SYMMETRY PROPERTIES OF THE CIRCULAR-POLARIZATION COVARIANCE-MATRIX

The circular polarization covariance matrix is a convenient method for expressing partially polarized response data with respect to a circul arly polarized basis. However, little concerning either the properties of the circular polarization covariance matrix or methods for transfo rming data expressed in this format has been previously reported in th e literature. Here we show (1) how to recover both the diagonal and of f-diagonal elements of the circular polarization covariance matrix fro m response data stored in either Stokes matrix or linear polarization covariance matrix format, (2) how the contribution of physical scatter ing mechanisms such as odd-bounce, even-bounce, and diffuse or volume scattering are expressed in circular polarization covariance matrix fo rmat, and (3) the form of the response after rotation of the target ab out the radar line-of-sight. Next, we derive the constraints on the ma trix elements (and thereby determine the dimensionality of the respons e) when a target exhibits reflection rotation, azimuthal, or centrical symmetry. Because the circular polarimetric rotation operator has a p articularly simple form, referring the polarization covariance matrix to a circularly polarized basis rather than a linearly polarized basis simplifies the formulation considerably. In many applications, circul ar polarimetric features are synthesized from data collected using a l inear polarization diversity radar. We show that residual amplitude an d phase imbalance between channels under a linear polarized basis tran sforms to cross-talk under the circularly polarized basis.