Abstract

In this paper, we present the theoretical background to electron scattering in an atomic potential and the differences between low- and high-energy electrons interacting with matter. We discuss several interferometric techniques that can be realized with low- and high-energy electrons and which can be applied to the imaging of non-crystalline samples and individual macromolecules, including in-line holography, point projection microscopy, off-axis holography, and coherent diffraction imaging. The advantages of using low- and high-energy electrons for particular experiments are examined, and experimental schemes for holography and coherent diffraction imaging are compared.

Highlights

  • We present the theoretical background to electron scattering in an atomic potential, and highlight the differences between low- and high-energy electrons interacting with matter

  • We discuss several interferometric techniques that can be realized with low- and high-energy electrons and which can be applied to the imaging of non-crystalline samples and individual macromolecules, including in-line holography, point projection microscopy, off-axis holography, and coherent diffraction imaging

  • We present several interferometric techniques that can be realized with electrons, following the chronological order in which they were discovered, and provide some examples

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Summary

Introduction

We present the theoretical background to electron scattering in an atomic potential, and highlight the differences between low- and high-energy electrons interacting with matter. This theoretical introduction provides the background and definitions necessary for the remaining sections. We present several interferometric techniques that can be realized with electrons, following the chronological order in which they were discovered (in-line holography, point projection microscopy, off-axis holography, and coherent diffraction imaging), and provide some examples. The advantages and disadvantages of various techniques realized with low- and high-energy electrons are discussed

The Wavelength of an Electron
The Schrödinger Equation
The Born Approximation
Scattering Amplitude
Examples of Scattering Amplitudes
Phase Shift of an Electron Wave in Electric and Magnetic Fields
Phase Shift of an Electron Wave in an Electric Potential
Transmission Functions
Phase Shift of an Electron Wave in a Magnetic Potential
Wavefront Propagation
Holography Principle
Coherence
Principle of Gabor Holography
The Electron Biprism
Electrostatic Potential
Magnetic Potential
Reconstruction of an Off-Axis Hologram
Low-Energy Electron Off-Axis Holography
Further Reading about Off-Axis Holography
In-Line Holography in TEM
Single In-Line Hologram and Its Reconstruction
Experimental Arrangement
Reconstruction of In-Line Holograms
Imaging Biological Samples and Individual Macromolecules
Imaging Electric Potentials
CDI with High-Energy Electrons
CDI with Low-Energy Electrons
10. Discussion
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