0.4 inch in 20 ms is about +/-12 G with a peak velocity of about 20 in/sec. Most of the accelerated mass will be in the straight line flexure and voice coil Voice coil bobbin aluminum, flexure EDMed titanium (low mass, high strength, good fatigue resistance). To keep the voice coil cool, ferrofluid in the voice coil-magnet housing gap.
Renishaw just came out with a self calibrating linear encoder.