Advances in Imaging and Electron Physics (eBook)

Cover 1
Contents 6
Contributors 10
Preface 12
Future Contributions 14
Chapter 1. Evanescent Waves in the Near and the Far Field 19
I. Introduction 19
II. Solution of Maxwell’s Equations 22
III. Green’s Tensor and Vector 24
IV. Electric Dipole 26
V. Angular Spectrum Representation of the Scalar Green’s Function 28
VI. Angular Spectrum Representation of Green’s Tensor and Vector 29
VII. Traveling and Evanescent Waves 30
VIII. The Auxiliary Functions 32
IX. Relations Between the Auxiliary Functions 35
X. The Evanescent Part 36
XI. The Traveling Part 38
XII. The z-Axis 39
XIII. The xy-Plane 41
XIV. Relation to Lommel Functions 44
XV. Expansion in Series with Bessel Functions 45
XVI. Asymptotic Series 47
XVII. Evanescent Waves in the Far Field 49
XVIII. Uniform Asymptotic Approximation 51
XIX. Traveling Waves in the Near Field 63
XX. The Coefficient Functions 65
XXI. Integral Representations 69
XXII. Evanescent Waves in the Near Field 71
XXIII. Integral Representations for Evanescent Waves 73
XXIV. Conclusions 78
Appendix A 78
Appendix B 81
References 83
Chapter 2. Symmetry and the Karhunen–Loève Decomposition 87
I. Introduction 88
II. The Karhunen–Loève Decomposition 89
III. Basics from the Group Representation Theory 97
IV. KL Decomposition and Symmetry 102
V. Applications 109
VI. Conclusion 123
References 123
Chapter 3. Analysis of Irregularly Sampled Data: A Review 127
I. Introduction 127
II. Application Areas 129
III. Noniterative Methods 131
IV. Iterative Methods 151
V. Incorporating the Uncertainty of the Data: Normalized and DiVerential Convolution 154
VI. A Comparative Study in 1D 166
VII. Survey of State of the Art 175
VIII. Conclusions 180
References 181
Chapter 4. Recent Developments in the Microscopy of Ceramics 185
I. Introduction 186
II. High-Resolution Microscopy of Ceramics 186
III. Electron Energy-Loss Spectroscopy of Ceramics 207
IV. Energy-Filtered TEM (EFTEM) 245
V. Concluding Comments 256
References 258
Chapter 5. Five-Dimensional Hamilton–Jacobi Approach to Relativistic Quantum Mechanics 265
I. Introduction 265
II. Covariant Hamilton Formalism for Spin-1/2 Particles 266
III. Spin Precession 271
IV. Reduced Relativistic Lagrangain and Hamiltonian 274
V. Properties of the Action Function 278
VI. Self-Action 279
VII. Multi-Particle System 284
VIII. Quantization of the Five-Dimensional Hamilton–Jacobi Equation 286
IX. Free-Particle Solutions 290
X. Integral Equation and Path Integral 293
XI. Eikonal Approximation of the Relativistic Propagator 298
XII. Conclusion 301
References 302
Chapter 6. Redundant Multiscale Transforms and Their Application for Morphological Component Separation 305
I. Introduction 306
II. Background. Part I. Wavelet 308
III. Background. Part II. From Wavelets to Curvelets 325
IV. Background. Part III. Sparsity in Transforms 338
V. Morphological Component Analysis 348
VI. Conclusion 360
References 363
Index 367