What does the fourier transform do

This is more a physics than a mathematics question. However, it's a very interesting one.

A pretty complicated topic in theoretical electromagnetism and optics is the scattering of electromagnetic waves on objects. The most simple approximation is Kirchhoff's scalar theory of diffraction. The idea is close to Huygen's principle, i.e., you shine with light on an opaque screen with some openings (like the one with regular holes shown on the left in your picture). Then from any point of the openings a spherical wave is emitted, and the total wave for an observer is given by the superposition of all these elementary spherical waves. The superposition of the spherical waves leads to partial destruction or amplifying, resulting in characteristic interference patterns.

In a certain limit, the socalled Fraunhofer-diffraction, where you observe the diffraction picture of your object in a distance very far from the extension of the object, the amplitude on this screen is given by the Fourier transform of the object.

Have a look at Wikipedia:

http://en.wikipedia.org/wiki/Fraunhofer_diffraction