page_title: High-resolution transmission electron microscopy
section_title: Exit wave reconstruction
hierarchical_section_title: High-resolution transmission electron microscopy / Image contrast and interpretation / Exit wave reconstruction
caption_attribution_description: Deutsch: (links) Die Elektronenwelle verlässt die Probe und wird durch das Mikroskop bis zur Bildebene geleitet. (unten) Der Fokus wird schrittweise geändert und eine Serie von Bildern wird aufgenommen. Das Interferenzmuster der Bilder ändert sich entsprechend der CTF und erlaubt Phasenbestimmung der Bildwelle. (rechts) Die Welle wird zur Probe zurück propagiert und die exit-Welle wird wiederhergestellt.
context_page_description: High-resolution transmission electron microscopy is an imaging mode of specialized transmission electron microscopes that allows for direct imaging of the atomic structure of the sample. HRTEM is a powerful tool to study properties of materials on the atomic scale, such as semiconductors, metals, nanoparticles and sp²-bonded carbon. While HRTEM is often also used to refer to high resolution scanning TEM, this article describes mainly the imaging of an object by recording the 2D spatial wave amplitude distribution in the image plane, in analogy to a "classic" light microscope. For disambiguation, the technique is also often referred to as phase contrast TEM. At present, the highest point resolution realised in phase contrast TEM is around 0.5 ångströms. At these small scales, individual atoms of a crystal and its defects can be resolved. For 3-dimensional crystals, it may be necessary to combine several views, taken from different angles, into a 3D map. This technique is called electron crystallography.
  One of the difficulties with HRTEM is that image formation relies on phase contrast.
context_section_description: To calculate back to φₑ(x,u) the wave in the image plane is back propagated numerically to the sample. If all properties of the microscope are well known, it is possible to recover the real exit wave with very high accuracy.
  First however, both phase and amplitude of the electron wave in the image plane must be measured. As our instruments only record amplitudes, an alternative method to recover the phase has to be used. There are two methods in use today:
  Holography, which was developed by Gabor expressly for TEM applications, uses a prism to split the beam into a reference beam and a second one passing through the sample. Phase changes between the two are then translated in small shifts of the interference pattern, which allows recovering both phase and amplitude of the interfering wave.
  Through focal series method takes advantage of the fact that the CTF is focus dependent. A series of about 20 pictures is shot under the same imaging conditions with the exception of the focus which is incremented between each take. Together with exact knowledge of the CTF the series allows for computation of φₑ(x,u) (see figure).
  Both methods extend the point resolution of the microscope past the information limit, which is the highest possible resolution achievable on a given machine. The ideal defocus value for this type of imaging is known as Lichte defocus and is usually several hundred nanometers negative.
caption: Exit wave reconstruction through focal series
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