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Lecture

Deviation from Bragg Scattering

In course

MSE-450: Electron microscopy: advanced methods

With this course, the student will learn about advanced methods in transmission electron microscopy, especially what is the electron optical setup involved in the acquisition, and how to interpret the data. After the course, students will be able to unders ...

Description

This lecture explores the effect of sample shape on the reciprocal lattice nodes in 2-beam electron diffraction, using Fourier transforms. It discusses scattering deviations from the perfect Bragg condition, introducing the 'excitation error' within a kinematical approximation.

In MOOC

Transmission Electron Microscopy for Materials Sciences

Instructors (2)

Cécile Hébert

Cécile Hébert was born in France in 1970. She obtained her Ingeneer degree (physics) and her PhD degree (design of a new energy filter for transmission electron microscopy, under the direction of Prof. B. Jouffrey) at the Ecole Centrale in Paris. As a post doc with Prof. P. Schattschneider, she was working on the calculation of the fine structure of ionisation edges in EELS. As a research assistant at the Vienna University of Technology, she was one of the main participant to the CHIRALTEM project dealing with the measurement of magnetic circular dichroism in the electron microscope.

Duncan Thomas Lindsay Alexander

Duncan Alexander graduated with a PhD in Materials Science and Metallurgy at the University of Cambridge in 2003 for a thesis on the kinetics of metallurgical phase transformations under the direction of Lindsay Greer. From 2003 to 2007 he held a Royal Society Overseas Research Fellowship at the University of Sydney, and then post-doctoral positions at the University of Cambridge and Arizona State University, working first on materials electrochemistry with Carsten Schwandt and Derek Fray, and then the characterization of atmospheric aerosol particles with Peter Crozier and Jim Anderson. In 2007 he came to EPFL as a scientific collaborator in the group of László Forró, and from 2008 to 2017 he was a staff scientist at EPFL’s Interdisciplinary Centre for Electron Microscopy (CIME), specializing in the application of advanced transmission electron microscopy techniques and enabling electron microscopy research activities for groups across EPFL through teaching, training and support. In 2018 he joined the Electron Spectrometry and Microscopy Laboratory (LSME) as a full-time research scientist dedicated to advancing transmission electron microscopy techniques, and was promoted to the status of Research and Teaching Associate. In 2019, together with LSME director Cécile Hébert, he launched the first MOOC on transmission electron microscopy for materials science: https://www.coursera.org/learn/microscopy/For a complete list of peer-reviewed publications, see:https://orcid.org/0000-0003-4350-8587

Official source

Related concepts (32)

Fourier transform

In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.

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.

Discrete Fourier transform

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies.

Non-uniform discrete Fourier transform

In applied mathematics, the nonuniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier transform, but in which the input signal is not sampled at equally spaced points or frequencies (or both). It is a generalization of the shifted DFT. It has important applications in signal processing, magnetic resonance imaging, and the numerical solution of partial differential equations.

Fractional Fourier transform

In mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to the n-th power, where n need not be an integer — thus, it can transform a function to any intermediate domain between time and frequency. Its applications range from filter design and signal analysis to phase retrieval and pattern recognition.

Related lectures (31)

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Explains how sample geometry affects the size and shape of reciprocal lattice nodes in multiple beam scattering.

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Discusses the point spread function and contrast transfer function in transmission electron microscopy.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.

Reciprocal lattice: basics and properties MOOC: Transmission Electron Microscopy for Materials Sciences

Covers the basics of the reciprocal lattice in electron diffraction, including diffraction vector geometry and properties of reciprocal lattice unit cell vectors.

Fourier Analysis: Fourier Series and Transform