  We present a method for 3D sub-nanometer displacement measurement using a set
of differential optical shadow sensor. It is based on using pairs of collimated
beams on opposite sides of an object that are partially blocked by it. Applied
to a sphere, our 3-axis sensor module consists of 8 parallel beam-detector sets
for redundancy. The sphere blocks half of each beam power in the nominal
centered position, and any displacement can be measured by the differential
optical power changes amongst the pairs of detectors. We have experimentally
demonstrated a displacement sensitivity of 0.87 nm/rtHz at 1 Hz and 0.39
nm/rtHz at 10 Hz. We describe the application of the module to the inertial
sensors of a drag-free satellite, which can potentially be used for navigation,
geodesy and fundamental science experiments as well as ground based
applications.
