Principles of Electron Optics, Volume 4 Advanced Wave Optics

Principles of Electron Optics: Second Edition, Advanced Wave Optics provides a self-contained, modern accounting of electron optical phenomena with the Dirac or Schrödinger equation as a starting point. Knowledge of this branch of the subject is essential to understanding electron propagation in ele...

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Main Authors Hawkes, Peter W, Kasper, Erwin
Format eBook
LanguageEnglish
Published Chantilly Elsevier Science & Technology 2022
Academic Press
Edition2
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Electron optics
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Abstract Principles of Electron Optics: Second Edition, Advanced Wave Optics provides a self-contained, modern accounting of electron optical phenomena with the Dirac or Schrödinger equation as a starting point. Knowledge of this branch of the subject is essential to understanding electron propagation in electron microscopes, electron holography and coherence. Sections in this new release include Principles of Electron Optics, Electron Interactions in Thin Specimens, Digital Image Processing, Acquisition, Sampling and Coding, Enhancement, Linear Restoration, Nonlinear Restoration - the Phase Problem, Three-dimensional Reconstruction, Image Analysis, Instrument Control, Instrumental Image Manipulation, and much more.
AbstractList Principles of Electron Optics: Second Edition, Advanced Wave Optics provides a self-contained, modern accounting of electron optical phenomena with the Dirac or Schrödinger equation as a starting point. Knowledge of this branch of the subject is essential to understanding electron propagation in electron microscopes, electron holography and coherence. Sections in this new release include Principles of Electron Optics, Electron Interactions in Thin Specimens, Digital Image Processing, Acquisition, Sampling and Coding, Enhancement, Linear Restoration, Nonlinear Restoration - the Phase Problem, Three-dimensional Reconstruction, Image Analysis, Instrument Control, Instrumental Image Manipulation, and much more.
Author Hawkes, Peter W
Kasper, Erwin
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DOI 10.1016/C2021-0-01238-4
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Academic Press
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Snippet Principles of Electron Optics: Second Edition, Advanced Wave Optics provides a self-contained, modern accounting of electron optical phenomena with the Dirac...
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SubjectTerms Electron optics
Subtitle Advanced Wave Optics
TableOfContents 78.11 The Propagation of Coherence Functions -- 78.11.1 Propagation of the Mutual Intensity in Free Space -- 78.11.2 Propagation of the Mutual Intensity Through a Lens System -- 78.11.3 Propagation of the Cross-Spectral Density and Brightness Through a Lens System -- 78.11.4 Introduction of a Specimen -- 78.12 Coherence and Illumination -- 78.13 Degeneracy and Brightness -- 78.14 Further Reading -- 79 Wigner Optics -- 79.1 Introduction -- 79.2 Image Formation Expressed in Terms of the Wigner Function -- 79.2.1 Source Properties -- 79.2.2 Effect of an Aperture -- 79.2.3 Passage through an Electron Lens -- 79.3 Holography -- 79.3.1 Propagation of the Density Matrix through a Conventional Transmission Electron Microscope -- 79.3.2 Propagation of the Density Matrix through an Electron Microscope Fitted with a Biprism -- 79.3.3 Related Holographic Techniques -- 79.4 Further Reading -- XVII. Vortex Studies, the Quantum Electron Microscope -- 80 Orbital Angular Momentum, Vortex Beams and the Quantum Electron Microscope -- 80.1 Introduction -- 80.2 Vortex Beams -- 80.2.1 Properties -- 80.2.2 Knots and Links -- 80.3 Interaction With Magnetic Fields -- 80.4 Production of Vortex Beams -- 80.4.1 Phase Plates -- 80.4.2 Holograms -- 80.4.3 Aberration Correctors as Vortex Generators -- 80.4.4 Mode Conversion -- 80.4.5 A Mirror-Based Method -- 80.4.6 Vortex Interferometry -- 80.4.7 Structured Illumination -- 80.4.8 Concluding Note -- 80.5 Measurement of Topological Charge -- 80.5.1 Diffraction -- 80.5.2 Stigmators -- 80.5.3 Azimuthal to Cartesian Mapping -- 80.5.4 Induced Currents -- 80.6 Interactions Between Vortex Beams and Specimens -- 80.7 Lensless Fourier Transform Holography -- 80.8 Further Reading -- 80.9 The Quantum Electron Microscope -- Appendix -- Appendix: Corrections and additions to volumes 1, 2 and 3 -- A1 Volume 1 -- Additions -- A2 Volume 2
Front Cover -- Principles of Electron Optics -- Copyright Page -- Dedication -- Contents -- Preface to the Second Edition -- Preface to the First Edition -- XIV. Electron-Specimen Interactions -- 69 Electron-Specimen Interactions -- 69.1 Introduction -- 69.2 Electron Interactions in Amorphous Specimens -- 69.2.1 Definition of the Elastic Cross-Sections -- 69.2.2 The First-Order Born Approximation for Elastic Scattering -- 69.2.3 The High-Energy Approximation -- 69.2.4 Partial Wave Analysis -- 69.2.4.1 Remaining Problems -- 69.2.5 Inelastic Electron Scattering -- 69.2.5.1 General Properties of Inelastic Scattering -- 69.2.5.2 Further Remarks -- 69.2.6 Plural and Multiple Electron Scattering -- 69.2.7 The Scattering Contrast -- 69.3 Electron Interactions in Crystalline Specimens -- 69.3.1 Introduction -- 69.3.2 Fundamentals of Crystallography -- 69.3.3 The Periodic Potential -- 69.3.4 Kinematic Theory of Electron Scattering -- 69.3.4.1 Geometrical Rules and Scattering -- 69.3.4.2 Intensity Formulae for Diffraction Peaks -- 69.3.4.3 Energy Spread of the Illumination -- 69.3.5 General Formulation of the Dynamical Theory -- 69.3.5.1 The Method of Oscillating Amplitudes -- 69.3.5.2 Formulation as an Eigenvalue Problem -- 69.3.5.3 The Equivalence of the Two Methods -- 69.3.5.4 Absorption -- 69.3.6 The Two-Beam Case -- 69.3.6.1 General Calculations -- 69.3.6.2 Interpretation of the Results -- 69.3.7 Applications and Extensions of the Dynamical Theory -- 69.3.7.1 Nearly Perfect Crystals -- 69.3.7.2 Imperfect Crystals -- 69.4 Simulation and Structure Retrieval -- 69.4.1 Introduction -- 69.4.2 Simulation -- 69.4.3 Reconstruction -- 69.5 Multislice Electron Optics -- XV. Digital Image Processing -- 70 Introduction -- 70.1 Organization of the Subject -- 70.2 Image Algebra -- 70.2.1 Introduction -- 70.2.2 Images and Templates -- 70.2.3 Operations
75.4 Three-Dimensional Reconstruction in Materials Science -- 75.5 Deep Learning, Machine Learning -- 75.5.1 Introduction and Principles -- 75.5.2 Noise -- 75.5.3 Segmentation -- 75.5.4 Labelling -- 75.5.5 Sparsity -- 75.5.6 Exit-Wave Reconstruction -- 75.5.7 Tomography -- 75.5.8 General Studies -- 75.6 Concluding Remarks -- 75.7 Further Reading -- 76 Image Analysis -- 76.1 Introduction -- 76.2 Digital Geometry -- 76.2.1 Neighbours -- 76.2.2 Distance -- 76.2.3 Connectedness -- 76.2.4 Border -- 76.2.5 Simplicity -- 76.3 Segmentation and Feature Extraction -- 76.3.1 Segmentation -- 76.3.2 Feature Extraction -- 76.3.3 Measurement -- 76.4 Classification -- 76.5 Description -- 76.6 Further Reading -- 77 Microscope Parameter Measurement and Instrument Control -- 77.1 Introduction -- 77.2 Measurement of Microscope Operating Parameters -- 77.2.1 The Transmission Electron Microscope -- 77.2.2 The Scanning Transmission Electron Microscope -- 77.2.3 Aberration Measurement for Corrected Optics -- 77.2.3.1 The Transmission Electron Microscope -- 77.2.3.2 The Scanning Transmission Electron Microscope -- 77.2.4 Aberration Determination Using Crystalline Materials -- 77.3 Control -- XVI. Coherence, Brightness and Spectral Functions -- 78 Coherence and the Brightness Functions -- 78.1 Introduction -- 78.2 Coherence -- 78.2.1 Definitions -- 78.2.2 Spectral Functions -- 78.3 Radiometry -- 78.4 The Brightness of Partially Coherent Sources -- 78.5 Consequences for the van Cittert-Zernike Theorem -- 78.6 Eigenfunction Expansions of the Coherence Functions -- 78.6.1 The Expansions -- 78.6.2 A New Set of Brightness Formulae -- 78.7 The Quasi-homogeneous Source -- 78.8 Brightness, Coherence and Quasi-homogeneity -- 78.9 Temporal and Spatial Coherence -- 78.10 Related Work -- 78.10.1 Operator Formalism -- 78.10.2 Use of Wigner and Ambiguity Functions
Omissions and additions
74.3.2 The Gerchberg-Saxton Algorithm -- 74.3.3 The Multiple-Image Algorithm -- 74.3.4 Bright-Field/Dark-Field Subtraction -- 74.3.5 Direct Methods -- 74.3.6 Modulation of the Incident Beam -- 74.3.7 One Image and Its Derivative with Respect to Defocus -- 74.3.8 Closely Spaced Images: The Transport-of-Intensity Equation -- 74.3.8.1 Introduction -- 74.3.8.2 Elementary Derivation of the Transport-of-Intensity Equation -- 74.3.8.3 Use of Schrödinger's Equation -- 74.3.8.4 The Notion of Phase -- 74.3.8.5 Further Developments -- 74.3.8.6 Aberration Space, Aberration Coefficients as Variables -- 74.3.9 Related Problems -- 74.4 Analyticity -- 74.4.1 Introduction -- 74.4.2 Analytic Continuation of Wavefunctions -- 74.4.3 Use of Half-Plane Apertures -- 74.4.4 Logarithmic Hilbert Transform Pairs -- 74.4.5 Uniqueness in One and Two Dimensions -- 74.4.5.1 Continuous Form -- 74.4.5.2 Discrete Form -- 74.4.5.3 One-Dimensional Case -- 74.4.5.4 Two- or Higher-Dimensional Case. Discrete Form -- 74.4.6 Summary and List of Further Reading -- 74.5 Maximum Entropy and Related Probabilistic Methods -- 74.6 Exit-Wave Reconstruction -- 75 Three-Dimensional Reconstruction -- 75.1 Introduction -- 75.2 Methods -- 75.2.1 Direct Methods -- 75.2.1.1 Discrete Data -- 75.2.2 Iterative Methods -- 75.2.3 Reconstruction From a Single View of an Oblique Section -- 75.2.4 Ptycho-Tomography -- 75.2.5 The Missing Wedge or Cone -- 75.2.6 Compressed Sensing -- 75.2.6.1 Introduction -- 75.2.6.2 Sparsity -- 75.2.6.3 Applied Compressed Sensing -- 75.2.6.4 Electron Tomography -- 75.2.7 Breakdown of the Projection Requirement -- Artificial Neural Networks -- 75.2.8 Reconstruction Quality -- 75.3 Preprocessing -- 75.3.1 Background -- 75.3.2 Alignment -- 75.3.3 Classification by Correspondence Analysis -- 75.3.4 Random Tilt Series -- 75.3.5 Removal of Distortion -- 75.3.6 Defocus Gradient
70.2.4 Operations Involving Images and Templates -- 70.2.4.1 General Definition -- 70.2.4.2 Special Cases -- 70.2.5 Concluding Remarks -- 70.3 Notation -- 71 Acquisition, Sampling and Coding -- 71.1 Acquisition -- 71.2 Sampling -- 71.2.1 The Sampling Theorem -- 71.2.2 Degrees of Freedom -- 71.3 Quantization -- 71.4 Coding -- 71.4.1 Use of Image Transforms -- 71.4.2 Predictive Coding -- 71.4.3 Huffman and Vector Codes -- 71.5 Electron Optical Considerations -- 71.5.1 Acquisition -- 71.5.2 Sampling -- 72 Enhancement -- 72.1 Operations on Individual Pixels -- 72.1.1 Elementary Operations -- 72.1.2 Histogram-Based Enhancement -- 72.1.2.1 Practical Difficulties -- 72.1.2.2 Refinements -- 72.2 Linear Filtering -- 72.2.1 Low-Pass Filters -- 72.2.2 High-Pass Filters -- 72.2.3 Hexagonal Sampling -- 72.2.4 Generalized Convolution -- 72.2.5 Periodic Specimens -- 72.3 Nonlinear Filters -- 72.3.1 Nonlinear Exploitation of Linear Filtering -- 72.3.2 Median and Rank-Order Filtering -- 72.3.3 Morphological Filters -- 72.3.3.1 Introduction -- 72.3.3.2 Binary Image Morphology -- 72.3.3.3 Interpretation in Terms of Convolution -- 72.3.3.4 Combinations of Dilation and Erosion -- 72.3.3.5 Grey-Level Image Morphology -- 72.3.3.6 Practical Applications -- 72.3.3.7 Linearity -- 72.4 Image Algebraic Representation of Enhancement -- 72.4.1 Formation of the Histogram -- 72.4.2 Convolutional Filters -- 72.5 Enhancement in Electron Microscopy -- 73 Linear Restoration -- 73.1 Introduction -- 73.2 Extended Wiener Filters -- 73.3 Filtering With Constraints -- 73.4 Hoenders' Procedure -- 73.5 Recursive Filtering -- 73.6 Other Approaches -- 74 Nonlinear Restoration - The Phase Problem -- 74.1 Introduction -- 74.1.1 Formal Statement of the Problem -- 74.2 Extended Linear Approximation -- 74.3 Multiple Recordings (Circular Symmetry) -- 74.3.1 Introduction
Title Principles of Electron Optics, Volume 4
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