Invariant quantities of a Mueller matrix under rotation and retarder transformations

Mueller matrices are defined with respect to appropriate Cartesian reference frames for the representation of the states of polarization of the input and output electromagnetic probe beams. The polarimetric quantities that are invariant under rotations of the said reference frames about the respective directions of propagation (rotation transformations) provide particularly interesting physical information. Moreover, certain properties are also invariant with respect to the action of birefringent devices located on both sides of the medium under consideration (retarder transformations). The polarimetric properties that remain invariant under rotation and retarder transformations are calculated from any given Mueller matrix and are then analyzed and interpreted, providing significant parameterizations of Mueller matrices in terms of meaningful physical quantities.