Useful Mueller matrix symmetries for ellipsometry

In this work we derive the five patterns of symmetry of a Mueller matrix, a differential Mueller matrix and a Jones matrix that can appear in ellipsometry measurements. While a general nondepolarizing measurement depends on six parameters, we show that there are certain orientations of uniaxial, orthorhombic and monoclinic crystals that result in highly symmetric Muller matrices over all the spectral range, allowing a reduction of the number of independent parameters to less than six. The matrix symmetries for media with optical activity are also examined.