Aberration-Corrected Imaging in Transmission Electron Microscopy

The following sections are included:

• Preface

• Contents

The following sections are included:

• Where are the Atoms?

• Brief Historical Overview

• Scope of the Book

• General Outline

The following sections are included:

• Overview

• The Exit-Plane Wave
  • The weak phase object approximation
  • Dynamic scattering theories

• Image Formation

• The Phase Contrast Transfer Function
  • The objective aperture
  • Lens effects
    • Scherzer focus
  • Partial spatial and partial temporal coherence
    • Partial temporal coherence
    • Partial spatial coherence
    • The phase contrast transfer function for partial coherent illumination
  • Point resolution and information limit
    • Point resolution
    • Information limit
  • Other factors
    • Non-ideal recording devices
    • Stability issues
    • The scattering amplitude
    • The finite field of view

• Non-Linear Imaging

• Summary

The following sections are included:

• Overview

• Geometrical Considerations
  • The diffraction limit
  • Lens effects — spherical aberration
  • Partial temporal coherence — chromatic aberration
  • Partial spatial coherence — the effective source size
  • Stability
  • Small electron probes

• Wave Optical Description of an Electron Probe
  • Diffraction
  • Defocus and spherical aberration
  • Geometrical source size
  • Energy spread of the electron beam
  • Concluding remarks

• Summary

The following sections are included:

• The Case of Transmission Electron Microscopy

• The Case of Scanning Transmission Electron Microscopy

• Summary

The following sections are included:

• The Electron Microscope

• Newton's Second Law of Motion and Electron Optics

• The Hamiltonian Analogy

• Geometrical Electron Optics

• Electrons in the Electrostatic Field
  • Snell's law of refraction
  • Snell's law of refraction for electrons
  • Fermat's principle: The shortest light optical path
  • The reduced principle of least action
  • The point eikonal

• Electrons in the Stationary Electromagnetic Field
  • Principle of Maupertius
  • The refractive index of electrons
  • Geometrical wave surfaces

• Summary

The following sections are included:

• Geometry and Coordinate Systems

• Fields and Lenses

• The Paraxial Approximation

• Path Equation of an Electrostatic Field

• Path Equation of a Stationary Magnetic Field
  • The homogeneous rotationally symmetric magnetic field
    • Three preliminary cases
    • Larmor precession
    • Properties of a homogeneous magnetic field
    • Application of the paraxial approximation
    • Deviation from the paraxial approximation
  • The rotationally symmetric magnetic field
    • General properties
    • The path equation
  • The rotationally symmetric electromagnetic field
    • Strategy
    • Equations of motion in the fixed cartesian coordinate system
    • Larmor precession
    • The path equation in the rotating coordinate system

• Series Expansion of the Fields

• Imaging Within the Paraxial Approximation
  • Theorem of optical imaging
  • Generalized theorem of Lippich
  • Real image and virtual image
  • Asymptotic cardinal elements
    • Real vs. asymptotic focal point
    • Object and image focal points
    • Object and image focal lengths
    • Newton's equation
    • Geometrical image construction
    • Lateral and longitudinal magnification
    • Telescopic system
    • Nodal ray and nodal points
    • The TEM objective lens

• Summary

The following sections are included:

• Overview

• Image Aberrations

• Types of Aberrations
  • Axial aberrations vs. off-axial aberrations
  • Chromatic aberrations vs. geometrical aberrations
    • Chromatic aberrations
    • Geometrical aberrations

• Geometrical Aberration of a Round Electron Lens
  • Spherical aberration
  • Coma
  • Field astigmatism and field curvature
  • Distortion
  • Summary

• Wave Surface, Aberration Function and Image Aberrations
  • HRTEM and STEM
  • Non-ideal geometrical wave surfaces
  • The aberration function
  • Other notations for axial aperture aberrations
  • Aberration function and image aberrations

• Summary

The following sections are included:

• Overview
  • Strategies to deal with the spherical aberration
  • Strategies to correct the spherical aberration

• Multi-Pole Lenses
  • Quadrupoles
  • Hexapoles
  • Octupoles

• The Basic Principles of Spherical Aberration Correctors
  • Hexapole spherical aberration corrector
  • Quadrupole–octupole spherical aberration corrector

• Beyond the Basic Principles — Parasitic Aberrations and Other Complications
  • The multitude of axial aberrations
  • Residual intrinsic axial aberrations
  • Balancing the effect of higher-order aberrations
  • Off-axial aberrations
  • The chromatic aberration
  • Dealing with the fifth-order spherical aberration

• Improved Correctors
  • Fifth-order correction with hexapole fields
  • Fifth-order correction with quadrupole–octupole fields
  • Correction of geometrical and chromatic aberrations
    • Stability
    • Spatial coherence
    • Monochromatic electron beams
    • Spherical and chromatic aberration corrector

• Summary

The following sections are included:

• Aberration Diagnosis
  • Geometrical resolution limit
  • Zemlin-tableau method
  • Tilt tableaux for probe-forming microscopes
  • Ronchigram methods
  • Other methods

• Aberration-Corrected HRTEM
  • The coherent phase contrast transfer function
  • Incoherent contributions
    • Enhanced instrument stability
    • Overcoming the limitation imposed by partial coherence
  • Summary

• Aberration-Corrected STEM
  • Illumination aperture
  • Geometrical aberrations
  • Partial coherence
    • Effective source size
    • Chromatic aberration
  • Considerations about small electron probes

• New Possibilities and New Limits

The following sections are included:

• Appendix A Physical Constants, Abbreviations, Acronyms and Symbols

• Bibliography

• Index

• About the Author