> It is amazing that this is done with only a single motor.
No. You misunderstood the video. There are 6 motors per mirror segment. Listen to video you linked at 9:11. It says:
“There are 6 actuators per mirror segment, and they are arranged in a hexapod or Stewart-platform configuration.”
What you are confused about is that there is only a single motor per actuator. One could naively think “oh we need a rough adjustment, and a fine adjustment so we will need two motors for each of those”. But they managed to make it more clever, and only use one motor for both the rough adjustment and the fine one. When they run the motor in one direction it adjusts the distance of the actuator roughly (minimum step size 0.058 micron) and when they run it in the other direction it adjusts finely (minimum step size is 7.7 nanometer).
Pedantry: when the motor starts moving, it's a fine correction, but after one rotation of one of the gears it hits a stop and changes to a coarse correction. It then continues to do coarse correction as long as you rotate in that one direction.
If you reverse the motor, you get fine correction again until that gear turns one rotation and hits the other side of the stop, reverting to coarse correction.
Once you have things coarsely aligned, you back the motor a bit and then operate within the single rotation of that gear, staying with fine correction.
https://youtu.be/5MxH1sfJLBQ
It is amazing that this is done with only a single motor.
It works something like this: one direction of the motor sets which axis to align, the other direction sets the alignment of the chosen axis.