Electron Beams, Lenses, and Optics (eBook)

Front Cover 1
Electron Beams, Lenses, and Optics 4
Copyright Page 5
Table of Contents 6
List of Symbols 10
Chapter 9. Geometrical Aberrations of Lenses 16
9.1 Types of Aberrations 16
9.2 Third-Order Theory 17
9.3 Geometrical Aberrations 18
9.4 Classification of the Geometrical Aberrations 25
9.5 Description of the Aberration Figures 26
9.6 Calculation of the Geometrical Aberration Coefficients 32
9.7 Solution for Paraxial Rays 35
9.8 Calculation of the Aberrations 38
9.9 Spherical Aberration 55
9.10 Coma Coefficient 61
9.11 Anisotropic Coma Coefficient 61
9.12 Curvature Coefficient 62
9.13 Astigmatism Coefficient 62
9.14 Anisotropic Astigmatism Coefficient 63
9.15 Distortion Coefficient 63
9.16 Anisotropic Distortion Coefficient 64
Further Reading 64
Chapter 10. The Spherical Aberration of Electric and Magnetic Lenses 65
10.1 The Impossibility of Canceling the Spherical Aberration 65
10.2 Definition of the Coefficient Cs 67
10.3 Disk of Minimum Confusion 68
10.4 The Spherical Aberration of the Combination of Two Thin Lenses 70
10.5 Conversion of Cs from One Object Position to Another 73
10.6 Derivation of the Coefficient of Spherical Aberration according to Glaser 74
10.7 Glaser's Expression for Cs of Purely Magnetic Fields 85
10.8 Spherical Aberration of a Magnetic Lens with a Bell-Shaped Field Distribution 87
10.9 Spherical Aberration of the Symmetrical Magnetic Lens 92
10.10 Spherical Aberration of an Electrostatic Immersion Lens 95
10.11 Spherical Aberration of Einzel Lenses 98
Further Reading 103
Chapter 11. Measurement of the Spherical Aberration of Various Electric and Magnetic Lenses 234
11.1 The Pepperpot Method or Hartmann's Test 234
11.2 The Shadow Method 237
11.3 The Halo Method 238
11.4 The Knife-Edge Method 241
11.5 The Tilt Method 244
11.6 The Diffraction Method 245
11.7 The Combined Tilt and Diffraction Method 247
Further Reading 248
Chapter 12. Theory of Diffraction 249
12.1 General Properties of a Wave 249
12.2 The Plane Wave 250
12.3 The de Broglie and Planck Relations 251
12.4 Huygens' Principle 253
12.5 Diffraction 255
12.6 The Wave Equation 256
12.7 Kirchhoff's Diffraction Equation 256
12.8 Fraunhofer's Diffraction through a Circular Aperture 259
12.9 Resolving Power of an Ideal Optical System 263
Chapter 13. The Influence of Space Charge in High Density Electron Beams 265
13.1 Force Due to Magnetic Attraction 266
13.2 Force Due to Coulomb Repulsion 268
13.3 The Universal Curve 271
13.4 Numerical Examples 283
Further Reading 284
Chapter 14. Chromatic Aberration 285
14.1 Development of the Expressions for Chromatic Aberration 285
14.2 Chromatic Aberration at the Focal Point 290
14.3 Upper Limit of the Chromatic Aberration of Magnetic Lenses 291
14.4 Upper Limit of the Chromatic Aberration of Electrostatic Lenses 294
14.5 Coefficient of Chromatic Aberration 296
14.6 Chromatic Aberration of a Magnetic Lens with the Glaser Bell-Shaped Field 296
14.7 Minimum Value of Cc and d 299
14.8 Chromatic Aberration of the Symmetrical Magnetic Lens 300
14.9 Current Limit at the Focus Due to the Velocity Spread of the Emitted Electrons 301
14.10 Numerical Example 308
14.11 Simplified Derivation 309
Further Reading 309
References 329
Index 331