The screen is split into three sections:
If you imagine the input image to be an atomic structure, the Fourier transform shows what X-rays would do to it: When X-rays interact with matter, they create an interference pattern. This pattern is the magnitude of the Fourier transform of the electron density structure in the matter, and is what we measure in an X-ray diffraction experiment.
You can use this tool to demonstrate what X-ray scattering / diffraction would look like for a variety of different structures. Simply hold a piece of paper with a structure on it to the camera and see the Fourier transform live. There are also a variety of examples built-in to the program.
The pattern on the right represents the reciprocal space of the input image. Because of the inverse relationship between real and reciprocal space, the size and orientation of your features will appear “flipped.”
If your particles are isotropic, you will see concentric rings in the scattering pattern. A small circle produces a broad, spread-out pattern, while a larger circle produces a tight, narrow pattern. If your particles are anisotropic, the scattering pattern will appear stretched in the opposite direction; e.g. a horizontal oval in your image will create a vertical streak in the Fourier transformed image.
When particles are arranged in an ordered lattice, the smooth rings break up into sharp, distinct spots (Bragg peaks). The positions of these spots tell you about the symmetry and spacing of the “crystal.” A closely packed lattice will push these spots further from the centre, while a sparse lattice brings them closer together. If the arrangement is disordered (like a liquid or glass), these sharp spots will blur back into diffuse “halos,” representing the average distance between particles rather than a fixed grid.
The Fourier transform of a finite lattice is effectively the transform of a single particle (the form factor) sampled by the transform of the lattice (the structure factor). For small lattices, the sampling functions are broad, allowing the intensity contribution from individual particles to remain visible as diffuse features. As the lattice extent increases, these functions narrow, resulting in the sharp, discrete peaks characteristic of an infinite periodic array.
The Radial Integration (below) converts these 2D patterns into a 1D plot. The peaks here give you a precise way to measure the average particle size or lattice spacing. Peaks further towards the left represent larger features than peaks towards the right hand side.