Completing an experimental non-depolarizing Mueller matrix with both a row and a column missing

Real-time imaging or spectroscopic applications of Mueller matrix polarimetry (or generalized ellipsometry) often require the acquisition of partial Mueller matrices only. We advance an efficient algebraic procedure allowing for the completion of a partial Mueller matrix, a row and a column of which are missing, i.e., only nine out of the 16 elements of which are measured, to a full Mueller matrix, assuming the measurement is non-depolarizing. Unlike already existing approaches, the novel one does not require the calculation of auxiliary quantities, such as the Jones matrix or the covariance matrix, and does not resort to any approximations, e.g., that of weak anisotropy, thus making it both fast and accurate. The algebraic procedure is validated under real-time experimental conditions during spectroscopic measurements using a snapshot instrument and can be used in both reflection and transmission measurement configurations.