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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