Some invariant properties of the polarization scattering matrix

A set of parameters can be based on properties of the polarization scattering matrix which are invariant to change in the axial ratio of the polarization ellipse for the measuring antenna, or to rotation of the antenna about the line of sight. These invariant quantities have the advantage that they are free of the effects of Faraday rotation and of certain errors in antenna polarization, yet depend upon the nature of the scattering body and as such can be used to classify certain characteristics of the body. Some of the parameters of special representations for the scattering matrix, such as the null polarization and eigenpolarization, are simply related to the invariant quantities. However, not all of the significant characteristics of the scattering matrix can be specified in terms of invariant quantities, since two degrees of freedom are necessary, one to account for the axial ratio of measuring antenna and one to account for the relative orientation of the antenna and scatterer about the line of sight. The decomposition of these effects into the product of a rotation operator and an ellipticity operator offers a convenient method for critical examination of polarization dependent characteristics.