Very low yield, though (below 1kt).

They were modified sounding rockets (typically used to gain scientific data from high altitudes) that left a smoke trail behind them at set distances from the detonation site. They were used to gather data on things such as the progression of the blast shock wave and other data.

Of course... because Photoshop was developed in the 50s!

This is not an exhaustive list, but 2 ways were... Cameras were set anywhere up to over 3000 metres away and were using state of the art lenses to film the effects. Cameras were also mounted in steel and lead housing set on top if concrete towers for closer filming. I believe they also had heavy steel pipes embedded in the ground and used mirrors like a periscope to send images to the buried cameras. Take for example the cameras on the launch pad for Apollo rockets, they were set behind inches thick quartz blocks that protected them from the rocket motors and the exhaust.