Optical Fourier transformations were performed using small lithographic patterns of different characters. A DLP projector can be used as a Fourier filter to do simple pattern recognition.

Video contents:

0:00 General introduction
1:44 Fourier explained (simple)
3:45 Digging a bit deeper (sorry, could not resist)
5:55 Fourier on images
9:27 Fourier transforms using optics
12:05 Setup and results
14:15 Fourier filtering

The 2D Fourier transformation images were calculated using freeware developed by Kobe University. You dan download this tool from:
http://cas.eedept.kobe-u.ac.jp/Welcom...

Conversions of 2D images to 3D were done using Gwyddion. This very advanced piece of software is can be downloaded for free from:
http://gwyddion.net/download.php

To illustrate 2D Fourier transform on an actual image, a small part of an M.C. Escher drawing was used.

While editing the material for this video I found out that the Applied Science channel made a somewhat similar video on "Optical Fourier" already in 2012:    • Intro to Fourier Optics and the 4F co...   . Luckily the angle is somewhat different.

This video gives a different (and deeper) perspective on the math behind Fourier transformations;
   • Lecture 6A Fourier Optics Basics  

If you want to go all the way, read the wiki page on Fourier. If you dare.
https://en.wikipedia.org/wiki/Fourier...