  High precision interferometers such as gravitational-wave detectors require
complex seismic isolation systems in order to decouple the experiment from
unwanted ground motion. Improved inertial sensors for active isolation
potentially enhance the sensitivity of existing and future gravitational-wave
detectors, especially below 30 Hz, and thereby increase the range of detectable
astrophysical signals. This paper presents a vertical inertial sensor which
senses the relative motion between an inertial test mass suspended by a blade
spring and a seismically isolated platform. An interferometric readout was used
which introduces low sensing noise, and preserves a large dynamic range due to
fringe-counting. The expected sensitivity is comparable to other
state-of-the-art interferometric inertial sensors and reaches values of
$10^{-10}\,\text{m}/\sqrt{\text{Hz}}$ at 100 mHz and
$10^{-12}\,\text{m}/\sqrt{\text{Hz}}$ at 1 Hz. The potential sensitivity
improvement compared to commercial L-4C geophones is shown to be about two
orders of magnitude at 10 mHz and 100 mHz and one order of magnitude at 1 Hz.
The noise performance is expected to be limited by thermal noise of the
inertial test mass suspension below 10 Hz. Further performance limitations of
the sensor, such as tilt-to-vertical coupling from a non-perfect levelling of
the test mass and nonlinearities in the interferometric readout, are also
quantified and discussed.
