Complete Mueller matrix from a partial polarimetry experiment: the 12-element case

Conventional generalized ellipsometry instrumentation is capable of measuring 12 out of the 16 elements of the Mueller matrix of the sample. The missing column (or row) of the experimental partial Mueller matrix can be analytically determined under additional assumptions. We identify the conditions necessary for completing the partial Mueller matrix to a full one. More specifically, such a completion is always possible if the sample is nondepolarizing; the fulfillment of additional conditions, such as the Mueller matrix exhibiting symmetries or being of a special two-component structure, are necessary if the sample is depolarizing. We report both algebraic and numerical procedures for completing the partial 12-element Mueller matrix in all tractable cases and validate them on experimental examples.