Blacklash from large gear
In creating MR !371 (merged) I have done a lot of looking at gears. One thing I have noticed is that the backlash in the large gear is approximate half a gear pitch which is 1/48 of a turn of the big gear. Which is then 1/24th of a turn of the little gear (or motor) to take up this slack. This is about 340 steps, which is higher than we measured in the autofocus paper.
I think it is worth inverting the nut trap used for the actuator and stage. This should hold the gear much firmer reducing backlash. It would be interesting to do it with the x motor and not the y and see if the difference is noticeable.