Course detail
Mathematics of Wave Optics
FSI-9MAV Acad. year: 2024/2025 Winter semester
Special functions are frequently used in monographs and papers dealing with wave optics. In spite of that they are not involved in the curricula (e. g. the Lommel functions of two variables or the Fresnel integrals). In some cases a mathematical literature does not exist at all (e. g. the Zernike polynomials). Most of the graduates from the technological universities never studied special functions, not even the standard ones (e. g. the Bessel functions). Therefore, the post-graduate students of optical engineering have troubles with the study of books and papers, with mathematical treatment of their own results, and with numerical calculations. The present course offers an overview of mathematics used in wave optics. The exposition is kept in frames of functions of real variables and applications are emphasized.
Language of instruction
Czech
Supervisor
Department
Entry knowledge
The exposition is kept in frames of functions of real variables and applications are emphasized.
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
To gain an overview of mathematics used in wave optics.
An overview of special functions.
Applications of special functions in wave optics.
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, optionally
Syllabus
1. Elementary functions.
2. Gamma and digamma functions.
3. Sine and cosine integrals.
4. The Fresnel integrals.
5. The Dirac distribution.
6. Orthogonal systems of functions. The Gramm-Schmidt orthogonalization process.
7. Hypergeometric functions.
8. The Bessel functions.
9. The Fourier transform.
10. The Hankel transforms.
11. The Jacobi polynomials.
12. The Gegenbauer polynomials.
13. The Chebyshev polynomials.
14. The Zernike polynomials.