Computer Processing of Electron Microscope Images

1. Image Processing Based on the Linear Theory of Image Formation.- 1.1 Transfer Functions.- 1.2 Transfer Functions with Partially Coherent Illumination.- 1.3 Practical Exploitation of the Linear Relationship.- 1.3.1 Measurement of the Microscope Operating Characteristics.- 1.3.2 On-Line Processing.- 1.3.3 Filtering and Reconstruction.- References.- 2. Recovery of Specimen Information for Strongly Scattering Objects.- 2.1 Image Formation and Interpretation.- 2.1.1 Recapitulation of Coherent Image Formation.- 2.1.2 Interpreting the Specimen Wave.- 2.1.3 Rendering Images Discrete.- 2.2 Methods Iterating the Linear Theory Solution.- 2.3 Methods Requiring No Special Apertures.- 2.3.1 The Data Used.- 2.3.2 The Iterative Transform Algorithm.- 2.3.3 Examples and Practical Applications.- 2.3.4 Uniqueness.- 2.3.5 Periodic Images and Complex Zeros.- 2.3.6 Other Methods of Analysis.- 2.3.7 Conclusions.- 2.4 Methods Using Half-Plane Apertures.- 2.4.1 Hilbert Transforms.- 2.4.2 Logarithmic Hilbert Transforms.- 2.4.3 Real Aperture Shapes.- 2.4.4 Dark-Field Conditions.- 2.5 Analytic Wave Functions and Complex Zeros.- 2.5.1 Zero-Distributions and Zero Flipping.- 2.5.2 An Example.- 2.5.3 Immediate Applications.- 2.5.4 Reformulation of Zero Flipping.- 2.5.5 Two-Dimensional Extensions.- 2.6 Holography.- 2.6.1 The Linear Case.- 2.6.2 The General Case.- 2.6.3 Some Particular Cases.- 2.6.4 Nonplanar Reference Waves.- 2.7 Ptychography and Related Methods.- 2.8 Bright-Field/Dark-Field Subtraction.- 2.9 Other Perspectives.- 2.9.1 Coherence.- 2.9.2 Inelastic Scattering.- 2.9.3 Recording Noise and Radiation Damage.- 2.9.4 Practical Details of Computer Processing.- 2.9.5 Other Constraints.- 2.10 Conclusions.- References.- 3. Computer Reconstruction of Regular Biological Objects.- 3.1 The Biological Object.- 3.1.1 General Remarks.- 3.1.2 Regular Biological Objects.- 3.1.3 Chemical and Physical Processing of the Object.- 3.1.4 Contrast in Bright-Field Images.- 3.1.5 Radiation Damage.- 3.2 Fourier Processing of Electron Micrographs.- 3.2.1 Quantization and Preprocessing.- 3.2.2 The Whittaker-Shannon Sampling Theorem.- 3.2.3 Fourier Transforms of Regular Objects.- 3.2.4 Processing of Two-Dimensional Structures with Translational Symmetry.- 3.2.5 Rotational Filtering.- 3.2.6 Three-Dimensional Reconstruction of Objects with Helical Symmetry.- 3.2.7 Three-Dimensional Reconstruction of Particles with Icosahedral Symmetry.- 3.3 Recent Applications to Image Processing of Regular Biological Structure.- 3.3.1 One-Dimensional Filtering: Tropomyosin Paracrystal Structure.- 3.3.2 The Structure of Polyheads.- 3.3.3 The Structure of Ribosomes.- 3.3.4 The Structure of the Purple Membrane.- 3.3.5 A Correction for Distorted Images.- 3.3.6 Rotational Filtering of Base Plates.- 3.3.7 The Structure of the Contractile Sheath from Bacteriophage Mu.- 3.3.8 The Three-Dimensional Structure of an Icosahedral Virus Particle.- 3.4. Outlook.- References.- 4. Three-Dimensional Structure Determination by Electron Microscopy (Nonperiodic Specimens).- 4.1 History and General Discussion of the Subject.- 4.2 The Fundamental Theoretical Background.- 4.2.1 The Use of a CTEM as a Diffractometer.- 4.2.2 The Description of Structures in Three-Dimensional Electron Microscopy.- 4.2.3 Two-Dimensional Reconstruction (Image Filtering).- 4.2.4 The Projection Theorem.- 4.3 The Problem of Reconstruction.- 4.3.1 The Whittaker-Shannon-Type Interpolation.- 4.3.2 An Alternative Way of Incorporating the Finite Body Concept.- 4.3.3 Back-Projection and Filtered Back-Projection.- a) Simple Back-Projection.- b) Filtered Back-Projection.- c) The Influence of the Reconstruction Body.- d) The Influence of Restricted Tilting Angle.- 4.3.4 Conical Tilting.- 4.3.5 Reconstruction by Series Expansion.- a) The Cormack Method.- b) Aliasing.- 4.3.6 Algebraic Reconstruction in Direct Space.- 4.3.7 Reconstruction of an "Infinite" Platelet with Restricted Tilting Angle.- a) One-Dimensional Whittaker-Shannon Treatment of Single-Axis Tilting.- b) Reconstruction by Interpolation in Projection Space.- c) The Partially Defined "Unit Cell".- 4.3.8 Determination of a Common Origin of the Projections.- 4.4 Aspects for the Future.- 4.4.1 The "Atom" Constraint.- 4.4.2 The Use of a STEM as a Diffractometer.- References.- 5. The Role of Correlation Techniques in Computer Image Processing.- 5.1 Correlation Functions.- 5.1.1 The Cross-Correlation Function.- 5.1.2 The Autocorrelation Function.- 5.1.3 Correlation and Similarity.- 5.2 Computation.- 5.3 Some Important Theorems.- 5.3.1 CCFs of Images Containing Signal and Noise.- 5.3.2 The CCF of Blurred Signals.- 5.3.3 Some Thoughts on Signal, Noise, and Correlation.- 5.4 Determination of Relative Positions.- 5.4.1 Translation.- 5.4.2 Alignment of Projections.- 5.4.3 Centering of a Centrosymmetric Particle.- 5.4.4 Determination of Relative Orientation.- 5.5 Matched Filtering.- 5.6 Characterization of Instrument Conditions.- 5.7 Signal-to-Noise Ratio Measurement.- 5.7.1 Theory.- 5.7.2 Measurement.- 5.7.3 Consequence for Phase Contrast Microscopy.- 5.7.4 Generalized Signal-to-Noise Ratio Measurement.- 5.8 Conclusions.- References.- 6. Holographic Methods in Electron Microscopy.- 6.1 Historical Background.- 6.2 Holographic Schemes.- 6.2.1 The Generalized Hologram.- 6.2.2 In-Line Fresnel and Fraunhofer Holograms.- 6.2.3 Sideband Fresnel Holograms.- 6.2.4 Fourier Transform Holograms.- 6.2.5 Single-Sideband Holograms.- 6.2.6 Zone Plate Interpretation.- 6.3 Experimental Electron Holography.- 6.4 Contrast Transfer and Holography.- 6.4.1 In-Line Fresnel Hologram.- 6.4.2 Fresnel Sideband Hologram.- 6.4.3 Single-Sideband Hologram.- 6.4.4 The Effect of Partial Coherence on Resolution.- 6.5 Additional Reading.- 6.6 Conclusions.- References.- 7. Analog Computer Processing of Scanning Transmission Electron Microscope Images.- 7.1 Organization.- 7.2 Characteristics of Analog Processing.- 7.2.1 Grey Scale Modification.- 7.2.2 Filters.- 7.2.3 Signal Mixing.- 7.3 Types of Signals Available in the STEM.- 7.3.1 Basic Signals.- 7.3.2 Detected Signals.- 7.3.3 Extraction of Basic Signals.- 7.3.4 Normalization.- 7.4 Instrumental Characteristics.- 7.4.1 The Analog Processor.- 7.4.2 Display System.- 7.5 Applications.- 7.5.1 Basic Operations.- 7.5.2 Color Conversion Techniques.- 7.6 Conclusion.- References.- Appendix: Publication Details of International and European Congresses on Electron Microscopy.- Additional References with Titles.