Mueller polarimetry measurements are increasingly being used to image
highly dynamic and short-lived phenomena such as plasma discharges.
For phenomena such as these, exposure times below 1 µs must be used.
Unfortunately, these low exposure times significantly reduce the
signal-to-noise ratio, making accurate and consistent measurements
difficult. To overcome this limitation, we investigated increasing the
number of Stokes vectors produced from a polarization state analyzer
and polarization state generator, a process known as
over-determination. To conduct our analysis, we used results from
physical experiments using Stokes vectors generated by liquid crystal
variable retarders. These results were then verified using data from
simulations. First, we conclude that increasing the degree of
over-determination is a simple and effective way of dealing with this
noise; however, we also convey that choosing the best scheme is not an
entirely trivial process. Second, we demonstrate that
over-determination gives rise to hitherto inaccessible information
that allows for the quantification of statistical noise and,
crucially, the pinpointing of the origin of systematic error, a highly
beneficial process that has been lacking until now.