Extended eigenvalue calibration method for overdetermined Mueller matrix polarimeters

The eigenvalue calibration method is a versatile approach that can be applied to any type of the Mueller matrix polarimetic setup because a precise knowledge of the optical response of the setup components is not required. The method has usually been employed in its original form to calibrate non-overdetermined polarimeters dealing with intensity data arranged in 4 × 4 matrices, but it can also be applied to calibrate overdetermined polarimeters with intensity data matrices of higher dimension. The main drawback with the original formulation of the method is its sensitivity to noise in the input data, especially if applied as it is to overdetermined intensity matrices. In the present work, we present a rigorous extension of the conventional eigenvalue calibration method to treat overdetermined data. We experimentally show that the proposed method does not enhance noise propagation, and therefore it does not degrade the quality of Mueller matrices measured with overdetermined polarimeters.