Charged Particle Optics Theory: An Introduction, 1st Edition (Hardback) book cover

Charged Particle Optics Theory

An Introduction, 1st Edition

By Timothy R. Groves

CRC Press

369 pages | 56 B/W Illus.

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pub: 2014-12-15
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Charged Particle Optics Theory: An Introduction identifies the most important concepts of charged particle optics theory, and derives each mathematically from the first principles of physics. Assuming an advanced undergraduate-level understanding of calculus, this book follows a logical progression, with each concept building upon the preceding one. Beginning witha non-mathematical survey of the optical nature of a charged particle beam, the text:

  • Discusses both geometrical and wave optics, as well as the correspondence between them
  • Describes the two-body scattering problem, which is essential to the interaction of a fast charged particle with matter
  • Introduces electron emission as a practical consequence of quantum mechanics
  • Addresses the Fourier transform and the linear second-order differential equation
  • Includes problems to amplify and fill in the theoretical details, with solutions presented separately

Charged Particle Optics Theory: An Introduction makes an ideal textbook as well as a convenient reference on the theoretical origins of the optics of charged particle beams. It is intended to prepare the reader to understand the large body of published research in this mature field, with the end result translated immediately to practical application.


"Groves focuses on the quantum physics of how the trajectory of a charged particle beam can be discussed in terms of photons. The book is written in a very accessible style with clear exposition of all topics. The author has surpassed the goal he explains in the preface. For graduate students in physics and optics, this text will be invaluable. I anticipate that this book will also find use among senior researchers and physics educators. I plan to assign it to my students."

—Christian Brosseau, OSA Fellow, Université de Bretagne Occidentale, Brest, France, from Optics & Photonics News, August 15, 2015

"This book starts at a very fundamental level of physics and provides a highly rigorous explanation of electron and matter optical systems. When working in the field, it is easy to forget the deep physical and mathematical underpinnings of the discipline. This book does a remarkable job clarifying and explaining those underpinnings."

—Karl K. Berggren, Massachusetts Institute of Technology, Cambridge, USA

"The book does a good job of discussing the physics behind how the trajectory of a beam of charged particles can be treated as a beam of photons, and thus illustrates what is meant by optics of charged particles."

—Professor Kanti Jain, University of Illinois at Urbana-Champaign, USA

"This is a nice scholarly review of charged-particle optics that’s easy to read and understand. It ties together topics from diverse areas quite well. I’d readily recommend this book to students."

—Henry I. Smith, Massachusetts Institute of Technology, Cambridge, USA

"After mastering the material in this book, the reader will be able to follow any of the other books and handbooks on the subject and so, beyond being a textbook, it is a valuable reference in itself."

—Jon Orloff, Professor Emeritus, University of Maryland at College Park, USA

Table of Contents



Introduction: The Optical Nature of a Charged Particle Beam

Geometrical Optics

Relativistic Classical Mechanics

Hamilton's Principle of Least Action

The Hamiltonian Function and Energy Conservation

Mechanical Analog of Fermat's Principle

Exact Trajectory Equation for a Single Particle

Conservation Laws

The Lagrange Invariant

Liouville's Theorem and Brightness Conservation

General Curvilinear Axis

Equation of Motion in Terms of Transverse Coordinates and Slopes

Natural Units

Axial Symmetry

Exact Equations of Motion for Axially Symmetric Fields

Paraxial Approximation, Gaussian Optics

Series Solution for the General Ray Equation

Space Charge

The Primary Geometrical Aberrations

Spherical Aberration

Field Aberrations

Chromatic Aberration

Intensity Point Spread Function

Stochastic Coulomb Scattering

Monte Carlo Simulation

Analytical Approximation by Markov's Method of Random Flights

Hamilton–Jacobi Theory

Canonical Transformations

Applications of Hamilton–Jacobi Theory

Hamilton–Jacobi Theory and Geometrical Optics

Wave Optics

Quantum Mechanical Description of Particle Motion

The Postulates of Quantum Mechanics

Particle Motion in a Field-Free Space

Wave Packet Propagation and the Heisenberg Uncertainty Principle

The Quantum Mechanical Analog of Fermat's Principle for Matter Waves

Particle Motion in a General Electromagnetic Potential

Path Integral Approach for the Time-Dependent Wave Function

Series Solution for a Particle in a General Electromagnetic Potential

Quantum Interference Effects in Electromagnetic Potentials

The Klein–Gordon Equation and the Covariant Wave Function

Physical Interpretation of the Wave Function and Its Practical Application


The Fresnel–Kirchhoff Relation

The Fresnel and Fraunhofer Approximations

Amplitude in the Gaussian Image Plane

Amplitude in the Diffraction Plane

Optical Transformation for a General Imaging System with Coherent Illumination

Optical Transformation for a General Imaging System with Incoherent Illumination

The Wave Front Aberration Function

Relationship between Diffraction and the Heisenberg Uncertainty Principle

Particle Scattering

Classical Particle Kinematics

Scattering Cross Section and Classical Scattering

Integral Expression of Schrodinger's Equation

Green's Function Solution for Elastic Scattering

Perturbation Theory

Perturbation Solution for Elastic Scattering

Inelastic Scattering of a Particle by a Target Atom

Slowing of a Charged Particle in a Dielectric Medium

Small Angle Plural Scattering of Fast Electrons

Electron Emission from Solids

The Image Force

The Incident Current Density

Thermionic Emission

Field Emission

Emission with Elevated Temperature and Field

Space Charge Limited Emission

Appendix A: The Fourier Transform

Appendix B: Linear Second-Order Differential Equation



About the Author

Timothy R. Groves is empire innovation professor of nanoscale science (2007 – 2014) at the College of Nanoscale Science and Engineering, SUNY Institute of Technology, State University of New York. Prior to this, he worked in industrial research and development at Vistec Lithography (2005 – 2007), Leica Microsystems (2000 – 2005), IBM’s Semiconductor Research and Development Center (1983 – 2000), Hewlett Packard Labs (1978 – 1983), and Zenith Corporation (1976 – 1978). He also served as consulting professor of electrical engineering at Stanford University (1998 – 2007). He holds a BS in physics from Stanford University, and an MS and Ph.D in physics from the University of Chicago.

About the Series

Optical Sciences and Applications of Light

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Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Physics