# Advances in Imaging and Electron Physics, Volume 172

## 1st Edition

### Part A

**Serial Volume Editors:**Jay Theodore Cremer, Jr.

**eBook ISBN:**9780123978141

**Hardcover ISBN:**9780123944221

**Imprint:**Academic Press

**Published Date:**2nd July 2012

**Page Count:**696

**View all volumes in this series:**Advances in Imaging and Electron Physics

## Table of Contents

Editor-in-Chief

Edited by

Foreword

Preface

Contributor

Future Contributions

Chapter 1 Introduction to Neutron and X-ray Optics

1 Compound Refractive Lenses for Neutrons and X-rays: Background and Theory

2 Experiments with Neutron Compound Refractive Lenses, Magnetic Lenses, and Microscopes

3 Experiments with X-ray Compound Refractive Lenses and Microscopes

4 Thermal Neutron Radiography, Coded Aperture, and Phase-Contrast Imaging

5 Experiments in Fast Neutron Radiography

6 A Brief History of Neutron Optics Before Compound Refractive Neutron Lenses

6 Background Reading

7 Brief History and Overview of Diffractive and Reflective X-ray Optics and Microscopy

Chapter 2 Compound Refractive Lenses and Prisms

1 The Compound Refractive Lens

2 Numerical Aperture and Thin Lenses

3 Biconcave Parabolic Lens: Path Length, Focal Length, and Absorption Aperture Radius

4 Biconcave Spherical Lens: Path Length, Focal Length, and Absorption Aperture Radius

5 Parabolic Aperture Radius in Spherical Biconcave CRLs

6 Matrix Representation of X-ray and Neutron Optics with Paraxial Approximation

7 Thin Lens Matrix and Ray Angle Deviation in a Thin Lens

8 Average CRL Transmission for X-rays or Neutrons

9 CRL Intensity Gain Including Attenuation

10 CRL Transverse and Axial Magnification

11 CRL Depth of Field and Depth of Focus

12 Modulation Transfer Function for CRL Resolution Determination

13 Calculation of CRL Modulation Transfer Function by Line Profile Measurements of Knife-Edge Images

14 CRL Field of View

15 Thick Lens CRLs

16 CRL Surface Roughness and Lens Alignment

17 Compound Refractive Prisms: X-ray and Neutron Deflection by a Single Prism

18 Deflection of X-rays and Neutrons in a Compound Refractive Prism

19 Calculation of X-ray or Neutron Absorption Aperture Depth and Transmission in a Compound Refractive Prism

20 Use of a Compound Refractive Prism to Offset Neutron Gravity Droop in Small-Angle Scattering

21 Curvature and Radius of Curvature of Lens Surface and Wave Surface

22 Measurement of Spherical and Parabolic Lens Curvature

23 Wave Vergence and Wave Vergence Change by Lens Surface

24 Refractive Index, Snell’s Law, Huygens’ Principle, and Fermat’s Principle of Least Time

25 The Paraxial Approximation and the Fundamental Paraxial Equation

26 The Gaussian Lens Equation for Thin Lenses

27 Thick Lens Power and Focal Length, and Wave Vergence Change in Thick Lenses

28 Wave Vergence Change and Power and Focal Length of a Separated Lens Doublet

Chapter 3 Geometric Neutron and X-ray Optics – Aberrations

1 Chromatic Aberration in Spherical and Parabolic Biconcave Lenses

2 Spherical Aberration in Spherical Biconcave Lenses and Total Object Resolution

3 CRL Image and Object Resolution: Spherical and Chromatic Aberration

4 CRL Aberrations: Astigmatism, Curvature of Field, Coma, and Distortion

5 Parabolic and Spherical Waves Converge to Different Focal Points by CRL

6 Monochromatic and Chromatic Aberrations Occur in Parabolic and Spherical Lenses

7 Aberrations from an Imperfect Spherical Lens Surface

8 Derivation of the Five Seidel Monochromatic Aberrations of a Spherical Biconcave Lens

9 Relation of the Optical Path Length Difference to its Associated Aberration

10 Spherical Aberration

11 Coma

12 Coma: The Abbe Sine Condition and the Coddington Shape Factor

13 Curvature of Field and the Petzval Condition

14 Astigmatism

15 Combined Astigmatism and Curvature of Field

16 Astigmatism: Sturm’s Interval and Remedy by Upstream Aperture Stop

17 Distortion

18 Images without and with Distortion

19 Prevention of Distortion and the Petzval Condition

20 Distortion in Compound Refractive Lens Imaging with Synchrotron X-ray Sources

Chapter 4 X-ray Optics

1 Damped Resonance for Driven Atomic Electron Oscillation and X-ray Emission

2 The Complex Atomic Scatter Factor for a Single Element

3 The Complex Atomic Scatter Factor for a Mixture or Compound

4 Maxwell’s Equations Yield the Electromagnetic Vector Wave Equation in Material Media

5 The Electromagnetic Vector Wave Equation Contains the Refractive Index

6 The Complex Refractive Index and the Complex Atomic Scatter Factor

7 The Complex Refractive Index—Decrement, Absorption Index, and Linear Attenuation

8 X-ray Complex Index of Refraction—Kramers–Kronig Relation

9 X-ray Rayleigh Scatter Total Cross Section and the Complex Atomic Scatter Factor

10 Differential Cross Section for the Rayleigh Scatter and Complex Atomic Scatter Factor

11 Rayleigh and Thomson X-ray Scatters are Coherent, Elastic Scatter

12 Compton Scatter of X-rays is Incoherent and Inelastic

13 X-ray Attenuation by Photoelectric Absorption

14 X-ray Absorptive Attenuation by Pair Production

15 Collision Losses of Charged Particle Passage in Matter

16 Bremsstrahlung from Charged Particle Passage in Matter

17 Forward-Directed Bremsstrahlung from Relativistic Electrons Undergoing Acceleration

18 X-ray Wave Packets—Phase Velocity and Group Velocity, Spatial and Spectral Widths

19 X-ray Wave Packets—Dispersion and Group Velocity, and Relation to Real Part of Complex Atomic Scatter Factor

20 X-rays in Material Medium—Phase and Group Velocity and Pulse Broadening

21 Reflection and Transmission of X-rays at a Planar Interface of Two Media

22 Fraction of Transmitted and Reflected Polarized X-rays with an Electric Field Component Parallel to the Planar Surface Interface

23 Fraction of Transmitted and Reflected Polarized X-rays with a Magnetic Field Component Parallel to the Planar Surface Interface

24 X-ray Brewster Angle Occurs Only for Electric Field Parallel to Plane of Incidence

Chapter 5 Neutron Optics

1 Neutron Phase and Group Velocity

2 Derivation of the Schrödinger Wave Equation for Neutron Wave

3 Derivation of the Schrödinger Wave Equation by the Electromagnetic Wave Equation Analogy

4 Derivation of the Schrödinger Wave Equation by Assumption of the Neutron Plane Wave Solution

5 Operator form of the Schrödinger Wave Equation for a Neutron Wave

6 Reflection and Transmission of Neutrons at Media Interfaces

7 Neutron Reflectometry

8 Measurement of the Complex Refractive Index via Refraction

9 X-ray and Neutron Interferometry

10 Interferometry and the FIZEAU Effect

11 Pendellösung Oscillations and Anomalous Absorption in Perfect Crystals

12 Measurement of Refractive Index via Interferometry

13 The Maxwell–Boltzmann Distribution for the Reactor Source of Thermal Neutrons

Chapter 6 X-ray and Neutron Optics

1 Derivation of the Index of Refraction for X-rays and Neutrons

2 Types of X-ray and Neutron Lenses and Significance of Delta/Mu Ratio

3 Coherent, Incoherent, Elastic, and Inelastic Scatter of X-rays and Neutrons

4 X-ray and Neutron Attenuation Comparison

5 Useful Formulas for X-rays and Neutrons

6 X-ray Multilayer Mirrors

7 Neutron Multilayer Mirrors

8 Capillary Optics and Kumakhov X-ray and Neutron Lenses

9 Bright-field, Dark-field, and Phase-Contrast Microscopy

Contents of Volumes 151–171

Index

## Description

This special volume of *Advances in Imaging and Electron Physics *details the current theory, experiments, and applications of neutron and x-ray optics and microscopy for an international readership across varying backgrounds and disciplines. Edited by Dr. Ted Cremer, these volumes attempt to provide rapid assimilation of the presented topics that include neutron and x-ray scatter, refraction, diffraction, and reflection and their potential application.

## Key Features

- Contributions from leading authorities
- Informs and updates on all the latest developments in the field

## Readership

Physicists, electrical engineers and applied mathematicians in all branches of image processing and microscopy as well as electron physics in general

## Details

- No. of pages:
- 696

- Language:
- English

- Copyright:
- © Academic Press 2012

- Published:
- 2nd July 2012

- Imprint:
- Academic Press

- eBook ISBN:
- 9780123978141

- Hardcover ISBN:
- 9780123944221

## About the Serial Volume Editors

### Jay Theodore Cremer, Jr. Serial Volume Editor

### Affiliations and Expertise

Chief Scientist, Adelphi Technology, Inc.