Polarimetric Channel Imbalance and Cross Talk Estimation in the Presence of Faraday Rotation Using Only Distributed Natural Scatterers

Kurzfassung

A methodology that allows the estimation of polarimetric Channel Imbalance (CI) and Cross Talk (CT) distortion in the presence of Faraday Rotation (FR) distortion for the calibration of spaceborne polarimetric data is proposed relying exclusively on distributed natural scatterers. A calibration schema appropriate for the calibration of CI and CT polarimetric data in the presence of FR is proposed without the need of a deterministic calibrator as for example a reflector or transponder. This is a significant contribution as - up to now – the calibration of CI always required a deterministic calibrator. The proposed methodology is applied and demonstrated on ALOS-2 data. The scattering matrix [O] measured by the radar system differs from the actual target scattering matrix [S]. The commonly used model to describe the system effects is a two-stage linear distortion model for receive and transmit given by [1], [2] . (1) [R] and [T] are 2x2 complex matrices describing amplitude and phase distortions in the receiver and transmitter path respectively; [N] contains the system-noise contributions in the four polarimetric channels which are usually assumed to be zero mean Gaussian random processes . (2) RIJ represents the system response in channel I to a stimulus in channel J and TIJ the transmission in channel I when channel J is excited. The system model, as stated in equation (1), assumes that the transmitter and receiver paths are independent. It is convenient to factorize (2) into an absolute (complex) gain factor Y= RHHTHH and relative transmitter and receiver chain distortions (3) where δTH and δTV are the cross-talk ratios for the transmitter channels (H and V respectively), δRH and δRV the corresponding cross-talk ratios for the receiver channels and fR and fT the channel imbalance ratios on transmit and receive . (4) Earth's ionosphere, in conjunction with its magnetic field, rotate the polarization plane of the transmitted and/or received radar pulse propagating through by a rotation angle Ω as a result of Faraday’s effect. The rotation is independent of the direction of propagation and applies in the same sense on both the transmit and receive path. Ignoring the additive noise term, the distortion model of (3) becomes (5) The FR angle Ω is linearly proportional to the component of the magnetic field in the direction of propagation (given by the scalar product of Earth’s magnetic field vector with the unitary wave propagation vector ), linearly proportional to the Total Electron Content TEC, i.e. the integrated value of the electron density along the propagation path and inverse proportional to the square of the central frequency of the radar pulse f0 (6) where ζ=40.31 m3/s2, qe and me are the charge and the mass of the electron, and c propagation speed of the wave through the ionosphere. In this paper, we propose, discuss and demonstrate a methodology that allows the separation of Faraday Rotation (FR) distortion from system induced distortion(s) and the estimation of polarimetric CT (e.g. the cross-talk ratios for the transmitter channels δTH and δTV and the corresponding cross-talk ratios for the receiver channels δRH and δRV ) and CI (and the channel imbalance ratios on transmit and receive)) distortion for the calibration of spaceborne polarimetric data relying exclusively on distributed natural scatterers. A calibration schema appropriate for the calibration of polarimetric data in the presence of FR is proposed. The proposed methodology is applied and demonstrated on ALOS-2 data and a performance analysis is attempted. 2. REFERENCES [1] A. Freeman, "SAR calibration: an overview," in IEEE Transactions on Geoscience and Remote Sensing, vol. 30, no. 6, pp. 1107-1121, Nov 1992. [2] S. Quegan, "A unified algorithm for phase and cross-talk calibration of polarimetric data-theory and observations," in IEEE Transactions on Geoscience and Remote Sensing, vol. 32, no. 1, pp. 89-99, Jan 1994. [3] J.S. Kim and K. Papathanassiou, “Faraday rotation estimation performance analysis,” In Proc. EUSAR, pp. 182-185, Aachen, Germany, Jun. 7-10, 2010 [4] J. S. Kim, K. P. Papathanassiou, R. Scheiber and S. Quegan, "Correcting Distortion of Polarimetric SAR Data Induced by Ionospheric Scintillation," in IEEE Transactions on Geoscience and Remote Sensing, vol. 53, no. 12, pp. 6319-6335, Dec. 2015. [5] S.H. Bickel and R.H.T. Bates, “Effects of magneto-ionic propagation on the polarization scattering matrix,” Proc. IEEE, vol. 53, pp.1089-1091, 1965. [6] Calibration Results of ALOS-2 / PALSAR-2 JAXA Standard Products, http://www.eorc.jaxa. jp/ALOS-2/ en/ calval/calval_index.htm.