Course detail

Fourier Optics

FSI-TFOAcad. year: 2011/2012

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.

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.


Wave optics. Calculus of functions of several variables.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Born M., Wolf E.: Principles of Optics. 7th ed., kap. 8, 9, Appendix VII, Cambridge University Press 1999.
Iizuka K.: Engineering Optics. 2nd ed., Springer Verlag, Berlin 1987.
Goodman J. W.: Introduction to Fourier Optics. 2nd ed., McGraw-Hill Co., New York 1996.
Saleh B. E. A., Teich C.: Základy fotoniky 1, Matfyzpress, Praha 1994.
Papoulis A.: Systems and Transforms with Applications in Optics., McGraw-Hill Co., New York 1968.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

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.

Language of instruction


Work placements

Not applicable.


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.

Classification of course in study plans

  • Programme M2A-P Master's

    branch M-FIN , 1. year of study, summer semester, 4 credits, compulsory-optional
    branch M-PMO , 1. year of study, summer semester, 3 credits, compulsory-optional

Type of course unit



26 hours, optionally

Teacher / Lecturer


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.


13 hours, compulsory

Teacher / Lecturer


Discussion, calculations and/or laboratory demonstrations of the topics specified during the lectures.