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Theory of Calculation of Images of Thick Specimens

  • Earl J. Kirkland
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Abstract

This chapter describes the theory of calculating transmission electron microscope image of thick specimens (more than a few atoms thick), including the effects of multiple (or plural) scattering. Two popular methods are presented: Bloch wave methods and multislice methods. These approximations are typically good for specimens up to a few thousand Angstroms thick.

References

  1. 3.
    G. P. Agrawal. Nonlinear Fiber Optics. Academic Press, San Diego, 2nd edition, 1995.zbMATHGoogle Scholar
  2. 6.
    L. J. Allen, A. J. D’Alfonso, and S. D. Findlay. Modeling the inelastic scattering of fast electrons. Ultramicroscopy, 151:11–22, 2015.CrossRefGoogle Scholar
  3. 7.
    L. J. Allen, H. M. L. Faulkner, and H. Leeb. Inversion of dynamical electron diffraction data including adsorption. Acta Cryst., A56:119–126, 2000.CrossRefGoogle Scholar
  4. 8.
    L. J. Allen, S. D. Findlay, M. P. Oxley, and C. J. Rossouw. Lattice-resolution contrast from a focused coherent electron probe. Part I. Ultramicroscopy, 96:47–63, 2003.CrossRefGoogle Scholar
  5. 9.
    L. J. Allen, T. W. Josefsson, and H. Leeb. Obtaining the crystal potential by inversion from electron scattering intensities. Acta Cryst., A54:388–398, 1998.CrossRefGoogle Scholar
  6. 10.
    L. J. Allen, H. Leeb, and A. E. C. Spargo. Retrieval of the projected potential by inversion from the scattering matrix in electron-crystal scattering. Acta Cryst., A55:105–111, 1999.CrossRefGoogle Scholar
  7. 12.
    J. G. Allpress, E. A. Hewat, A. F. Moodie, and J. V. Sanders. n-beam lattice images. I. experimental and computed images of W4Nb26O77. Acta Cryst., A28:528–536, 1972.Google Scholar
  8. 13.
    J. G. Allpress and J. V. Sanders. The direct observation of the structure of real crystals by lattice imaging. J. Appl. Cryst., 6:165–190, 1973.CrossRefGoogle Scholar
  9. 15.
    E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen. LAPACK Users’ Guide. Society for Industrial and Applied Mathematics, Philadelphia, PA, third edition, 1999.Google Scholar
  10. 19.
    G. R. Anstis and D. J. H. Cockayne. The calculation and interpretation of high-resolution electron microscope images of lattice defects. Acta Cryst., A35:511–524, 1979.CrossRefGoogle Scholar
  11. 20.
    N. W. Ashcroft and N. D. Mermin. Solid State Physics. Holt, Rinehart and Winston, New York, 1976.Google Scholar
  12. 24.
    J. Barthel. Dr. Probe: A software for high-resolution STEM image simulation. Ultramicroscopy, 193:1–11, 2018.CrossRefGoogle Scholar
  13. 25.
    B. W. Batterman and H. Cole. Dynamical diffraction of X-rays by perfect crystals. Reviews of Modern Physics, 36:681–717, 1964.ADSMathSciNetCrossRefGoogle Scholar
  14. 27.
    M. J. Beeching and A. E. C. Spargo. A method for crystal potential retrieval in HRTEM. Ultramicroscopy, 52:243–247, 1993.CrossRefGoogle Scholar
  15. 28.
    M. J. Beeching and A. E. C. Spargo. Inversion of nonperiodic wavefields to determine localized defect structure. J. Microscopy, 190:262–266, 1998.CrossRefGoogle Scholar
  16. 31.
    H. Bethe. Theorie der beugung von elektronen an kristallen. Annalen der Physik, 87:55–129, 1928.ADSCrossRefGoogle Scholar
  17. 36.
    D. M. Bird. Theory of zone axis electron diffraction. J. of Elect. Micros. Tech., 13:77–97, 1989.CrossRefGoogle Scholar
  18. 42.
    M. Born and E. Wolf. Principles of Optics. Pergamon Press, Oxford, 6th edition, 1980.zbMATHGoogle Scholar
  19. 51.
    L. A. Bursill and A. R. Wilson. Electron-optical imaging of the hollandite structure at 3 Å resolution. Acta Cryst., A33:672–676, 1977.CrossRefGoogle Scholar
  20. 54.
    C. Cai and J. Chen. An accurate multislice method for low-energy transmission electron microscopy. Micron, 43:374–379, 2012.CrossRefGoogle Scholar
  21. 55.
    Can Ying Cai, Song Jun Zeng, Hong Rong Liu, and Qi Bin Yang. Computational comparison of the conventional multislice method and the real space multislice method for simulating exit wavefunctions. Micron, 40:313–319, 2009.CrossRefGoogle Scholar
  22. 57.
    E. Carlino, V. Grillo, and P. Palazzari. Accurate and fast multislice simulations of HAADF image contrast by parallel computing. In A. G. Cullis and P. A. Midgley, editors, Springer Proc. in Phys., volume 120, pages 177–180, 2008.Google Scholar
  23. 60.
    J. H. Chen and D. Van Dyck. Accurate multislice theory for elastic electron scattering in transmission electron microscopy. Ultramicroscopy, 70:29–44, 1997.CrossRefGoogle Scholar
  24. 61.
    J. H. Chen, D. Van Dyck, and M. Op de Beck. Multislice method for large beam tilt with applications to HOLZ effects in triclinic and monoclinic crystals. Acta Cryst., A53:576–589, 1997.CrossRefGoogle Scholar
  25. 62.
    J. H. Chen, D. Van Dyck, M. Op de Beck, and J. Van Landuyt. Computational comparisons between the conventional multislice method and the third-order multislice method for calculating high-energy electron diffraction and imaging. Ultramicroscopy, 69:219–240, 1997.CrossRefGoogle Scholar
  26. 64.
    W. Coene and D. Van Dyck. The real space method for dynamical electron diffraction calculation in high resolution electron microscopy, II. critical analysis of the dependency on the input parameters. Ultramicroscopy, 15:41–50, 1984.CrossRefGoogle Scholar
  27. 65.
    W. Coene and D. Van Dyck. The real space method for dynamical electron diffraction calculations in high resolution electron microscopy III. a computational algorithm for the electron propagation with practical applications. Ultramicroscopy, 15:287–300, 1984.CrossRefGoogle Scholar
  28. 69.
    J. M. Cordes, A. Pidwerbetsky, and R. V. E. Lovelace. Refractive and diffractive scattering in the interstellar medium. The Astrophysical J., 310:737–767, 1986.ADSCrossRefGoogle Scholar
  29. 74.
    J. M. Cowley. Diffraction Physics. North-Holland, Amsterdam, 2nd edition, 1975.Google Scholar
  30. 78.
    J. M. Cowley and A. F. Moodie. The scattering of electrons by atoms and crystals. I. a new theoretical approach. Acta Cryst., 10:609–619, 1957.MathSciNetCrossRefGoogle Scholar
  31. 81.
    J. M. Cowley and J. C. H. Spence. Innovative imaging and microdiffraction in STEM. Ultramicroscopy, 3:433–438, 1979.CrossRefGoogle Scholar
  32. 101.
    D. Drouin, A. R. Couture, D. Joly, X. Tastet, V. Aimez, and R. Gauvin. CASINO V 2.42 - a fast and easy-to-use modeling tool for scanning electron microscopy and microanalysis users. Scanning, 29:92–101, 2007.CrossRefGoogle Scholar
  33. 102.
    D. Drouin, P. Hovington, and R. Gauvin. CASINO: A new Monte Carlo code in C language for electron beam interaction–part II: Tabulated values of the Mott cross section. Scanning, 19:20–28, 1997.CrossRefGoogle Scholar
  34. 103.
    D. E. Dudgeon and R. M. Mersereau. Multidimensional Digital Signal Processing. Prentice Halls, New Jersey, 1984.zbMATHGoogle Scholar
  35. 104.
    B. J. Dulong, R. D. Haynes, and M. D. Robertson. A study in the computation time required for the inclusion of strain field effects in Bloch-wave simulations of TEM diffraction contrast images. Ultramicroscopy, 108:415–425, 2008.CrossRefGoogle Scholar
  36. 105.
    C. Dwyer. Multislice simulation of scanning transmission electron microscope images. In L. N. Brewer, S. McKernan, J. P. Shields, F. E. Schmidt Jr, J. H. Woodward, and N. J. Zaluzec, editors, Microscopy and Microanalysis 2009, volume 15, suppl. 2, pages 754–755, Cambridge, UK, 2009. Cambridge Univ. Press.Google Scholar
  37. 106.
    C. Dwyer. Simulation of scanning transmission electron microscope images on desktop computers. Ultramicroscopy, 110:195–198, 2010.CrossRefGoogle Scholar
  38. 110.
    A. S. Eggeman, A. London, and P. A. Midgley. Ultrafast electron diffraction pattern simulations using GPU technology. applications to lattice vibrations. Ultramicroscopy, 134:44–47, 2013.CrossRefGoogle Scholar
  39. 126.
    M. D. Feit and J. A. Fleck. Light propagation in graded-index optical fibers. Applied Optics, 17:3990–3998, 1978.ADSCrossRefGoogle Scholar
  40. 128.
    J. Fertig and H. Rose. Resolution and contrast of crystalline objects in high-resolution scanning transmission electron microscopy. Optik, 59:407–429, 1981.Google Scholar
  41. 132.
    R. P. Feynman. An operator calculus having applications in quantum electrodynamics. Phys. Rev., 84:108–128, 1951.ADSMathSciNetzbMATHCrossRefGoogle Scholar
  42. 133.
    P. M. Fields and J. M. Cowley. Computed electron microscope images of atomic defects in fcc metals. Acta Cryst., A34:103–112, 1978.CrossRefGoogle Scholar
  43. 138.
    J. A. Fleck(Jr.), J. R. Morris, and M. D. Feit. Time-dependent propagation of high energy laser beams through the atmosphere. Appl. Phys., 10:129–160, 1976.Google Scholar
  44. 148.
    R. G. French and R. V. E. Lovelace. Strong turbulence and atmospheric waves in stellar occultations. Icarus, 56:122–146, 1983.ADSCrossRefGoogle Scholar
  45. 149.
    Matteo Frigo and Steven G. Johnson. The design and implementation of FFTW3. Proc. of the IEEE, 93:216–231, 2005. www.fftw.org.CrossRefGoogle Scholar
  46. 152.
    F. Fujimoto. Dynamical theory of electron diffraction in Laue-case I. general theory. J. Physical Soc. Japan, 14:1558–1568, 1959.ADSCrossRefGoogle Scholar
  47. 159.
    A. Gómez-Rodríguez, L. M. Beltrán-del-Río, and R. Herrera-Becerra. SimulaTEM: Multislice simulations for general objects. Ultramicroscopy, 110:95–104, 2010.CrossRefGoogle Scholar
  48. 162.
    P. Goodman and A. F. Moodie. Numerical evaluation of N-beam wave functions in electron scattering by the multislice method. Acta Cryst., A30:280–290, 1974.CrossRefGoogle Scholar
  49. 164.
    M. De Graf. Intro. to Conventional Transmission Electron Microscopy. Cambridge Univ. Press, Cambridge, UK, 2003.Google Scholar
  50. 168.
    M. A. Gribelyuk. Structure retrieval in HREM. Acta Cryst., A47:715–723, 1991.CrossRefGoogle Scholar
  51. 170.
    V. Grillo, E. Carlino, and F. Glas. Influence of the static atomic displacement on atomic resolution Z-contrast imaging. Phys. Rev. B, 77:054103, 2008.ADSCrossRefGoogle Scholar
  52. 171.
    V. Grillo and F. Rossi. STEM_CELL: a software tool for electron microscopy: Part ii analysis of crystalline materials. Ultramicroscopy, 125:112–129, 2013.CrossRefGoogle Scholar
  53. 172.
    V. Grillo and E. Rotunno. STEM_CELL: a software tool for electron microscopy: Part i simulations. Ultramicroscopy, 125:97–111, 2013.CrossRefGoogle Scholar
  54. 173.
    G. R. Grinton and J. M. Cowley. Phase and amplitude contrast in electron microscopy of biological materials. Optik, 34:221–233, 1971.Google Scholar
  55. 206.
    S. C. Hiller, E. T. Robertson, G. D. Reid, R. D. Haynes, and M. D. Robertson. On the role of the second-order derivative term in the calculation of convergent beam diffraction patterns. Ultramicroscopy, 179:73–80, 2017.CrossRefGoogle Scholar
  56. 208.
    P. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley, and M. J. Whelan. Electron Microscopy of Thin Crystals. Krieger, Huntington, New York, second edition, 1977.Google Scholar
  57. 212.
    F. Hosakawa, T. Shinkawa, Y. Arai, and T. Sannomiya. Benchmark test of accelerated multi-slice simulation by GPGPU. Ultramicroscopy, 158:56–64, 2015.CrossRefGoogle Scholar
  58. 215.
    P. Hovington, D. Drouin, and R. Gauvin. CASINO: A new Monte Carlo code in C language for electron beam interaction—part I: Description of the program. Scanning, 19:1–14, 1997.CrossRefGoogle Scholar
  59. 216.
    P. Hovington, D. Drouin, R. Gauvin, D. C. Joy, and N. Evans. CASINO: A new Monte Carlo code in C language for electron beam interaction—part III: Stopping power at low energies. Scanning, 19:29–35, 1997.CrossRefGoogle Scholar
  60. 218.
    A. Howie and Z. S. Basinski. Approx. of the dynamical theory of diffraction contrast. Phil. Mag, 17:1039–1063, 1968.Google Scholar
  61. 219.
    A. Howie and M. J. Whelan. Diffraction contrast of electron microscope images of crystal lattice defects, II. the development of a dynamical theory. Proc. Royal Society of London, A263:217–237, 1961.Google Scholar
  62. 220.
    C. J. Humphreys. The scattering of fast electrons by crystals. Rep. Prog. Phys., 42:1825–1887, 1979.ADSCrossRefGoogle Scholar
  63. 231.
    K. Ishizuka. Multislice formula for inclined illumination. Acta Cryst., A38:773–779, 1982.CrossRefGoogle Scholar
  64. 233.
    K. Ishizuka. A practical approach for STEM image simulation based on the FFT multislice method. Ultramicroscopy, 90:71–83, 2002.CrossRefGoogle Scholar
  65. 234.
    K. Ishizuka. FFT multislice method - the silver anniversary. Microsc. and Microanalysis, 10:34–40, 2004.ADSCrossRefGoogle Scholar
  66. 235.
    K. Ishizuka, 2006. www.hremresearch.com.
  67. 236.
    K. Ishizuka and N. Uyeda. A new theoretical and practical approach to the multislice method. Acta Cryst., A33:740–749, 1977.CrossRefGoogle Scholar
  68. 243.
    B. K. Jap and R. M. Glaeser. The scattering of high-energy electrons. I. Feynman path-integral formulation. Acta. Cryst., A34:94–102, 1978.ADSMathSciNetCrossRefGoogle Scholar
  69. 251.
    Nicholas H. Julian, Tian T. Li, Robert E. Rudd, and Jaime Martian. MS-STEM-FEM: A parallelized multi-slice fluctuation TEM simulation tool. Ultramicroscopy, 194:117–125, 2018.CrossRefGoogle Scholar
  70. 256.
    R. Kilaas. Interactive simulation of high-resolution electron micrographs. In G. W. Bailey, editor, Proceedings of the 45th Annual Meeting of the Microscopy Society of America, pages 66–69. San Francisco Press, 1987.Google Scholar
  71. 257.
  72. 258.
    R. Kilaas and R. Gronsky. Real space image simulation in high resolution electron microscopy. Ultramicroscopy, 11:289–298, 1983.CrossRefGoogle Scholar
  73. 260.
    R. Kilaas, M. A. O’Keefe, and K. M. Krishman. On the inclusion of upper Laue layers in computational methods in high resolution transmission electron microscopy. Ultramicroscopy, 21:47–62, 1987.CrossRefGoogle Scholar
  74. 273.
    E. J. Kirkland. Advanced Computing in Electron Microscopy. Plenum, New York, 1998.CrossRefGoogle Scholar
  75. 276.
    E. J. Kirkland, 2013. www.sourceforge.com/computem.
  76. 277.
    E. J. Kirkland. Computation in electron microscopy. Acta Cryst. A, 72:1–27, 2016.CrossRefGoogle Scholar
  77. 279.
    E. J. Kirkland, R. F. Loane, and J. Silcox. Simulation of annular dark field STEM images using a modified multislice method. Ultramicroscopy, 23:77–96, 1987.CrossRefGoogle Scholar
  78. 286.
    C. Kittel. Intro. to Solid State Physics. Wiley, New York, 7th edition, 1996.Google Scholar
  79. 290.
    C. Koch, 2015. elim.physik.uni-ulm.de.Google Scholar
  80. 292.
    D. Koslof and R. Kosloff. A Fourier method solution for the time dependent Schrodinger equation as a tool in molecular dynamics. J. Comp. Phys., 52:35–53, 1983.ADSzbMATHCrossRefGoogle Scholar
  81. 293.
    R. Kosloff. Time-dependent quantum-mechanical methods for molecular dynamics. J. Phys. Chem., 92:2087–2100, 1988.CrossRefGoogle Scholar
  82. 295.
    Florian F. Krause, Knut Müller, Dennis Zillmann, Jacob Jansen, and Marco Schowalter. Comparison of intensity and absolute contrast of simulated and experimental high-resolution transmission electron microscopy images for different multislice simulation methods. Ultramicroscopy, 134:94–101, 2013.CrossRefGoogle Scholar
  83. 311.
    A. L. Lewis, R. B. Hammond, and R. E. Villagrana. The importance of second-order partial derivatives in the theory of high-energy-electron diffraction from imperfect crystals. Acta. Cryst., A31:221–227, 1975.CrossRefGoogle Scholar
  84. 319.
    I. Lobato and D. van Dyck. MULTEM: a new multislice program to perform accurate and fast electron diffraction and imaging simulations using graphics processing unit with CUDA. Ultramicroscopy, 156:9–17, 2015.CrossRefGoogle Scholar
  85. 324.
    D. F. Lynch and A. F. Moodie. Numerical evaluation of low energy electron diffraction intensities I. the perfect crystal with no upper layer lines and no absorption. Surface Science, 32:422–438, 1972.ADSCrossRefGoogle Scholar
  86. 325.
    D. F. Lynch and M. A. O’Keefe. n-beam lattice images II. methods of calculation. Acta Cryst., A28:536–548, 1972.Google Scholar
  87. 327.
    D. S. MacLagan, L. A. Bursill, and A. E. C. Spargo. Experimental and calculated images of planar defects at high resolution. Phil. Mag., 35:757–780, 1977.ADSCrossRefGoogle Scholar
  88. 332.
  89. 335.
    H. Matsuhata, D. Van Dyck, J. Van Lanuyt, and S. Amelincjx. A practical approach to the periodic continuation method for the simulation of high resolution TEM images of isolated crystal defects. Ultramicroscopy, 13:343–348, 1984.CrossRefGoogle Scholar
  90. 347.
    W. Q. Ming and J. H. Chen. Validities of three multislice algorithms for quantitative low-energy transmission electron microscopy. Ultramicroscopy, 134:135–143, 2013.CrossRefGoogle Scholar
  91. 350.
    K. Mitsuishi, K. Iakoubovskii, M. Takeguchi, M. Shimojo, A. Hashimoto, and K. Furuya. Bloch wave-based calculations of imaging properties of high-resolution scanning confocal electron microscopy. Ultramicroscopy, 108:981–988, 2008.CrossRefGoogle Scholar
  92. 360.
    Gordon E. Moore. Cramming more components onto integrated circuits. Proc. IEEE, 86:82–85, 1998. reprinted from Electronics, April 19, 1965, p. 114–117.CrossRefGoogle Scholar
  93. 368.
    P. D. Nellist and S. J. Pennycook. Incoherent imaging using dynamically scattered coherent electrons. Ultramicroscopy, 78:111–124, 1999.CrossRefGoogle Scholar
  94. 369.
    P. D. Nellist and S. J. Pennycook. The principles and interpretation of annular dark-field Z-contrast imaging. In P. W. Hawkes, editor, Adv. in Imaging and Electron Physics, vol. 113, pages 147–203. Academic Press, San Diego, 2000.Google Scholar
  95. 373.
    H. Niehrs and E. H. Wagner. Die amplituden der wellenfelder bei elektroneninterferenzen im Laue-fall. Z. Physik, 143:285–299, 1955.ADSCrossRefGoogle Scholar
  96. 376.
    Jan Oliver Oelerich, Lennart Duschek, Jürgen Belz, Andreas Beyer, Sergei D. Baranovskii, and Kerstin Volz. STEMsalabim: A high-performance computing cluster friendly code for scanning transmission electron microscopy image simulations of thin specimens. Ultramicroscopy, 177:91–96, 2017.Google Scholar
  97. 378.
    M. A. O’Keefe. Advances in image simulation for high resolution TEM. In G. W. Bailey, M. H. Ellisman, R. A. Hennigar, and N. J. Zaluzec, editors, Proc. Micros. and Microanal. 1995, pages 38–39, New York, 1995. Jones and Begell.Google Scholar
  98. 379.
    M. A. O’Keefe and P. R. Buseck. Computation of high resolution TEM images of materials. Trans. American Crystallography Assoc., 15:27–46, 1979.Google Scholar
  99. 380.
    M. A. O’Keefe, P. R. Buseck, and S. Iijima. Computed crystal structure images for high resolution electron microscopy. Nature, 274:322–324, 1978.ADSCrossRefGoogle Scholar
  100. 381.
    M. A. O’Keefe and R. Kilaas. Advances in high-resolution image simulation. In P. W. Hawkes, F. P. Ottensmeyer, W. O. Saxton, and A. Rosenfeld, editors, Image and Signal Processing in Electron Microscopy, Scanning Microscopy, Supplement 2, pages 225–244, Chicago, 1988. Scanning Microscopy Intern.Google Scholar
  101. 382.
    M. A. O’Keefe and J. V. Sanders. n-beam lattice images. VI. degradation of image resolution by a combination of incident-beam divergence and spherical aberration. Acta Cryst., A31:307–310, 1975.ADSCrossRefGoogle Scholar
  102. 385.
    N. L. O’Leary and L. J. Allen. Quantitative structure retrieval at atomic resolution. Acta Cryst., A61:252–259, 2005.CrossRefGoogle Scholar
  103. 387.
    Colin Ophus. A fast image simulation algorithm for scanning transmission electron microscopy. Advanced Structural and Chemical Imaging, 3:13, 2017.CrossRefGoogle Scholar
  104. 398.
    S. J. Pennycook and D. E. Jesson. High-resolution incoherent imaging of crystals. Phys. Rev. Let., 64:938–941, 1990.ADSCrossRefGoogle Scholar
  105. 400.
    S. J. Pennycook and D. E. Jesson. Atomic resolution Z-contrast imaging of interfaces. Acta Metall. Mater., 40:S149–S159, 1992.CrossRefGoogle Scholar
  106. 402.
    A. Pidwerbetsky and R. V. E. Lovelace. Chaotic wave propagation in a random medium. Physics Letters A, 140:411–415, 1989.ADSCrossRefGoogle Scholar
  107. 406.
    W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes. Cambridge University Press, Cambridge, 3rd edition, 2007.zbMATHGoogle Scholar
  108. 409.
    M. J. Quinn. Parallel Programming in C with MPI and openMP. McGraw Hill, New York, 2004.Google Scholar
  109. 410.
    M. Radek, J.-G. Tenberge, S. Hilke, G. Wilde, and M. Peterlechner. STEMcl- a multi-GPU multislice algorithm for simulation of large structure and imaging parameter series. Ultramicroscopy, 188:24–30, 2018.CrossRefGoogle Scholar
  110. 414.
    L. Reimer. Transmission Electron Microscopy, volume 36 of Spring Series in Optical Sciences. Springer-Verlag, New York, third edition, 1993.Google Scholar
  111. 422.
    M. D. Robertson, J. C. Bennett, M. M. J. Burns, and D. Currie. The simulation of annular dark field images of InAs/InP quantum dots. In P. Kotula, M. Marko, J.-H. Scott, R. Gauvin, D. Beniac, G. Lucas, S. McKernan, and J. Shields, editors, Microscopy and Microanalysis 2006, volume 12, suppl. 2, pages 714–715, Cambridge, UK, 2006. Cambridge Univ. Press.Google Scholar
  112. 431.
    H. Rullgård, L.-G. Öfverstedt, S. Masich, B. Daneholt, and O. Öktem. Simulation of transmission electron microscope images of biological specimens. J. Microscopy, 243:234–256, 2011.CrossRefGoogle Scholar
  113. 433.
    Jason Sanders and Edward Kandrot. CUDA by Example, An Intr. to General-Purpose GPU Programming. Addison-Wesley, Boston, 2011.Google Scholar
  114. 448.
    Noah Schnitzer, Suk Hyun Sung, and Robert Hovden. Intro. to the ronchigram and its calculation with ronchigram.com. Microscopy Today, May:12–15, 2019.Google Scholar
  115. 452.
    P. G. Self, M. A. O’Keefe, P. R. Buseck, and A. E. C. Spargo. Practical computation of amplitudes and phases in electron diffraction. Ultramicroscopy, 11:35–52, 1983.CrossRefGoogle Scholar
  116. 467.
    A. E. C. Spargo, M. J. Beeching, and L. J. Allen. Inversion of electron scattering intensity for crystal structure analysis. Ultramicroscopy, 55:329–333, 1994.CrossRefGoogle Scholar
  117. 469.
    J. C. H. Spence. Direct inversion of dynamical electron diffraction patterns to structure factors. Acta Cryst., A54:7–18, 1998.CrossRefGoogle Scholar
  118. 470.
    J. C. H. Spence. High-Resolution Electron Microscopy. Oxford University Press, New York, fourth edition, 2013.Google Scholar
  119. 471.
    J. C. H. Spence, B. Calef, and J. M. Zuo. Dynamic inversion by the method of generalized projections. Acta Cryst., A55:112–118, 1999.CrossRefGoogle Scholar
  120. 474.
    J. C. H. Spence and J. M. Zuo. Electron Microdiffraction. Plenum Press, New York, 1992.CrossRefGoogle Scholar
  121. 475.
    P. A. Stadelmann. EMS - a software package for electron diffraction analysis and HREM image simulation in materials science. Ultramicroscopy, 21:131–146, 1987.CrossRefGoogle Scholar
  122. 476.
    P. A. Stadelmann. JEMS - EMS java version, 2004. www.cimewww.epfl.ch/people/stadelmann/jemsWebSite/jems.html.
  123. 478.
    L. Sturkey. The calculation of electron diffraction intensities. Proc. Phys. Soc., 80:321–354, 1962.ADSzbMATHCrossRefGoogle Scholar
  124. 493.
    M. Tournaire. Recent developments of the matrical and semi-reciprocal formulation in the field of dynamical theory. J. of the Physical Society of Japan, Suppl. B II, 17:98–100, 1962.Google Scholar
  125. 500.
    W. van den Broek, X. Jiang, and C. T. Koch. FDES, a GPU-based multislice algorithm with increased efficiency of the computation of the potential. Ultramicroscopy, 158:89–97, 2015.CrossRefGoogle Scholar
  126. 501.
    D. van Dyck. The path integral formalism as a new description for the diffraction of high-energy electrons in crystals. Phys. Stat. Sol., B72:321–336, 1975.ADSCrossRefGoogle Scholar
  127. 502.
    D. van Dyck. On the optimisation of methods for the computation of many-beam structure images. In J. M. Sturgess, V. I. Kalnins, F. P. Ottensmeyer, and G. T. Simon, editors, Electron Microscopy 1978, Vol. 1, Ninth Intern. Congress on Electron Microscopy (Toronto), pages 196–197, Ontario, 1978. The Imperial Press.Google Scholar
  128. 503.
    D. van Dyck. Improved methods for the high speed calculation of electron microscopic structure images. Phys. Stat. Sol., A52:283–292, 1979.ADSCrossRefGoogle Scholar
  129. 504.
    D. van Dyck. Fast computational procedures for the simulation of structures in complex or disordered crystal: A new approach. J. of Microscopy, 119:141–152, 1980.CrossRefGoogle Scholar
  130. 505.
    D. van Dyck. High-speed computation techniques for the simulation of high resolution electron micrographs. J. of Microscopy, 132:31–42, 1983.CrossRefGoogle Scholar
  131. 506.
    D. van Dyck. Image calculations in high-resolution electron microscopy: Problems, progress, and prospects. In P. W. Hawkes, editor, Advances in Electronics and Electron Physics, Vol. 65, pages 295–355. Academic Press, Orlando, 1985.Google Scholar
  132. 507.
    D. van Dyck and W. Coene. The real space method for dynamical electron diffraction calculation in high resolution electron microscopy, I. principles of the method. Ultramicroscopy, 15:29–40, 1984.CrossRefGoogle Scholar
  133. 514.
    C. Wacker and R. R. Schröder. Multislice algorithms revisited: Solving the Schrödinger equation numerically for imaging electrons. Ultramicroscopy, 151:211–223, 2015.CrossRefGoogle Scholar
  134. 526.
    K. Watanabe. n-beam dynamical calculations. In P. W. Hawkes, editor, Advances in Electronics and Electron Physics, Vol. 86, pages 173–224. Academic Press, San Diego, 1993.Google Scholar
  135. 527.
    K. Watanabe, Y. Kikuchi, K. Hiratsuka, and H. Yamaguchi. A new approach for n-beam lattice image calculation. Phys. Status Solidi, A109:119–126, 1988.ADSCrossRefGoogle Scholar
  136. 528.
    K. Watanabe, Y. Kikuchi, K. Hiratsuka, and H. Yamaguchi. A new approach for n-beam dynamical calculations. Acta. Cryst., A46:94–98, 1990.CrossRefGoogle Scholar
  137. 529.
    K. Watanabe, T. Yamazaki, I. Hashimoto, and M. Shiojiri. Atomic-resolution annular dark-field STEM image calculations. Phys. Rev. B, 64:115432, 2001.ADSCrossRefGoogle Scholar
  138. 531.
    G. H. Weiss and A. A. Maradudin. The Baker-Hausdorff formula and a problem in crystal physics. J. Math. Phys., 3:771–777, 1962.ADSMathSciNetzbMATHCrossRefGoogle Scholar
  139. 533.
    R. M. Wilcox. Exponential operators and parameter differentiation in quantum physics. J. Math. Physics, 8:962–982, 1967.ADSMathSciNetzbMATHCrossRefGoogle Scholar
  140. 535.
    A. R. Wilson and A. E. C. Spargo. Calculation of the scattering from defects using periodic continuation methods. Phil. Mag., A46:435–449, 1982.ADSCrossRefGoogle Scholar
  141. 549.
    J. M. Zuo. Web electron microscopy applications software (WebEMAPS), 2009. emaps.mrl.uiuc.edu/.Google Scholar
  142. 550.
    Jian Min Zuo and John C. H. Spence. Advanced Transmission Electron Microscopy, Imaging and Diffraction in Nanoscience. Springer, New York, 2017.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Earl J. Kirkland
    • 1
  1. 1.School of Applied & Engineering PhysicsCornell UniversityIthacaUSA

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