What are those vertical lines of smoke we see in many old photos of atomic bomb tests before the ban?
The Five Biggest Nuclear Bomb Tests Ever | The National Interest
How were they made and what function did they serve? I’m assuming they had something to do with providing a measure of scale to compare the size of a blast, but don’t know that for a fact.
They launched rockets to make the smoke trails. As you said, it was to study the blast.
Did the rockets have any sort of instrumentation or telemetry on them?
The shock wave from the explosion compresses their air as it passes through, changing its index of refraction and causing a lensing effect. The rocket’s smoke trails are on the far side of the explosion from the camera, and provide straight lines that the lensing effect distorts, pinpointing where the shock wave is (and possibly also how strong it is) at any given moment.