A unified algorithm for phase and cross-talk calibration of polarimetric data-theory and observations

A unified approach to phase and cross-talk calibration of polarimetric data which can be applied to calibrating scattering matrix data or to extraction of the descriptors of distributed targets is described. It relies on the scene being dominated by targets with uncorrelated like and cross-polarized backscattering coefficients, but provides cross-talk calibration of targets for which this is not true. The algorithm needs unsymmetrized data, but uses only quantities derived from the covariance matrix of large areas. It makes no assumptions about system reciprocity, permits ready interpretation of the terms in the calibration procedure, allows comparison of the relative magnitude of the system-induced mixing of terms in the observed covariance matrix, is noniterative, and produces indicators which allow testing of whether it meets its own underlying assumptions. The linear distortion model is shown to lead to an inconsistent system of equations; this inconsistency can be removed by introducing an extra parameter which has properties expected of system noise. The modulus of the copolarized correlation coefficient, which is important in polarimetric classification and as a phase descriptor, is shown to be invariant under all effects embodied in the linear distortion model. Calibration of the scattering matrix data is based on a minimum least squares principle. This suggests that current methods of symmetrization are not optimal. The same analysis shows that estimates of parameters needed to form an equivalent reciprocal system are also nonoptimal. The method is more general than the well-known van Zyl algorithm for cross-talk removal, and permits an analysis of the conditions under which the van Zyl algorithm will yield valid results. Correction of phase distortion induced by channel imbalance Is treated as an optional extra step relying on a known HH-VV phase difference in some region of the image. Results from the algorithm are discussed using scattering matrix data from the 1989 MAESTRO campaign