An introduction to Fourier transforms

What is a Fourier transform?

The Fourier transform is fundamental to the scattering of all radiation, including neutrons. The scattering interaction between radiation and some sample essentially performs a Fourier transform on the radiation, leading to the scattering pattern that we measure..

Before we look in more detail at Fourier transforms and scattering, watch the video below from 3Blue1Brown which gives a great overview of the Fourier transform.

Note

This video focuses on the decomposition of something in the time domain, but for elastic scattering, we are interested in the analogous decomposition in the space domain (hence we measure \(q\) in units of Å^-1).

Now let’s take a look at the impact of Fourier transforms in neutron reflectometry.