COMPENSATION OF FARADAY ROTATION IN MULTI-POLARIZATION SCATTEROMETRY M. T. Frankford and J. T. Johnson The Ohio State University Department of Electrical and Computer Engineering and Electroscience Laboratory 1320 Kinnear Road, Columbus, OH 43212, USA. Email:
[email protected] 1. INTRODUCTION Faraday rotation can have a significant influence on spaceborne radar systems operating at L-band and lower frequencies [1, 2, 3]. While methods for compensating Faraday rotation in polarimetric SAR systems have received substantial attention in the literature, the compensation of Faraday rotation in multi-polarization scatterometers, as included in NASA’s Aquarius mission [4], has not been discussed extensively. Multi-polarization scatterometer systems measure surface backscattered powers without phase information as a function of the transmit and receive polarization. Measurements are reported in terms of the normalized radar cross section (NRCS) per unit area of the scene, represented here as σαβ where (α, β) = H or V refer to the scattered and transmitted polarization, respectively. Assuming that Faraday rotation causes a rotation of the polarization by an angle Ω, it has been shown [5] that the NRCS F values measured by the sensor (σαβ ) are: ⎡ F ⎤ ⎡ ⎤ cos4 Ω sin4 Ω −2 sin2 Ω cos2 Ω 0 0 σHH ⎢ σF ⎥ ⎢ ⎥ cos4 Ω −2 sin2 Ω cos2 Ω 0 0 sin4 Ω ⎢ VF V ⎥ = ⎢ ⎥ ⎣ σHV ⎦ ⎣ sin2 Ω cos2 Ω sin2 Ω cos2 Ω 2 sin2 Ω cos2 Ω 1 2 sin Ω cos Ω ⎦ · σVF H sin2 Ω cos2 Ω sin2 Ω cos2 Ω 2 sin2 Ω cos2 Ω 1 −2 sin Ω cos Ω ⎤ ⎡ σHH ⎥ ⎢ σV V ⎥ ⎢ ∗ ⎥ ⎢ Re{< SHH SV V >} (1) ⎥ ⎢ ⎦ ⎣ σHV ∗ Re{< SHH SHV > + < SHV SV∗ V >} 2
where the Sαβ quantities refer to field values including phases, and are defined so that |Sαβ | = σαβ . F An important relationship between NRCS values in the presence (σαβ ) and absence (σαβ ) of Faraday rotation can be derived by adding all the rows of equation (1): F F σHH + σV V + 2σHV = σHH + σVF H + σHV + σVF V
(2)
This “total cross section” quantity is unaffected by Faraday rotation and can be used in developing retrievals of geophysical quantities of interest. However, further manipulation of equation (1) produces four additional relationships: cos 2Ω − 1 cos 2Ω + 1 F F + σHH σV V + σHV = A + σV V 2 cos 2Ω 2 cos 2Ω cos 2Ω − 1 cos 2Ω + 1 F F σHH + σHV = A + σV V + σHH 2 cos 2Ω 2 cos 2Ω
σHV
F − σVF H σHV ∗ > + < SHV SV∗ V >} = Re{< SHH SHV 2 sin 2Ω F 2 sin2 2Ω 2Ω sin σHH + σVF V ∗ + Re{< SHH SV V >} = A− 2 2 − sin2 2Ω 2 − sin2 2Ω
(3)
F where A = (σHV + σVF H )/2. If an estimate of Ω is available, it is possible to compute the first three quantities on the left hand sides in equation (3). The polarized information obtained can be useful for improving geophysical retrievals given the strong polarization signatures exhibited by some classes of geophysical media, including the sea surface. It is interesting to note that the third equation above shows that multi-polarization incoherent measurements in the presence of Faraday rotation may produce the ability to measure a polarimetric quantity involving the cross correlation of co- and cross-polarized fields. This quantity has been shown to be useful in estimating the sea surface wind direction in polarimetric scatterometry [6]. The final equation shows that interpreting the combined σHV and co-pol correlation term Re{< SHH SV∗ V >} is likely to be difficult, due to the small size of σHV which is added to the larger co-pol correlation term multiplied by a small coefficient that is very sensitive to Ω.
2. DESCRIPTION OF STUDY AND RESULTS Predictions of expected Faraday rotation (Ω) can be produced as a function of a single ionospheric parameter, the total electron content (TEC). TEC forecasts are readily available from the International Reference Ionosphere [7], which assimilates real time information from the Global Positioning System. Tests of these forecasts have shown them to produce TEC values accurate to within 10 to 20 percent. This paper analyzes the impact of errors in the TEC forecast as well as instrument measurement errors on the computed σV V + σHV and σHH + σHV quantities from equation (3). It is shown that errors in Ω within 20% produce errors less than 0.1 dB for σV V + σHV and 0.2 dB for σHH + σHV for modeled sea scenes in an Aquarius-like observation ∗ geometry. Additionally, errors in the co-cross correlation term Re{< SHH SHV > + < SHV SV∗ V >}, although more sensitive to variations in Ω, can be bounded to within 3 dB when Ω is greater than 7 degrees. Implications of these results for future L-band scatterometer systems will be discussed. 3. REFERENCES [1] S. H. Yueh, “Estimates of Faraday Rotation with Passive Microwave Polarimetry for Microwave Remote Sensing of Earth Surfaces,” Geoscience and Remote Sensing, IEEE Transactions on, vol. 38, no. 5, pp. 2434–2438, Sep 2000. [2] D. M. Le Vine and S. Abraham, “The Effect of the Ionosphere on Remote Sensing of Sea Surface Salinity from Space: Absorption and Emission at L-band,” Geoscience and Remote Sensing, IEEE Transactions on, vol. 40, no. 4, pp. 771–782, Apr 2002. [3] S. Abraham and D. M. Le Vine, “Use of IRI to Model the Effect of Ionosphere Emission on Earth Remote Sensing at L-band,” Advances in Space Research, vol. 34, pp. 2059–2066, 2004. [4] A. Freedman, D. McWatters, and M. Spencer, “The Aquarius Scatterometer: an Active System for Measuring Surface Roughness for Sea-Surface Brightness Temperature Correction,” 2006. [5] R. Y. Qi and Y. Q. Jin, “Analysis of the Effects of Faraday Rotation on Spaceborne Polarimetric SAR Observations at P-Band,” Geoscience and Remote Sensing, IEEE Transactions on, vol. 45, no. 5, pp. 1115–1122, May 2007. [6] S. H. Yueh, “Modeling of Wind Direction Signals in Polarimetric Sea Surface Brightness Temperatures,” Geoscience and Remote Sensing, IEEE Transactions on, vol. 35, no. 6, pp. 1400–1418, Nov 1997. [7] International Reference Ionosphere, available online at http://modelweb.gsfc.nasa.gov/ionos/iri.html, 2007.
