Compact multi-fringe interferometry with sub-picometer precision

Deep frequency modulation interferometry combines optical minimalism with multi-fringe readout. Precision however is key for applications such as optical gradiometers for satellite geodesy or as dimensional sensor for ground-based gravity experiments. We present a single-component interferometer smaller than a cubic inch. Two of these are compared to each other to demonstrate tilt and displacement measurements with a precision of less than $20\mathrm{n}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{/}\sqrt{\mathrm{H}\mathrm{z}}$ and $1\mathrm{p}\mathrm{m}\mathrm{/}\sqrt{\mathrm{H}\mathrm{z}}$ at frequencies below $1\mathrm{H}\mathrm{z}$.