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).


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  • 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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