Basis of High-Resolution Electron Microscopy

  • Daisuke Shindo
  • Kenji Hiraga


We first describe the main principles of electron microscopy. The formation of images in a transmission electron microscope can be understood from an optical ray diagram with an optical objective lens, as shown in Fig. 1.1. When a crystal of lattice spacing d is irradiated with electrons of wavelength λ, diffracted waves will be produced at specific angles 2θ Satisfying the Bragg condition, i.e.,
$$ 2d\sin \theta = \lambda . $$
The diffracted waves form diffraction spots on the back focal plane. In an electron microscope, the use of electron lenses allows the regular arrangement of the diffraction spots to be projected on a screen and the so-called electron diffraction pattern can then be observed. If the transmitted and the diffracted beams interfere on the image plane, a magnified image (electron microscope image) can be observed. The space where the diffraction pattern forms is called the reciprocal space, while the space at the image plane or at a specimen is called the real space. As shown in the following section, the scattering from the specimen to the back focal plane, in other words, the transformation from the real space to the reciprocal space, is mathematically given by the Fourier transform.


Reciprocal Space Incident Electron Diffract Beam Transmission Function Chromatic Aberration 
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Copyright information

© Springer-Verlag Tokyo 1998

Authors and Affiliations

  • Daisuke Shindo
    • 1
  • Kenji Hiraga
    • 2
  1. 1.Institute for Advanced Materials ProcessingTohoku UniversityAoba-ku, Sendai, MiyagiJapan
  2. 2.Institute for Materials ResearchTohoku UniversityAoba-ku, Sendai, MiyagiJapan

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