Lecture

Fourier Optics: Wavefront Analysis

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In course

CH-417: Optical methods in chemistry

Introduction and application of photon based tools for chemical sciences: from basic concepts to optical and x-ray lasers ...

Description

This lecture covers the principles of Fourier optics, starting with a review of diffraction and the Huygens-Fresnel principle. It then delves into the Fourier analysis, explaining how any function can be represented by harmonic functions. The lecture explores the Fourier transform, providing examples of its application in optics. It discusses the diffraction patterns of 2D objects, Babinet's principle, and the mathematical description of Fourier analysis. The concept of diffraction as a Fourier transform is explained, along with Abbe image formation. The lecture concludes with a note on optical tricks for creating Gaussian beams and a summary of the key concepts covered.

Instructor

Christoph Bostedt

Teaching & PhD PhD Students Eloisa Florence Manetti, Wenyi Jiang, Hankai Zhang, Loïc Lucien Cédric Bassement, Silas Strebel, Eliot Jermann Past EPFL PhD Students Jonas Knurr, Ningchen Yang Courses Optical methods in chemistry CH-417 Introduction and application of photon based tools for chemical sciences: from basic concepts to optical and x-ray lasers Physical Chemistry Seminar 1: Trends CH-643 Students can learn about the broader research in Phyiscal Chemistry and broaden

Official source

Related concepts (32)

Fourier analysis

In mathematics, Fourier analysis (ˈfʊrieɪ,_-iər) is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics.

Fourier series

A Fourier series (ˈfʊrieɪ,_-iər) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series, but not all trigonometric series are Fourier series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation.

Fresnel diffraction

In optics, the Fresnel diffraction equation for near-field diffraction is an approximation of the Kirchhoff–Fresnel diffraction that can be applied to the propagation of waves in the near field. It is used to calculate the diffraction pattern created by waves passing through an aperture or around an object, when viewed from relatively close to the object. In contrast the diffraction pattern in the far field region is given by the Fraunhofer diffraction equation. The near field can be specified by the Fresnel number, F, of the optical arrangement.

Harmonic analysis

Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on the real line, or by Fourier series for periodic functions. Generalizing these transforms to other domains is generally called Fourier analysis, although the term is sometimes used interchangeably with harmonic analysis.

Huygens–Fresnel principle

The Huygens–Fresnel principle (named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel) states that every point on a wavefront is itself the source of spherical wavelets, and the secondary wavelets emanating from different points mutually interfere. The sum of these spherical wavelets forms a new wavefront. As such, the Huygens-Fresnel principle is a method of analysis applied to problems of luminous wave propagation both in the far-field limit and in near-field diffraction as well as reflection.

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