zaalexander

The only way to get that kind of accuracy ( 1 Micron ) is to use Ball-screws,which would be ground from C1 to C3 Grade, 3mm pitch, is a normal size that would work,then ac servos with 16 Bit to 20 Bit high count per rev encoders

You also could use a linear motor most can do ( 1 Micron ) positioning accuracy

Steppers belts, rack & pinion lead-screws, Etc it's not going to happen