Fourier Optics (FSI-TFO)

Academic year 2020/2021
Supervisor: prof. RNDr. Jiří Komrska, CSc.  
Supervising institute: ÚFI all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
The aim of the course is to provide students with basic ideas and history of Fourier optics.
Learning outcomes and competences:
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.
Course contents:
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, of optics of Gaussian beams, of laser speckles and their metrological applications. Also dealt with are the fundamentals of holography. The course involves also the history of the Fourier optics as a whole.
Teaching methods and criteria:
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.
Controlled participation in lessons:
Course-unit credit is conditional on active participation in lessons. The way of compensation for missed lessons is specified by the teacher.
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Exercise  13 × 1 hrs. compulsory                  
Course curriculum:
    Lecture The Bessel functions.
The intensity distribution near the focus.
The Fourier transform in polar coordinates. The Hankel transforms.
The Fourier transform in spherical coordinates. The atomic factor.
The Zernike polynomials.
The wave description of the image formation by a lens.
Linear systems. The transfer function.
Image processing. Dark field method.
The method of phase contrast. The schlieren method. Confocal microscopy.
Image formation by zone plates. Diffraction optics.
The Gaussian beams.
Laser speckles and their applications.
History of the diffraction theory and of the Fourier optics. Biography of J. B. Fourier, A. J. Fresnel, J. Fraunhofer, E. Abbe, F. Zernike.
    Exercise Discussion, calculations and/or laboratory demonstrations of the topics specified during the lectures.
Literature - fundamental:
1. Born M., Wolf E.: Principles of Optics. 7th ed., kap. 8, 9, Appendix VII, Cambridge University Press 1999.
2. Goodman J. W.: Introduction to Fourier Optics. 2nd ed., McGraw-Hill Co., New York 1996.
3. Papoulis A.: Systems and Transforms with Applications in Optics., McGraw-Hill Co., New York 1968.
Literature - recommended:
1. Iizuka K.: Engineering Optics. 2nd ed., Springer Verlag, Berlin 1987.
2. Saleh B. E. A., Teich C.: Základy fotoniky 1, Matfyzpress, Praha 1994.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
M2A-P full-time study M-PMO Precise Mechanics and Optics -- Cr,Ex 4 Compulsory-optional 2 1 S
N-FIN-P full-time study --- no specialisation -- Cr,Ex 4 Compulsory-optional 2 1 S