Mueller Matrix Associated with an Arbitrary 4×4 Real Matrix. The Effective Component of a Mueller Matrix

Due to the limited accuracy of experimental data, Mueller polarimetry can produce real 4×4 matrices that fail to meet required covariance or passivity conditions. A general and simple procedure to convert any real 4×4 matrix into a valid Mueller matrix by adding a portion of polarimetric white noise is presented. This approach provides deeper insight into the structure of Mueller matrices and has a subtle relation to the effective component of the Mueller matrix, which is defined through the subtraction of the fully random component of the characteristic decomposition. Up to a scale coefficient determined by the third index of polarimetric purity of the original Mueller matrix, the effective component retains complete information on the polarimetric anisotropies.