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

We show that an incomplete, nine-element Mueller matrix with a row and a column missing, obtained in a partial polarimetry experiment, can be completed to a full, 16-element Mueller matrix, provided depolarization is absent experimentally. There exist exactly two solutions for the missing row and column, differing from one another only by the signs of the respective row and column elements. To select the correct solution, additional information on the sample properties, such as weak anisotropy or special symmetry, is needed. We provide analytical and numerical procedures for completing the partial Mueller matrix for the cases of practical interest and illustrate the approach on an experimental example.