Fourier Optics and Optical Signal Processing

Course guarantor:

Ivan Richter

Lecturer:

Pavel Kwiecien, Ivan Richter

Tutor:

Pavel Kwiecien, Ivan Richter

Supervisor:

Department of Laser Physics and Photonics

Synopsis:

The lecture covers the basics of the Fourier optics and optical information processing. It systematically discusses the Fourier formalism in optics, it mentions also other optical transforms. The propagation and diffraction of light is described in terms of the Fourier optics, using the impulse response, the optical transfer function, the thin transparency, and the phase corrector. Within the recording and modulation of the optical information, the special attention is given, apart from the traditional photographic films, especially to the holography, the spatial light modulators, and the diffractive structures. The lecture also describes the basic processing of analogue, discrete, and logic optical information.

Requirements:

A prerequisite for studying this course is completion of the course Physical Optics (12FOPT) or a similar optics course.

Two credit tests during the semester. The first test will take place approximately halfway through the semester, the second at the end.

Syllabus of lectures:

1. Fourier transform and its properties, discrete signals and transforms.

2. Selected non-fourier transforms in optics (cosine, sine, Fresnel, Hilbert, Radon, Mellin, wavelet transforms).

2. Linear transfer systems.

4. Light propagation and diffraction within the concept of Fourier optics, the scalar signals, the thin transparent, the free space, the quadratic phase corrector, optical realization of the Fourier transform, the impulse response and the transfer function.

5. Coherently and incoherently imaging diffraction limited systems.

6. Aberation limited systems, resolution limits.

7. Diffractive structures in Fourier optics, the thin and volume diffraction gratings, general diffractive structures.

8. Recording and modulation of the optical information, the intensity record, the amplitude and phase records.

9. Optical memories, holographic memories.

10.Analogue optical information processing, the optical realization of various mathematical operations.

11.Coherent and incoherent Fourier processors, correlation and convolution processors.

12.Applications of optical processors - optical pattern and image recognition.

13.Processing of discrete optical information, vector a matrix multiplication, optical interconnection and switching.

14.Processing of logic optical information, digital logic optical processors, optical neural networks.

Syllabus of tutorials:

Study Objective:

Knowledge:

The goal of study is to acquaint with the wave optics approach to the propagation of the optical signal, the fundamentals of Fourier optics, optical realization of various mathematical transforms and its application in the analogue, digital, and logic optical information processing.

Skills:

Wave analysis of the optical transfer and imaging systems, optical realization of various mathematical operations, optical image recognition.

Study materials:

Key references:

[1] Goodman J. W.: Introduction to Fourier Optics, 4st edition, W. H. Freeman, 2017.

[2] Electronic texts stored in Microsoft Teams

Recommended references:

[3] C. S. Adams, I. G. Hughes, Optics f2f: From Fourier to Fresnel, Oxford University Press, 2019.

[4] K. Khare, M. Butola, S. Rajora, Fourier Optics and Computational Imaging, Springer, 2023.

[5] T. Yatagai, Fourier Theory in Optics and Optical Information Processing, CRC Press, 2022.

[6] R. K. Tyson, Principles and Applications of Fourier Optics, IOP Publishing, 2014.

[7] Saleh B.E.A., Teich M.C.: Fundamentals of Photonics, 3rd edition, John Wiley & Sons, New York, 2019.

[8] D. Voelz, Computational Fourier Optics - a Matlab tutorial, SPIE Press, 2011.

[9] Yu F. T. S., Jutamulia S.: Optical Signal Processing, Computing, and Neural Networks, John Wiley & Sons, New York, 1992.

[10] Papoulis A.: Systems and Transforms with Applications in Optics, McGraw Hill, New York, 1968.

Note:

Time-table for winter semester 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans:

• Fyzikální elektronika - Fotonika (PS)
• Fyzikální elektronika - Laserová fyzika a technika (elective course)