Advances in Imaging and Electron Physics

Editor-In-Chief

Preface

Future Contributions

Contributors

Chapter One. Small Angle Scatter with Correlation, Scatter and Intermediate Functions

1 Overview of Scatter: Neutron and X-ray Small-angle Scatter in Perspective

2 Neutron and X-ray Scatter Amplitude from Non–bravais Lattice Crystal

3 Neutron and X-ray Scatter Intensity from Non–Bravais Lattice Crystal

4 Small-angle Scatter: Scatter Length Density and Particle Structure Factor

5 Small-angle Scatter: Scatter Amplitudes and Intensity

6 The Rayleigh–Gans Equation, Babinet’s Principle, and Differential Cross Sections

7 Random Variables: Correlation and Independence

8 The Scattering Vector Resolution of SANS Instruments for Neutrons and X-rays

9 Macroscopic Differential Cross Section: Scatter Length Density Convolution and Correlation

10 The Pair Correlation Function

11 The Macroscopic Differential Cross Section for Elastic Scatter Expressed by Intermediate Function, and Fourier Transform of Patterson Function

12 Scatter Function for Elastic and Inelastic Scatter from Sample Solute Particles Obtained from Neutron (X-ray), Sample-Averaged Scatter Intensity

13 Sample-averaged Scatter Intensity Versus Scattering Vector q for the Guinier, Intermediate, and Porod Regimes

14 Small-angle Scatter: Measurement of Solute Particle Size and Shape—Guinier Regime

15 Small-angle Scatter from Spherical Particles—Guinier Regime

16 Small-angle Scatter from Particles of Various Shapes, Log-log Plots, Method of Contrast Variation—Guinier Regime

17 Small-angle Scatter—Intermediate Regime and Porod Regime

18 Small-angle Scatter—Porod Regime and Porod’s Law

19 Neutron Incoherent Scatter: Solution of the Diffusion Equation with Self-Correlation and Incoherent Scatter Functions, Measurable by Small-angle Scatter

20 Neutron Coherent Partial Differential Cross Section: The Scatter Function and the Principle of Detailed Balance

21 The Coherent and Incoherent Pair Correlation Function, Intermediate Function, and Scatter Function: The Static Approximation

22 The Particle Number Density Operator and the Coherent Intermediate and Pair Correlation Functions

23 Neutron Elastic Scatter Occurs Only in Forward Direction for Liquids and Gases Shown by Coherent Intermediate and Scatter Functions

24 Neutron Coherent Differential Cross Sections in Crystals Derived from Coherent Scatter and Intermediate Functions

25 Pair Correlation Function Expressed by Particle Density Operator and the Patterson Function

26 Neutron Coherent Differential Cross Section in Crystals Expressed by Particle Density Operators

27 Neutron Incoherent Elastic Differential Cross Section in Crystals Derived from Incoherent Intermediate Function

28 Neutron Incoherent Differential Cross Section in Crystals Derived from Incoherent Pair Correlation Function

29 No Elastic Scatter Except Forward Direction in Liquids and Gases is Shown by Intermediate and Pair Correlation Functions

30 Moments of the Neutron Scatter Function

References

Chapter Two. Nuclear Scatter of Neutron Spin States

1 Angular Momentum Vectors, Spin Vectors, and Vector Operators

2 Heisenberg Uncertainty Principle and Commutation of Operators

3 The Neutron Spin Operator

4 The Neutron Spin–Lowering and –Raising Operators

5 Nuclear Scatter of Neutron Spin States: Partial Differential Cross Section

6 Combined Neutron and Nuclear spin Operators for Polarized Neutron Scatter

7 Neutron Nuclear Scatter Lengths for Neutron Spin States

8 Partial Differential Cross Section for Single Transition Neutron Spin-State Scatter

9 Thermal Averaging: Total Partial Differential Cross Section for Neutron Spin-State Scatter

10 Neutron Spin-State Scatter Lengths for Ensemble of Nuclear Spins and Isotopes

11 Coherent Partial Differential Cross Section for Neutron Spin-State Scatter

12 Incoherent Partial Differential Cross Section for Neutron Spin-State Scatter

References

Chapter Three. Atomic-Resolution Core-Level Spectroscopy in the Scanning Transmission Electron Microscope

1 Introduction

2 Practical Aspects

3 Theoretical Aspects

4 Selected Applications

5 Concluding Remarks

References

Chapter Four. Point Spread Function Engineering for Super-Resolution Single-Photon and Multiphoton Fluorescence Microscopy

1 Introduction

2 Theory

3 Results and Discussions

4 Conclusions

Acknowledgments

References

Chapter Five. A Review of Recent Advances in the Hit-or-Miss Transform

1 Introduction

2 Preliminaries and Properties of Mathematical Morphology

3 Fundamental Morphological Operations

4 Extensions of the Hit-or-Miss Transform

5 Conclusions

References

Chapter Six. Perspectives on Color Image Processing by Linear Vector Methods Using Projective Geometric Transformations

1 History and Background

2 Linear Filtering

3 Linear Quaternion Systems and Homogeneous Coordinates

4 Quaternion Derivations of Geometric Operations

5 The Difficulty Of Designing Linear Filters

6 Conclusion

References

Subject Index

Contents of Volumes 151-174

Color Plates