  Tracking moving masses in several degrees of freedom with high precision and
large dynamic range is a central aspect in many current and future
gravitational physics experiments. Laser interferometers have been established
as one of the tools of choice for such measurement schemes. Using sinusoidal
phase modulation homodyne interferometry allows a drastic reduction of the
complexity of the optical setup, a key limitation of multi-channel
interferometry. By shifting the complexity of the setup to the signal
processing stage, these methods enable devices with a size and weight not
feasible using conventional techniques. In this paper we present the design of
a novel sensor topology based on deep frequency modulation interferometry: the
self-referenced single-element dual-interferometer (SEDI) inertial sensor,
which takes simplification one step further by accommodating two
interferometers in one optic. Using a combination of computer models and
analytical methods we show that an inertial sensor with sub-picometer precision
for frequencies above 10 mHz, in a package of a few cubic inches, seems
feasible with our approach. Moreover we show that by combining two of these
devices it is possible to reach sub-picometer precision down to 2 mHz. In
combination with the given compactness, this makes the SEDI sensor a promising
approach for applications in high precision inertial sensing for both
next-generation space-based gravity missions employing drag-free control, and
ground-based experiments employing inertial isolation systems with optical
readout.
