Charged Particle Optics Theory

Table of contents

1. Cover Page
2. Title Page
3. Copyright Page
4. Contents
5. Preface
6. 1 Introduction: The optical nature of a charged particle beam
7. 2 Geometrical optics
   1. 2.1 Relativistic classical mechanics
      1. 2.1.1 Hamilton’s principle of least action
      2. 2.1.2 The Hamiltonian function and energy conservation
      3. 2.1.3 Mechanical analog of Fermat’s principle
   2. 2.2 Exact trajectory equation for a single particle
   3. 2.3 Conservation laws
      1. 2.3.1 The Lagrange invariant
      2. 2.3.2 Liouville’s theorem and brightness conservation
   4. 2.4 General curvilinear axis
      1. 2.4.1 Equation of motion in terms of transverse coordinates and slopes
      2. 2.4.2 Natural units
   5. 2.5 Axial symmetry
      1. 2.5.1 Exact equations of motion for axially symmetric fields
      2. 2.5.2 Paraxial approximation, Gaussian optics
      3. 2.5.3 Series solution for the general ray equation
      4. 2.5.4 Space charge
      5. 2.5.5 The primary geometrical aberrations
      6. 2.5.6 Spherical aberration
      7. 2.5.7 Field aberrations
      8. 2.5.8 Chromatic aberration
      9. 2.5.9 Intensity point spread function
   6. 2.6 Stochastic Coulomb scattering
      1. 2.6.1 Monte Carlo simulation
      2. 2.6.2 Analytical approximation by Markov’s method of random flights
   7. 2.7 Hamilton–Jacobi theory
      1. 2.7.1 Canonical transformations
      2. 2.7.2 Applications of Hamilton–Jacobi theory
      3. 2.7.3 Hamilton–Jacobi theory and geometrical optics
8. 3 Wave optics
   1. 3.1 Quantum mechanical description of particle motion
      1. 3.1.1 The postulates of quantum mechanics
      2. 3.1.2 Particle motion in a field-free space
      3. 3.1.3 Wave packet propagation and the Heisenberg uncertainty principle
      4. 3.1.4 The quantum mechanical analog of Fermat’s principle for matter waves
   2. 3.2 Particle motion in a general electromagnetic potential
      1. 3.2.1 Path integral approach for the time-dependent wave function
      2. 3.2.2 Series solution for a particle in a general electromagnetic potential
      3. 3.2.3 Quantum interference effects in electromagnetic potentials
      4. 3.2.4 The Klein–Gordon equation and the covariant wave function
      5. 3.2.5 Physical interpretation of the wave function and its practical application
   3. 3.3 Diffraction
      1. 3.3.1 The Fresnel–Kirchhoff relation
      2. 3.3.2 The Fresnel and Fraunhofer approximations
      3. 3.3.3 Amplitude in the Gaussian image plane
      4. 3.3.4 Amplitude in the diffraction plane
      5. 3.3.5 Optical transformation for a general imaging system with coherent illumination
      6. 3.3.6 Optical transformation for a general imaging system with incoherent illumination
      7. 3.3.7 The wave front aberration function
      8. 3.3.8 Relationship between diffraction and the Heisenberg uncertainty principle
9. 4 Particle scattering
   1. 4.1 Classical particle kinematics
   2. 4.2 Scattering cross section and classical scattering
   3. 4.3 Integral expression of Schrödinger’s equation
   4. 4.4 Green’s function solution for elastic scattering
   5. 4.5 Perturbation theory
   6. 4.6 Perturbation solution for elastic scattering
   7. 4.7 Inelastic scattering of a particle by a target atom
   8. 4.8 Slowing of a charged particle in a dielectric medium
   9. 4.9 Small angle plural scattering of fast electrons
10. 5 Electron emission from solids
    1. 5.1 The image force
    2. 5.2 The incident current density
    3. 5.3 Thermionic emission
    4. 5.4 Field emission
    5. 5.5 Emission with elevated temperature and field
    6. 5.6 Space charge limited emission
11. Appendix A The Fourier transform
12. Appendix B Linear second-order differential equation
13. Bibliography
14. Index