Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools, do not necessarily understand all the richness that can be derived from joint analysis in the temporal and spectral domains, particularly in the field of optics. As part of the second year of the Master's degree in Physics Lasers and Materials at the University of Burgundy, we have set up a set of experiments to highlight these concepts and to show, on a non-trivial example of periodic phase modulation, the precautions to be taken in the interpretation of the various experimentally accessible spectra. This hands-on session, made possible through the use of the research infrastructure, is also an introduction to the use of standard optical telecommunications equipment.

https://iopscience.iop.org/article/10.1088/1361-6404/ab1a54/pdf

Applications of sinusoidal phase modulation in temporal optics to highlight some properties of the Fourier transform

Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency ω = 2π/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students should be familiar with this subject. A suitable device for demonstrating spectra of electrical signals is a digital storage oscilloscope. Spectra of various waveforms and of AM and FM signals are demonstrated, as well as AM signals from a broadcasting station. Changes in the signals filtered by frequency-selective circuits are seen by comparing the spectra of the input and output voltages. All the experiments are suitable for undergraduate laboratories and usable as classroom demonstrations.

http://iopscience.iop.org/article/10.1088/0143-0807/33/5/1249/pdf

Some applications of Fourier's great discovery for beginners

As a concept and as a tool, the Fourier transform is pervasive in applied mathematics, computing, mathematics, probability and statistics as well as in substantive sciences such as chemistry, geophysics and physics This chapter presents a review of such applications and then four personal analyses of scientific data based on Fourier transforms Specific points made include: Fourier analysis is conceptually simple, its concepts often have direct physical interpretations, useful statistical properties are available, and there are various interesting connections between the mathematical and physical concepts

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Some Examples of Empirical Fourier Analysis in Scientific Problems

The authors systematically bring together the standard mathematical properties of Fourier transforms and the experimental characteristics of diffraction phenomena. They display in detail an experimental realisation of a particular case of the convolution theorem.

https://iopscience.iop.org/article/10.1088/0143-0807/7/3/007/pdf

S Moss de Oliveira

Papers

Experimental demonstrations of the mathematical properties of Fourier transforms using diffraction phenomena