FSI-TCOAcad. year: 2018/2019
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.
Recommended optional programme components
Recommended or required reading
M. Lenc, B. Lencová: Optické prvky elektronových mikroskopů. Metody analýzy povrchů. Elektronová mikroskopie a difrakce. (L. Eckertová, L. Frank ed.), Academia 1996.
V. Hulínský a K. Jurek: Zkoumání látek elektronovým paprskem. SNTL 1982.
B. Urgošík: Dynamické hmotové spektrometry. SNTL 1972.
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. Sedlák, I. Štoll: Elektřina a magnetismus. Academia 1993.
S. Humphries, Jr.: Charged Particle Beams. J. Wiley 1990.
J. Orloff (ed.), Handbook of Charged Particle Optics. CRC Press, 2008. (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
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.
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
seminars in computer labs
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