Error propagation in decomposition of Mueller matrices

Abstract

A decomposition for Mueller matrices into three physically descriptive components was recently developed by Shih-Yau Lu. The effect of experimental error on this decomposition was studied. Both analytical and numerical methods were employed. Symbolic expression of the component matrices in terms of the original Mueller matrix elements shows how errors in the original matrix propagate through the decomposition. Complete symbolic decomposition was given for non-depolarizing Mueller matrices and their associated physical parameters; however, the depolarizing case produced unmanageably large expressions, so approximations were used. For the numerical results, Mathcad was used to randomly generate Mueller matrices, incorporate matrices is proportional to the original error within the measured Mueller matrix, and that the proportional constant increases with each subsequent step in the decomposition. In addition, Cloude's method for eliminating 'noise' in a Mueller matrix was employed, and its effect on error distribution was analyzed.