As for eliminating backlash, that's fundamentally impossible
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Basicaly true , but, you can minimize it. Very often the culprit is the thrust bearings and proper pre-load can reduce backlash.
If you realy get anal about this one can profile the ball screws movement over it's entire length in both forward and backward direction, test the ball nut play, measure the preload, etc. Based on measurements from a known standard, of resolution greater than the compnents, you can know exactly what you have.
BTW, I do my checking using optics. Also don't have servo's so Hood is a good source on that subject.
Good stuff to do if your borded on a rainy day and have the equipment to do it.
RICH