Issue
Eur. Phys. J. Appl. Phys.
Volume 100, 2025
Special Issue on ‘Imaging, Diffraction, and Spectroscopy on the micro/nanoscale (EMC 2024)’, edited by Jakob Birkedal Wagner and Randi Holmestad
Article Number 20
Number of page(s) 37
DOI https://doi.org/10.1051/epjap/2025018
Published online 30 July 2025
  1. L. Zhou, J. Song, J.S. Kim, X. Pei, C. Huang, M. Boyce, L. Mendonça, D. Clare, A. Siebert, C.S. Allen, E. Liberti, D. Stuart, X. Pan, P.D. Nellist, P. Zhang, A.I. Kirkland, P. Wang, Low-dose phase retrieval of biological specimens using cryo-electron ptychography, Nat. Commun. 11, 2773 (2020). https://doi.org/10.1038/s41467-020-16391-6 [Google Scholar]
  2. I. Lazić, M. Wirix, M.L. Leidl, F. de Haas, D. Mann, M. Beckers, E.V. Pechnikova, K. Müller-Caspary, R. Egoavil, E.G. Bosch, C. Sachse, Single-particle cryo-EM structures from iDPC-STEM at near-atomic resolution, Nat. Methods 19, 1126 (2022). https://doi.org/10.1038/s41592-022-01586-0 [Google Scholar]
  3. K. Müller-Caspary, M. Duchamp, M. Rösner, V. Migunov, F. Winkler, H. Yang, M. Huth, R. Ritz, M. Simson, S. Ihle, H. Soltau, T. Wehling, R.E. Dunin-Borkowski, S. Van Aert, A. Rosenauer, Atomic-scale quantification of charge densities in two-dimensional materials, Phys. Rev. B 98 (2018). https://doi.org/10.1103/PhysRevB.98.121408 [Google Scholar]
  4. Y. Wen, C. Ophus, C.S. Allen, S. Fang, J. Chen, E. Kaxiras, A.I. Kirkland, J.H. Warner, Simultaneous identification of low and high atomic number atoms in monolayer 2D materials using 4D scanning transmission electron microscopy, Nano Lett. 19, 6482 (2019). https://doi.org/10.1021/acs.nanolett.9b02717 [Google Scholar]
  5. Y. Chen, T.-C. Chou, C.-H. Fang, C.-Y. Lu, C.-N. Hsiao, W.-T. Hsu, C.-C. Chen, Direct observation of single-atom defects in monolayer two-dimensional materials by using electron ptychography at 200 kV acceleration voltage, Sci. Rep. 14, 277 (2024). https://doi.org/10.1038/s41598-023-50784-z [Google Scholar]
  6. L. Liu, N. Wang, C. Zhu, X. Liu, Y. Zhu, P. Guo, L. Alfilfil, X. Dong, D. Zhang, Y. Han, Direct imaging of atomically dispersed molybdenum that enables location of aluminum in the framework of zeolite ZSM-5, Angew. Chem. In. Ed. 59, 819 (2020). https://doi.org/10.1002/anie.201909834 [Google Scholar]
  7. H. Sha, J. Cui, J. Li, Y. Zhang, W. Yang, Y. Li, R. Yu, Ptychographic measurements of varying size and shape along zeolite channels, Sci. Adv. 9, 1 (2023). https://doi.org/10.1126/sciadv.adf1151 [Google Scholar]
  8. H. Zhang, G. Li, J. Zhang, D. Zhang, Z. Chen, X. Liu, P. Guo, Y. Zhu, C. Chen, L. Liu, X. Guo, Y. Han, Three-dimensional inhomogeneity of zeolite structure and composition revealed by electron ptychography, Science 380, 633 (2023). https://doi.org/10.1126/science.adg3183 [Google Scholar]
  9. Z. Dong, E. Zhang, Y. Jiang, Q. Zhang, A. Mayoral, H. Jiang, Y. Ma, Atomic-level imaging of zeolite local structures using electron ptychography, J. Am. Chem. Soc. 145, 6628 (2023). https://doi.org/10.1021/jacs.2c12673 [Google Scholar]
  10. K. Mitsuishi, K. Nakazawa, R. Sagawa, M. Shimizu, H. Matsumoto, H. Shima, T. Takewaki, Direct observation of Cu in high-silica chabazite zeolite by electron ptychography using Wigner distribution deconvolution, Sci. Rep. 13, 316 (2023). https://doi.org/10.1038/s41598-023-27452-3 [CrossRef] [Google Scholar]
  11. J.G. Lozano, G.T. Martinez, L. Jin, P.D. Nellist, 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). https://doi.org/10.1021/acs.nanolett.8b02718 [Google Scholar]
  12. W. Song, M.A. Pérez-Osorio, J.-J. Marie, E. Liberti, X. Luo, C. O'Leary, R.A. House, P.G. Bruce, P.D. Nellist, Direct imaging of oxygen shifts associated with the oxygen redox of Li-rich layered oxides, Joule 6, 1049 (2022). https://doi.org/10.1016/j.joule.2022.04.008 [Google Scholar]
  13. W. Song, M.A. Pérez-Osorio, J. Chen, Z. Ding, J.-J. Marie, M. Juelsholt, R.A. House, P.G. Bruce, P.D. Nellist, Visualization of Tetrahedral Li in the Alkali Layers of Li-Rich Layered Metal Oxides, J. Am. Chem. Soc. 146, 23814 (2024). https://doi.org/10.1021/jacs.4c05556 [Google Scholar]
  14. B. Hao, Z. Ding, X. Tao, P.D. Nellist, H.E. Assender, Atomic-scale imaging of polyvinyl alcohol crystallinity using electron ptychography, Polymer 284, 126305 (2023). https://doi.org/10.1016/j.polymer.2023.126305 [Google Scholar]
  15. M. Ma, X. Zhang, X. Chen, H. Xiong, L. Xu, T. Cheng, J. Yuan, F. Wei, B. Shen, In situ imaging of the atomic phase transition dynamics in metal halide perovskites, Nat. Commun. 14, 7142 (2023). https://doi.org/10.1038/s41467-023-42999-5 [Google Scholar]
  16. A. Scheid, Y. Wang, M. Jung, T. Heil, D. Moia, J. Maier, P.A. van Aken, Electron ptychographic phase imaging of beam-sensitive all-inorganic halide perovskites using four-dimensional scanning transmission electron microscopy, Microsc. Microanal. 29, 869 (2023). https://doi.org/10.1093/micmic/ozad017 [Google Scholar]
  17. N.J. Schrenker, T. Braeckevelt, A. De Backer, N. Livakas, C.-P. Yu, T. Friedrich, M.B.J. Roeffaers, J. Hofkens, J. Verbeeck, L. Manna, V. Van Speybroeck, S. Van Aert, S. Bals, Investigation of the octahedral network structure in formamidinium lead bromide nanocrystals by low-dose scanning transmission electron microscopy, Nano Lett. 24, 10936 (2024). https://doi.org/10.1021/acs.nanolett.4c02811 [Google Scholar]
  18. X. Li, J. Wang, X. Liu, L. Liu, D. Cha, X. Zheng, A.A. Yousef, K. Song, Y. Zhu, D. Zhang, Y. Han, Direct imaging of tunable crystal surface structures of mof mil-101 using high-resolution electron microscopy, J. Am. Chem. Soc. 141, 12021 (2019). https://doi.org/10.1021/jacs.9b04896 [Google Scholar]
  19. G. Li, M. Xu, W.-q. Tang, Y. Liu, C. Chen, D. Zhang, L. Liu, S. Ning, H. Zhang, Z.-y. Gu, Z. Lai, D.A. Muller, Y. Han, Atomically resolved imaging of radiation-sensitive metal-organic frameworks via electron ptychography, Nat. Commun. 16, 914 (2025). https://doi.org/10.1038/s41467-025-56215-z [Google Scholar]
  20. R. Egerton, Radiation damage to organic and inorganic specimens in the TEM, Micron 119, 72 (2019). https://doi.org/10.1016/j.micron.2019.01.005 [Google Scholar]
  21. W.E. King, R. Benedek, K. Merkle, M. Meshii, Damage effects of high energy electrons on metals, Ultramicroscopy 23, 345 (1987). https://doi.org/10.1016/0304-3991(87)90245-2 [Google Scholar]
  22. L.W. Hobbs, F.W. Clinard, S.J. Zinkle, R.C. Ewing, Radiation effects in ceramics, J. Nucl. Mater. 216, 291 (1994). https://doi.org/10.1016/0022-3115(94)90017-5 [Google Scholar]
  23. B. Bornes, W. Glaser, Über die Temperaturerhöhung der Objekte im Übermikroskop, Kolloid-Z. 106, 123 (1944). https://doi.org/10.1007/BF01502110 [Google Scholar]
  24. D.T. Grubb, Radiation damage and electron microscopy of organic polymers, J. Mater. Sci. 9, 1715 (1974). https://doi.org/10.1007/BF00540772 [Google Scholar]
  25. R.F. Egerton, Dose measurement in the TEM and STEM, Ultramicroscopy 229, 113363 (2021). https://doi.org/10.1016/j.ultramic.2021.113363 [Google Scholar]
  26. R. Egerton, Limits to the spatial, energy and momentum resolution of electron energy-loss spectroscopy, Ultramicroscopy 107, 575 (2007). https://doi.org/10.1016/j.ultramic.2006.11.005 [Google Scholar]
  27. P. Rez, Coherent and incoherent imaging of biological specimens with electrons and X-rays, Ultramicroscopy 231, 113301 (2021). https://doi.org/10.1016/j.ultramic.2021.113301 [Google Scholar]
  28. G. McMullan, D. Cattermole, S. Chen, R. Henderson, X. Llopart, C. Summerfield, L. Tlustos, A. Faruqi, Electron imaging with Medipix2 hybrid pixel detector, Ultramicroscopy 107, 401 (2007). https://doi.org/10.1016/j.ultramic.2006.10.005 [Google Scholar]
  29. X. Llopart, R. Ballabriga, M. Campbell, L. Tlustos, W. Wong, Timepix, a 65k programmable pixel readout chip for arrival time, energy and/or photon counting measurements, Nucl. Instrum. Methods Phys. Res. A 581, 485 (2007). https://doi.org/10.1016/j.nima.2007.08.079 [Google Scholar]
  30. R. Ballabriga, M. Campbell, E. Heijne, X. Llopart, L. Tlustos, W. Wong, Medipix3: A 64k pixel detector readout chip working in single photon counting mode with improved spectrometric performance, Nucl. Instrum. Methods Phys. Res. A 633, S15 (2011). https://doi.org/10.1016/j.nima.2010.06.108 [Google Scholar]
  31. R. Plackett, I. Horswell, E.N. Gimenez, J. Marchal, D. Omar, N. Tartoni, Merlin: a fast versatile readout system for Medipix3, JINST 8, C01038 (2013). https://doi.org/10.1088/1748-0221/8/01/C01038 [Google Scholar]
  32. T. Poikela, J. Plosila, T. Westerlund, M. Campbell, M.D. Gaspari, X. Llopart, V. Gromov, R. Kluit, M.V. Beuzekom, F. Zappon, V. Zivkovic, C. Brezina, K. Desch, Y. Fu, A. Kruth, Timepix3: a 65K channel hybrid pixel readout chip with simultaneous ToA/ToT and sparse readout, JINST 9, C05013 (2014). https://doi.org/10.1088/1748-0221/9/05/C05013 [CrossRef] [Google Scholar]
  33. H. Ryll, M. Simson, R. Hartmann, P. Holl, M. Huth, S. Ihle, Y. Kondo, P. Kotula, A. Liebel, K. Müller-Caspary, A. Rosenauer, R. Sagawa, J. Schmidt, H. Soltau, L. Strüder, A pnCCD-based, fast direct single electron imaging camera for TEM and STEM, JINST 11, P04006 (2016). https://doi.org/10.1088/1748-0221/11/04/P04006 [Google Scholar]
  34. 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, D.C. Ralph, G.D. Fuchs, K.S. Shanks, H.T. Philipp, D.A. Muller, S.M. Gruner, High dynamic range pixel array detector for scanning transmission electron microscopy, Microsc. Microanal. 22, 237 (2016). https://doi.org/10.1017/S1431927615015664 [CrossRef] [PubMed] [Google Scholar]
  35. H.T. Philipp, M.W. Tate, K.S. Shanks, L. Mele, M. Peemen, P. Dona, R. Hartong, G. van Veen, Y.-T. Shao, Z. Chen, J. Thom-Levy, D.A. Muller, S.M. Gruner, Very-high dynamic range, 10,000 frames/second pixel array detector for electron microscopy, Microsc. Microanal. 28, 425 (2022). https://doi.org/10.1017/S1431927622000174 [Google Scholar]
  36. X. Llopart, J. Alozy, R. Ballabriga, M. Campbell, R. Casanova, V. Gromov, E. Heijne, T. Poikela, E. Santin, V. Sriskaran, L. Tlustos, A. Vitkovskiy, Timepix4, a large area pixel detector readout chip which can be tiled on 4 sides providing sub-200 ps timestamp binning, JINST 17, C01044 (2022). https://doi.org/10.1088/1748-0221/17/01/C01044 [Google Scholar]
  37. P. Zambon, S. Bottinelli, R. Schnyder, D. Musarra, D. Boye, A. Dudina, N. Lehmann, S. De Carlo, M. Rissi, C. Schulze-Briese, M. Meffert, M. Campanini, R. Erni, L. Piazza, KITE: High frame rate, high count rate pixelated electron counting ASIC for 4D STEM applications featuring high-Z sensor, Nucl. Instrum. Methods Phys. Res. A 1048, 167888 (2023). https://doi.org/10.1016/j.nima.2022.167888 [Google Scholar]
  38. P. Ercius, I.J. Johnson, P. Pelz, B.H. Savitzky, L. Hughes, H.G. Brown, S.E. Zeltmann, S.-L. Hsu, C.C.S. Pedroso, B.E. Cohen, R. Ramesh, D. Paul, J.M. Joseph, T. Stezelberger, C. Czarnik, M. Lent, E. Fong, J. Ciston, M.C. Scott, C. Ophus, A.M. Minor, P. Denes, The 4D Camera: An 87 kHz direct electron detector for scanning/transmission electron microscopy, Microsc. Microanal. 30, 903 (2024) https://doi.org/10.1093/mam/ozae086 [Google Scholar]
  39. R.S. Ruskin, Z. Yu, N. Grigorieff, Quantitative characterization of electron detectors for transmission electron microscopy, J. Struct. Biol. 184, 385 (2013). https://doi.org/10.1016/j.jsb.2013.10.016 [Google Scholar]
  40. A.-C. Milazzo, G. Moldovan, J. Lanman, L. Jin, J.C. Bouwer, S. Klienfelder, S.T. Peltier, M.H. Ellisman, A.I. Kirkland, N.-H. Xuong, Characterization of a direct detection device imaging camera for transmission electron microscopy, Ultramicroscopy 110, 741 (2010). https://doi.org/10.1016/j.ultramic.2010.03.007 [Google Scholar]
  41. J.A. Mir, R. Clough, R. MacInnes, C. Gough, R. Plackett, I. Shipsey, H. Sawada, I. MacLaren, R. Ballabriga, D. Maneuski, V. O'Shea, D. McGrouther, A.I. Kirkland, Characterisation of the Medipix3 detector for 60 and 80 keV electrons, Ultramicroscopy 182, 44 (2017). https://doi.org/10.1016/j.ultramic.2017.06.010 [Google Scholar]
  42. K.A. Paton, M.C. Veale, X. Mu, C.S. Allen, D. Maneuski, C. Kübel, V. O'Shea, A.I. Kirkland, D. McGrouther, Quantifying the performance of a hybrid pixel detector with GaAs:Cr sensor for transmission electron microscopy, Ultramicroscopy 227, 113298 (2021). https://doi.org/10.1016/j.ultramic.2021.113298 [Google Scholar]
  43. K. Müller, H. Ryll, I. Ordavo, S. Ihle, L. Strüder, K. Volz, J. Zweck, H. Soltau, A. Rosenauer, Scanning transmission electron microscopy strain measurement from millisecond frames of a direct electron charge coupled device, Appl. Phys. Lett. 101, 212110 (2012). https://doi.org/10.1063/1.4767655 [Google Scholar]
  44. K. Müller-Caspary, F.F. Krause, F. Winkler, A. Béché, J. Verbeeck, S. Van Aert, A. Rosenauer, S. VanAert, A. Rosenauer, Comparison of first moment STEM with conventional differential phase contrast and the dependence on electron dose, Ultramicroscopy 203, 95 (2018) in print. https://doi.org/10.1016/j.ultramic.2018.12.018 [Google Scholar]
  45. H. Yang, L. Jones, H. Ryll, M. Simson, H. Soltau, Y. Kondo, R. Sagawa, H. Banba, I. MacLaren, P.D. Nellist, 4D STEM: High efficiency phase contrast imaging using a fast pixelated detector, J. Phys.: Conf. Ser. 644, 12032 (2015). https://doi.org/10.1088/1742-6596/644/1/012032 [Google Scholar]
  46. G. Fan, P. Datte, E. Beuville, J.-F. Beche, J. Millaud, K. Downing, F. Burkard, M. Ellisman, N.-H. Xuong, ASIC-based event-driven 2D digital electron counter for TEM imaging, Ultramicroscopy 70, 107 (1998). https://doi.org/10.1016/S0304-3991(97)00109-5 [Google Scholar]
  47. E. Frojdh, M. Campbell, M.D. Gaspari, S. Kulis, X. Llopart, T. Poikela, L. Tlustos, Timepix3: first measurements and characterization of a hybrid-pixel detector working in event driven mode, JINST 10, C01039 (2015). https://doi.org/10.1088/1748-0221/10/01/C01039 [Google Scholar]
  48. D. Jannis, C. Hofer, C. Gao, X. Xie, A. Béché, T. Pennycook, J. Verbeeck, Event driven 4D STEM acquisition with a Timepix3 detector: Microsecond dwell time and faster scans for high precision and low dose applications, Ultramicroscopy 233, 113423 (2022). https://doi.org/10.1016/j.ultramic.2021.113423 [Google Scholar]
  49. Y. Auad, J. Baaboura, J.D. Blazit, M. Tencé, O. Stéphan, M. Kociak, L.H. Tizei, Time calibration studies for the Timepix3 hybrid pixel detector in electron microscopy, Ultramicroscopy 257, 113889 (2024). https://doi.org/10.1016/j.ultramic.2023.113889 [Google Scholar]
  50. J. Kuttruff, J. Holder, Y. Meng, P. Baum, Real-time electron clustering in an event-driven hybrid pixel detector, Ultramicroscopy 255, 113864 (2024). https://doi.org/10.1016/j.ultramic.2023.113864 [Google Scholar]
  51. W. Hoppe, Beugung im inhomogenen Primärstrahlwellenfeld. I. Prinzip einer Phasenmessung von Elektronenbeungungsinterferenzen, Acta Crystallogr. A 25, 495 (1969). https://doi.org/10.1107/S0567739469001045 [Google Scholar]
  52. W. Hoppe, G. Strube, Beugung in inhomogenen Primärstrahlenwellenfeld. II. Lichtoptische Analogieversuche zur Phasenmessung von Gitterinterferenzen, Acta Crystallogr. A 25, 502 (1969). https://doi.org/10.1107/S0567739469001057 [Google Scholar]
  53. W. Hoppe, Beugung im inhomogenen Primärstrahlwellenfeld. III. Amplituden- und Phasenbestimmung bei unperiodischen Objekten, Acta Crystallogr. A 25, 508 (1969). https://doi.org/10.1107/S0567739469001069 [Google Scholar]
  54. A. Drenth, A. Huiser, H. Ferwerda, The problem of phase retrieval in light and electron microscopy of strong objects, Optica Acta 22, 615 (1975). https://doi.org/10.1080/713819083 [Google Scholar]
  55. J.R. Fienup, Reconstruction of an object from the modulus of its Fourier transform, Opt. Lett. 3, 27 (1978). https://doi.org/10.1364/OL.3.000027 [NASA ADS] [CrossRef] [Google Scholar]
  56. J. Miao, D. Sayre, H.N. Chapman, Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects, J. Opt. Soc. Am. A 15, 1662 (1998). https://doi.org/10.1364/JOSAA.15.001662 [NASA ADS] [CrossRef] [Google Scholar]
  57. J. Miao, P. Charalambous, J. Kirz, D. Sayre, Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens, Nature 400, 342 (1999). https://doi.org/10.1038/22498 [Google Scholar]
  58. U. Weierstall, Q. Chen, J. Spence, M. Howells, M. Isaacson, R. Panepucci, Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation, Ultramicroscopy 90, 171 (2002). https://doi.org/10.1016/S0304-3991(01)00134-6 [Google Scholar]
  59. G.J. Williams, H.M. Quiney, B.B. Dhal, C.Q. Tran, K.A. Nugent, A.G. Peele, D. Paterson, M.D. de Jonge, Fresnel coherent diffractive imaging, Phys. Rev. Lett. 97, 025506 (2006). https://doi.org/10.1103/PhysRevLett.97.025506 [Google Scholar]
  60. J.R. Fienup, Phase retrieval algorithms: a comparison, Appl. Opt. 21, 2758 (1982). https://doi.org/10.1364/AO.21.002758 [NASA ADS] [CrossRef] [Google Scholar]
  61. P.M. Pelz, W.X. Qiu, R. Bücker, G. Kassier, R.J. Miller, Low-dose cryo electron ptychography via non-convex Bayesian optimization, Sci. Rep. 7, 1 (2017). https://doi.org/10.1038/s41598-017-07488-y [CrossRef] [Google Scholar]
  62. X. Pei, L. Zhou, C. Huang, M. Boyce, J.S. Kim, E. Liberti, Y. Hu, T. Sasaki, P.D. Nellist, P. Zhang, D.I. Stuart, A.I. Kirkland, P. Wang, Cryogenic electron ptychographic single particle analysis with wide bandwidth information transfer, Nat. Commun. 14, 3027 (2023). https://doi.org/10.1038/s41467-023-38268-0 [Google Scholar]
  63. B. Küçükoğlu, I. Mohammed, R.C. Guerrero-Ferreira, S.M. Ribet, G. Varnavides, M.L. Leidl, K. Lau, S. Nazarov, A. Myasnikov, M. Kube, J. Radecke, C. Sachse, K. Müller-Caspary, C. Ophus, H. Stahlberg, Low-dose cryo-electron ptychography of proteins at sub-nanometer resolution, Nat. Commun. 15, 8062 (2024). https://doi.org/10.1038/s41467-024-52403-5 [Google Scholar]
  64. W. Mao, W. Zhang, C. Huang, L. Zhou, J.S. Kim, S. Gao, Y. Lei, X. Wu, Y. Hu, X. Pei, W. Fang, X. Liu, J. Song, C. Fan, Y. Nie, A.I. Kirkland, P. Wang, Multi-Convergence-Angle Ptychography with Simultaneous Strong Contrast and High Resolution (2024) arXiv:2403.16902. https://doi.org/10.48550/arXiv.2403.16902 [Google Scholar]
  65. V. Elser, Phase retrieval by iterated projections, J. Opt. Soc. Am. A 20, 40 (2003). https://doi.org/10.1364/JOSAA.20.000040 [Google Scholar]
  66. H.M. Faulkner, J.M. Rodenburg, Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm, Phys. Rev. Lett. 93, 2 (2004). https://doi.org/10.1103/PhysRevLett.93.023903 [Google Scholar]
  67. J.M. Rodenburg, H.M. Faulkner, A phase retrieval algorithm for shifting illumination, Appl. Phys. Lett. 85, 4795 (2004). https://doi.org/10.1063/1.1823034 [Google Scholar]
  68. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, High-resolution scanning X-ray diffraction microscopy, Science 321, 379 (2008). https://doi.org/10.1126/science.1158573 [Google Scholar]
  69. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, F. Pfeiffer, Probe retrieval in ptychographic coherent diffractive imaging, Ultramicroscopy 109, 338 (2009). https://doi.org/10.1016/j.ultramic.2008.12.011 [Google Scholar]
  70. A.M. Maiden, J.M. Rodenburg, An improved ptychographical phase retrieval algorithm for diffractive imaging, Ultramicroscopy 109, 1256 (2009). https://doi.org/10.1016/j.ultramic.2009.05.012 [Google Scholar]
  71. A. Maiden, D. Johnson, P. Li, Further improvements to the ptychographical iterative engine, Optica 4, 736 (2017). https://doi.org/10.1364/optica.4.000736 [Google Scholar]
  72. A. Maiden, W. Mei, P. Li, WASP: Weighted Average of Sequential Projections for ptychographic phase retrieval, Optics Express 32, 21327 (2024). https://doi.org/10.1364/oe.516946 [Google Scholar]
  73. R. Gerchberg, W. Saxton, Optik 35, 237 (1972). http://ci.nii.ac.jp/naid/10010556614/ [Google Scholar]
  74. R. Gerchberg, Super-resolution through error energy reduction, Optica Acta 21, 709 (1974). https://doi.org/10.1080/713818946 [Google Scholar]
  75. M. Guizar-Sicairos, J.R. Fienup, Phase retrieval with transverse translation diversity: a nonlinear optimization approach, Opt. Express 16, 7264 (2008). https://doi.org/10.1364/oe.16.007264 [Google Scholar]
  76. P. Godard, M. Allain, V. Chamard, J. Rodenburg, Noise models for low counting rate coherent diffraction imaging, Opt. Express 20, 25914 (2012). https://doi.org/10.1364/OE.20.025914 [Google Scholar]
  77. L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, Q. Dai, Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient, Sci. Rep. 6, 1 (2016). https://doi.org/10.1038/srep27384 [CrossRef] [Google Scholar]
  78. M. Odstrčil, A. Menzel, M. Guizar-Sicairos, Iterative least-squares solver for generalized maximum-likelihood ptychography, Opt. Express 26, 3108 (2018). https://doi.org/10.1364/oe.26.003108 [Google Scholar]
  79. P. Thibault, M. Guizar-Sicairos, Maximum-likelihood refinement for coherent diffractive imaging, New J. Phys. 14, 1 (2012). https://doi.org/10.1088/1367-2630/14/6/063004 [Google Scholar]
  80. M. Pham, P. Yin, A. Rana, S. Osher, J. Miao, Generalized proximal smoothing (GPS) for phase retrieval, Opt. Express 27, 2792 (2019). https://doi.org/10.1364/OE.27.002792 [Google Scholar]
  81. M. Schloz, T.C. Pekin, Z. Chen, W. Van den Broek, D.A. Muller, C.T. Koch, Overcoming information reduced data and experimentally uncertain parameters in ptychography with regularized optimization, Opt. Express 28, 28306 (2020). https://doi.org/10.1364/oe.396925 [Google Scholar]
  82. K.C. Lee, H. Chae, S. Xu, K. Lee, R. Horstmeyer, S.A. Lee, B.-W. Hong, Anisotropic regularization for sparsely sampled and noise-robust Fourier ptychography, Opt. Express 32, 25343 (2024). https://doi.org/10.1364/OE.529023 [Google Scholar]
  83. Z. Herdegen, B. Diederichs, K. Müller-Caspary, Thermal vibrations in the inversion of dynamical electron scattering, Phys. Rev. B 110, 064102 (2024). https://doi.org/10.1103/PhysRevB.110.064102 [Google Scholar]
  84. B. Diederichs, Z. Herdegen, A. Strauch, F. Filbir, K. Müller-Caspary, Exact inversion of partially coherent dynamical electron scattering for picometric structure retrieval, Nat. Commun. 15 (2024). https://doi.org/10.1038/s41467-023-44268-x [Google Scholar]
  85. W. Yang, H. Sha, J. Cui, L. Mao, R. Yu, Local-orbital ptychography for ultrahigh-resolution imaging, Nat. Nanotechnol. 19, 612 (2024). https://doi.org/10.1038/s41565-023-01595-w [Google Scholar]
  86. W. Yang, H. Sha, J. Cui, R. Yu, Imaging thick objects with deep-sub-angstrom resolution and deep-sub-picometer precision (2025) arXiv:2502.18294. https://doi.org/10.48550/arXiv.2502.18294 [Google Scholar]
  87. H. Chang, P. Enfedaque, J. Zhang, J. Reinhardt, B. Enders, Y.-S. Yu, D. Shapiro, C.G. Schroer, T. Zeng, S. Marchesini, Advanced denoising for X-ray ptychography, Opt. Express 27, 10395 (2019). https://doi.org/10.1364/OE.27.010395 [Google Scholar]
  88. M.L. Leidl, B. Diederichs, C. Sachse, K. Müller-Caspary, Influence of loss function and electron dose on ptychography of 2D materials using the Wirtinger flow, Micron 185, 103688 (2024). https://doi.org/10.1016/j.micron.2024.103688 [Google Scholar]
  89. J. Seifert, Y. Shao, R. van Dam, D. Bouchet, T. van Leeuwen, A.P. Mosk, Maximum-likelihood estimation in ptychography in the presence of Poisson-Gaussian noise statistics, Opt. Lett. 48, 6027 (2023). https://doi.org/10.1364/OL.502344 [Google Scholar]
  90. O. Melnyk, Convergence properties of gradient methods for blind ptychography (2023) arXiv:2306.08750. https://doi.org/10.48550/arXiv.2306.08750 [Google Scholar]
  91. V. Katkovnik, J. Astola, Sparse ptychographical coherent diffractive imaging from noisy measurements, J. Optical Soc. Am. A 30, 367 (2013). https://doi.org/10.1364/JOSAA.30.000367 [Google Scholar]
  92. S. Marchesini, H. Krishnan, B.J. Daurer, D.A. Shapiro, T. Perciano, J.A. Sethian, F.R. Maia, SHARP: a distributed GPU-based ptychographic solver, J. Appl. Crystallogr. 49, 1245 (2016). https://doi.org/10.1107/S1600576716008074 [Google Scholar]
  93. X. Yu, V. Nikitin, D.J. Ching, S. Aslan, D. Gürsoy, T. Biçer, Scalable and accurate multi-GPU-based image reconstruction of large-scale ptychography data, Sci. Rep. 12, 1 (2022). https://doi.org/10.1038/s41598-022-09430-3 [CrossRef] [Google Scholar]
  94. X. Wang, A. Tsaris, D. Mukherjee, M. Wahib, P. Chen, M. Oxley, O. Ovchinnikova, J. Hinkle, Image gradient decomposition for parallel and memory-efficient ptychographic reconstruction, in SC22: International Conference for High Performance Computing, Networking, Storage and Analysis (IEEE, 2022) Vol. 2022-Novem, pp. 1–13. arXiv:2205.06327. https://doi.org/10.1109/SC41404.2022.00013 [Google Scholar]
  95. D. Mukherjee, K.M. Roccapriore, A. Al-Najjar, A. Ghosh, J.D. Hinkle, A.R. Lupini, R.K. Vasudevan, S.V. Kalinin, O.S. Ovchinnikova, M.A. Ziatdinov, N.S. Rao, A roadmap for edge computing enabled automated multidimensional transmission electron microscopy, Microscopy Today 30, 10 (2022). https://doi.org/10.1017/S1551929522001286 [Google Scholar]
  96. S.S. Welborn, C. Harris, S.M. Ribet, G. Varnavides, C. Ophus, B. Enders, P. Ercius, Streaming large-scale microscopy data to a supercomputing facility (2024) arXiv:2407.03215. https://doi.org/10.48550/arXiv.2407.03215 [Google Scholar]
  97. R. Bates, J. Rodenburg, Sub-ångström transmission microscopy: A fourier transform algorithm for microdiffraction plane intensity information, Ultramicroscopy 31, 303 (1989). https://doi.org/10.1016/0304-3991(89)90052-1 [Google Scholar]
  98. J.M. Rodenburg, R.H.T. Bates, The theory of super-resolution electron microscopy via Wigner-distribution deconvolution, Philos. Trans. R. Soc. Lond. A 339, 521 (1992). https://doi.org/10.1098/rsta.1992.0050 [Google Scholar]
  99. J. Rodenburg, B. McCallum, P. Nellist, Experimental tests on double-resolution coherent imaging via STEM, Ultramicroscopy 48, 304 (1993). https://doi.org/10.1016/0304-3991(93)90105-7 [Google Scholar]
  100. A. Strauch, D. Weber, A. Clausen, A. Lesnichaia, A. Bangun, B. März, F.J. Lyu, Q. Chen, A. Rosenauer, R. Dunin-Borkowski, K. Müller-Caspary, Live processing of momentum-resolved STEM data for first moment imaging and ptychography, Microsc. Microanal. 27, 1078 (2021). https://doi.org/10.1017/S1431927621012423 [Google Scholar]
  101. A. Bangun, P.F. Baumeister, A. Clausen, D. Weber, R.E. Dunin-Borkowski, Wigner distribution deconvolution adaptation for live ptychography reconstruction, Microsc. Microanal. 29, 994 (2023). https://doi.org/10.1093/micmic/ozad021 [Google Scholar]
  102. D. Weber, S. Ehrig, A. Schropp, A. Clausen, S. Achilles, N. Hoffmann, M. Bussmann, R.E. Dunin-Borkowski, C.G. Schroer, Live Iterative Ptychography, Microsc. Microanal. 30, 103 (2024). https://doi.org/10.1093/mam/ozae004 [Google Scholar]
  103. T.J. Pennycook, A.R. Lupini, H. Yang, M.F. Murfitt, L. Jones, P.D. Nellist, Efficient phase contrast imaging in STEM using a pixelated detector. Part 1: Experimental demonstration at atomic resolution, Ultramicroscopy 151, 160 (2015). https://doi.org/10.1016/j.ultramic.2014.09.013 [Google Scholar]
  104. H. Yang, T.J. Pennycook, P.D. Nellist, Efficient phase contrast imaging in STEM using a pixelated detector. Part II: Optimisation of imaging conditions, Ultramicroscopy 151, 232 (2015). https://doi.org/10.1016/j.ultramic.2014.10.013 [Google Scholar]
  105. C.M. O'Leary, C.S. Allen, C. Huang, J.S. Kim, E. Liberti, P.D. Nellist, A.I. Kirkland, Phase reconstruction using fast binary 4D STEM data, Appl. Phys. Lett. 116, 124101 (2020). https://doi.org/10.1063/1.5143213 [Google Scholar]
  106. C.M. O'Leary, G.T. Martinez, E. Liberti, M.J. Humphry, A.I. Kirkland, P.D. Nellist, Contrast transfer and noise considerations in focused-probe electron ptychography, Ultramicroscopy 221, 113189 (2021). https://doi.org/10.1016/j.ultramic.2020.113189 [Google Scholar]
  107. H. Yang, R.N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T.J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B.G. Davis, P.D. Nellist, Simultaneous atomic-resolution electron ptychography and Z-contrast imaging of light and heavy elements in complex nanostructures, Nat. Commun. 7, 1 (2016). https://doi.org/10.1038/ncomms12532 [CrossRef] [Google Scholar]
  108. H. Yang, I. MacLaren, L. Jones, G.T. Martinez, M. Simson, M. Huth, H. Ryll, H. Soltau, R. Sagawa, Y. Kondo, C. Ophus, P. Ercius, L. Jin, A. Kovács, P.D. Nellist, Electron ptychographic phase imaging of light elements in crystalline materials using Wigner distribution deconvolution, Ultramicroscopy 180, 173 (2017). https://doi.org/10.1016/j.ultramic.2017.02.006 [Google Scholar]
  109. P. Wang, F. Zhang, S. Gao, M. Zhang, A.I. Kirkland, Electron ptychographic diffractive imaging of boron atoms in LaB 6 crystals, Sci. Rep. 7, 1 (2017). https://doi.org/10.1038/s41598-017-02778-x [CrossRef] [Google Scholar]
  110. M.L. Leidl, C. Sachse, K. Müller-Caspary, Dynamical scattering in ice-embedded proteins in conventional and scanning transmission electron microscopy, IUCrJ 10, 867 (2023). https://doi.org/10.1107/S2052252523004505 [Google Scholar]
  111. B. McCallum, J. Rodenburg, Two-dimensional demonstration of Wigner phase-retrieval microscopy in the STEM configuration, Ultramicroscopy 45, 371 (1992). https://doi.org/10.1016/0304-3991(92)90149-E [Google Scholar]
  112. P. Nellist, J. Rodenburg, Beyond the conventional information limit: the relevant coherence function, Ultramicroscopy 54, 61 (1994). https://doi.org/10.1016/0304-3991(94)90092-2 [Google Scholar]
  113. P. Li, T.B. Edo, J.M. Rodenburg, Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design, Ultramicroscopy 147, 106 (2014). https://doi.org/10.1016/j.ultramic.2014.07.004 [Google Scholar]
  114. K. Müller, F.F. Krause, A. Béché, M. Schowalter, V. Galioit, S. Löffler, J. Verbeeck, J. Zweck, P. Schattschneider, A. Rosenauer, Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction, Nat. Commun. 5, 5653 (2014). https://doi.org/10.1038/ncomms6653 [Google Scholar]
  115. I. Lazić, E.G.T. Bosch, S. Lazar, Phase contrast {STEM} for thin samples: Integrated differential phase contrast, Ultramicroscopy 160, 265 (2016). https://doi.org/10.1016/j.ultramic.2015.10.011 [Google Scholar]
  116. H. Yang, P. Ercius, P.D. Nellist, C. Ophus, Enhanced phase contrast transfer using ptychography combined with a pre-specimen phase plate in a scanning transmission electron microscope, Ultramicroscopy 171, 117 (2016). https://doi.org/10.1016/j.ultramic.2016.09.002 [Google Scholar]
  117. F. Hüe, J.M. Rodenburg, A.M. Maiden, F. Sweeney, P.A. Midgley, Wave-front phase retrieval in transmission electron microscopy via ptychography, Phys. Rev. B 82, 1 (2010). https://doi.org/10.1103/PhysRevB.82.121415 [CrossRef] [Google Scholar]
  118. J. Song, C.S. Allen, S. Gao, C. Huang, H. Sawada, X. Pan, J. Warner, P. Wang, A.I. Kirkland, Atomic resolution defocused electron ptychography at low dose with a fast, direct electron detector, Sci. Rep. 9, 3919 (2019). https://doi.org/10.1038/s41598-019-40413-z [Google Scholar]
  119. D.J. Vine, G.J. Williams, B. Abbey, M.A. Pfeifer, J.N. Clark, M.D. de Jonge, I. McNulty, A.G. Peele, K.A. Nugent, Ptychographic Fresnel coherent diffractive imaging, Phys. Rev. A 80, 063823 (2009). https://doi.org/10.1103/PhysRevA.80.063823 [Google Scholar]
  120. J.M. Cowley, I. Sumio, S. Iijima, Electron microscope image contrast for thin crystal, Z. Naturforsch. A 27, 445 (1972). https://doi.org/10.1515/zna-1972-0312 [Google Scholar]
  121. K. van Benthem, A.R. Lupini, M. Kim, H.S. Baik, S. Doh, J.-H. Lee, M.P. Oxley, S.D. Findlay, L.J. Allen, J.T. Luck, S.J. Pennycook, Three-dimensional imaging of individual hafnium atoms inside a semiconductor device, Appl. Phys. Lett. 87, 034104 (2005). https://doi.org/10.1063/1.1991989 [Google Scholar]
  122. K. van Benthem, A.R. Lupini, M.P. Oxley, S.D. Findlay, L.J. Allen, S.J. Pennycook, Three-dimensional ADF imaging of individual atoms by through-focal series scanning transmission electron microscopy, Ultramicroscopy 106, 1062 (2006). https://doi.org/10.1016/j.ultramic.2006.04.020 [Google Scholar]
  123. D. Van Dyck, M. Op de Beeck, A simple intuitive theory for electron diffraction, Ultramicroscopy 64, 99 (1996). https://doi.org/10.1016/0304-3991(96)00008-3 [Google Scholar]
  124. C.J. Humphreys, P.B. Hirsch, Absorption parameters in electron diffraction theory, Philos. Mag. 18, 115 (1968). https://doi.org/10.1080/14786436808227313 [Google Scholar]
  125. H. Yoshioka, Effect of inelastic waves on electron diffraction, J. Phys. Soc. Jpn. 12, 618 (1957). https://doi.org/10.1143/JPSJ.12.618 [Google Scholar]
  126. Z.L. Wang, W.D. Mo, The “ Optical potential ” and multiple diffuse scattering in dynamical electron diffraction and imaging, Scanning Microsc. 12, 91 (1998) [Google Scholar]
  127. K.A. Mkhoyan, S.E. MacCagnano-Zacher, M.G. Thomas, J. Silcox, Critical role of inelastic interactions in quantitative electron microscopy, Phys. Rev. Lett. 100, 1 (2008). https://doi.org/10.1103/PhysRevLett.100.025503 [Google Scholar]
  128. A. Beyer, F.F. Krause, H.L. Robert, S. Firoozabadi, T. Grieb, P. Kükelhan, D. Heimes, M. Schowalter, K. Müller-Caspary, A. Rosenauer, K. Volz, Influence of plasmon excitations on atomic-resolution quantitative 4D scanning transmission electron microscopy, Sci. Rep. 10, 17890 (2020). https://doi.org/10.1038/s41598-020-74434-w [Google Scholar]
  129. J. Barthel, M. Cattaneo, B.G. Mendis, S.D. Findlay, L.J. Allen, Angular dependence of fast-electron scattering from materials, Phys. Rev. B 101, 1 (2020). https://doi.org/10.1103/PhysRevB.101.184109 [Google Scholar]
  130. H.L. Robert, B. Diederichs, K. Müller-Caspary, Contribution of multiple plasmon scattering in low-angle electron diffraction investigated by energy-filtered atomically resolved 4D-STEM, Appl. Phys. Lett. 121, 213502 (2022). https://doi.org/10.1063/5.0129692 [Google Scholar]
  131. C.R. Hall, The scattering of high energy electrons by the thermal vibrations of crystals, Philos. Mag. 12, 815 (1965). https://doi.org/10.1080/14786436508218919 [Google Scholar]
  132. C.R. Hall, P.B. Hirsch, Effect of thermal diffuse scattering on propagation of high energy electrons through crystals, Proc. R. Soc. Lond. A 286, 158 (1965). https://doi.org/10.1098/rspa.1965.0136 [Google Scholar]
  133. D. Van Dyck, Is the frozen phonon model adequate to describe inelastic phonon scattering? Ultramicroscopy 109, 677 (2009). https://doi.org/10.1016/j.ultramic.2009.01.001 [Google Scholar]
  134. K. Fujiwara, Relativistic dynamical theory of electron diffraction, J. Phys. Soc. Jpn. 16, 2226 (1961). https://doi.org/10.1143/JPSJ.16.2226 [Google Scholar]
  135. O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, Influence of the overlap parameter on the convergence of the ptychographical iterative engine, Ultramicroscopy 108, 481 (2008). https://doi.org/10.1016/j.ultramic.2007.08.003 [Google Scholar]
  136. J.M. Cowley, Image contrast in a transmission scanning electron microscope, Appl. Phys. Lett. 15, 58 (1969). https://doi.org/10.1063/1.1652901 [Google Scholar]
  137. F.F. Krause, A. Rosenauer, Reciprocity relations in transmission electron microscopy: a rigorous derivation, Micron 92, 1 (2017). https://doi.org/10.1016/j.micron.2016.09.007 [Google Scholar]
  138. E. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40, 749 (1932). https://doi.org/10.1103/PhysRev.40.749 [CrossRef] [Google Scholar]
  139. R.T. Bates, M.J. McDonnell, Image restoration and reconstruction (Oxford University Press, Inc., 1986) [Google Scholar]
  140. G. Möllenstedt, H. Düker, Fresnelscher Interferenzversuch mit einem Biprisma für Elektronenwellen, Naturwissenschaften 42, 41 (1955) [Google Scholar]
  141. A. Tonomura, T. Matsuda, T. Komoda, Two beam interference with field emission electron beam, Jpn. J. Appl. Phys. 17, 1137 (1978). https://doi.org/10.1143/JJAP.17.1137 [Google Scholar]
  142. F. Winkler, J. Barthel, R.E. Dunin-Borkowski, K. Müller-Caspary, Direct measurement of electrostatic potentials at the atomic scale: a conceptual comparison between electron holography and scanning transmission electron microscopy, Ultramicroscopy 210, 112926 (2020). https://doi.org/10.1016/j.ultramic.2019.112926 [Google Scholar]
  143. D. Sayre, Some implications of a theorem due to Shannon, Acta Crystallogr. 5, 843 (1952). https://doi.org/10.1107/S0365110X52002276 [Google Scholar]
  144. P.D. Nellist, B.C. McCallum, J.M. Rodenburg, Resolution beyond the 'information limit' in transmission electron microscopy, Nature 374, 630 (1995). https://doi.org/10.1038/374630a0 [Google Scholar]
  145. A.M. Maiden, M.J. Humphry, F. Zhang, J.M. Rodenburg, Superresolution imaging via ptychography, J. Opt. Soc. Am. A 28, 604 (2011). https://doi.org/10.1364/josaa.28.000604 [NASA ADS] [CrossRef] [Google Scholar]
  146. M. Humphry, B. Kraus, A. Hurst, A. Maiden, J. Rodenburg, Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging, Nat. Commun. 3, 730 (2012). https://doi.org/10.1038/ncomms1733 [Google Scholar]
  147. Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M.W. Tate, J. Park, S.M. Gruner, V. Elser, D.A. Muller, Electron ptychography of 2D materials to deep sub-ångström resolution, Nature 559, 343 (2018). https://doi.org/10.1038/s41586-018-0298-5 [Google Scholar]
  148. S. Li, N. Gauquelin, H.L. Lalandec Robert, A. Annys, C. Gao, C. Hofer, T.J. Pennycook, J. Verbeeck, Improving the low-dose performance of aberration correction in single sideband ptychography (2025). arXiv:2505.09555 [Google Scholar]
  149. T. Seki, Y. Ikuhara, N. Shibata, Theoretical framework of statistical noise in scanning transmission electron microscopy, Ultramicroscopy 193, 118 (2018). https://doi.org/10.1016/j.ultramic.2018.06.014 [Google Scholar]
  150. J. Luczka, M. Niemiec, A master equation for quantum systems driven by Poisson white noise, J. Phys. A: Math. Gen. 24, L1021 (1991). https://doi.org/10.1088/0305-4470/24/17/010 [Google Scholar]
  151. L. Clark, G.T. Martinez, C.M. O'Leary, H. Yang, Z. Ding, T.C. Petersen, S.D. Findlay, P.D. Nellist, The effect of dynamical scattering on single-plane phase retrieval in electron ptychography, Microsc. Microanal. 29, 384 (2023). https://doi.org/10.1093/micmic/ozac022 [CrossRef] [PubMed] [Google Scholar]
  152. C. Hofer, T.J. Pennycook, Reliable phase quantification in focused probe electron ptychography of thin materials, Ultramicroscopy 254, 113829 (2023). https://doi.org/10.1016/j.ultramic.2023.113829 [Google Scholar]
  153. J. Verbeeck, A. Béché, K. Müller-Caspary, G. Guzzinati, M.A. Luong, M. Den Hertog, Demonstration of a 2 × 2 programmable phase plate for electrons, Ultramicroscopy 190, 58 (2018). https://doi.org/10.1016/j.ultramic.2018.03.017 [Google Scholar]
  154. F. Vega Ibáñez, A. Béché, J. Verbeeck, Can a programmable phase plate serve as an aberration corrector in the transmission electron microscope (TEM)? Microsc. Microanal. 29, 341 (2023). https://doi.org/10.1017/S1431927622012260 [Google Scholar]
  155. C.-P. Yu, F. Vega Ibañez, A. Béché, J. Verbeeck, Quantum wavefront shaping with a 48-element programmable phase plate for electrons, SciPost Phys. 15, 223 (2023). https://doi.org/10.21468/SciPostPhys.15.6.223 [CrossRef] [Google Scholar]
  156. N. Shibata, Y. Kohno, S.D. Findlay, H. Sawada, Y. Kondo, Y. Ikuhara, New area detector for atomic-resolution scanning transmission electron microscopy, J. Electron Microsc. 59, 473 (2010). https://doi.org/10.1093/jmicro/dfq014 [Google Scholar]
  157. M. Lohr, R. Schregle, M. Jetter, C. Wächter, T. Wunderer, F. Scholz, J. Zweck, Differential phase contrast 2.0—Opening new “fields” for an established technique, Ultramicroscopy 117, 7 (2012). https://doi.org/10.1016/j.ultramic.2012.03.020 [Google Scholar]
  158. N.H. Dekkers, H. de Lang, Differential Phase Contrast in a STEM, Optik 41, 452 (1974) [Google Scholar]
  159. H. Rose, Nonstandard imaging methods in electron microscopy, Ultramicroscopy 2, 251 (1977). https://doi.org/10.1016/S0304-3991(76)91538-2 [Google Scholar]
  160. T. Seki, G. Sanchez-Santolino, R. Ishikawa, S.D. Findlay, Y. Ikuhara, N. Shibata, G. Sánchez-Santolino, R. Ishikawa, S.D. Findlay, Y. Ikuhara, N. Shibata, Quantitative electric field mapping in thin specimens using a segmented detector: revisiting the transfer function for differential phase contrast, Ultramicroscopy 182, 258 (2017). https://doi.org/10.1016/j.ultramic.2017.07.013 [Google Scholar]
  161. F. Schwarzhuber, P. Melzl, S. Pöllath, J. Zweck, Introducing a non-pixelated and fast centre of mass detector for differential phase contrast microscopy, Ultramicroscopy 192, 21 (2018). https://doi.org/10.1016/j.ultramic.2018.05.003 [Google Scholar]
  162. E. Yücelen, I. Lazic, E.G.T. Bosch, Phase contrast scanning transmission electron microscopy imaging of light and heavy atoms at the limit of contrast and resolution, Sci. Rep. 8, 1 (2018). https://doi.org/10.1038/s41598-018-20377-2 [Google Scholar]
  163. R. Close, Z. Chen, N. Shibata, S.D. Findlay, Towards quantitative, atomic-resolution reconstruction of the electrostatic potential via differential phase contrast using electrons, Ultramicroscopy 159, 124 (2015). https://doi.org/10.1016/j.ultramic.2015.09.002 [Google Scholar]
  164. C. Addiego, W. Gao, X. Pan, Thickness and defocus dependence of inter-atomic electric fields measured by scanning diffraction, Ultramicroscopy 208, 112850 (2020). https://doi.org/10.1016/j.ultramic.2019.112850 [Google Scholar]
  165. J. Bürger, T. Riedl, J.K. Lindner, Influence of lens aberrations, specimen thickness and tilt on differential phase contrast STEM images, Ultramicroscopy 219, 113118 (2020). https://doi.org/10.1016/j.ultramic.2020.113118 [Google Scholar]
  166. H. Robert, I. Lobato, F. Lyu, Q. Chen, S. Van Aert, D. Van Dyck, K. Müller-Caspary, Dynamical diffraction of high-energy electrons investigated by focal series momentum-resolved scanning transmission electron microscopy at atomic resolution, Ultramicroscopy 233, 113425 (2022). https://doi.org/10.1016/j.ultramic.2021.113425 [Google Scholar]
  167. Z. Liang, D. Song, B. Ge, Optimizing experimental parameters of integrated differential phase contrast (iDPC) for atomic resolution imaging, Ultramicroscopy 246, 113686 (2023). https://doi.org/10.1016/j.ultramic.2023.113686 [Google Scholar]
  168. G. Black, E.H. Linfoot, Spherical aberration and the information content of optical images, Proc. R. Soc. Lond. A 239, 522 (1957). https://doi.org/10.1098/rspa.1957.0059 [Google Scholar]
  169. C. Gao, C. Hofer, D. Jannis, A. Béché, J. Verbeeck, T.J. Pennycook, Overcoming contrast reversals in focused probe ptychography of thick materials: An optimal pipeline for efficiently determining local atomic structure in materials science, Appl. Phys. Lett. 121, 081906 (2022). https://doi.org/10.1063/5.0101895 [Google Scholar]
  170. N. Shibata, S.D. Findlay, H. Sasaki, T. Matsumoto, H. Sawada, Y. Kohno, S. Otomo, R. Minato, Y. Ikuhara, Imaging of built-in electric field at a p-n junction by scanning transmission electron microscopy, Sci. Rep. 5, 10040 (2015). [Google Scholar]
  171. J.N. Chapman, The investigation of magnetic domain structures in thin foils by electron microscopy, J. Phys. D: Appl. Phys. 17, 623 (1984) [Google Scholar]
  172. C. Mahr, T. Grieb, F.F. Krause, M. Schowalter, A. Rosenauer, Towards the interpretation of a shift of the central beam in nano-beam electron diffraction as a change in mean inner potential, Ultramicroscopy 236, 113503 (2022). https://doi.org/10.1016/j.ultramic.2022.113503 [Google Scholar]
  173. M. Wu, E. Spiecker, Correlative micro-diffraction and differential phase contrast study of mean inner potential and subtle beam-specimen interaction, Ultramicroscopy 176, 233 (2017). https://doi.org/10.1016/j.ultramic.2017.03.029 [Google Scholar]
  174. S. McVitie, S. Hughes, K. Fallon, S. McFadzean, D. McGrouther, M. Krajnak, W. Legrand, D. Maccariello, S. Collin, K. Garcia, N. Reyren, V. Cros, A. Fert, K. Zeissler, C.H. Marrows, A transmission electron microscope study of Néel skyrmion magnetic textures in multilayer thin film systems with large interfacial chiral interaction, Sci. Rep. 8, 5703 (2018). https://doi.org/10.1038/s41598-018-23799-0 [Google Scholar]
  175. J.F. Dushimineza, J. Jo, R.E. Dunin-Borkowski, K. Müller-Caspary, Quantitative electric field mapping between electrically biased needles by scanning transmission electron microscopy and electron holography, Ultramicroscopy 253, 113808 (2023). https://doi.org/10.1016/j.ultramic.2023.113808 [Google Scholar]
  176. A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Kopf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, S. Chintala, PyTorch: An Imperative Style, High-Performance Deep Learning Library, in Advances in Neural Information Processing Systems 32 (Curran Associates, Inc., 2019) p. 8024. https://doi.org/10.48550/arXiv.1912.01703 [Google Scholar]
  177. P.G. Self, M.A. O'Keefe, P.R. Buseck, A.E.C. Spargo, Practical computation of amplitudes and phases in electron diffraction, Ultramicroscopy 11, 35 (1983). https://doi.org/10.1016/0304-3991(83)90053-0 [Google Scholar]
  178. E.J. Kirkland, Advanced Computing in Electron Microscopy (Springer International Publishing, Cham, 2020). https://doi.org/10.1007/978-3-030-33260-0 [Google Scholar]
  179. J.M. Cowley, Coherent interference in convergent-beam electron diffraction and shadow imaging, Ultramicroscopy 4, 435 (1979) [Google Scholar]
  180. G.C. Capitani, P. Oleynikov, S. Hovmöller, M. Mellini, A practical method to detect and correct for lens distortion in the TEM, Ultramicroscopy 106, 66 (2006). https://doi.org/10.1016/j.ultramic.2005.06.003 [Google Scholar]
  181. J.M. Cowley, A.F. Moodie, The scattering of electrons by atoms and crystals. I. A new theoretical approach, Acta Crystallogr. 10, 609 (1957). https://doi.org/10.1107/S0365110X57002194 [Google Scholar]
  182. P. Goodman, A.F. Moodie, Numerical evaluations of N‐beam wave functions in electron scattering by the multi‐slice method, Acta Crystallogr. A 30, 280 (1974). https://doi.org/10.1107/S056773947400057X [Google Scholar]
  183. K. Ishizuka, N. Uyeda, A new theoretical and practical approach to the multislice method, Acta Crystallogr. A 33, 740 (1977). https://doi.org/10.1107/S0567739477001879 [Google Scholar]
  184. I. Lobato, D. Van Dyck, An accurate parameterization for scattering factors, electron densities and electrostatic potentials for neutral atoms that obey all physical constraints, Acta Crystallogr. A 70, 636 (2014). https://doi.org/10.1107/S205327331401643X [Google Scholar]
  185. Z.L. Wang, The ‘Frozen-Lattice' approach for incoherent phonon excitation in electron scattering. How accurate is it?, Acta Crystallogr. A 54, 460 (1998). https://doi.org/10.1107/S0108767398001457 [Google Scholar]
  186. D.A. Muller, B. Edwards, E.J. Kirkland, J. Silcox, Simulation of thermal diffuse scattering including a detailed phonon dispersion curve, Ultramicroscopy 86, 371 (2001) [Google Scholar]
  187. R.F. Loane, P. Xu, J. Silcox, Thermal vibrations in convergent‐beam electron diffraction, Acta Crystallogr. A 47, 267 (1991). https://doi.org/10.1107/S0108767391000375 [Google Scholar]
  188. N. Denisov, D. Jannis, A. Orekhov, K. Müller-Caspary, J. Verbeeck, Characterization of a Timepix detector for use in SEM acceleration voltage range, Ultramicroscopy 253, 113777 (2023). https://doi.org/10.1016/j.ultramic.2023.113777 [CrossRef] [PubMed] [Google Scholar]
  189. J.M. LeBeau, S. Stemmer, Experimental quantification of annular dark-field images in scanning transmission electron microscopy, Ultramicroscopy 108, 1653 (2008). https://doi.org/10.1016/j.ultramic.2008.07.001 [Google Scholar]
  190. A. Rosenauer, K. Gries, K. Müller, A. Pretorius, M. Schowalter, A. Avramescu, K. Engl, S. Lutgen, Measurement of specimen thickness and composition in Alx Ga1 − x N / GaN using high-angle annular dark field images, Ultramicroscopy 109, 1171 (2009). https://doi.org/10.1016/j.ultramic.2009.05.003 [Google Scholar]
  191. A.J. D'Alfonso, L.J. Allen, H. Sawada, A.I. Kirkland, Dose-dependent high-resolution electron ptychography, J. Appl. Phys. 119, 054302 (2016). https://doi.org/10.1063/1.4941269 [Google Scholar]
  192. J.N. Cederquist, C.C. Wackerman, Phase-retrieval error: a lower bound, J. Opt. Soc. Am. A 4, 1788 (1987). https://doi.org/10.1364/JOSAA.4.001788 [Google Scholar]
  193. X. Wei, H.P. Urbach, W.M. Coene, Cramér-Rao lower bound and maximum-likelihood estimation in ptychography with Poisson noise, Phys. Rev. A 102 (2020). https://doi.org/10.1103/PhysRevA.102.043516 [Google Scholar]
  194. D. Bouchet, J. Dong, D. Maestre, T. Juffmann, Fundamental bounds on the precision of classical phase microscopes, Phys. Rev. Appl. 15, 024047 (2021). https://doi.org/10.1103/PhysRevApplied.15.024047 [Google Scholar]
  195. S. Koppell, M. Kasevich, Information transfer as a framework for optimized phase imaging, Optica 8, 493 (2021). https://doi.org/10.1364/OPTICA.412129 [CrossRef] [Google Scholar]
  196. C. Dwyer, D.M. Paganin, Quantum and classical Fisher information in four-dimensional scanning transmission electron microscopy, Phys. Rev. B 110, 024110 (2024). https://doi.org/10.1103/PhysRevB.110.024110 [Google Scholar]
  197. F. Vega Ibáñez, J. Verbeeck, Retrieval of phase information from low-dose electron microscopy experiments: are we at the limit yet?, Microsc. Microanal. 31 (2025). https://doi.org/10.1093/mam/ozae125 [Google Scholar]
  198. C.R. Rao, Information and the Accuracy Attainable in the Estimation of Statistical Parameters, in Breakthroughs in Statistics. Springer Series in Statistics (Springer, New York, 1992) Vol. 37, p. 235. https://doi.org/10.1007/978-1-4612-0919-5_16 [Google Scholar]
  199. R.F. Egerton, Control of radiation damage in the TEM, Ultramicroscopy 127, 100 (2013). https://doi.org/10.1016/j.ultramic.2012.07.006 [Google Scholar]
  200. M.G. van Heel, W. Keegstra, W. Schutter, E.F.J. van Bruggen, Life chemistry reports, Life Chem. Rep. 5, 69 (1982) [Google Scholar]
  201. W.O. Saxton, W. Baumeister, The correlation averaging of a regularly arranged bacterial cell envelope protein, J. Microsc. 127, 127 (1982). https://doi.org/10.1111/j.1365-2818.1982.tb00405.x [Google Scholar]
  202. T.B. Edo, D.J. Batey, A.M. Maiden, C. Rau, U. Wagner, Z.D. Pešić, T.A. Waigh, J.M. Rodenburg, Sampling in X-ray ptychography, Phys. Rev. A 87, 053850 (2013). https://doi.org/10.1103/PhysRevA.87.053850 [Google Scholar]
  203. B. Kabius, P. Hartel, M. Haider, H. Müller, S. Uhlemann, U. Loebau, J. Zach, H. Rose, First application of Cc-corrected imaging for high-resolution and energy-filtered TEM, J. Electron Microsc. 58, 147 (2009). https://doi.org/10.1093/jmicro/dfp021 [Google Scholar]
  204. H. Sawada, T. Sasaki, F. Hosokawa, K. Suenaga, Atomic-resolution STEM imaging of graphene at low voltage of 30 kV with resolution enhancement by using large convergence angle, Phys. Rev. Lett. 114, 166102 (2015). https://doi.org/10.1103/PhysRevLett.114.166102 [Google Scholar]
  205. R. Ishikawa, A.R. Lupini, Y. Hinuma, S.J. Pennycook, Large-angle illumination STEM: toward three-dimensional atom-by-atom imaging, Ultramicroscopy 151, 122 (2015). https://doi.org/10.1016/j.ultramic.2014.11.009 [Google Scholar]
  206. H.G. Brown, R. Ishikawa, G. Śanchez-Santolino, N. Shibata, Y. Ikuhara, L.J. Allen, S.D. Findlay, Large angle illumination enabling accurate structure reconstruction from thick samples in scanning transmission electron microscopy, Ultramicroscopy 197, 112 (2019). https://doi.org/10.1016/j.ultramic.2018.12.010 [Google Scholar]
  207. Y. Ma, J. Shi, R. Guzman, A. Li, W. Zhou, Aberration correction for large-angle illumination scanning transmission electron microscopy by using iterative electron ptychography algorithms, Microsc. Microanal. 30, 226 (2024). https://doi.org/10.1093/mam/ozae027 [Google Scholar]
  208. T. Susi, J.C. Meyer, J. Kotakoski, Quantifying transmission electron microscopy irradiation effects using two-dimensional materials, Nature Rev. Phys. 1, 397 (2019). https://doi.org/10.1038/s42254-019-0058-y [Google Scholar]
  209. J. Müller, M. Heyl, T. Schultz, K. Elsner, M. Schloz, S. Rühl, H. Seiler, N. Koch, E.J. List-Kratochvil, C.T. Koch, Probing crystallinity and grain structure of 2D materials and 2D‐like van der Waals heterostructures by low‐voltage electron diffraction, Phys. Status Solidi 221, 2300148 (2023). https://doi.org/10.1002/pssa.202300148 [Google Scholar]
  210. Y. Cheng, N. Grigorieff, P.A. Penczek, T. Walz, A primer to single-particle cryo-electron microscopy, Cell 161, 438 (2015). https://doi.org/10.1016/j.cell.2015.03.050 [Google Scholar]
  211. T. Nakane, A. Kotecha, A. Sente, G. McMullan, S. Masiulis, P.M.G.E. Brown, I.T. Grigoras, L. Malinauskaite, T. Malinauskas, J. Miehling, T. Uchański, L. Yu, D. Karia, E.V. Pechnikova, E. de Jong, J. Keizer, M. Bischoff, J. McCormack, P. Tiemeijer, S.W. Hardwick, D.Y. Chirgadze, G. Murshudov, A.R. Aricescu, S.H.W. Scheres, Single-particle cryo-EM at atomic resolution, Nature 587, 152 (2020). https://doi.org/10.1038/s41586-020-2829-0 [CrossRef] [PubMed] [Google Scholar]
  212. H. Bethe, Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie, Ann. Phys. 5, 325 (1930). https://doi.org/10.1002/andp.19303970303 [CrossRef] [Google Scholar]
  213. N.F. Mott, The scattering of electrons by atoms, Proc. Roy. Soc. Lond. A 127, 658 (1930). https://doi.org/10.1098/rspa.1930.0082 [Google Scholar]
  214. J. Dubochet, M. Adrian, J.-J. Chang, J.-C. Homo, J. Lepault, A.W. McDowall, P. Schultz, Cryo-electron microscopy of vitrified specimens, Q. Rev. Biophys. 21, 129 (1988). https://doi.org/10.1017/S0033583500004297 [Google Scholar]
  215. R. Henderson, The potential and limitations of neutrons, electrons and X-rays for atomic resolution microscopy of unstained biological molecules, Q. Rev. Biophys. 28, 171 (1995). https://doi.org/10.1017/S003358350000305X [CrossRef] [PubMed] [Google Scholar]
  216. C. Gao, C. Hofer, T. Pennycook, On central focusing for contrast optimization in direct electron ptychography of thick samples, Ultramicroscopy 256, 113879 (2024). https://doi.org/10.1016/j.ultramic.2023.113879 [Google Scholar]
  217. W.T. Baxter, R.A. Grassucci, H. Gao, J. Frank, Determination of signal-to-noise ratios and spectral SNRs in cryo-EM low-dose imaging of molecules, J. Struct. Biol. 166, 126 (2009). https://doi.org/10.1016/j.jsb.2009.02.012 [Google Scholar]
  218. M. Vulović, R.B. Ravelli, L.J. van Vliet, A.J. Koster, I. Lazić, U. Lücken, H. Rullgård, O. Öktem, B. Rieger, Image formation modeling in cryo-electron microscopy, J. Struct. Biol. 183, 19 (2013). https://doi.org/10.1016/j.jsb.2013.05.008 [Google Scholar]
  219. J.M. Parkhurst, A. Cavalleri, M. Dumoux, M. Basham, D. Clare, C.A. Siebert, G. Evans, J.H. Naismith, A. Kirkland, J.W. Essex, Computational models of amorphous ice for accurate simulation of cryo-EM images of biological samples, Ultramicroscopy 256, 113882 (2024). https://doi.org/10.1016/j.ultramic.2023.113882 [Google Scholar]
  220. T. Plamann, J.M. Rodenburg, Electron ptychography. II. Theory of three-dimensional propagation effects, Acta Crystallogr. A 54, 61 (1998). https://doi.org/10.1107/S0108767397010507 [Google Scholar]
  221. A.M. Maiden, M.J. Humphry, J.M. Rodenburg, Ptychographic transmission microscopy in three dimensions using a multi-slice approach, J. Opt. Soc. Am. A 29, 1606 (2012). https://doi.org/10.1364/JOSAA.29.001606 [Google Scholar]
  222. E.H.R. Tsai, I. Usov, A. Diaz, A. Menzel, M. Guizar-Sicairos, X-ray ptychography with extended depth of field, Opt. Express 24, 29089 (2016). https://doi.org/10.1364/OE.24.029089 [Google Scholar]
  223. S. Gao, P. Wang, F. Zhang, G.T. Martinez, P.D. Nellist, X. Pan, A.I. Kirkland, Electron ptychographic microscopy for three-dimensional imaging, Nat. Commun. 8, 163 (2017). https://doi.org/10.1038/s41467-017-00150-1 [Google Scholar]
  224. Z. Chen, Y. Jiang, Y.-T.T. Shao, M.E. Holtz, M. Odstrčil, M. Guizar-Sicairos, I. Hanke, S. Ganschow, D.G. Schlom, D.A. Muller, Electron ptychography achieves atomic-resolution limits set by lattice vibrations, Science 372, 826 (2021). https://doi.org/10.1126/science.abg2533 [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
  225. T. Susi, Quantifying phase magnitudes of open‐source focused‐probe 4D‐STEM ptychography reconstructions, J. Microsc. (2025). https://doi.org/10.1111/jmi.13409 [Google Scholar]
  226. R. Ballabriga, M. Campbell, X. Llopart, Asic developments for radiation imaging applications: the medipix and timepix family, Nucl. Instrum. Methods Phys. Res. Sect. A 878, 10 (2018). https://doi.org/10.1016/j.nima.2017.07.029 [Google Scholar]
  227. D. Pennicard, R. Ballabriga, X. Llopart, M. Campbell, H. Graafsma, Simulations of charge summing and threshold dispersion effects in Medipix3, Nucl. Instrum. Methods Phys. Res. Sect. A 636, 74 (2011). https://doi.org/10.1016/j.nima.2011.01.124 [Google Scholar]
  228. J.P. van Schayck, E. van Genderen, E. Maddox, L. Roussel, H. Boulanger, E. Fröjdh, J.-P. Abrahams, P.J. Peters, R.B. Ravelli, Sub-pixel electron detection using a convolutional neural network, Ultramicroscopy 218, 113091 (2020). https://doi.org/10.1016/j.ultramic.2020.113091 [Google Scholar]
  229. J.P. van Schayck, Y. Zhang, K. Knoops, P.J. Peters, R.B.G. Ravelli, Integration of an event-driven timepix3 hybrid pixel detector into a cryo-EM workflow, Microsc. Microanal. 29, 352 (2023). https://doi.org/10.1093/micmic/ozac009 [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.