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This is an author produced version of a paper published in IEEE Transactions
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Published paper
Chen, J., Quegan, S., Calibration of spaceborne CTLR compact polarimetric low-
frequency SAR using mixed radar calibrators, IEEE Transactions on Geoscience
and Remote Sensing, 49 (7), pp. 2712-2723
http://dx.doi.org/10.1109/TGRS.2011.2109065
1
Calibration of Spaceborne CTLR Compact
Polarimetric Low Frequency SAR Using Mixed
Radar Calibrators
Jie Chen
(1)
, Member, IEEE, Shaun Quegan
(2)
, Member, IEEE
(1) School of Electronic and Information Engineering, Beihang University (BUAA), Beijing, 100191, China
e-mail: chenjie@buaa.edu.cn; Jie.Chen@sheffield.ac.uk
(2) School of Mathematics and Statistics, University of Sheffield, Sheffield, S37RH, UK
e-mail: s.quegan@sheffield.ac.uk
Abstract—Spaceborne synthetic aperture radar (SAR) systems operating at lower
frequencies, such as P-band, are significantly affected by Faraday rotation (FR) effects. A novel
algorithm for calibrating the circular transmit and linear receive mode spaceborne compact
polarimetric SAR using mixed calibrators is proposed, which is able to correct precisely both FR
and radar system errors (i.e. channel imbalance and cross-talk). Six sets of mixed calibrators,
consisting of both passive calibrators and polarimetric active radar calibrators (PARCs), are
investigated. Theoretical analysis and simulations demonstrate that the optimal calibration
scheme combines four polarimetric selective mixed calibrators, including two gridded trihedrals
and two PARCs, together with total electron content measurements by the GNSS system.
Index Terms— Calibration, Faraday rotation, Ionosphere, Compact polarimetry, Synthetic
aperture radar (SAR).
I. INTRODUCTION
There is growing interest in deploying lower frequency spaceborne Synthetic Aperture Radars (SARs)
for monitoring of the Earth, such as the P-band BIOMASS mission to measure forest biomass [1],
which is currently under Phase-A study by the European Space Agency. However, the ionosphere can
2
significantly affect such systems; in particular, L- and P-band spaceborne SAR measurements will
suffer from Faraday rotation (FR) [1]–[4]. Furthermore, two conflicting factors often affect the design
of such systems, namely the need for frequent global coverage and the need to maximize information
content, which often requires polarimetric information. Full polarimetry (FP) suffers from reduced
swath width compared to SAR systems transmitting on a single polarization, thus increasing the time
needed for global coverage. As a result, there has been growing interest in the compact polarimetric (CP)
SAR mode [5]-[14], because, for a given swath width, it operates with reduced data rate, system power
and pulse repetition frequency compared to a FP system, while still allowing estimates of some of the
key polarimetric quantities.
The first system of this type, proposed by Souyris et al. [5], [6], used the /4 CP mode, which
transmits H+V (45
o
linearly polarized) and receives echoes in the H and V polarizations. However, such
a system could also be severely affected by FR [11]–[14]. A way to reduce the effects of FR was
suggested by Raney [8] when he introduced the hybrid mode (also called the /2 mode [11] or CTLR
mode [12]) which transmits on circular polarization and receives on the two linear (H, V) polarizations.
This is a promising approach, since circular polarizations are preserved under FR [6], [10], [12] and
[13]; hence the polarization of the incident wave would be undistorted and only FR effects on the return
signal would need to be corrected.
Freeman [14] developed a system model for CTLR mode compact polarimetry with FR. On the basis
of this model, this paper proposes a novel algorithm for calibrating the CTLR mode using both passive
and active calibration targets. After an introduction to the system model in Section II, the mathematical
analysis in Section III leads to a set of new calibration algorithms and an optimized set of calibrators.
Computer simulations presented in Section IV verify the effectiveness of the approach; these include
simulations accounting just for radar system errors and FR, and simulations that also take calibrator
3
errors into account.
II. SYSTEM MODEL FOR CTLR COMPACT POLARIMETRY
A. Faraday Rotation
When a polarized electromagnetic wave traverses the ionosphere, its interaction with free electrons
and the Earth’s magnetic field leads to rotation of the polarization vector [4], [15]. This phenomenon is
known as Faraday rotation. The one-way FR for a SAR signal can be approximated as [15]
TECseccos
400
2
0
B
f
K
(1)
where f
0
is the carrier frequency in Hz, K is a constant of value 2.36510
4
[Am
2
/kg], B is the magnetic
flux density in Wb/m
2
, and
and
are the angles the wave-normal makes with the Earth’s magnetic
field and the downward vertical, respectively. TEC is the total electron content in TEC units (1 TECU =
10
16
electrons m
-2
). The “magnetic field factor”,
400
seccos
B
, is calculated at a height of 400 km.
B. System Model
We assume a CTLR mode SAR system that transmits right-circular polarization chirps and receives
linear (H, V) polarization echoes. In the presence of cross-talk, the transmitted electric field will include
a component from the orthogonal left-circular polarization, so has the form [14]
c
c
c
V
H
j
jj
T
T
1
1
2
1
11
2
1
where
c
is a cross-talk parameter.
With Faraday rotation, , the electric field incident on the Earth’s surface will be [14]
j
c
j
j
c
j
V
H
i
V
i
H
eej
ee
T
T
E
E
2
1
cossin
sincos
(2)
Freeman [14] introduced a system model for this CTLR mode, in which the measured scattering vectors
are given by
4
2
1
1
2
cossin
sincos
1
2
1
,
N
N
eej
ee
SS
SS
f
erA
M
M
j
c
j
j
c
j
VVVH
HVHH
j
RV
RH
(3)
where S
HH
, S
HV
, S
VH
and S
VV
are the components of the true scattering matrix, M
RH
and M
RV
are the
components of the measured scattering vector, f denotes channel imbalance,
i
, i = 1-2, are crosstalk
terms in the receiving channel, and N
i
, i = 1-2, are additive noise terms present in each measurement.
III. CALIBRATION ALGORITHM VIA MIXED CALIBRATORS
A. Signatures of Mixed Calibrators
By mixed calibrators we refer to a set of passive and active radar calibrators operating in combination.
Their use for calibrating spaceborne FP SAR systems is discussed in [16]-[22]. Passive radar calibrators
usually consist of the dihedral, trihedral and gridded trihedral (the classical trihedral with gridded base
wires or thin plates [22], see Fig.1(c)), while the polarimetric active radar calibrators (PARCs) include
three types [16], denoted as PARC
X
, PARC
Y
and PARC
P
, respectively, having signature matrices:
01
00
X
S
00
10
Y
S
11
11
P
S
(4)
where PARC
X
and PARC
Y
are polarimetric selective active calibrators.
For the passive calibrators illustrated in Fig.1, the scattering matrixes can be written as [22]
10
01
,
,
Tri
j
TriTri
eAS
(5)
2cos2sin
2sin2cos
,
,
Di
j
DiDi
eAS
(6)
22
2
222
,
sincossincossin
sincossinsin
sincossin
,
Gt
j
Gt
Gt
eA
S
(7)
where A
Tri
, A
Di
and A
Gt
are gain factors,
Tri
,
Di
and
Gt
are phase factors,
and
are the azimuth and
elevation angles, and
is the rotation angle of the dihedral.
Without loss of generality, we assume that the gain and phase factors in the ideal responses of (4)-(7)
are known, and can be normalized for simplicity. Then we have
10
01
Tri
S
10
01
Di
S
00
01
1Gt
S
10
00
2Gt
S
(8)
where S
Tri
, S
Di
, S
Gt1
and S
Gt2
denote the signature matrices of the trihedral, dihedral (
= 0) and gridded
