Course detail
Fourier Methods in Optics
FSI-TFO Acad. year: 2021/2022 Summer semester
The course consists of three parts.
The first part is a mathematical one. The Fourier transform of two variables is transformed to polar coordinates and expressed in terms of Hankel's transforms. The Zernike polynomials are used for the description of wave aberrations.
The second part of the course deals with the wave description of an image formation by lenses. The problem is exposed by a direct application of the diffraction theory on one hand, and by the use of the formalism of linear systems (transfer function) on the other hand. The light distribution near the focus, the Abbe theory of image formation, the dark field method, the method of the phase contrast, schlieren method, the image processing by influencing the spectrum of spatial frequencies, and the principle of confocal microscopy are discussed.
The third part of the course provides an overview of the diffractive optics, of the image formation by zone plates and of optics of Gaussian beams. The course involves also the history of the Fourier optics as a whole.
Language of instruction
Czech
Number of ECTS credits
7
Supervisor
Department
Learning outcomes of the course unit
Working knowledge of the Bessel functions, Lommel functions of two variables, Hankel transforms, Zernike polynomials and their applications for calculation in wave optics. A grasp of the Fourier optics.
Prerequisites
Wave optics. Calculus of functions of several variables.
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
Examination: Oral. The examined student has 90 minutes to prepare the solution of the problems and he/she may use books and notes.
Aims
The aim of the course is to provide students with basic ideas and history of Fourier optics.
Specification of controlled education, way of implementation and compensation for absences
Course-unit credit is conditional on active participation in lessons. The way of compensation for missed lessons is specified by the teacher.
The study programmes with the given course
Programme N-PMO-P: Precise Mechanics and Optics, Master's, compulsory
Programme N-FIN-P: Physical Engineering and Nanotechnology, Master's, compulsory-optional
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
1. The Dirac distribution, its definition, properties and expressions in various coordinate systems. Examples.
2. The Fourier transform, definition, fundamental theorem. Examples. The diffraction of plane wave by a three-dimensional structure. The Ewald spherical surface.
3. The Fraunhofer diffraction as the Fourier transform of the transmission function. Meanings of variables in the Fourier transform. Spatial frequencies.
4. Linearity of the Fourier transform and the Babinet theorem. Examples. Rayleigh-Parseval theorem. Examples. Symmetry properties of the Fourier transform. Central symmetry, mirror symmetry, places of zero amplitude. The Friedel law.Convolution and the Fourier transform of convolution.
5. The Bessel functions. The intensity distribution near the focus.
6. The Fourier transform in polar coordinates. The Hankel transforms.
7. The Fourier transform in spherical coordinates.
8. The Zernike polynomials. The wave description of the image formation by a lens.
9. Linear systems. The transfer function.
Image processing. Dark field method.
10. Image formation by the zone plates. Diffraction optics.
11. image processing. Spatial frequencies filtration. Dark field method.
12. The method of phase contrast. The schlieren method. Confocal microscopy.
Exercise
26 hours, compulsory
Teacher / Lecturer
Syllabus
Discussion, calculations and/or laboratory demonstrations of the topics specified during the lectures.