Electron Beams, Lenses, and Optics

List of Symbols

IX. Geometrical Aberrations of Lenses


9.1 Types of Aberrations


9.2 Third-Order Theory


9.3 Geometrical Aberrations


9.4 Classification of the Geometrical Aberrations


9.5 Description of the Aberration Figures


9.6 Calculation of the Geometrical Aberration Coefficients


9.7 Solution for Paraxial Rays


9.8 Calculation of the Aberrations


9.9 Spherical Aberration


9.10 Coma Coefficient


9.11 Anisotropie Coma Coefficient


9.12 Curvature Coefficient


9.13 Astigmatism Coefficient


9.14 Anisotropie Astigmatism Coefficient


9.15 Distortion Coefficient


9.16 Anisotropie Distortion Coefficient

Further Reading

X. The Spherical Aberration of Electric and Magnetic Lenses


10.1 The Impossibility of Canceling the Spherical Aberration


10.2 Definition of the Coefficient Cs


10.3 Disk of Minimum Confusion


10.4 The Spherical Aberration of the Combination of Two Thin Lenses


10.5 Conversion of Cs from One Object Position to Another


10.6 Derivation of the Coefficient of Spherical Aberration according to Glaser


10.7 Glaser's Expression for Cs of Purely Magnetic Fields


10.8 Spherical Aberration of a Magnetic Lens with a Bell-Shaped Field Distribution


10.9 Spherical Aberration of the Symmetrical Magnetic Lens


10.10 Spherical Aberration of an Electrostatic Immersion Lens


10.11 Spherical Aberration of Einzel Lenses

Further Reading

XI. Measurement of the Spherical Aberration of Various Electric and Magnetic Lenses


11.1 The Pepperpot Method or Hartmann's Test


11.2 The Shadow Method


11.3 The Halo Method


11.4 The Knife-Edge Method


11.5 The Tilt Method


11.6 The Diffraction Method


11.7 The Combined Tilt and Diffraction Method

Further Reading

XII. Theory of Diffraction


12.1 General Properties of a Wave


12.2 The Plane Wave


12.3 The de Broglie and Planck Relations


12.4 Huygens' Principle


12.5 Diffraction


12.6 The Wave Equation


12.7 Kirchhoff's Diffraction Equation


12.8 Fraunhofers Diffraction through a Circular Aperture


12.9 Resolving Power of an Ideal Optical System

XIII. The Influence of Space Charge in High Density Electron Beams


13.1 Force Due to Magnetic Attraction


13.2 Force Due to Coulomb Repulsion


13.3 The Universal Curve


13.4 Numerical Examples

Further Reading

XIV. Chromatic Aberration


14.1 Development of the Expressions for Chromatic Aberration


14.2 Chromatic Aberration at the Focal Point


14.3 Upper Limit of the Chromatic Aberration of Magnetic Lenses


14.4 Upper Limit of the Chromatic Aberration of Electrostatic Lenses


14.5 Coefficient of Chromatic Aberration


14.6 Chromatic Aberration of a Magnetic Lens with the Glaser Bell-Shaped Field


14.7 Minimum Value of Cc and 8


14.8 Chromatic Aberration of the Symmetrical Magnetic Lens


14.9 Current Limit at the Focus Due to the Velocity Spread of the Emitted Electrons


14.10 Numerical Example


14.11 Simplified Derivation

Further Reading

References

Index