M. H. Lee, S. H. Lee, Y.-C. Lai, C. H. Du, and C. H. Chen, Probing charge order and hidden topology at the atomic scale by cryogenic scanning transmission electron microscopy and spectroscopy, Phys. Rev. B 103, 115130 (2021).
  70. E. Bianco and L. F. Kourkoutis, Atomic-resolution cryogenic scanning transmission electron microscopy for quantum materials, Acc. Chem. Res. 54, 3277 (2021).
  71. J. Mun, D. Potemkin, H. Jang, S. Park, S. Mick, C. Petrovic, S.-W. Cheong, M.-G. Han, and Y. Zhu, Atomic resolution scanning transmission electron microscopy at liquid helium temperatures for quantum materials, Ultramicroscopy 267, 114039 (2024).
  72. N. Schnitzer, B. H. Goodge, G. Powers, J. Kim, S.-W. Cheong, I. El Baggari, and L. F. Kourkoutis, Atomic-scale tracking of topological defect motion and incommensurate charge order melting, Phys. Rev. X 15, 011007 (2025).
  73. J. Cui, H. Sha, W. Yang, and R. Yu, Antiferromagnetic imaging via ptychographic phase retrieval, Sci. Bull. 69, 466 (2024).
  74. Z. Chen, E. Turgut, Y. Jiang, K. X. Nguyen, M. J. Stolt, S. Jin, D. C. Ralph, G. D. Fuchs, and D. A. Muller, Lorentz electron ptychography for imaging magnetic textures beyond the diffraction limit, Nat. Nanotechnol. 17, 1165 (2022).
  75. C. Hofer, J. Madsen, T. Susi, and T. J. Pennycook, Detecting charge transfer at defects in 2D materials with electron ptychography, J. Microsc. 300, 156 (2025).
  76. C. Gilgenbach, T. Defferriere, H. L. Tuller, and J. M. LeBeau, Direct quantification of grain boundary space charge layers using multislice electron ptychography, Microsc. Microanal. 30 (2024).
  77. Y. Tokura, M. Kawasaki, and N. Nagaosa, Emergent functions of quantum materials, Nat. Phys. 13, 1056 (2017).
  78. E. Rennich, S. H. Sung, N. Agarwal, M. Gates, R. Kerns, R. Hovden, and I. E. Baggari, Ultracold cryogenic TEM with liquid helium and high stability, Proc. Natl. Acad. Sci. U.S.A. 122, e2509736122 (2025).
  79. Y.-H. Kim, F. S. Yasin, N. Y. Kim, M. Birch, X. Yu, A. Kikkawa, Y. Taguchi, J. Yan, and M. Chi, Ultralow-temperature cryogenic transmission electron microscopy using a new helium flow cryostat stage, Ultramicroscopy 280, 114263 (2026).
  80. M. Huth, B. Eckert, S. Aschauer, E. Hedley, P. Nellist, P. Majewski, L. Strüder, and H. Soltau, Combine 4D STEM and EELS using a fast pixelated direct detector with center hole, Microsc. Microanal. 29, 401 (2023).
  81. D. G. Stroppa, M. Meffert, C. Hoermann, P. Zambon, D. Bachevskaya, H. Remigy, C. Schulze-Briese, and L. Piazza, From STEM to 4D STEM: Ultrafast diffraction mapping with a hybrid-pixel detector, Microsc. Today 31, 10 (2023).
  82. W. Koibuchi and R. Sagawa, High-resolution STEM image acquisition method for tilted specimen using a new type of aberration corrector, Microsc. Microanal. 30 (2024).
  83. O. L. Krivanek, T. C. Lovejoy, N. Dellby, T. Aoki, R. W. Carpenter, P. Rez, E. Soignard, J. Zhu, P. E. Batson, M. J. Lagos et al., Vibrational spectroscopy in the electron microscope, Nature (London) 514, 209 (2014).
  84. https://github.com/799040451/MultiHollowPtycho.

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