I am looking for some mirror setup where rotation one or more elements in the mirror setup will allow to shift the beam along its axis.
Two mirrors in a galvanometer scanner type setup work well for controlling the angle of the beam.
Rotating risley prisms can be used to only offset the beam without changing its angle but the possible positions are limited.
Dove prisms are great for rotating the beam along itself or rotate in a circular fashion if prism center is shifted.
But as for offsetting (shifting) a beam along its axis from a (-1,-1) position to (1,1) without changing the angle of the beam, I can't find any setup which involves a rotating mirror rather than shifting mirror. But I feel there may be something missing from my limited optics knowledge.
4 rotating galvo scanner mirrors may do this but this may be an overkill and the size of the mirrors on the last two will increase to impractical sizes for decent 45 degree FOVs or more. So I'm crossing this one out.
In case not clear, https://i.stack.imgur.com/ITNSL.jpg