Obtainment of Mueller-Jones matrix from the outer product of input and output Stokes vectors

Implementation of a theorem that was recently put forward is discussed. The theorem states that there exists a relation between input-output Stokes vectors and complex vectors. Complex vectors are obtained as a result of transformation of Stokes vectors by Z matrices. Z matrices are 4x4 analogues of Jones matrices. Jones matrices and Z matrices can be characterized by one real and three complex parameters. It is shown that, in general, six Stokes vector measurements are needed to find all parameters by the proposed theorem. The method becomes more efficient as the number of parameters decreases. If one of the complex parameters is zero (optical system has a symmetry) only two Stokes vector measurements is enough. Besides the symmetry condition, if the optical system is a pure diattenuator or pure retarder (all nonzero complex parameters are real or pure imaginary), then single Stokes vector measurement is enough to determine the parameters that characterize the optical system. It is also discussed that complex parameters can be altered by a rotation about the z-axis, and it is shown that in some cases it is possible to make one complex parameter zero by simply rotating the optical system.symmetries and rotations, rotations about the z-axi