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Electron Holography

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References

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Electron Holographic Tomography and Dark-Field Electron Holography

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Author information

Authors and Affiliations

  1. Institute for Optics and Atomic Physics, TU Berlin, Berlin, Germany

    Michael Lehmann

  2. Triebenberg Laboratory, TU Dresden, Dresden, Germany

    Hannes Lichte

Authors
  1. Michael Lehmann
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  2. Hannes Lichte
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Corresponding author

Correspondence to Michael Lehmann .

Editor information

Editors and Affiliations

  1. University of Connecticut, Storrs, Connecticut, USA

    C. Barry Carter

  2. Ohio State University, Columbus, Ohio, USA

    David B. Williams

Appendix

Appendix

8.1.1 People

Dennis Gábor, born June 5, 1900 in Budapest, died February 8, 1979 in London; inventor of holography, 1947; received Nobel Prize, 1971.

Gottfried Möllenstedt , born September 14, 1912 in Versmold, died September 11, 1997 in Tübingen; fundamental experiments on electron interferometry; inventor of the Möllenstedt biprism (together with Heinrich Düker in 1954), initially using a metal-coated spider’s web.

Akira Tonomura, born April 25, 1942, died May 2, 2012; known for his work on electron holography and in particular for the experimental verification of the Aharonov–Bohm effect. His family moved away from Hiroshima two months before August 1945. He worked in Tübingen 1973–4.

8.1.2 Self-Assessment Questions

Q9.1:

Why should you consider using electron holography in an image C s-corrected TEM for atomic imaging?

Q9.2:

Why it is not possible to image the potential distribution of a p–n junction in a fully image C s-corrected TEM?

Q9.3:

Why it is so important to image the phase of the object exit-wave? How this is done at least partially in conventional TEM?

Q9.4:

What is the difference between a diffractogram and a diffraction pattern?

Q9.5:

Name the contributions to shifting the phase of an electron wave.

Q9.6:

Why is there a difference between an object exit-wave and an image wave?

Q9.7:

What are experimental prerequisites for imaging electric potentials on the mesoscopic scale?

Q9.8:

Why does electron holography use an elliptically shaped illumination ?

Q9.9:

Why it is so important to first maximize the interference fringe contrast and only second the number of registered electrons?

Q9.10:

What are the possible applications of electron holography in material sciences?

Q9.11:

What is the difference between the phase of the electron wave and the geometric phase?

Q9.12:

What are the reasons that reconstructions from electron holograms are not 3D?

Q9.13:

What is the difference between strain and displacement field?

8.1.3 Text-Specific Questions

T9.1:

Calculate the imaging of an object exit-wave into the image wave and its recording as intensity on the detector within the weak object approximation.

T9.2:

Perform the tricky integration to show that the phase shift of the electron wave is caused by the projected potential and the enclosed magnetic flux .

T9.3:

Look up the mathematical formulation of the wave aberration χ. Which aberrations are included and which are not? Why?

T9.4:

Show that two coherent inclined waves brought to an overlap produce a cosinusoidal interference pattern on the detector.

T9.5:

Show by calculation that distortion-induced phase modulations can indeed be corrected by an empty hologram.

T9.6:

How are aberrations corrected numerically?

T9.7:

What are dead layers in the context of imaging p–n junctions, and why is this model too simple?

T9.8:

Make a sketch of the ray paths for dark-field electron holography.

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Lehmann, M., Lichte, H. (2016). Electron Holography. In: Carter, C., Williams, D. (eds) Transmission Electron Microscopy. Springer, Cham. https://doi.org/10.1007/978-3-319-26651-0_8

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