Principles of Electron Optics, Three Volume Set: Principles of Electron Optics: Basic Geometrical Optics

665 Pages·1996·20.31 MB·English

by  Peter W. Hawkes

Principles of
Electron Optics
Corrections for this volume are to be found after the index.
Principles of
Electron Optics
Volume 1
Basic Geometrical Optics
by
P. W. HAWKES
CNRS Laboratory of Electron Optics,
Toulouse, France
and
E. KASPER
Institut f~r Angewandte Physik
Universit~t T6bingen,
Federal Republic of Germany
•
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Copyright © 1996
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British Library Cataloguing in Publication Data
Hawkes, P. W.
Principles of electron optics.
Vol 1: Basic Geometrical Optics
1. Electron Optics
I. Title II. Kasper, E.
537.5'6
ISBN 0-12-333341-5
Printed in Great Britain by St Edmundsbury Press Limited,
Bury St Edmunds, Suffolk.
Contents of Volume 1
Basic Geometrical Optics
Preface
Chapter 1 Introduction
1.1 Organization of the subject
1.2 History
PART I- CLASSICAL MECHANICS
Chapter 2 Relativistic Kinematics 17
2.1 The Lorentz equation and general
considerations 17
2.2 Conservation of energy 18
2.3 The acceleration potential 19
2.4 Definition of coordinate systems 22
2.5 Conservation of axial angular momentum 24
Chapter 3 Different Forms of Trajectory Equations 27
3.1 Parametric representation in terms of the
arc-length 27
3.2 Relativistic proper-time representation 29
3.3 The cartesian representation 30
3.4 Scaling rules 33
Chapter 4 Variational Principles 35
4.1 The Lagrange formalism 35
4.2 General rotational ly symmetric systems 38
4.3 The canonical formalism 41
4.4 The time-independent form of the
variational principle 43
4.5 Static rotational ly symmetric systems 44
Chapter 5 Hamiltonian Optics 46
5.1 Introduction of the characteristic function 46
5.2 The Hamilton-Jacobi equation 48
5.3 The analogy with light optics 49
5.4 The influence of vector potentials 51
5.5 Gauge transformations 53
vi Contents
5.6 Poincar~'s integral invariant 54
5.7 The problem of uniqueness 57
5.8 R~sum6 58
PART II- CALCULATION OF STATIC FIELDS
Chapter 6 Basic Concepts and Equations 61
6.1 General considerations 61
6.2 Field equations 62
6.3 Variational principles 65
6.4 Rotationally symmetric fields 67
6.5 Planar fields 69
Chapter 7 Series Expansions 73
7.1 Azimuthal Fourier series expansions 73
7.2 Radial series expansions 78
7.3 Rotationally symmetric fields 85
7.4 Multipole fields 88
7.5 Planar fields 90
7.6 Fourier-Bessel series expansions 91
Chapter 8 Boundary-Value Problems 94
8.1 Boundary-value problems in electrostatics 94
8.2 Boundary conditions in magnetostatics 96
8.3 Examples of boundary-value problems in
magnetostatics 101
Chapter 9 Integral Equations 107
9.1 Integral equations for scalar potentials 107
9.2 Problems with interface conditions 111
9.3 Reduction of the dimensions 113
9.4 Important special cases 117
9.5 R~sum~ 124
Chapter 10 The Boundary-Element Method 125
10.1 Evaluation of the Fourier integral kernels 125
10.2 Numerical solution of one-dimensional
integral equations 131
10.3 Superposition of aperture fields 143
10.4 Three-dimensional Dirichlet problems 149
10.5 Examples of applications of the
boundary-element method 158
Chapter 11 The Finite-Difference Method (FDM) 159
11.1 The choice of grid 159
Contents vii
11.2 The Taylor series method 160
11.3 The integration method 162
11.4 Nine-point formulae 165
11.5 Iterative solution techniques 170
Chapter 12 The Finite-Element Method (FEM) 175
12.1 Formulation for round magnetic lenses 175
12.2 Formulation for self-adjoint elliptic
equations 179
12.3 Solution of the finite-element equations 182
12.4 Improvement of the finite-element method 183
12.5 Comparison and combination of different
methods 184
Chapter 13 Field-Interpolation Techniques 188
13.1 One-dimensional differentiation and
interpolation 188
13.2 Two-dimensional interpolation 194
PART III- THE PARAXlAL APPROXIMATION
Chapter 14 Introduction 201
Chapter 15 Systems with an Axis of Rotational
Symmetry 202
15.1 Derivation of the paraxial ray equations
from the general ray equations 207
15.2 Variational derivation of the paraxial
equations 212
15.3 Forms of the paraxial equations and
general properties of their solutions 213
15.4 The Abbe sine condition and Herschel's
condition 219
15.5 Some other transformations 222
Chapter 16 Gaussian Optics of Rotationally Symmetric
Systems: Asymptotic Image Formation 225
16.1 Real and asymptotic image formation 225
16.2 Asymptotic cardinal elements and transfer
matrices 226
16.3 Gaussian optics as a projective
transformation 235
16.4 Use of the angle characteristic to establish
the optical quantities 237
viii Contents
16.5 The existence of asymptotes 239
Chapter 17 Gaussian Optics of Rotationally Symmetric
Systems: Real Cardinal Elements 242
17.1 Real cardinal elements for high
magnification and high demagnification 242
17.2 Osculating cardinal elements 246
17.3 Inversion of the principal planes 253
17.4 Approximate formulae for the cardinal
elements: the thin-lens approximation and
the weak-lens approximation 257
Chapter 18 Electron Mirrors 261
18.1 Introduction 261
18.2 A time-like parameter as independent
variable 264
18.3 The cartesian representation 271
18.4 A quadratic transformation 274
Chapter 19 Quadrupole Lenses 276
19.1 Paraxial equations for quadrupoles 277
19.2 Transaxial lenses 286
Chapter 20 Cylindrical Lenses 290
PART IV- ABERRATIONS
Chapter 21 Introduction 297
Chapter 22 Perturbation Theory: General
Formalism 3O3
Chapter 23 The Relation Between Permitted Types of
Aberration and System Symmetry 315
23.1 Introduction 315
23.2 N=I 322
23.3 N=2 325
23.4 N=3 329
23.5 N=4 330
23.6 N = 5 and 6 333
23.7 Systems with an axis of rotational
symmetry 334
23.8 Note on the classification of aberrations 336
Chapter 24 The Geometrical Aberrations of Round
Lenses 339
24.1 Introduction 339
Contents ix
24.2 Derivation of the real aberration
coefficients 339
24.3 Spherical aberration 350
24.4 Coma 365
24.5 Astigmatism and field curvature 369
24.6 Distortion 378
24.7 The variation of the aberration coefficients
with aperture position 382
24.8 Reduced coordinates 384
24.9 Seman's transformation of the
characteristic function 387
Chapter 25 Asymptotic Aberration Coefficients 393
Chapter 26 Chromatic Aberrations 409
26.1 Real chromatic aberrations 409
26.2 Asymptotic chromatic aberrations 415
Chapter 2 7 Aberration Matrices and the Aberrations
of Lens Combinations 418
Chapter 28 The Aberrations of Mirrors and Cathode
Lenses 425
28.1 The parametric form of the theory 425
28.2 Systems with curved cathodes 429
28.3 Structure of the aberrations 430
28.4 The cartesian form of the aberration theory 432
Chapter 29 The Aberrations of Quadrupole Lenses
and Octopoles 434
29.1 Introduction 434
29.2 Geometrical aberration coefficients 434
29.3 Aperture aberrations 453
29.4 Chromatic aberrations 460
29.5 Quadrupole multiplets 461
Chapter 30 The Aberrations of Cylindrical Lenses 466
Chapter 31 Parasitic Aberrations 470
31.1 Small deviations from rotational symmetry;
axial astigmatism 470
31.2 Classification of the parasitic aberrations 472
31.3 Numerical determination of parasitic
aberrations 475
31.4 The isoplanatic approximation 477