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