Course detail
The Fourier Transform of Lattices and the Kinematical Theory of Difraction
FSI-9KTD Acad. year: 2024/2025 Summer semester
The course deals with the Fourier transform of functions of several variables and its use in diffraction theory and in structure analysis. The introductory parts are focused on the definition of the Fourier transform, spatial frequencies, spectrum of spatial frequencies, and on the relevance of the Fourier transform to the diffraction theory. Then, the properties of the Fourier transform are presented via mathematical theorems and are illustrated by the Fraunhofer diffraction patterns. In this way a view of the general properties of the diffraction phenomena of this type is obtained. At the end the kinematical theory of diffraction by crystals is presented as an application of the Fourier transform of three-dimensional lattices.
Language of instruction
Czech
Supervisor
Department
Entry knowledge
Basic mathematical description of light propagation (diffraction), basic knowledge of Theory of solid state physics (structural analysis).
Rules for evaluation and completion of the course
Examination: Oral. Both practical and theoretical knowledge of the course is checked in detail. The examined student has 90 minutes to prepare the solution of the problems and he/she may use books and notes.
The presence of students at practice is obligatory and is monitored by a tutor. The way how to compensate missed practice lessons will be decided by a tutor depending on the range and content of the missed lessons.
Aims
Knowledge of the kinematical diffraction in structure analysis.
Practice in analytical calculations of the Fourier transform.
Ability to calculate Fourier transform.
Knowledge of kinematic theory of diffraction in structural analysis
The study programmes with the given course
Programme D-FIN-K: Physical Engineering and Nanotechnology, Doctoral, recommended course
Programme D-FIN-P: Physical Engineering and Nanotechnology, Doctoral, recommended course
Type of course unit
Lecture
20 hours, compulsory
Syllabus
1. Summary of the crystal lattice geometry.
2. The Dirac distribution.
3. The Fourier transform of functions of several variables and its relevance for structure analysis.
4. Linearity of the Fourier transform and the Babinet theorem.
5. The Fourier transform of the lattice function and the reciprocal lattice.
6. Symmetry of the Fourier transform and the Friedel law.
7. Convolution and the Fourier transform of convolution. Cross-correlation and autocorrelation.
8. Kinematical theory of diffraction.
9. The Laue equations and the Bragg equation.
10. Calculations of the shape amplitudes.
11. Addenda.