Geometric Polarimetry—Part II: The Antenna Height Spinor and the Bistatic Scattering Matrix

This paper completes the fundamental development of the basic coherent entities in radar polarimetry for coherent reciprocal scattering involving polarized wave states, antenna states, and scattering matrices. The concept of antenna polarization states as contravariant spinors is validated from fundamental principles in terms of Schelkunoff's reaction theorem and the Lorentz reciprocity theorem. In the general bistatic case, polarization states of different wavevectors must be related by the linear scattering matrix. It is shown that the relationship can be expressed geometrically, and that each scattering matrix has a unique complex scalar invariant characterizing a homographic mapping relating pairs of transmit/receive states for which the scattering amplitude vanishes. We show how the scalar invariant is related to the properties of the bistatic Huynen fork in both its conventional form and according to a new definition. Results are presented illustrating the invariant k for a range of spheroidal Rayleigh scatterers.