Increasing signal-to-noise ratio in over-determined Mueller matrices

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.