SCIENCE CHINA Information Sciences, Volume 61 , Issue 2 : 022301(2018) https://doi.org/10.1007/s11432-016-9032-6

Equivalent system model for the calibration of polarimetric SAR under Faraday rotation conditions

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  • ReceivedDec 5, 2016
  • AcceptedFeb 16, 2017
  • PublishedAug 25, 2017


An equivalent system model (ESM) that can be used to calibrate a SAR system affected by both the effect of system errors and the Faraday rotation (FR) is proposed. This ESM contains only system-distortion-like parameters but includes a distortion matrix (DM) that is identical to the original, which contains the effects of both the system errors and the Faraday rotation angle (FRA). With this model, the conventional distributed-target-based (DT-based) algorithms which have not taken FR effect into account are readily applicable. The conditions on FRA for the successful application of DT-based algorithms are studied, and the results suggest that reliable estimates can be obtained for a well-designed system whose true system crosstalk level is lower than $-20$ dB provided that the mean FRA at the calibration site is within ${\pm~15^{\circ}}$ and that the FRA can be suitably modeled as Gaussian. Thus, the requirements on the crosstalk level or the FRA that are commonly employed in other calibration methods designed for data affected by FR are relaxed.


This work was supported by State Key Program of National Natural Science of China (Grant No. 61430118).


[1] Rignot E J, Zimmermann R, van Zyl J J. Spaceborne applications of P-band imaging radars for measuring forest biomass. IEEE Trans Geosci Remote Sens, 1995, 33: 1162--1169. Google Scholar

[2] Lopez-Sanchez J M, Hajnsek I, Ballester-Berman J D. First demonstration of agriculture height retrieval with PolInSAR airborne data. IEEE Geosci Remote Sens Lett, 2012, 9: 242--246. Google Scholar

[3] Guo S L, Li Y, Hong W, et al. Model-based target decomposition with the $\pi$/4 mode compact polarimetry data. Sci China Inf Sci, 2016, 59: 062307. Google Scholar

[4] Freeman A. Calibration of linearly polarized polarimetric SAR data subject to Faraday rotation. IEEE Trans Geosci Remote Sens, 2004, 42: 1617--1624. Google Scholar

[5] Touzi R, Shimada M. Polarimetric PALSAR calibration. IEEE Trans Geosci Remote Sens, 2009, 47: 3951--3959. Google Scholar

[6] Kimura H. Calibration of polarimetric PALSAR imagery affected by Faraday rotation using polarization orientation. IEEE Trans Geosci Remote Sens, 2009, 47: 3943--3950. Google Scholar

[7] Villa A, Iannini L, Giudici D, et al. Calibration of SAR polarimetric images by means of a covariance matching approach. IEEE Trans Geosci Remote Sens, 2015, 53: 674--686. Google Scholar

[8] van Zyl J J. Calibration of polarimetric radar images using only image parameters and trihedral corner reflector responses. IEEE Trans Geosci Remote Sens, 1990, 28: 337--348. Google Scholar

[9] Freeman A, van Zyl J J, Klein J D, et al. Calibration of stokes and scattering matrix format polarimetric SAR data. IEEE Trans Geosci Remote Sens, 1992, 30: 531--539. Google Scholar

[10] Klein J D. Calibration of complex polarimetric SAR imagery using backscatter correlations. IEEE Trans Aerosp Electron Syst, 1992, 28: 183--194. Google Scholar

[11] Touzi R, Livingstone C E, Lafontaine J R C, et al. Consideration of antenna gain and phase patterns for calibration of polarimetric SAR data. IEEE Trans Geosci Remote Sens, 1993, 31: 1132--1145. Google Scholar

[12] Quegan S. A unified algorithm for phase and cross-talk calibration of polarimetric data — theory and observations. IEEE Trans Geosci Remote Sens, 1994, 32: 89--99. Google Scholar

[13] Ainsworth T L, Ferro-Famil L, Lee Jong-Sen. Orientation angle preserving a posteriori polarimetric SAR calibration. IEEE Trans Geosci Remote Sens, 2006, 44: 994--1003. Google Scholar

[14] Goh A, Preiss M, Gray D, et al. Comparison of parameter estimation accuracy of distributed-target polarimetric calibration techniques. In: IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Barcelona, 2007. 4175--4178. Google Scholar

[15] Zhang H, Lu W, Zhang B, et al. Improvement of polarimetric SAR calibration based on the Ainsworth algorithm for Chinese airborne PolSAR data. IEEE Geosci Remote Sens Lett, 2013, 10: 898--902. Google Scholar

[16] Meyer F J, Nicoll J B. Prediction, detection, and correction of Faraday rotation in full-polarimetric L-band SAR data. IEEE Trans Geosci Remote Sens, 2008, 46: 3076--3086. Google Scholar

[17] Gail W. A simplified calibration technique for polarimetric radars. In: Proceedings of IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Tokyo, 1993. 2: 377--379. Google Scholar

[18] Freeman A, Saatchi S S. On the detection of Faraday rotation in linearly polarized L-band SAR backscatter signatures. IEEE Trans Geosci Remote Sens, 2004, 42: 1607--1616. Google Scholar

[19] Wright P A, Quegan S, Wheadon N S, et al. Faraday rotation effects on L-band spaceborne SAR data. IEEE Trans Geosci Remote Sens, 2003, 41: 2735--2744. Google Scholar

[20] Sandberg G, Eriksson L E B, Ulander L M H. Measurements of Faraday rotation using polarimetric PALSAR images. IEEE Geosci Remote Sens Lett, 2009, 6: 142--146. Google Scholar

[21] Wright P, Meadows P, Mack G, et al. Aden ALOS-PALSAR product verification. In: Proceedings of European Space Agency Special Publication (ESA SP), Rhodes, 2008. 664. Google Scholar

[22] Lavalle M, Solimini D, Pottier E, et al. Faraday rotation estimation from unfocussed raw data: analysis using ALOS-PALSAR data. In: Proceedings of European Space Agency Special Publication (ESA SP), Frascati, 2009. 668. Google Scholar

[23] Bickel S H, Bates R H T. Effects of magneto-ionic propagation on the polarization scattering matrix. Proc IEEE, 1965, 53: 1089--1091. Google Scholar

[24] Wang Y T, Ainsworth T L, Lee J-S. Assessment of system polarization quality for polarimetric SAR imagery and target decomposition. IEEE Trans Geosci Remote Sens, 2011, 49: 1755--1771. Google Scholar

  • Figure 1

    Equivalent crosstalk level versus mean FRA. The dashed line corresponds to an ideal system with zero crosstalk and unit imbalances. The solid line corresponds to an imperfect system with the following distortion parameters: mbox$k~=~1/\sqrt{2}$ mbox$\alpha~=~2\angle~30^{\circ}$ mbox$u~=~0.1~\angle~60^{\circ}$ mbox$v~=~0.1~\angle~90^{\circ}$ mbox$w~=~0.1~\angle~120^{\circ}$ and mbox$z~=~0.1~\angle~150^{\circ}$

  • Figure 5

    Mean value of ${\rm~MNE}_{\XMatSym\!\AMatSym}^{}$ versus true crosstalk level obtained as the average from $10^4$ Monte Carlo trials with ${\rm~SNR}_{\times}=12~{~\:~\rm~dB}$, $\overline{\omega}=~0^{\circ}$, $\sigma_{\omega}=~0^{\circ}$, $f~=~3{~\:~\rm~dB}$, and $f_{1}^{}=~1$. The length of each error bar corresponds to twice the standard deviation.

  • Table 1   Ranges of the true system distortions for a well-designed system
    Parameter Range
    Crosstalk level (dB) $[-50,~-20]$
    Crosstalk phase (${^{\circ}}$) $(-180^{\circ},~+180^{\circ}]$
    Transceiver imbalance level (dB) $[0,~3]$
    Transceiver phase imbalance ($^{\circ}$) $(-180^{\circ},~+180^{\circ}]$
  • Table 2   Conservative estimates of the allowable ranges of the mean FRA for typical combinations of channel imbalance and crosstalk level
    $f$ (dB) $x$ (dB) $\Omega$
    $3~$ $-20~$ $[-15^{\circ},~\:~+15^{\circ}]$
    $3$ $-30~$ $[-18^{\circ},~\:~+18^{\circ}]$
    $3~$ $-40~$ $[-19^{\circ},~\:~+19^{\circ}]$
    $1~$ $-20~$ $[-17^{\circ},~\:~+17^{\circ}]$
    $1~$ $-30~$ $[-20^{\circ},~\:~+20^{\circ}]$
    $1~$ $-40~$ $[-21^{\circ},~\:~+21^{\circ}]$
    $0~$ $-\infty~$ $[-26^{\circ},~\:~+26^{\circ}]$
  • Table 3   Parameters used to generate the natural target data
    Parameter Unit Value
    Seed covariance $\varSigma_{11}^{}~,~\varSigma_{\times}~,~\varSigma_{44}^{}$ ${\rm~m}^2$ $1~,~0.2~,~1$
    matrix elements $\displaystyle~\frac{\varSigma_{14}}{\sqrt{\varSigma_{11}^{}{\varSigma_{44}}}}$ $0.4~{\rm~e}^{{\rm~j}~10^{\circ}}$
    Cross-pol SNR $\varSigma_{\times}~/~\varSigma_{\:\!~\sss~+}$ dB $[0,~20]$
    Number of looks $L$ $10^5$
    FRA at DT $\omega~\sim~\mathcal{N}~\big(\overline{\omega},~\sigma_{\omega}^{\sss~2}~\big)$ ${^\circ}$ $\overline{\omega}~\in~[0^\circ,~15^\circ]$
    calibration site $\sigma_{\omega}~\in~[0^\circ,~10^\circ]$
  • Table 4   Calibration requirements for polarimetry and interferometry$^{1)}$
    Item Value
    Residual crosstalk level $<-35{~\:~\rm~dB}$
    Channel amplitude imbalance $0.2{~\:~\rm~dB}$ (soil moisture)
    Channel phase imbalance $2^{\circ}~\sim~5^{\circ}$


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