Three Dimensional Electron Microscopy/Fourier transforms

What You Need To Know About A Fourier Transform

By David J DeRosier

Professor Emeritus,
Department of Biology & Rosenstiel Basic Medical Sciences Research Center,
Brandeis University

Introduction

Most students of molecular electron microscopy keep well away from learning about Fourier transforms. At schools whose aim is to train students in molecular electron microscopy, however, the gathered class must sit through a lecture or two on the Fourier transform. A mathematical lecture on the topic is usually more satisfying to the faculty than it is to students, who use the occasion to day dream or simply sleep having been up half the previous night at some bar. I guess it is not obvious why such a mathematical operation would be of interest to those who simply wants to know the molecular architecture of some cellular machine.

My aim is to tell you why you want a Fourier transform of your electron micrographs, what you can learn from a Fourier transform, how to think about a Fourier transform without having to waddle through the mathematics, and how to generate a Fourier transform when you want one. Since microscopy and image analysis are visual, I am presenting many of the lessons as pictures. I do not intend to prove the properties of various transforms but rather to show the results. There are lots of books on the theory.

Why you want a Fourier transform.

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