Electron Tomography in Materials Science

  • Rowan K. Leary
  • Paul A. MidgleyEmail author
Part of the Springer Handbooks book series (SHB)


This chapter illustrates how electron tomography has become a technique of primary importance in the three-dimensional () microscopic analysis of materials. The foundations of tomography are set out with descriptions of the Radon transform and its inverse and its relationship to the Fourier transform and the Fourier slice theorem. The acquisition of a tilt series of images is described and how the angular sampling in the series affects the overall 3-D resolution in the tomogram. The imaging modes available in the (scanning) transmission electron microscope are explored with reference to their application in electron tomography and how each mode can provide complementary information on the structural, chemical, electronic, and magnetic properties of the material studied. The chapter also sets out in detail methods for tomographic reconstruction from backprojection and iterative methods, such as simultaneous iterative reconstruction technique () and algebraic reconstruction technique (), through to more recent compressed sensing approaches that aim to build in prior knowledge about the specimen into the reconstruction process. The chapter concludes with a look to the future.

Electron tomography STEM HAADF imaging compressed sensing reconstructions Radon transform analytical electron tomography algebraic iterative reconstruction 3D imaging 



The research leading to these results was possible through funding from the European Union Seventh Framework Program under Grant Agreement 312483-ESTEEM2 (Integrated Infrastructure Initiative–I3), from the European Research Council under the European Union's Seventh Framework Program (FP/2007–2013)/ERC Grant Agreement 291522–3-DIMAGE, and funding from the EPSRC, grant number EP/R008779/1. R.K.L. acknowledges a Junior Research Fellowship at Clare College. The authors acknowledge the many people with whom they have worked, including most recently Sir John Meurig Thomas, Francisco de la Pena, Sean Collins, Adam Lee, Emilie Ringe, Alex Eggeman, Jon Barnard, Duncan Johnstone, and David Rossouw.


  1. A.J. Koster, R. Grimm, D. Typke, R. Hegerl, A. Stoschek, J. Walz, W. Baumeister: Perspectives of molecular and cellular electron tomography, J. Struct. Biol. 120(3), 276–308 (1997)Google Scholar
  2. P.A. Midgley, M. Weyland: 3D electron microscopy in the physical sciences: the development of Z-contrast and EFTEM tomography, Ultramicroscopy 96(3/4), 413–431 (2003)Google Scholar
  3. J. Radon: Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten, Ber. Verh. K. Sächs. Ges. Wiss. Leipz. Math.-Phys. Kl. 69, 262–277 (1917)Google Scholar
  4. R.N. Bracewell: Two-dimensional aerial smoothing in radio astronomy, Aust. J. Phys. 9, 297–314 (1956)Google Scholar
  5. J. Frank: Three-Dimensional Electron Microscopy of Macromolecular Assemblies: Visualization of Biological Molecules in Their Native State (Oxford Univ. Press, New York 2006)Google Scholar
  6. S.R. Deans: The Radon Transform and Some of its Applications (Wiley, New York, Chichester 1983)Google Scholar
  7. A.C. Kak, M. Slaney: Principles of Computerized Tomographic Imaging (IEEE, New York 1988)Google Scholar
  8. G.T. Herman, A. Kuba: Advances in Discrete Tomography and Its Applications (Birkhauser, Boston 2007)Google Scholar
  9. P.A. Penczek, J.J. Grant: Fundamentals of three-dimensional reconstruction from projections, Methods Enzymol. 482, 1–33 (2010)Google Scholar
  10. J. Banhart: Advanced Tomographic Methods in Materials Research and Engineering (Oxford Univ. Press, Oxford 2008)Google Scholar
  11. D.J. De Rosier, A. Klug: Reconstruction of three dimensional structures from electron micrographs, Nature 217(5124), 130–134 (1968)Google Scholar
  12. W. Hoppe, R. Langer, G. Knesch, C. Poppe: Proteinkristallstrukturanalyse mit Elektronenstrahlen, Naturwissenschaften 55(7), 333–336 (1968)Google Scholar
  13. R.G. Hart: Electron microscopy of unstained biological material: The polytropic montage, Science 159(3822), 1464–1467 (1968)Google Scholar
  14. T. Dahmen, P. Trampert, N. De Jonge, P. Slusallek: Advanced recording schemes for electron tomography, MRS Bulletin 41(7), 537–541 (2016)Google Scholar
  15. R. Leary, R. Brydson: Chromatic aberration correction: The next step in electron microscopy, Adv. Imaging Electron Phys. 165, 73–130 (2011)Google Scholar
  16. R.A. Crowther, D.J. DeRosier, A. Klug: The reconstruction of a three-dimensional structure from projections and its application to electron microscopy, Proc. Royal Soc. A 317(1530), 319–340 (1970)Google Scholar
  17. D.N. Mastronarde: Dual-axis tomography: An approach with alignment methods that preserve resolution, J. Struct. Biol. 120(3), 343–352 (1997)Google Scholar
  18. P. Penczek, M. Marko, K. Buttle, J. Frank: Double-tilt electron tomography, Ultramicroscopy 60(3), 393–410 (1995)Google Scholar
  19. J. Tong, I. Arslan, P. Midgley: A novel dual-axis iterative algorithm for electron tomography, J. Struct. Biol. 153(1), 55–63 (2006)Google Scholar
  20. I. Arslan, J.R. Tong, P.A. Midgley: Reducing the missing wedge: High-resolution dual axis tomography of inorganic materials, Ultramicroscopy 106(11/12), 994–1000 (2006)Google Scholar
  21. N. Kawase, M. Kato, H. Nishioka, H. Jinnai: Transmission electron microtomography without the ‘‘missing wedge'' for quantitative structural analysis, Ultramicroscopy 107(1), 8–15 (2007)Google Scholar
  22. K. Jarausch, P. Thomas, D.N. Leonard, R. Twesten, C.R. Booth: Four-dimensional STEM-EELS: Enabling nano-scale chemical tomography, Ultramicroscopy 109(4), 326–337 (2009)Google Scholar
  23. M. Koguchi, H. Kakibayashi, R. Tsuneta, M. Yamaoka, T. Niino, N. Tanaka, K. Kase, M. Iwaki: Three-dimensional STEM for observing nanostructures, J. Electron Microsc. 50(3), 235–241 (2001)Google Scholar
  24. M. Kato, N. Kawase, T. Kaneko, S. Toh, S. Matsumura, H. Jinnai: Maximum diameter of the rod-shaped specimen for transmission electron microtomography without the ‘‘missing wedge'', Ultramicroscopy 108(3), 221–229 (2008)Google Scholar
  25. E. Biermans, L. Molina, K.J. Batenburg, S. Bals, G. Van Tendeloo: Measuring porosity at the nanoscale by quantitative electron tomography, Nano Lett. 10(12), 5014–5019 (2010)Google Scholar
  26. J. Leschner, J. Biskupek, A. Chuvilin, U. Kaiser: Accessing the local three-dimensional structure of carbon materials sensitive to an electron beam, Carbon 48(14), 4042–4048 (2010)Google Scholar
  27. H. Friedrich, P.E. de Jongh, A.J. Verkleij, K.P. de Jong: Electron tomography for heterogeneous catalysts and related nanostructured materials, Chem. Rev. 109(5), 1613–1629 (2009)Google Scholar
  28. S.S. van Bavel, J. Loos: Volume organization of polymer and hybrid solar cells as revealed by electron tomography, Adv. Funct. Mater. 20, 3217–3234 (2010)Google Scholar
  29. X.Y. Wang, R. Lockwood, M. Malac, H. Furukawa, P. Li, A. Meldrum: Reconstruction and visualization of nanoparticle composites by transmission electron tomography, Ultramicroscopy 113, 96–105 (2012)Google Scholar
  30. H. Sugimori, T. Nishi, H. Jinnai: Dual-axis electron tomography for three-dimensional observations of polymeric nanostructures, Macromolecules 38(24), 10226–10233 (2005)Google Scholar
  31. M. Radermacher, W. Hoppe: Properties of 3-D reconstruction from projections by conical tilting compared to single-axis tilting. In: 7th Eur. Congr. Electron Microsc., Den Haag, Leiden, The Netherlands, ed. by P. Brederoo, G. Boom (1980) pp. 132–133Google Scholar
  32. D. Chen, H. Friedrich, G. de With: On resolution in electron tomography of beam sensitive materials, J. Phys. Chem. C 118(2), 1248–1257 (2013)Google Scholar
  33. R.N. Bracewell, A.C. Riddle: Inversion of fan-beam scans in radio astronomy, Astrophys. J. 150, 427–434 (1967)Google Scholar
  34. H. Heidari Mezerji, W. Van den Broek, S. Bals: A practical method to determine the effective resolution in incoherent experimental electron tomography, Ultramicroscopy 111(5), 330–336 (2011)Google Scholar
  35. P.A. Midgley, M. Weyland, J.M. Thomas, B.F.G. Johnson: Z-contrast tomography: A technique in three-dimensional nanostructural analysis based on Rutherford scattering, Chem. Commun. 18(10), 907–908 (2001)Google Scholar
  36. A.J. Koster, U. Ziese, A.J. Verkleij, A.H. Janssen, K.P. de Jong: Three-dimensional transmission electron microscopy: A novel imaging and characterization technique with nanometer scale resolution for materials science, J. Phys. Chem. B 104(40), 9368–9370 (2000)Google Scholar
  37. M. Bar Sadan, L. Houben, S.G. Wolf, A. Enyashin, G. Seifert, R. Tenne, K. Urban: Toward atomic-scale bright-field electron tomography for the study of fullerene-like nanostructures, Nano Lett. 8(3), 891–896 (2008)Google Scholar
  38. S. Van Aert, K.J. Batenburg, M.D. Rossell, R. Erni, G. Van Tendeloo: Three-dimensional atomic imaging of crystalline nanoparticles, Nature 470(7334), 374–377 (2011)Google Scholar
  39. B. Goris, S. Bals, W. Van den Broek, E. Carbó-Argibay, S. Gómez-Graña, L.M. Liz-Marzán, G. Van Tendeloo: Atomic-scale determination of surface facets in gold nanorods, Nat. Mater. 11, 930–935 (2012)Google Scholar
  40. J.-P. Baudoin, J.R. Jinschek, C.B. Boothroyd, R.E. Dunin-Borkowski, N. de Jonge: Chromatic aberration-corrected tilt series transmission electron microscopy of nanoparticles in a whole mount macrophage cell, Microsc. Microanal. 19(04), 814–820 (2013)Google Scholar
  41. J.S. Barnard, J. Sharp, J.R. Tong, P.A. Midgley: High-resolution three-dimensional imaging of dislocations, Science 313(5785), 319 (2006)Google Scholar
  42. S. Bals, G. Van Tendeloo, C. Kisielowski: A new approach for electron tomography: Annular dark-field transmission electron microscopy, Adv. Mater. 18(7), 892–895 (2006)Google Scholar
  43. J.M. Rebled, L. Yedra, S. Estradé, J. Portillo, F. Peiró: A new approach for 3D reconstruction from bright field TEM imaging: Beam precession assisted electron tomography, Ultramicroscopy 111(9/10), 1504–1511 (2011)Google Scholar
  44. A.A. Sousa, A.A. Azari, G. Zhang, R.D. Leapman: Dual-axis electron tomography of biological specimens: extending the limits of specimen thickness with bright-field STEM imaging, J. Struct. Biol. 174(1), 107–114 (2011)Google Scholar
  45. P. Ercius, M. Weyland, D.A. Muller, L.M. Gignac: Three-dimensional imaging of nanovoids in copper interconnects using incoherent bright field tomography, Appl. Phys. Lett. 88(24), 243116 (2006)Google Scholar
  46. J.H. Sharp, J.S. Barnard, K. Kaneko, K. Higashida, P.A. Midgley: Dislocation tomography made easy: a reconstruction from ADF STEM images obtained using automated image shift correction, J. Phys. Conf. Ser. 126(1), 012013 (2008)Google Scholar
  47. P. Jornsanoh, G. Thollet, J. Ferreira, K. Masenelli-Varlot, C. Gauthier, A. Bogner: Electron tomography combining ESEM and STEM: a new 3D imaging technique, Ultramicroscopy 111(8), 1247–1254 (2011)Google Scholar
  48. M. Weyland, P.A. Midgley: 3D-EFTEM: Tomographic reconstruction from tilt series of energy loss images. In: Proc. Inst. Phys. EMAG Conf. Ser. 2001, Vol. 161 (2001) p. 239Google Scholar
  49. G. Möbus, B.J. Inkson: Three-dimensional reconstruction of buried nanoparticles by element-sensitive tomography based on inelastically scattered electrons, Appl. Phys. Lett. 79, 1369 (2001)Google Scholar
  50. G. Möbus, R.C. Doole, B.J. Inkson: Spectroscopic electron tomography, Ultramicroscopy 96, 433 (2003)Google Scholar
  51. K. Lepinay, F. Lorut, R. Pantel, T. Epicier: Chemical 3D tomography of 28 nm high K metal gate transistor: STEM XEDS experimental method and results, Micron 47, 43–49 (2013)Google Scholar
  52. U. Kolb, T. Gorelik, C. Kübel, M.T. Otten, D. Hubert: Towards automated diffraction tomography: Part I—Data acquisition, Ultramicroscopy 107(6/7), 507–513 (2007)Google Scholar
  53. A.C. Twitchett-Harrison, T.J.V. Yates, S.B. Newcomb, R.E. Dunin-Borkowski, P.A. Midgley: High-resolution three-dimensional mapping of semiconductor dopant potentials, Nano Lett. 7(7), 2020–2023 (2007)Google Scholar
  54. O.-H. Kwon, A.H. Zewail: 4D electron tomography, Science 328(5986), 1668–1673 (2010)Google Scholar
  55. D.B. Williams, C.B. Carter: Transmission Electron Microscopy: A Textbook for Materials Science (Springer, New York 2009)Google Scholar
  56. J.C.H. Spence: High-Resolution Electron Microscopy, 4th edn. (Oxford Univ. Press, Oxford 2013)Google Scholar
  57. D. Cockayne, A.I. Kirkland, P.D. Nellist, A. Bleloch: New possibilities with aberration-corrected electron microscopy, Philos. Trans. Royal Soc. A 367(1903), 3633–3870 (2009)Google Scholar
  58. M. Weyland, P.A. Midgley, J.M. Thomas: Electron tomography of nanoparticle catalysts on porous supports: A new technique based on Rutherford scattering, J. Phys. Chem. B 105(33), 7882–7886 (2001)Google Scholar
  59. P.A. Midgley, R.E. Dunin-Borkowski: Electron tomography and holography in materials science, Nat. Mater. 8(4), 271–280 (2009)Google Scholar
  60. P.A. Midgley, M. Weyland, T.J.V. Yates, I. Arslan, R.E. Dunin-Borkowski, J.M. Thomas: Nanoscale scanning transmission electron tomography, J. Microsc. 223(3), 185–190 (2006)Google Scholar
  61. P.A. Midgley, E.P.W. Ward, A.B. Hungria, J.M. Thomas: Nanotomography in the chemical, biological and materials sciences, Chem. Soc. Rev. 36, 1477–1494 (2007)Google Scholar
  62. M. Weyland, P.A. Midgley: Electron tomography. In: Nanocharacterisation, 2nd edn., ed. by A.I. Kirkland, S.J. Haigh (Royal Society of Chemistry, Cambridge 2007)Google Scholar
  63. H. Jinnai, R.J. Spontak: Transmission electron microtomography in polymer research, Polymer 50(5), 1067–1087 (2009)Google Scholar
  64. H. Jinnai, R.J. Spontak, T. Nishi: Transmission electron microtomography and polymer nanostructures, Macromolecules 43(4), 1675–1688 (2010)Google Scholar
  65. C. Kübel, A. Voigt, R. Schoenmakers, M. Otten, D. Su, T.-C. Lee, A. Carlsson, J. Bradley: Recent advances in electron tomography: TEM and HAADF-STEM tomography for materials science and semiconductor applications, Microsc. Microanal. 11, 378–400 (2005)Google Scholar
  66. G. Möbus, B.J. Inkson: Nanoscale tomography in materials science, Mater. Today 10(12), 18–25 (2007)Google Scholar
  67. Z. Saghi, X. Xu, G. Möbus: Electron tomography of regularly shaped nanostructures under non-linear image acquisition, J. Microsc. 232(1), 186–195 (2008)Google Scholar
  68. H. Friedrich, M.R. McCartney, P.R. Buseck: Comparison of intensity distributions in tomograms from BF TEM, ADF STEM, HAADF STEM, and calculated tilt series, Ultramicroscopy 106(1), 18–27 (2005)Google Scholar
  69. F. Leroux, E. Bladt, J.-P. Timmermans, G. Van Tendeloo, S. Bals: Annular dark-field transmission electron microscopy for low contrast materials, Microsc. Microanal. 19(03), 629–634 (2013)Google Scholar
  70. G. Prieto, J. Zečević, H. Friedrich, K.P. de Jong, P.E. de Jongh: Towards stable catalysts by controlling collective properties of supported metal nanoparticles, Nat. Mater. 12(1), 34–39 (2013)Google Scholar
  71. R.J. Spontak, M.C. Williams, D.A. Agard: Three-dimensional study of cylindrical morphology in a styrene-butadiene-styrene block copolymer, Polymer 29(3), 387–395 (1988)Google Scholar
  72. H. Jinnai, X. Jiang: Electron tomography in soft materials, Curr. Opin. Solid State Mater. Sci. 17(3), 135–142 (2013)Google Scholar
  73. P. Yuan, L. Tan, D. Pan, Y. Guo, L. Zhou, J. Yang, J. Zou, C. Yu: A systematic study of long-range ordered 3D-SBA-15 materials by electron tomography, New J. Chem. 35, 2456–2461 (2011)Google Scholar
  74. K.P. de Jong, J. Zečević, H. Friedrich, P.E. de Jongh, M. Bulut, S. van Donk, R. Kenmogne, A. Finiels, V. Hulea, F. Fajula: Zeolite Y crystals with trimodal porosity as ideal hydrocracking catalysts, Angew. Chem. Int. Ed. 49, 10074–10078 (2010)Google Scholar
  75. J. Zečević, K.P. de Jong, P.E. de Jongh: Progress in electron tomography to assess the 3D nanostructure of catalysts, Curr. Opin. Solid State Mater. Sci. 17(3), 115–125 (2013)Google Scholar
  76. R. Leary, P.A. Midgley, J.M. Thomas: Recent advances in the application of electron tomography to materials chemistry, Acc. Chem. Res. 45(10), 1782–1791 (2012)Google Scholar
  77. M. Weyland: Electron tomography of catalysts, Top. Catal. 21(4), 175–183 (2002)Google Scholar
  78. S.J. Pennycook, P.D. Nellist: Scanning Transmission Electron Microscopy (Springer, New York 2011)Google Scholar
  79. O.L. Krivanek, M.F. Chisholm, V. Nicolosi, T.J. Pennycook, G.J. Corbin, N. Dellby, M.F. Murfitt, C.S. Own, Z.S. Szilagyi, M.P. Oxley, S.T. Pantelides, S.J. Pennycook: Atom-by-atom structural and chemical analysis by annular dark-field electron microscopy, Nature 464(7288), 571–574 (2010)Google Scholar
  80. M.M.J. Treacy: Z dependence of electron scattering by single atoms into annular dark-field detectors, Microsc. Microanal. 17(06), 847–858 (2011)Google Scholar
  81. P. Ercius, O. Alaidi, M.J. Rames, G. Ren: Electron tomography: A three-dimensional analytic tool for hard and soft materials research, Adv. Mater. 27, 5638–5663 (2015)Google Scholar
  82. M. Weyland, P.A. Midgley: Electron tomography, Mater. Today 7(12), 32–40 (2004)Google Scholar
  83. E.P.W. Ward, T.J.V. Yates, J.-J. Fernandez, D.E.W. Vaughan, P.A. Midgley: Three-dimensional nanoparticle distribution and local curvature of heterogeneous catalysts revealed by electron tomography, J. Phys. Chem. C 111(31), 11501–11505 (2007)Google Scholar
  84. J.C. Hernández-Garrido, K. Yoshida, P.L. Gai, E.D. Boyes, C.H. Christensen, P.A. Midgley, N.C. Greenham: The location of gold nanoparticles on titania: A study by high resolution aberration-corrected electron microscopy and 3D electron tomography, Catal. Today 160, 165–169 (2011)Google Scholar
  85. J.M. Thomas, P.A. Midgley, T.J.V. Yates, J.S. Barnard, R. Raja, I. Arslan, M. Weyland: The chemical application of high-resolution electron tomography: Bright field or dark field?, Angew. Chem. Int. Ed. 43(48), 6745–6747 (2004)Google Scholar
  86. K. Lu, E. Sourty, R. Guerra, G. Bar, J. Loos: Critical comparisonof volume data obtained by different electron tomography techniques, Macromolecules 43(3), 1444–1448 (2010)Google Scholar
  87. P.B. Hirsch, A. Howie, P.B. Nicholson, D.W. Pashley, W.J. Whelan: Electron Microscopy of Thin Crystals (Krieger, New York 1977)Google Scholar
  88. I. Arslan, T.J.V. Yates, N.D. Browning, P.A. Midgley: Embedded nanostructures revealed in three dimensions, Science 309(5744), 2195–2198 (2005)Google Scholar
  89. Z.Y. Li, N.P. Young, M.D. Vece, S. Palomba, R.E. Palmer, A.L. Bleloch, B.C. Curley, R.L. Johnston, J. Jiang, J. Yuan: Three-dimensional atomic-scale structure of size-selected gold nanoclusters, Nature 451, 46 (2008)Google Scholar
  90. M. Azubel, J. Koivisto, S. Malola, D. Bushnell, G.L. Hura, A. Koh, H. Tsunoyama, T. Tsukuda, M. Pettersson, H. Häkkinen, R.D. Kornberg: Electron microscopy of gold nanoparticles at atomic resolution, Science 345(6199), 909–912 (2014)Google Scholar
  91. C.-C. Chen, C. Zhu, E.R. White, C.-Y. Chiu, M.C. Scott, B.C. Regan, L.D. Marks, Y. Huang, J. Miao: Three-dimensional imaging of dislocations in a nanoparticle at atomic resolution, Nature 496(7443), 74–77 (2013)Google Scholar
  92. B. Goris, J. De Beenhouwer, A. De Backer, D. Zanaga, K.J. Batenburg, A. Sánchez-Iglesias, L.M. Liz-Marzán, S. Van Aert, S. Bals, J. Sijbers, G. Van Tendeloo: Measuring lattice strain in three dimensions through electron microscopy, Nano Lett. 15, 6996–7001 (2015)Google Scholar
  93. G. Haberfehlner, P. Thaler, D. Knez, A. Volk, F. Hofer, W.E. Ernst, G. Kothleitner: Formation of bimetallic clusters in superfluid helium nanodroplets analysed by atomic resolution electron tomography, Nat. Commun. 6, 8779 (2015)Google Scholar
  94. M.C. Scott, C.-C. Chen, M. Mecklenburg, C. Zhu, R. Xu, P. Ercius, U. Dahmen, B.C. Regan, J. Miao: Electron tomography at 2.4-ångström resolution, Nature 483(7390), 444–447 (2012)Google Scholar
  95. J. Park, H. Elmlund, P. Ercius, J.M. Yuk, D.T. Limmer, Q. Chen, K. Kim, S.H. Han, D.A. Weitz, A. Zettl, A.P. Alivisatos: 3D structure of individual nanocrystals in solution by electron microscopy, Science 349, 290–295 (2015)Google Scholar
  96. T. Willhammar, K. Sentosun, S. Mourdikoudis, B. Goris, M. Kurttepeli, M. Bercx, D. Lamoen, B. Partoens, I. Pastoriza-Santos, J. Perez-Juste, L.M. Liz-Marzan, S. Bals, G. Van Tendeloo: Structure and vacancy distribution in copper telluride nanoparticles influence plasmonic activity in the near-infrared, Nat. Commun. 8, 14925–14932 (2017)Google Scholar
  97. B. Goris, T. Roelandts, K.J. Batenburg, H. Heidari Mezerji, S. Bals: Advanced reconstruction algorithms for electron tomography: From comparison to combination, Ultramicroscopy 127, 40–47 (2013)Google Scholar
  98. Y. Yang, C.-C. Chen, M.C. Scott, C. Ophus, R. Xu, A. Pryor, L. Wu, F. Sun, W. Theis, J. Zhou, M. Eisenbach, P.R.C. Kent, R.F. Sabirianov, H. Zeng, P. Ercius, J. Miao: Deciphering chemical order/disorder and material properties at the single-atom level, Nature 542(7639), 75–79 (2017)Google Scholar
  99. L.D. Marks: Experimental studies of small particle structures, Rep. Prog. Phys. 57(6), 603–649 (1994)Google Scholar
  100. T.J.A. Slater, A. Macedo, S.L.M. Schroeder, M.G. Burke, P. O'Brien, P.H.C. Camargo, S.J. Haigh: Correlating catalytic activity of Ag-Au nanoparticles with 3D compositional variations, Nano Lett. 14, 1921 (2014)Google Scholar
  101. P. Burdet, Z. Saghi, A.N. Filippin, A. Borrás, P.A. Midgley: A novel 3D absorption correction method for quantitative EDX-STEM tomography, Ultramicroscopy 160, 118 (2016)Google Scholar
  102. G. Haberfehlner, A. Orthacker, M. Albu, J. Li, G. Kothleitner: Nanoscale voxel spectroscopy by simultaneous EELS and EDS tomography, Nanoscale 6, 14563 (2014)Google Scholar
  103. B. Goris, S. Turner, S. Bals, G. Van Tendeloo: Three-dimensional valency mapping in ceria nanocrystals, ACS Nano 8, 10878 (2014)Google Scholar
  104. O. Nicoletti, F. de la Pena, R.K. Leary, D.J. Holland, C. Ducati, P.A. Midgley: Three-dimensional imaging of localized surface plasmon resonances of metal nanoparticles, Nature 502, 80 (2013)Google Scholar
  105. N.Y. Jin-Phillipp, C.T. Koch, P.A. van Aken: Toward quantitative core-loss EFTEM tomography, Ultramicroscopy 111, 1255 (2011)Google Scholar
  106. M.H. Gass, K.K.K. Koziol, A.H. Windle, P.A. Midgley: Four-dimensional spectral tomography of carbonaceous nanocomposites, Nano Lett. 6(3), 376–379 (2006)Google Scholar
  107. P. Torruella, R. Arenal, F. de la Peña, Z. Saghi, L. Yedra, A. Eljarrat, L. López-Conesa, M. Estrader, A. López-Ortega, G. Salazar-Alvarez, J. Nogués, C. Ducati, P.A. Midgley, F. Peiró, S. Estradé: 3D visualization of the iron oxidation state in FeO/Fe3O4 core–shell nanocubes from electron energy loss tomography, Nano Lett. 16, 5068–5073 (2016)Google Scholar
  108. F. de la Peña, T. Ostaševičius, R.K. Leary, C. Ducati, P.A. Midgley, R. Arenal: Quantitative elemental and bonding EELS tomography of a complex nanoparticle. In: Proc. Eur. Microsc. Congr. (2016), Scholar
  109. A. Yurtsever, M. Weyland, D.A. Muller: Three-dimensional imaging of nonspherical silicon nanoparticles embedded in silicon oxide by plasmon tomography, Appl. Phys. Lett. 89, 151920 (2006)Google Scholar
  110. A.C. Atre, B.J.M. Brenny, T. Coenen, A. García-Etxarri, A. Polman, J.A. Dionne: Nanoscale optical tomography with cathodoluminescence spectroscopy, Nat. Nanotechnol. 10, 429 (2015)Google Scholar
  111. R.F. Egerton: Electron Energy-Loss Spectroscopy in the Electron Microscope (Springer, New York 2011)Google Scholar
  112. J. Scott, P.J. Thomas, M. Mackenzie, S. McFadzean, J. Wilbrink, A.J. Craven, W.A. Nicholson: Near-simultaneous dual energy range EELS spectrum imaging, Ultramicroscopy 108(12), 1586–1594 (2008)Google Scholar
  113. A. Al-Afeef, W.P. Cockshott, I. MacLaren, S. McVitie: Electron tomography image reconstruction using data-driven adaptive compressed sensing, Scanning 38, 251–276 (2016)Google Scholar
  114. Z. Saghi, X. Xu, Y. Peng, B. Inkson, G. Mobus: Three-dimensional chemical analysis of tungsten probes by energy dispersive x-ray nanotomography, Appl. Phys. Lett. 91, 251906 (2007)Google Scholar
  115. T.J.A. Slater, A. Janssen, P.H.C. Camargo, M.G. Burke, N.J. Zaluzec, S.J. Haigh: STEM-EDX tomography of bimetallic nanoparticles: A methodological investigation, Ultramicroscopy 162, 61–73 (2016)Google Scholar
  116. C.S. Yeoh, D. Rossouw, Z. Saghi, P. Burdet, R.K. Leary, P.A. Midgley: The dark side of EDX tomography: Modeling detector shadowing to aid 3D elemental signal analysis, Microsc. Microanal. 21(3), 759–764 (2015)Google Scholar
  117. D. Zanaga, T. Altantzis, J. Sanctorum, B. Freitag, S. Bals: An alternative approach for ζ-factor measurement using pure element nanoparticles, Ultramicroscopy 164, 11–16 (2016)Google Scholar
  118. Z. Saghi, G. Divitini, B. Winter, R. Leary, E. Spiecker, C. Ducati, P.A. Midgley: Compressed sensing electron tomography of needle-shaped biological specimens – Potential for improved reconstruction fidelity with reduced dose, Ultramicroscopy 160, 230–238 (2016)Google Scholar
  119. D. Wolf, A. Lubk, F. Röder, H. Lichte: Electron holographic tomography, Curr. Opin. Solid State Mater. Sci. 17(3), 126–134 (2013)Google Scholar
  120. U. Kolb, E. Mugnaioli, T.E. Gorelik: Automated electron diffraction tomography—A new tool for nano crystal structure analysis, Cryst. Res. Technol. 46(6), 542–554 (2011)Google Scholar
  121. K. Kimura, S. Hata, S. Matsumura, T. Horiuchi: Dark-field transmission electron microscopy for a tilt series of ordering alloys: Toward electron tomography, J. Electron Microsc. 54(4), 373–377 (2005)Google Scholar
  122. R. Beanland, A. Sánchez, J. Hernandez-Garrido, D. Wolf, P. Midgley: Electron tomography of III-V quantum dots using dark field 002 imaging conditions, J. Microsc. 237(2), 148–154 (2010)Google Scholar
  123. H.H. Liu, S. Schmidt, H.F. Poulsen, A. Godfrey, Z.Q. Liu, J.A. Sharon, X. Huang: Three-dimensional orientation mapping in the transmission electron microscope, Science 332, 833–834 (2011)Google Scholar
  124. A.S. Eggeman, R. Krakow, P.A. Midgley: Scanning precession electron tomography for three-dimensional nanoscale orientation imaging and crystallographic analysis, Nat. Commun. 6, 7267 (2015)Google Scholar
  125. Y. Meng, J.-M. Zuo: Three-dimensional nanostructure determination from a large diffraction data set recorded using scanning electron nanodiffraction, IUCr Journal 3, 300–308 (2016)Google Scholar
  126. D. Johnstone, A. Van Helvoort, P. Midgley: Nanoscale strain tomography by scanning precession electron diffraction, Microsc. Microanal. 23(S1), 1710–1711 (2017)Google Scholar
  127. S.J. Lade, D. Paganin, M.J. Morgan: Electron tomography of electromagnetic fields, potentials and sources, Opt. Commun. 253(4–6), 392–400 (2005)Google Scholar
  128. G. Lai, T. Hirayama, K. Ishizuka, T. Tanji, A. Tonomura: Three-dimensional reconstruction of electric-potential distribution in electron-holographic interferometry, Appl. Opt. 33(5), 829–833 (1994)Google Scholar
  129. C. Phatak, M. Beleggia, M. De Graef: Vector field electron tomography of magnetic materials: Theoretical development, Ultramicroscopy 108, 503–513 (2008)Google Scholar
  130. V. Stolojan, R.E. Dunin-Borkowski, M. Weyland, P.A. Midgley: Three-dimensional magnetic fields of nanoscale elements determined by electron-holographic tomography, Electron Microsc. Anal. 2001, 243–246 (2001)Google Scholar
  131. C. Phatak, A.K. Petford-Long, M. De Graef: Three-dimensional study of the vector potential of magnetic structures, Phys. Rev. Lett. 104, 253901 (2010)Google Scholar
  132. D. Wolf, L.A. Rodriguez, A. Béché, E. Javon, L. Serrano, C. Magen, C. Gatel, A. Lubk, H. Lichte, S. Bals, G. Van Tendeloo, A. Fernández-Pacheco, J.M. De Teresa, E. Snoeck: 3D magnetic induction maps of nanoscale materials revealed by electron holographic tomography, Chem. Mater. 27(19), 6771–6778 (2015)Google Scholar
  133. P. Simon, D. Wolf, C. Wang, A.A. Levin, A. Lubk, S. Sturm, H. Lichte, G.H. Fecher, C. Felser: Synthesis and three-dimensional magnetic field mapping of Co2FeGa Heusler nanowires at 5 nm resolution, Nano Lett. 16, 114 (2016)Google Scholar
  134. V. Migunov, H. Ryll, X. Zhuge, M. Simson, L. Strüder, K.J. Batenburg, L. Houben, R.E. Dunin-Borkowski: Rapid low dose electron tomography using a direct electron detection camera, Sci. Rep. 5, 14516 (2015)Google Scholar
  135. R. Guckenberger: Determination of a common origin in the micrographs of tilt series in three-dimensional electron microscopy, Ultramicroscopy 9, 167–173 (1982)Google Scholar
  136. L. Houben, M. Bar Sadan: Refinement procedure for the image alignment in high-resolution electron tomography, Ultramicroscopy 111(9/10), 1512–1520 (2011)Google Scholar
  137. T. Sanders, M. Prange, C. Akatay, P. Binev: Physically motivated global alignment method for electron tomography, Adv. Struct. Chem. Imaging 1, 1–11 (2015)Google Scholar
  138. D. Gürsoy, Y.P. Hong, K. He, K. Hujsak, S. Yoo, S. Chen, Y. Li, M. Ge, L.M. Miller, Y.S. Chu, V. De Andrade, K. He, O. Cossairt, A.K. Katsaggelos, C. Jacobsen: Rapid alignment of nanotomography data using joint iterative reconstruction and reprojection, Sci. Rep. 7, 11818 (2017)Google Scholar
  139. C.O. Sanchez Sorzano, C. Messaoudi, M. Eibauer, J.R. Bilbao-Castro, R. Hegerl, S. Nickell, S. Marco, J.M. Carazo: Marker-free image registration of electron tomography tilt-series, BMC Bioinformatics 10, 124 (2009)Google Scholar
  140. J. Kwon, J.E. Barrera, T.Y. Jung, S.P. Most: Measurements of orbital volume change using computed tomography in isolated orbital blowout fractures, Arch. Facial Plast. Surg. 11(6), 395–398 (2009)Google Scholar
  141. T. Furnival, R.K. Leary, P.A. Midgley: Denoising time-resolved microscopy image sequences with singular value thresholding, Ultramicroscopy 178, 112–124 (2017)Google Scholar
  142. P.C. Hansen, M. Saxild-Hansen: AIR Tools—a MATLAB package of algebraic iterative reconstruction methods, J. Comput. Appl. Math. 236(8), 2167–2178 (2012)Google Scholar
  143. P.F.C. Gilbert: The reconstruction of a three-dimensional structure from projections and its application to electron microscopy, II. Direct methods, Proc. Royal Soc. B 182(1066), 89–102 (1972)Google Scholar
  144. E. Lee, B.P. Fahimian, C.V. Iancu, C. Suloway, G.E. Murphy, E.R. Wright, D. Castaño Díez, G.J. Jensen, J. Miao: Radiation dose reduction and image enhancement in biological imaging through equally-sloped tomography, J. Struct. Biol. 164(2), 221–227 (2008)Google Scholar
  145. Y. Chen, F. Förster: Iterative reconstruction of cryo-electron tomograms using nonuniform fast Fourier transforms, J. Struct. Biol. 185(3), 309–316 (2014)Google Scholar
  146. Z. Saghi, D.J. Holland, R. Leary, A. Falqui, G. Bertoni, A.J. Sederman, L.F. Gladden, P.A. Midgley: Three-dimensional morphology of iron oxide nanoparticles with reactive concave surfaces, a compressed sensing-electron tomography (CS-ET) approach, Nano Lett. 11(11), 4666–4673 (2011)Google Scholar
  147. R. Leary, Z. Saghi, P.A. Midgley, D.J. Holland: Compressed sensing electron tomography, Ultramicroscopy 131, 70–91 (2013)Google Scholar
  148. J. Miao, F. Förster, O. Levi: Equally sloped tomography with oversampling reconstruction, Phys. Rev. B 72(5), 052103 (2005)Google Scholar
  149. C. Zhu, C.-C. Chen, J. Du, M.R. Sawaya, M.C. Scott, P. Ercius, J. Ciston, J. Miao: Towards three-dimensional structural determination of amorphous materials at atomic resolution, Phys. Rev. B 88, 100201 (2013)Google Scholar
  150. M.I. Sezan: An overview of convex projections theory and its application to image recovery problems, Ultramicroscopy 40(1), 55–67 (1992)Google Scholar
  151. R. Gordon, R. Bender, G.T. Herman: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography, J. Theor. Biol. 29(3), 471–481 (1970)Google Scholar
  152. P. Gilbert: Iterative methods for the three-dimensional reconstruction of an object from projections, J. Theor. Biol. 36(1), 105–117 (1972)Google Scholar
  153. J.I. Agulleiro, J.J. Fernandez: Fast tomographic reconstruction on multicore computers, Bioinformatics 27(4), 582–583 (2011)Google Scholar
  154. S. Kaczmarz: Angenäherte Auflösung von Systemen linearer Gleichungen, Bull. Int. Acad. Pol. Sci. Lett. A 35, 355–357 (1937)Google Scholar
  155. P.P.B. Eggermont, G.T. Herman, A. Lent: Iterative algorithms for large partitioned linear systems, with applications to image reconstruction, Linear Algebra Appl. 40, 37–67 (1981)Google Scholar
  156. Y. Censor, S.A. Zenios: Parallel Optimization: Theory and Algorithms (Oxford Univ. Press, New York 1997)Google Scholar
  157. A.H. Andersen, A.C. Kak: Simultaneous algebraic reconstruction technique (SART): A superior implementation of the ART algorithm, Ultrason. Imaging 6(1), 81–94 (1984)Google Scholar
  158. L. Landweber: An iteration formula for Fredholm integral equations of the first kind, Am. J. Math. 73(3), 615–624 (1951)Google Scholar
  159. J. Gregor, T. Benson: Computational analysis and improvement of SIRT, IEEE Trans. Med. Imaging 27(7), 918–924 (2008)Google Scholar
  160. E. Elfving, T. Nikazad, P.C. Hansen: Semi-convergence and relaxation parameters for a class of SIRT algorithms, Electron. Trans. Numer. Anal. 37, 321–336 (2010)Google Scholar
  161. J. Tong, I. Arslan, P. Midgley: A novel dual-axis iterative algorithm for electron tomography, J. Struct. Biol. 153(1), 55–63 (2006)Google Scholar
  162. D. Wolf, A. Lubk, H. Lichte: Weighted simultaneous iterative reconstruction technique for single-axis tomography, Ultramicroscopy 136, 15–25 (2014)Google Scholar
  163. A. Lange, A. Kupsch, M.P. Hentschel, I. Manke, N. Kardjilov, T. Arlt, R. Grothausmann: Reconstruction of limited computed tomography data of fuel cell components using direct iterative reconstruction of computed tomography trajectories, J. Power Sources 196(12), 5293–5298 (2011)Google Scholar
  164. S. Lück, A. Kupsch, A. Lange, M.P. Hentschel, V. Schmidt: Statistical analysis of tomographic reconstruction algorithms by morphological image characteristics, Image Anal. Stereol. 29(2), 61–77 (2010)Google Scholar
  165. E.J. Candès, J. Romberg, T. Tao: Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inf. Theory 52(2), 489–509 (2006)Google Scholar
  166. D.L. Donoho: Compressed sensing, IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)Google Scholar
  167. E.Y. Sidky, X.C. Pan: Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization, Phys. Med. Biol. 53(17), 4777–4807 (2008)Google Scholar
  168. D.J. Holland, D.M. Malioutov, A. Blake, A.J. Sederman, L.F. Gladden: Reducing data acquisition times in phase-encoded velocity imaging using compressed sensing, J. Magn. Reson. 203(2), 236–246 (2010)Google Scholar
  169. M. Lustig, D. Donoho, J.M. Pauly: Sparse MRI: The application of compressed sensing for rapid MR imaging, Magn. Reson. Med. 58(6), 1182–1195 (2007)Google Scholar
  170. M.W. Kim, J. Choi, L. Yu, K.E. Lee, S.S. Han, J.C. Ye: Cryo-electron microscopy single particle reconstruction of virus particles using compressed sensing theory, Proceedings SPIE 6498, 64981G (2007)Google Scholar
  171. C. Vonesch, W. Lanhui, Y. Shkolnisky, A. Singer: Fast wavelet-based single-particle reconstruction in cryo-EM. In: IEEE Symp. Biomed. Imaging (2011), Scholar
  172. D.S. Taubman, M.W. Marcellin: JPEG2000: Standard for interactive imaging, Proceedings IEEE 90(8), 1336–1357 (2002)Google Scholar
  173. J.L. Starck, F. Murtagh, J.M. Fadili: Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity (Cambridge Univ. Press, Cambridge 2010)Google Scholar
  174. L. Rudin, S. Osher, E. Fatemi: Non-linear total variation noise removal algorithm, Physica D 60, 259–268 (1992)Google Scholar
  175. S. Mallat: A Wavelet Tour of Signal Processing (Academic Press, Burlington 2008)Google Scholar
  176. A. Stoschek, R. Hegerl: Denoising of electron tomographic reconstructions using multiscale transformations, J. Struct. Biol. 120(3), 257–265 (1997)Google Scholar
  177. C.O.S. Sorzano, E. Ortiz, M. López, J. Rodrigo: Improved Bayesian image denoising based on wavelets with applications to electron microscopy, Pattern Recognit. 39(6), 1205–1213 (2006)Google Scholar
  178. C.O.S. Sorzano, S. Jonić, C. El-Bez, J.M. Carazo, S. De Carlo, P. Thévenaz, M. Unser: A multiresolution approach to orientation assignment in 3D electron microscopy of single particles, J. Struct. Biol. 146(3), 381–392 (2004)Google Scholar
  179. K. Song, L.R. Comolli, M. Horowitz: Removing high contrast artifacts via digital inpainting in cryo-electron tomography: An application of compressed sensing, J. Struct. Biol. 178(2), 108–120 (2012)Google Scholar
  180. J.L. Starck, M. Elad, D.L. Donoho: Image decomposition via the combination of sparse representations and a variational approach, IEEE Trans. Image Process. 14(10), 1570–1582 (2005)Google Scholar
  181. G.T. Herman, A. Kuba: Discrete Tomography: Foundations, Algorithms and Applications (Birkhauser, Boston 1999)Google Scholar
  182. K.J. Batenburg, S. Bals, J. Sijbers, C. Kübel, P.A. Midgley, J.C. Hernandez, U. Kaiser, E.R. Encina, E.A. Coronado, G. Van Tendeloo: 3D imaging of nanomaterials by discrete tomography, Ultramicroscopy 109(6), 730–740 (2009)Google Scholar
  183. J.R. Jinschek, K.J. Batenburg, H.A. Calderon, R. Kilaas, V. Radmilovic, C. Kisielowski: 3-D reconstruction of the atomic positions in a simulated gold nanocrystal based on discrete tomography: Prospects of atomic resolution electron tomography, Ultramicroscopy 108(6), 589–604 (2008)Google Scholar
  184. K. Batenburg, J. Sijbers: DART: A practical reconstruction algorithm for discrete tomography, IEEE Trans. Image Process. 20(9), 2542–2553 (2011)Google Scholar
  185. S. Bals, M. Casavola, M.A. van Huis, S. Van Aert, K.J. Batenburg, G. Van Tendeloo, D.L. Vanmaekelbergh: Three-dimensional atomic imaging of colloidal core-shell nanocrystals, Nano Lett. 11(8), 3420–3424 (2011)Google Scholar
  186. F.J. Maestre-Deusto, G. Scavello, J. Pizarro, P.L. Galindo: ADART: an adaptive algebraic reconstruction algorithm for discrete tomography, IEEE Trans. Image Process. 20(8), 2146–2152 (2011)Google Scholar
  187. K.J. Batenburg, W. van Aarle, J. Sijbers: A semi-automatic algorithm for grey level estimation in tomography, Pattern Recognit. Lett. 32(9), 1395–1405 (2011)Google Scholar
  188. A. Zürner, M. Döblinger, V. Cauda, R. Wei, T. Bein: Discrete tomography of demanding samples based on a modified SIRT algorithm, Ultramicroscopy 115, 41–49 (2012)Google Scholar
  189. T. Roelandts, K.J. Batenburg, E. Biermans, C. Kübel, S. Bals, J. Sijbers: Accurate segmentation of dense nanoparticles by partially discrete electron tomography, Ultramicroscopy 114, 96–105 (2012)Google Scholar
  190. X. Zhuge, W.J. Palenstijn, K.J. Batenburg: TVR-DART: A more robust algorithm for discrete tomography from limited projection data with automated gray value estimation, IEEE Trans. Image Process. 25(1), 455–468 (2016)Google Scholar
  191. A. Alpers, R.J. Gardner, S. König, R.S. Pennington, C.B. Boothroyd, L. Houben, R.E. Dunin-Borkowski, K.J. Batenburg: Geometric reconstruction methods for electron tomography, Ultramicroscopy 128, 42–54 (2013)Google Scholar
  192. M. Wollgarten, M. Habeck: Autonomous reconstruction and segmentation of tomographic data, Micron 63, 20–27 (2014)Google Scholar
  193. R.J. Gardner: Geometric Tomography (Cambridge Univ. Press, Cambridge 2006)Google Scholar
  194. T.C. Petersen, S.P. Ringer: Electron tomography using a geometric surface-tangent algorithm: Application to atom probe specimen morphology, J. Appl. Phys. 105(10), 103518 (2009)Google Scholar
  195. W.O. Saxton, W. Baumeister, M. Hahn: Three-dimensional reconstruction of imperfect two-dimensional crystals, Ultramicroscopy 13(1/2), 57–70 (1984)Google Scholar
  196. Y. Cheng: Single-particle cryo-EM at crystallographic resolution, Cell 161(3), 450–457 (2015)Google Scholar
  197. M. Shalev-Benami, Y. Zhang, D. Matzov, Y. Halfon, A. Zackay, H. Rozenberg, E. Zimmerman, A. Bashan, C.L. Jaffe, A. Yonath, G. Skiniotis: 2.8-Å cryo-EM structure of the large ribosomal subunit from the eukaryotic parasite Leishmania, Cell Rep. 16(2), 288–294 (2016)Google Scholar
  198. E. Callaway: The revolution will not be crystallized: A new method sweeps through structural biology, Nature 525, 172–174 (2015)Google Scholar
  199. N. Grigorieff: Direct detection pays off for electron cryo-microscopy, eLife 2, e00573 (2013)Google Scholar
  200. D. Rossouw, R. Krakow, Z. Saghi, C.S.M. Yeoh, P. Burdet, R.K. Leary, F. de la Peña, C. Ducati, C.M.F. Rae, P.A. Midgley: Blind source separation aided characterization of the γ' strengthening phase in an advanced nickel-based superalloy by spectroscopic 4D electron microscopy, Acta Mater. 107, 229–238 (2016)Google Scholar
  201. S.M. Collins, E. Ringe, M. Duchamp, Z. Saghi, R.E. Dunin-Borkowski, P.A. Midgley: Eigenmode tomography of surface charge oscillations of plasmonic nanoparticles by electron energy loss spectroscopy, ACS Photonics 2(11), 1628–1635 (2015)Google Scholar
  202. S.M. Collins, S. Fernandez-Garcia, J.J. Calvino, P.A. Midgley: Sub-nanometer surface chemistry and orbital hybridization in lanthanum-doped ceria nano-catalysts revealed by 3D electron microscopy, Sci. Rep. 7, 5406 (2017)Google Scholar
  203. J.-J. Fernandez: Computational methods for materials characterization by electron tomography, Curr. Opin. Solid State Mater. Sci. 17(3), 93–106 (2013)Google Scholar
  204. N. Volkmann, J.J. Grant: Methods for segmentation and interpretation of electron tomographic reconstructions, Methods Enzymol. 483, 31–46 (2010)Google Scholar
  205. R. Narasimha, I. Aganj, A.E. Bennett, M.J. Borgnia, D. Zabransky, G. Sapiro, S.W. McLaughlin, J.L.S. Milne, S. Subramaniam: Evaluation of denoising algorithms for biological electron tomography, J. Struct. Biol. 164(1), 7–17 (2008)Google Scholar
  206. J.-J. Fernández, S. Li: An improved algorithm for anisotropic nonlinear diffusion for denoising cryo-tomograms, J. Struct. Biol. 144(1/2), 152–161 (2003)Google Scholar
  207. C. Bajaj, Z. Yu, M. Auer: Volumetric feature extraction and visualization of tomographic molecular imaging, J. Struct. Biol. 144(1/2), 132–143 (2003)Google Scholar
  208. J.-J. Fernandez: TOMOBFLOW: feature-preserving noise filtering for electron tomography, BMC Bioinformatics 10, 178 (2009)Google Scholar
  209. E. Garduño, M. Wong-Barnum, N. Volkmann, M.H. Ellisman: Segmentation of electron tomographic data sets using fuzzy set theory principles, J. Struct. Biol. 162(3), 368–379 (2008)Google Scholar
  210. K. Sandberg, M. Brega: Segmentation of thin structures in electron micrographs using orientation fields, J. Struct. Biol. 157(2), 403–415 (2007)Google Scholar
  211. R. Leary, Z. Saghi, M. Armbrüster, G. Wowsnick, R. Schlögl, J.M. Thomas, P.A. Midgley: Quantitative high-angle annular dark-field scanning transmission electron microscope (HAADF-STEM) tomography and high-resolution electron microscopy of unsupported intermetallic GaPd2 catalysts, J. Phys. Chem. C 116(24), 13343–13352 (2012)Google Scholar
  212. R. Thiedmann, A. Spettl, O. Stenzel, T. Zeibig, J.C. Hindson, Z. Saghi, N.C. Greenham, P.A. Midgley, V. Schmidt: Networks of nanoparticles in organic-inorganic composites: Algorithmic extraction and statistical analysis, Image Anal. Stereol. 31(1), 27–42 (2011)Google Scholar
  213. C.J. Gommes, K. de Jong, J.-P. Pirard, S. Blacher: Assessment of the 3D localization of metallic nanoparticles in Pd/SiO2 cogelled catalysts by electron tomography, Langmuir 21(26), 12378–12385 (2005)Google Scholar
  214. R. Grothausmann, G. Zehl, I. Manke, S. Fiechter, P. Bogdanoff, I. Dorbandt, A. Kupsch, A. Lange, M.P. Hentschel, G. Schumacher, J. Banhart: Quantitative structural assessment of heterogeneous catalysts by electron tomography, J. Am. Chem. Soc. 133(45), 18161–18171 (2011)Google Scholar
  215. J.C. Russ, F.B. Neal: The Image Processing Handbook, 7th edn. (CRC, Boca Raton 2015)Google Scholar
  216. H. Li, H.L. Xin, D.A. Muller, L.A. Estroff: Visualizing the 3D internal structure of calcite single crystals grown in agarose hydrogels, Science 326(5957), 1244–1247 (2009)Google Scholar
  217. M. Sezgin, B. Sankur: Survey over image thresholding techniques and quantitative performance evaluation, J. Electron. Imaging 13(1), 146–168 (2004)Google Scholar
  218. W. van Aarle, K.J. Batenburg, J. Sijbers: Optimal threshold selection for segmentation of dense homogeneous objects in tomographic reconstructions, IEEE Trans. Med. Imaging 30(4), 980–989 (2011)Google Scholar
  219. N. Otsu: A threshold selection method from gray-level histograms, IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (1979)Google Scholar
  220. J.C. Hindson, Z. Saghi, J.-C. Hernandez-Garrido, P.A. Midgley, N.C. Greenham: Morphological study of nanoparticle-polymer solar cells using high-angle annular dark-field electron tomography, Nano Lett. 11(2), 904–909 (2011)Google Scholar
  221. H. Friedrich, S. Guo, P.E. de Jongh, X. Pan, X. Bao, K.P. de Jong: A quantitative electron tomography study of ruthenium particles on the interior and exterior surfaces of carbon nanotubes, ChemSusChem 4(7), 957–963 (2011)Google Scholar
  222. K.J. Batenburg, J. Sijbers: Optimal threshold selection for tomogram segmentation by projection distance minimization, IEEE Trans. Med. Imaging 28(5), 676–686 (2009)Google Scholar
  223. M.N. Lebbink, W.J.C. Geerts, T.P. van der Krift, M. Bouwhuis, L.O. Hertzberger, A.J. Verkleij, A.J. Koster: Template matching as a tool for annotation of tomograms of stained biological structures, J. Struct. Biol. 158(3), 327–335 (2007)Google Scholar
  224. N. Volkmann: A novel three-dimensional variant of the watershed transform for segmentation of electron density maps, J. Struct. Biol. 138(1/2), 123–129 (2002)Google Scholar
  225. H. Katz-Boon, C.J. Rossouw, M. Weyland, A.M. Funston, P. Mulvaney, J. Etheridge: Three-dimensional morphology and crystallography of gold nanorods, Nano Lett. 11(1), 273–278 (2011)Google Scholar
  226. C.M.A. Parlett, M.A. Isaacs, S.K. Beaumont, L.M. Bingham, N.S. Hondow, K. Wilson, A.F. Lee: Spatially orthogonal chemical functionalization of a hierarchical pore network for catalytic cascade reactions, Nat. Mater. 15, 178–182 (2016)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dept. of Materials Science & MetallurgyUniversity of CambridgeCambridgeUK

Personalised recommendations