Uniform polarimetric matrix rotation theory

This paper presents the development of a uniform polarimetric matrix rotation theory in the rotation domain along the radar line of sight for polarimetric SAR (PolSAR) data interpretation. The uniform representation of each coherency matrix element is a sinusoidal function in the rotation domain. A set of oscillation parameters, including oscillation amplitude, oscillation center, angular frequency and initial angle, is proposed to fully characterize the scattering behavior in the rotation domain. A set of rotation angle parameters, including stationary angle, null angle, and minimization/maximization angles, is derived from the angular frequency and initial angle to indicate the specific states of the rotation property. A look-up table for these parameters is provided and their physical meanings are interpreted. The proposed theory generalizes both the classic polarization orientation (PO) angle originally derived from the covariance matrix in a circular polarization basis and the deorientation theory developed from the minimization of the cross-polarization term. The roll-invariant terms have also been summarized. Finally, multi-frequency AIRSAR and Pi-SAR PolSAR data sets are used to demonstrate the derived parameters.