Principles of Electron Optics, Volume 1 : Basic Geometrical Optics.
Hawkes, Peter W.
Principles of Electron Optics, Volume 1 : Basic Geometrical Optics. - 2nd ed. - 1 online resource (729 pages)
Front Cover -- Principles of Electron Optics -- Copyright Page -- Contents -- Preface to the Second Edition -- Preface to the First Edition (Extracts) -- Acknowledgments -- 1 Introduction -- 1.1 Organization of the Subject -- 1.2 History -- I. Classical Mechanics -- 2 Relativistic Kinematics -- 2.1 The Lorentz Equation and General Considerations -- 2.2 Conservation of Energy -- 2.3 The Acceleration Potential -- 2.4 Definition of Coordinate Systems -- 2.5 Conservation of Axial Angular Momentum -- 3 Different Forms of Trajectory Equations -- 3.1 Parametric Representation in Terms of the Arc-Length -- 3.2 Relativistic Proper-Time Representation -- 3.3 The Cartesian Representation -- 3.4 Scaling Rules -- 4 Variational Principles -- 4.1 The Lagrange Formalism -- 4.2 General Rotationally Symmetric Systems -- 4.3 The Canonical Formalism -- 4.4 The Time-Independent Form of the Variational Principle -- 4.5 Static Rotationally Symmetric Systems -- 5 Hamiltonian Optics -- 5.1 Introduction of the Characteristic Function -- 5.2 The Hamilton-Jacobi Equation -- 5.3 The Analogy With Light Optics -- 5.4 The Influence of Vector Potentials -- 5.5 Gauge Transformations -- 5.6 Poincaré's Integral Invariant -- 5.7 The Problem of Uniqueness -- 5.8 Lie Algebra -- 5.9 Summary -- II. Calculation of Static Fields -- 6 Basic Concepts and Equations -- 6.1 General Considerations -- 6.2 Field Equations -- 6.3 Variational Principles -- 6.4 Rotationally Symmetric Fields -- 6.5 Planar Fields -- 7 Series Expansions -- 7.1 Azimuthal Fourier Series Expansions -- 7.1.1 Scalar Potentials -- 7.1.2 Vector Potentials -- 7.2 Radial Series Expansions -- 7.2.1 Scalar Potentials -- 7.2.2 Vector Potentials -- 7.2.3 Explicit Representations -- 7.3 Rotationally Symmetric Fields -- 7.3.1 Electrostatic Fields -- 7.3.2 Magnetic Fields -- 7.4 Multipole Fields -- 7.5 Planar Fields. 7.6 Fourier-Bessel Series Expansions -- 8 Boundary-Value Problems -- 8.1 Boundary-Value Problems in Electrostatics -- 8.2 Boundary Conditions in Magnetostatics -- 8.3 Examples of Boundary-Value Problems in Magnetostatics -- 8.3.1 Devices with Superconducting Yokes -- 8.3.2 Conventional Round Magnetic Lenses -- 8.3.3 Unconventional Round Magnetic Lenses -- 8.3.4 Toroidal Magnetic Deflection Systems -- 9 Integral Equations -- 9.1 Integral Equations for Scalar Potentials -- 9.1.1 General Theory -- 9.1.2 Dirichlet Problems -- 9.1.3 Neumann Problems -- 9.2 Problems with Interface Conditions -- 9.3 Reduction of the Dimensions -- 9.3.1 Dirichlet Problems -- 9.3.2 Interface Conditions -- 9.3.3 Planar Fields -- 9.4 Important Special Cases -- 9.4.1 Rotationally Symmetric Scalar Potentials -- 9.4.2 Rotationally Symmetric Vector Potentials -- 9.4.3 Unconventional Magnetic Lenses -- 9.4.4 Magnetic Deflection Coils -- 9.4.5 Multipole Systems -- 9.4.6 Small Perturbations of the Rotational Symmetry -- 9.5 Résumé -- 10 The Boundary-Element Method -- 10.1 Evaluation of the Fourier Integral Kernels -- 10.1.1 Introduction of Moduli -- 10.1.2 Radial Series Expansions -- 10.1.3 Recurrence Relations -- 10.1.4 Analytic Differentiation -- 10.2 Numerical Solution of One-Dimensional Integral Equations -- 10.2.1 Conventional Solution Techniques -- 10.2.2 The Charge Simulation Method -- 10.2.3 Combination with Interpolation Kernels -- 10.2.3.1 General formalism -- 10.2.3.2 Marginal positions -- 10.2.3.3 General properties -- 10.2.3.4 Solution of integral equations -- 10.2.3.5 Application to field calculations -- 10.2.4 Evaluation of Improper Integrals -- 10.3 Superposition of Aperture Fields -- 10.3.1 Electric Field of a Single Aperture -- 10.3.2 Superposition Procedure -- 10.3.3 Combination with the BEM -- 10.3.4 Extrapolation of the Number of Segments. 10.4 Three-Dimensional Dirichlet Problems -- 10.5 Examples of Applications of the Boundary-Element Method -- 11 The Finite-Difference Method (FDM) -- 11.1 The Choice of Grid -- 11.2 The Taylor Series Method -- 11.3 The Integration Method -- 11.4 Nine-Point Formulae -- 11.5 The Finite-Difference Method in Three Dimensions -- 11.6 Other Aspects of the Method -- 11.6.1 Expanding Spherical-Mesh Grid -- 11.6.2 Extrapolation on Multiple Grids -- 11.6.3 Combination with the BEM -- 11.7 Iterative Solution Techniques -- 12 The Finite-Element Method (FEM) -- 12.1 Formulation for Round Magnetic Lenses -- 12.2 Formulation for Self-adjoint Elliptic Equations -- 12.3 Solution of the Finite-Element Equations -- 12.4 Improvement of the Finite-Element Method -- 12.4.1 Introduction -- 12.4.2 Alternative Formulations -- 12.4.3 First- and Second-Order Finite-Element Methods (FOFEM and SOFEM) -- 12.5 Comparison and Combination of Different Methods -- 12.6 Deflection Units and Multipoles -- 12.7 Related Work -- 13 Field-Interpolation Techniques -- 13.1 One-Dimensional Differentiation and Interpolation -- 13.1.1 Hermite Interpolation -- 13.1.2 Cubic Splines -- 13.1.3 Differentiation Using Difference Schemes -- 13.1.4 Evaluation of Radial Series Expansions -- 13.2 Two-Dimensional Interpolation -- 13.2.1 Hermite Interpolation -- 13.2.2 The Use of Derivatives of Higher Order -- 13.3 Interpolation and the Finite-Element Method -- III. The Paraxial Approximation -- 14 Introduction to Paraxial Equations -- 15 Systems with an Axis of Rotational Symmetry -- 15.1 Derivation of the Paraxial Ray Equations from the General Ray Equations -- 15.1.1 Physical Significance of the Coordinate Rotation -- 15.2 Variational Derivation of the Paraxial Equations -- 15.3 Forms of the Paraxial Equations and General Properties of their Solutions -- 15.3.1 Reduced Coordinates. 15.3.2 Stigmatic Image Formation -- 15.3.3 The Wronskian -- 15.4 The Abbe Sine Condition and Herschel's Condition -- 15.5 Some Other Transformations -- 16 Gaussian Optics of Rotationally Symmetric Systems: Asymptotic Image Formation -- 16.1 Real and Asymptotic Image Formation -- 16.2 Asymptotic Cardinal Elements and Transfer Matrices -- 16.3 Gaussian Optics as a Projective Transformation (Collineation) -- 16.4 Use of the Angle Characteristic to Establish the Gaussian Optical Quantities -- 16.5 The Existence of Asymptotes -- 17 Gaussian Optics of Rotationally Symmetric Systems: Real Cardinal Elements -- 17.1 Real Cardinal Elements for High Magnification and High Demagnification -- 17.2 Osculating Cardinal Elements -- 17.3 Inversion of the Principal Planes -- 17.4 Approximate Formulae for the Cardinal Elements: The Thin-Lens Approximation and the Weak-Lens Approximation -- Magnetic Lenses -- Electrostatic Lenses -- 18 Electron Mirrors -- 18.1 Introduction -- 18.2 The Modified Temporal Representation -- 18.3 The Cartesian Representation -- 18.4 A Quadratic Transformation -- 19 Quadrupole Lenses -- 19.1 Paraxial Equations for Quadrupoles -- 19.2 Transaxial Lenses -- 20 Cylindrical Lenses -- IV. Aberrations -- 21 Introduction to Aberration Theory -- 22 Perturbation Theory: General Formalism -- 23 The Relation Between Permitted Types of Aberration and System Symmetry -- 23.1 Introduction -- 23.2 N=1 -- 23.2.1 N=1. Systems with a Plane of Symmetry -- 23.3 N=2 -- 23.3.1 N=2. Systems Possessing a Plane of Symmetry -- 23.4 N=3 -- 23.5 N=4 -- 23.6 N=5 and 6 -- 23.7 Systems with an Axis of Rotational Symmetry -- 23.8 Note on the Classification of Aberrations -- 23.8.1 Terms Independent of xo, yo (p=q=0): Aperture Aberrations -- 23.8.2 Terms Independent of xa, ya (r=s=0): Distortions -- 23.8.3 Intermediate Terms -- 23.8.4 Phase Shifts. 23.8.5 Parasitic Aberrations -- 24 The Geometrical Aberrations of Round Lenses -- 24.1 Introduction -- 24.2 Derivation of the Real Aberration Coefficients -- 24.2.1 The Trajectory Method -- 24.2.2 The Eikonal Method -- 24.3 Spherical Aberration (Terms in xa and ya only) -- 24.3.1 Electrostatic case (B=0, ϕ ≠ const) -- General Relativistic Expression -- General Nonrelativistic Expression -- 24.3.2 Magnetic case (ϕ=const, B≠0) -- General Relativistic Case -- 24.3.3 Scherzer's Theorem -- 24.3.4 Thin-Lens Approximation -- 24.4 Coma (Terms Linear in xo, yo) -- 24.4.1 Thin-Lens Formulae -- 24.5 Astigmatism and Field Curvature (Terms Linear in xa, ya) -- 24.5.1 Thin-Lens Formulae -- 24.6 Distortion (Terms in xo and yo only) -- 24.6.1 Thin-Lens Formulae -- 24.7 The Variation of the Aberration Coefficients with Aperture Position -- 24.8 Reduced Coordinates -- 24.9 Seman's Transformation of the Characteristic Function -- 24.10 Fifth-Order Aberrations -- 24.10.1 Isotropic Aberration Coefficients -- 24.10.2 Anisotropic Aberration Coefficients -- 25 Asymptotic Aberration Coefficients -- 25.1 Spherical Aberration -- 25.2 Coma -- 25.3 Astigmatism and Field Curvature -- 25.4 Distortion -- 25.5 Aberration Matrices and the Integrals ij -- 25.6 Dependence on Object Position or Magnification -- 25.7 Dependence on Aperture Position -- 25.8 Thin-Lens Approximations -- 26 Chromatic Aberrations -- 26.1 Real Chromatic Aberrations -- 26.2 Asymptotic Chromatic Aberrations -- 26.3 Higher Order Chromatic Aberration Coefficients -- 26.3.1 Third-Order (Fourth-Rank) Aberrations -- 26.3.1.1 Isotropic Aberrations -- 26.3.1.2 Anisotropic Aberrations -- 26.3.1.3 Definitions -- 26.3.2 Third-Rank Aberrations -- 27 Aberration Matrices and the Aberrations of Lens Combinations -- 28 The Aberrations of Mirrors and Cathode Lenses -- 28.1 The Modified Temporal Theory. 28.2 The Cartesian Theory.
9780081022573
Electron optics.
Electronic books.
QC447 .H395 2018
535.32
Principles of Electron Optics, Volume 1 : Basic Geometrical Optics. - 2nd ed. - 1 online resource (729 pages)
Front Cover -- Principles of Electron Optics -- Copyright Page -- Contents -- Preface to the Second Edition -- Preface to the First Edition (Extracts) -- Acknowledgments -- 1 Introduction -- 1.1 Organization of the Subject -- 1.2 History -- I. Classical Mechanics -- 2 Relativistic Kinematics -- 2.1 The Lorentz Equation and General Considerations -- 2.2 Conservation of Energy -- 2.3 The Acceleration Potential -- 2.4 Definition of Coordinate Systems -- 2.5 Conservation of Axial Angular Momentum -- 3 Different Forms of Trajectory Equations -- 3.1 Parametric Representation in Terms of the Arc-Length -- 3.2 Relativistic Proper-Time Representation -- 3.3 The Cartesian Representation -- 3.4 Scaling Rules -- 4 Variational Principles -- 4.1 The Lagrange Formalism -- 4.2 General Rotationally Symmetric Systems -- 4.3 The Canonical Formalism -- 4.4 The Time-Independent Form of the Variational Principle -- 4.5 Static Rotationally Symmetric Systems -- 5 Hamiltonian Optics -- 5.1 Introduction of the Characteristic Function -- 5.2 The Hamilton-Jacobi Equation -- 5.3 The Analogy With Light Optics -- 5.4 The Influence of Vector Potentials -- 5.5 Gauge Transformations -- 5.6 Poincaré's Integral Invariant -- 5.7 The Problem of Uniqueness -- 5.8 Lie Algebra -- 5.9 Summary -- II. Calculation of Static Fields -- 6 Basic Concepts and Equations -- 6.1 General Considerations -- 6.2 Field Equations -- 6.3 Variational Principles -- 6.4 Rotationally Symmetric Fields -- 6.5 Planar Fields -- 7 Series Expansions -- 7.1 Azimuthal Fourier Series Expansions -- 7.1.1 Scalar Potentials -- 7.1.2 Vector Potentials -- 7.2 Radial Series Expansions -- 7.2.1 Scalar Potentials -- 7.2.2 Vector Potentials -- 7.2.3 Explicit Representations -- 7.3 Rotationally Symmetric Fields -- 7.3.1 Electrostatic Fields -- 7.3.2 Magnetic Fields -- 7.4 Multipole Fields -- 7.5 Planar Fields. 7.6 Fourier-Bessel Series Expansions -- 8 Boundary-Value Problems -- 8.1 Boundary-Value Problems in Electrostatics -- 8.2 Boundary Conditions in Magnetostatics -- 8.3 Examples of Boundary-Value Problems in Magnetostatics -- 8.3.1 Devices with Superconducting Yokes -- 8.3.2 Conventional Round Magnetic Lenses -- 8.3.3 Unconventional Round Magnetic Lenses -- 8.3.4 Toroidal Magnetic Deflection Systems -- 9 Integral Equations -- 9.1 Integral Equations for Scalar Potentials -- 9.1.1 General Theory -- 9.1.2 Dirichlet Problems -- 9.1.3 Neumann Problems -- 9.2 Problems with Interface Conditions -- 9.3 Reduction of the Dimensions -- 9.3.1 Dirichlet Problems -- 9.3.2 Interface Conditions -- 9.3.3 Planar Fields -- 9.4 Important Special Cases -- 9.4.1 Rotationally Symmetric Scalar Potentials -- 9.4.2 Rotationally Symmetric Vector Potentials -- 9.4.3 Unconventional Magnetic Lenses -- 9.4.4 Magnetic Deflection Coils -- 9.4.5 Multipole Systems -- 9.4.6 Small Perturbations of the Rotational Symmetry -- 9.5 Résumé -- 10 The Boundary-Element Method -- 10.1 Evaluation of the Fourier Integral Kernels -- 10.1.1 Introduction of Moduli -- 10.1.2 Radial Series Expansions -- 10.1.3 Recurrence Relations -- 10.1.4 Analytic Differentiation -- 10.2 Numerical Solution of One-Dimensional Integral Equations -- 10.2.1 Conventional Solution Techniques -- 10.2.2 The Charge Simulation Method -- 10.2.3 Combination with Interpolation Kernels -- 10.2.3.1 General formalism -- 10.2.3.2 Marginal positions -- 10.2.3.3 General properties -- 10.2.3.4 Solution of integral equations -- 10.2.3.5 Application to field calculations -- 10.2.4 Evaluation of Improper Integrals -- 10.3 Superposition of Aperture Fields -- 10.3.1 Electric Field of a Single Aperture -- 10.3.2 Superposition Procedure -- 10.3.3 Combination with the BEM -- 10.3.4 Extrapolation of the Number of Segments. 10.4 Three-Dimensional Dirichlet Problems -- 10.5 Examples of Applications of the Boundary-Element Method -- 11 The Finite-Difference Method (FDM) -- 11.1 The Choice of Grid -- 11.2 The Taylor Series Method -- 11.3 The Integration Method -- 11.4 Nine-Point Formulae -- 11.5 The Finite-Difference Method in Three Dimensions -- 11.6 Other Aspects of the Method -- 11.6.1 Expanding Spherical-Mesh Grid -- 11.6.2 Extrapolation on Multiple Grids -- 11.6.3 Combination with the BEM -- 11.7 Iterative Solution Techniques -- 12 The Finite-Element Method (FEM) -- 12.1 Formulation for Round Magnetic Lenses -- 12.2 Formulation for Self-adjoint Elliptic Equations -- 12.3 Solution of the Finite-Element Equations -- 12.4 Improvement of the Finite-Element Method -- 12.4.1 Introduction -- 12.4.2 Alternative Formulations -- 12.4.3 First- and Second-Order Finite-Element Methods (FOFEM and SOFEM) -- 12.5 Comparison and Combination of Different Methods -- 12.6 Deflection Units and Multipoles -- 12.7 Related Work -- 13 Field-Interpolation Techniques -- 13.1 One-Dimensional Differentiation and Interpolation -- 13.1.1 Hermite Interpolation -- 13.1.2 Cubic Splines -- 13.1.3 Differentiation Using Difference Schemes -- 13.1.4 Evaluation of Radial Series Expansions -- 13.2 Two-Dimensional Interpolation -- 13.2.1 Hermite Interpolation -- 13.2.2 The Use of Derivatives of Higher Order -- 13.3 Interpolation and the Finite-Element Method -- III. The Paraxial Approximation -- 14 Introduction to Paraxial Equations -- 15 Systems with an Axis of Rotational Symmetry -- 15.1 Derivation of the Paraxial Ray Equations from the General Ray Equations -- 15.1.1 Physical Significance of the Coordinate Rotation -- 15.2 Variational Derivation of the Paraxial Equations -- 15.3 Forms of the Paraxial Equations and General Properties of their Solutions -- 15.3.1 Reduced Coordinates. 15.3.2 Stigmatic Image Formation -- 15.3.3 The Wronskian -- 15.4 The Abbe Sine Condition and Herschel's Condition -- 15.5 Some Other Transformations -- 16 Gaussian Optics of Rotationally Symmetric Systems: Asymptotic Image Formation -- 16.1 Real and Asymptotic Image Formation -- 16.2 Asymptotic Cardinal Elements and Transfer Matrices -- 16.3 Gaussian Optics as a Projective Transformation (Collineation) -- 16.4 Use of the Angle Characteristic to Establish the Gaussian Optical Quantities -- 16.5 The Existence of Asymptotes -- 17 Gaussian Optics of Rotationally Symmetric Systems: Real Cardinal Elements -- 17.1 Real Cardinal Elements for High Magnification and High Demagnification -- 17.2 Osculating Cardinal Elements -- 17.3 Inversion of the Principal Planes -- 17.4 Approximate Formulae for the Cardinal Elements: The Thin-Lens Approximation and the Weak-Lens Approximation -- Magnetic Lenses -- Electrostatic Lenses -- 18 Electron Mirrors -- 18.1 Introduction -- 18.2 The Modified Temporal Representation -- 18.3 The Cartesian Representation -- 18.4 A Quadratic Transformation -- 19 Quadrupole Lenses -- 19.1 Paraxial Equations for Quadrupoles -- 19.2 Transaxial Lenses -- 20 Cylindrical Lenses -- IV. Aberrations -- 21 Introduction to Aberration Theory -- 22 Perturbation Theory: General Formalism -- 23 The Relation Between Permitted Types of Aberration and System Symmetry -- 23.1 Introduction -- 23.2 N=1 -- 23.2.1 N=1. Systems with a Plane of Symmetry -- 23.3 N=2 -- 23.3.1 N=2. Systems Possessing a Plane of Symmetry -- 23.4 N=3 -- 23.5 N=4 -- 23.6 N=5 and 6 -- 23.7 Systems with an Axis of Rotational Symmetry -- 23.8 Note on the Classification of Aberrations -- 23.8.1 Terms Independent of xo, yo (p=q=0): Aperture Aberrations -- 23.8.2 Terms Independent of xa, ya (r=s=0): Distortions -- 23.8.3 Intermediate Terms -- 23.8.4 Phase Shifts. 23.8.5 Parasitic Aberrations -- 24 The Geometrical Aberrations of Round Lenses -- 24.1 Introduction -- 24.2 Derivation of the Real Aberration Coefficients -- 24.2.1 The Trajectory Method -- 24.2.2 The Eikonal Method -- 24.3 Spherical Aberration (Terms in xa and ya only) -- 24.3.1 Electrostatic case (B=0, ϕ ≠ const) -- General Relativistic Expression -- General Nonrelativistic Expression -- 24.3.2 Magnetic case (ϕ=const, B≠0) -- General Relativistic Case -- 24.3.3 Scherzer's Theorem -- 24.3.4 Thin-Lens Approximation -- 24.4 Coma (Terms Linear in xo, yo) -- 24.4.1 Thin-Lens Formulae -- 24.5 Astigmatism and Field Curvature (Terms Linear in xa, ya) -- 24.5.1 Thin-Lens Formulae -- 24.6 Distortion (Terms in xo and yo only) -- 24.6.1 Thin-Lens Formulae -- 24.7 The Variation of the Aberration Coefficients with Aperture Position -- 24.8 Reduced Coordinates -- 24.9 Seman's Transformation of the Characteristic Function -- 24.10 Fifth-Order Aberrations -- 24.10.1 Isotropic Aberration Coefficients -- 24.10.2 Anisotropic Aberration Coefficients -- 25 Asymptotic Aberration Coefficients -- 25.1 Spherical Aberration -- 25.2 Coma -- 25.3 Astigmatism and Field Curvature -- 25.4 Distortion -- 25.5 Aberration Matrices and the Integrals ij -- 25.6 Dependence on Object Position or Magnification -- 25.7 Dependence on Aperture Position -- 25.8 Thin-Lens Approximations -- 26 Chromatic Aberrations -- 26.1 Real Chromatic Aberrations -- 26.2 Asymptotic Chromatic Aberrations -- 26.3 Higher Order Chromatic Aberration Coefficients -- 26.3.1 Third-Order (Fourth-Rank) Aberrations -- 26.3.1.1 Isotropic Aberrations -- 26.3.1.2 Anisotropic Aberrations -- 26.3.1.3 Definitions -- 26.3.2 Third-Rank Aberrations -- 27 Aberration Matrices and the Aberrations of Lens Combinations -- 28 The Aberrations of Mirrors and Cathode Lenses -- 28.1 The Modified Temporal Theory. 28.2 The Cartesian Theory.
9780081022573
Electron optics.
Electronic books.
QC447 .H395 2018
535.32