## Abstract

The Microwave Imager (MWI) on the Weather System Follow-on – Microwave (WSF-M) satellite contains fully polarimetric channels at 10.85, 18.85, and 36.75 GHz. Like its predecessor WindSat, fully polarimetric channels provide observations of the ocean wind vectors due to the polarimetric dependency of ocean emissivity on both wind speed and direction. Like dual-polarization radiometers, the MWI measures both vertical polarization (v-pol) and horizontal polarization (h-pol) through the antenna. The MWI computes the other polarization states (3rd and 4th Stokes) by digitally correlating the v-pol and h-pol inputs.

For a dual-polarization conical scanning radiometer, the sensor calibration reduces to a handful of corrections for the receiver and antenna. The receiver calibration is performed in the Temperature Data Record (TDR) algorithm. The antenna calibration is performed in the Sensor Data Record (SDR) calibration.

In dual-polarized receiver calibration, hot load and cold sky calibration targets above the feedhorns serve to linearly relate the output counts to Antenna Temperature. With a fully polarimetric system, signal coherency and purity become important, and the forward receiver model becomes a 4x4 matrix equation. For the v-pol and h-pol channels, the receiver off-diagonal matrix terms are negligible, reducing the equations to the dual-polarized form. For the 3rd and 4th Stokes terms, the cross-terms are significant. The coupling between 3rd and 4th is defined mostly by the phase difference between v-pol and h-pol chains. The phase is computed on-board using a correlated noise source combined with ground measurements of the orthomode transducer (OMT) phase. The v/h into 3rd/4th Stokes cross-coupling terms are defined mainly by the cross-coupling in the OMT and cross-coupling in the receiver. The symmetric, part of these (from 1st Stokes) are computed on-board using the hot and cold loads. The anti-symmetric part (from 2nd Stokes) is obtained from ground measurements. The TDR estimates the parameters and inverting the matrix equation.

The effects of the antenna and ionosphere are corrected in the Sensor Data Record (SDR) algorithm. The SDR algorithm inverts an integral equation that is expanded to individual correction terms and inverted, piece by piece. The only spatially varying part of the integral equation is the squint matrix and Earth brightness temperature. The squint matrix accounts for non-spatially homogenous effects and captures the well-known 4th Stokes beam squint issue in off-axis reflectors, which can be recast into a spatially varying integral over 1st Stokes coupling into 4th Stokes. There is a smaller spatially varying integral over 2nd Stokes that couples into 3rd Stokes. The spatially varying coupling captured in the squint matrix is corrected using an adapted optimal interpolation method. All other corrections are straight-forward inversions of the expanded equation.

The methods have been derived and implemented in the ground software for WSF-M. Full characterization of the sensor has been performed to estimate all necessary terms for the polarimetric calibration.

Calibration of the Fully Polarimetric Microwave Imager (MWI) on the Weather System Follow- on-Microwave (WSF-M) Satellite

The Microwave Imager (MWI) on the Weather System Follow-on – Microwave (WSF-M) satellite contains fully polarimetric channels at 10.85, 18.85, and 36.75 GHz. Like its predecessor WindSat, fully polarimetric channels provide observations of the ocean wind vectors due to the polarimetric dependency of ocean emissivity on both wind speed and direction. Like dual-polarization radiometers, the MWI measures both vertical polarization (v-pol) and horizontal polarization (h-pol) through the antenna. The MWI computes the other polarization states (3rd and 4th Stokes) by digitally correlating the v-pol and h-pol inputs.

For a dual-polarization conical scanning radiometer, the sensor calibration reduces to a handful of corrections for the receiver and antenna. The receiver calibration is performed in the Temperature Data Record (TDR) algorithm. The antenna calibration is performed in the Sensor Data Record (SDR) calibration.

In dual-polarized receiver calibration, hot load and cold sky calibration targets above the feedhorns serve to linearly relate the output counts to Antenna Temperature. With a fully polarimetric system, signal coherency and purity become important, and the forward receiver model becomes a 4x4 matrix equation. For the v-pol and h-pol channels, the receiver off-diagonal matrix terms are negligible, reducing the equations to the dual-polarized form. For the 3rd and 4th Stokes terms, the cross-terms are significant. The coupling between 3rd and 4th is defined mostly by the phase difference between v-pol and h-pol chains. The phase is computed on-board using a correlated noise source combined with ground measurements of the orthomode transducer (OMT) phase. The v/h into 3rd/4th Stokes cross-coupling terms are defined mainly by the cross-coupling in the OMT and cross-coupling in the receiver. The symmetric, part of these (from 1st Stokes) are computed on-board using the hot and cold loads. The anti-symmetric part (from 2nd Stokes) is obtained from ground measurements. The TDR estimates the parameters and inverting the matrix equation.

The effects of the antenna and ionosphere are corrected in the Sensor Data Record (SDR) algorithm. The SDR algorithm inverts an integral equation that is expanded to individual correction terms and inverted, piece by piece. The only spatially varying part of the integral equation is the squint matrix and Earth brightness temperature. The squint matrix accounts for non-spatially homogenous effects and captures the well-known 4th Stokes beam squint issue in off-axis reflectors, which can be recast into a spatially varying integral over 1st Stokes coupling into 4th Stokes. There is a smaller spatially varying integral over 2nd Stokes that couples into 3rd Stokes. The spatially varying coupling captured in the squint matrix is corrected using an adapted optimal interpolation method. All other corrections are straight-forward inversions of the expanded equation.

The methods have been derived and implemented in the ground software for WSF-M. Full characterization of the sensor has been performed to estimate all necessary terms for the polarimetric calibration.