Polarization Symmetric Scatterer Metric Space

The coherent polarization scattering matrix decomposition presented in Cameron et al. brought attention to the importance of Symmetric Scatterer Space, the space of scattering matrices corresponding to symmetric scatterers. Each symmetric scatterer scattering matrix can be associated with a complex numberz, the scatterer-type parameter, where |z| les 1. A distance measure,d(z1,z2), was defined on Symmetric Scatterer Space providing a means of comparing scattering matrices. It will be demonstrated that Symmetric Scatterer Space is a metric space with metricd(z1,z2). A new mapping of the Unit Disc representation of Symmetric Scatterer Space to a sphere is also presented along with a metric on the sphere,ds(thetas1, phi1; thetas2, phi2), that is equivalent to the metricd(z1,z2) on the Unit Disc.