Course detail

Particle Optics

FSI-TCOAcad. year: 2020/2021

The course deals with problems of optics of charged particles in focusing and deflection systems and spectrometers. The sources of electrons and ions are characterized as well as electron and ion optical elements and instruments utilizing the beams of charged particles. In addition to the practical implementation of individual elements, the theory of imaging and aberrations is emphasized to allow students effectivelly use software for design of charged particle systems.

Learning outcomes of the course unit

Knowledge of motion of charged particles in electromagnetic fields of electron and ion lenses, deflectors and spectrometers as well as the knowledge of instruments using them for microscopic or technological applications.


Knowledge of electromagnetism on the level defined by the textbook HALLIDAY, D. - RESNICK, R. - WALKER, J.: Fundamentals of Physics. J. Wiley and Sons. MATHEMATICS: Basics of vector analysis.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

V. Hulínský a K. Jurek: Zkoumání látek elektronovým paprskem. SNTL 1982.
M. Lenc, B. Lencová: Optické prvky elektronových mikroskopů. Metody analýzy povrchů. Elektronová mikroskopie a difrakce. (L. Eckertová, L. Frank ed.), Academia 1996.
B. Lencová, M. Lenc: Optika iontových svazků. Metody analýzy povrchů. Iontové, sondové a speciální metody. (L. Frank, J.Král, ed.), Academia 2002, 65-103.
B. Urgošík: Dynamické hmotové spektrometry. SNTL 1972.
S. Humphries, Jr.: Charged Particle Beams. J. Wiley 1990.
B. Sedlák, I. Štoll: Elektřina a magnetismus. Academia 1993.
J. Orloff (ed.), Handbook of Charged Particle Optics. CRC Press, 2008. (EN)
L. Reimer, Scanning Electron Microscopy (2nd ed.), Springer,1998 (EN)
D. B. Williams, C. B. Carter, Transmission Electron Microscopy (2nd ed.), Springer, 2009 (EN)

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Active participation at tutorials and correct protocols. Exam is oral, two questions from the list of subjects given above. The preparation takes 30 minutes, lecture notes and literature are allowed.

Language of instruction


Work placements

Not applicable.


The course improves the knowledge of the students about the most important instruments used in microscopy and microanalysis, in electron and ion beam technology and in the physics of surfaces and thin films.

Specification of controlled education, way of implementation and compensation for absences

Compulsory participation at tutorials, protocol with solution of all sample problems and on CAD projects. Auxiliary lecture notes will be provided to the students on Internet.

Classification of course in study plans

  • Programme M2A-P Master's

    branch M-PMO , 2. year of study, winter semester, 6 credits, compulsory

  • Programme N-FIN-P Master's, 2. year of study, winter semester, 6 credits, compulsory

Type of course unit



26 hours, optionally

Teacher / Lecturer


Overview of instruments utilizing the beams of charged particles for the study of structure and composition of solids and in technological applications.
Wave and relativistic properties of charged particles. Equation of motion for charged particles in electrostatic and magnetic fields.
Qualitative description of electrostatic and magnetic lenses and deflectors, based on equation of motion.
The series expansion of potential near an optical axis. Multipole fields for particle optics and their realization.
General expression of trajectory equation for systems with straight axis.
Paraxial equation for rotationally symmetric and quadrupole lenses and for lenses with deflection systems.
Aberrations of charged particle optical systems.
Transport of particles – the use of matrix notation. The description of particle optics with variational methods (Lagrange function, index of refraction) and with Hamiltonian methods.
Basic numerical methods of computing fields in electron optics and their optical properties.
Sources of electrons and ions. Basic properties and utilization.
Scanning electron microscope – the principle of image formation, depth of field, dependence of spot current on spot size, image resolution.
Image formation in a transmission electron microscope, the image resolution.
Optics of systems with curved axis, electron and ion spectrometers – basic types and properties.


14 hours, compulsory

Teacher / Lecturer


Electron movement in the homogeneous electrostatic and magnetic field
Derivation of trajectorz equation and paraxial equation
Expansion of the potential near optical axis
Geometric aberrations of 3rd order of electrostatic and magnetic lens
Spherical aberration of magnetic lens

Computer-assisted exercise

12 hours, compulsory

Teacher / Lecturer


Aberration polynomial - visualisation of aberrations, spot size, resolution
Finite element method - solution of 1D electrostatic field
Intoduction to EOD (Electron Optical Design) software
EOD - electrostatic lens design, focussing, computation of aberrations
EOD - magnetic lens and deflectors
Work on individial project