Nonlinearities in Fringe-Counting Compact Michelson Interferometers

Compact Michelson interferometers are well positioned to replace existing displacement sensors in the readout of seismometers and suspension systems, such as those used in contemporary gravitational-wave detectors. Here, we continue our previous investigation of a customised compact displacement sensor built by SmarAct that operates on the principle of deep frequency modulation. The focus of this paper is the linearity of this device and its subsequent impact on sensitivity. We show the three primary sources of nonlinearity that arise in the sensor: residual ellipticity, intrinsic distortion of the Lissajous figure, and distortion caused by exceeding the velocity limit imposed by the demodulation algorithm. We verify the theoretical models through an experimental demonstration, where we show the detrimental impact that these nonlinear effects have on device sensitivity. Finally, we simulate the effect that these nonlinearities are likely to have if implemented in the readout of the Advanced LIGO suspensions and show that the noise from nonlinearities should not dominate across the key sub-10 Hz frequency band.