Principles of Electron Optics

Volume 1 Basic Geometrical Optics

CLASSICAL MECHANICS

• Relativistic Kinematics
  • The Lorentz equation and general
  • considerations
  • Conservation of energy
  • The acceleration potential
  • Definition of coordinate systems
  • Conservation of axial angular momentum
• Different Forms of Trajectory Equations
  • Parametric representation in terms of the arc-length
  • Relativistic proper-time representation
  • The cartesian representation
  • Scaling rules
• Variational Principles
  • The Lagrange formalism
  • General rotationally symmetric systems
  • The canonical formalism
  • The time-independent form of the
  • variational principle
  • Static rotational ly symmetric systems
• Hamiltonian Optics
  • Introduction of the characteristic function
  • The Hamilton-Jacobi equation
  • The analogy with light optics
  • The influence of vector potentials
  • Gauge transformations
  • Poincare’s integral invariant
  • The problem of uniqueness

CALCULATION OF STATIC FIELDS

• Basic Concepts and Equations
• Series Expansions
• Boundary-Value Problems
• Integral Equations
• The Boundary-Element Method
• The Finite-Difference Method (FDM)
• The Finite-Element Method (FEM)
• Field-Interpolation Techniques

THE PARAXlAL APPROXIMATION

• Introduction
• Systems with an Axis of Rotational Symmetry
• Gaussian Optics of Rotationally Symmetric Systems: Asymptotic Image Formation
• Gaussian Optics of Rotationally Symmetric Systems: Real Cardinal Elements
• Electron Mirrors
• Quadrupole Lenses
• Cylindrical Lenses

ABERRATIONS

• Introduction
• Perturbation Theory: General Formalism
• The Relation Between Permitted Types of Aberration and System Symmetry
• The Geometrical Aberrations of Round Lenses
• Asymptotic Aberration Coefficients
• Chromatic Aberrations
• Aberration Matrices and the Aberrations of Lens Combinations
• The Aberrations of Mirrors and Cathode Lenses
• The Aberrations of Quadrupole Lenses and Octopoles
• The Aberrations of Cylindrical Lenses
• Parasitic Aberrations

DEFLECTION SYSTEMS

• Deflection Systems and their Aberrations

COMPUTER-AIDED ELECTRON OPTICS

• Numerical Calculation of Trajectories, Paraxial Properties and Aberrations
• The Use of Computer Algebra Languages