We never really thought about it before, but this post about Rapatronic Shutters answers the question of how to photograph an atomic bomb detonation. The post includes an MIT video where [Charles Wyckoff] explains how he and [Harold Edgerton] developed the Rapatronic Camera. It is designed to snap a photograph based on zero time, marked by the X-ray transmission emanating from the bomb before it actually explodes. This pulse is picked up by a light sensor on a delay circuit, allowing for very precise exposure timing. Many of these cameras were used at the same time, all with slightly different delays so that the images could be viewed in order to show what happens during each stage of detonation.
[Thanks Petrus]