Optimizing Mueller Polarimetry in Noisy Systems Through Over-determination

Mueller polarimetry measurements are increasingly being used to image highly dynamic and short-lived phenomena such as plasma discharges. For phenomena such as this, exposure times below 1𝜇s 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 the Polarisation State Analyser and Polarisation 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. Secondly, we demonstrate that overdetermination gives rise to hitherto inaccessible information that allows for the quantification of statistical noise and crucially, the pinpointing of the origin of systematic noise, a highly beneficial process that has been lacking until now.