Free Electron Laser Time

In this case, the x-ray data is already the constructive interference of the Fourier transform of the object shot by the X-ray beam. The raw diffraction data is actually just the intensities of the Fourier transform of whatever is providing the constructive interference (i.e. diffracting).

What they actually had to calculate were the phases of the data, which is arguably much more challenging. Once those phases are calculated, you can do a reverse Fourier transform (also significant, also called a Fourier synthesis in that paper and elsewhere) and get your real-space map. This is an iterative process, so you don't usually just do it once, although I'm not sure what Kendrew, Perutz and Rossman did in the early days.

https://en.wikipedia.org/wiki/Phase_problem

Structural biology and cutting edge computing are inextricably linked, and probably always will be, which is actually how I fell into the field. My (not yet then) P.I. was trying to get Nvidia 3d vision working on Linux for refining the atomic structure into an X-ray map and had exhausted all the IT knowledge on campus before I stumbled in.

The lab my wife worked in, 20+ years ago, still had a mahogany chest of "bones" to calculate Fourier transforms, by hand. Once you had phases, you'd plot density on transparent cels, and put them in a stack.

What are you wondering about? I'm a structural biologist and just got home for the day from running some electron diffraction samples. I could probably provide pretty pictures and accompanying explanations of anything up to the free-electron laser portion.