This work investigates how the signal-to-noise ratio (SNR) of an over-determined Mueller matrix can be improved by changing the method of calculation. Specifically, our investigation focused on comparing SNRs achieved using the vector methodology from the field of partial Mueller polarimetry, and the matrix methodology. We use experimentally derived measurements from an investigation into the time-varying signal produced by the Mueller matrix of an electro-optic Bismuth Silicon Oxide (BSO) crystal undergoing cyclical impact of a Helium plasma ionisation wave. Our findings show that the vector methodology is superior to the matrix methodology, with a maximum SNR of 7.54 versus 4.97. We put forth that the superiority of the vector methodology is due to its greater flexibility, which results in the Mueller matrix being calculated with better condition matrices, and higher levels of SNR in the intensity measurements used for calculation.

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.