Polarimetric Mode of MIRAS
Manuel Martín-Neira,Member,IEEE,Serni Ribó,and Arturo J.Martín-Polegre Abstract—The L-band Microwave Imaging Radiometer with
Aperture Synthesis(MIRAS),scheduled to be flown as single
payload on board the European Soil Moisture and Ocean Salinity
(SMOS)mission,has a very wide field of view and synthesizes
narrow beams by means of two-dimensional(2-D)interferometry,
the same concept used in radio astronomy.Wide field of view is
indeed a key feature of this radiometer,which leads naturally to
the measurement of the full vector of brightness temperatures of the image.This paper analyzes the theory of polarimetry in the2-D wide-field-of-view microwave interferometry and describes the way MIRAS will measure the polarimetric bright-ness temperatures.
Index Terms—Aperture synthesis,microwave radiometers,po-larimetry,Soil Moisture and Ocean Salinity(SMOS)mission.
I.I NTRODUCTION
T HE European Soil Moisture and Ocean Salinity(SMOS) mission is the second Earth Explorer Opportunity Mission of the European Space Agency(ESA),with an expected launch date near the beginning of2007.The industrial Phase A study of SMOS was completed by October2001,the result of which, together with the detailed scientific assessment of the mission, should end up in a decision for its full implementation.SMOS carries a single payload,Microwave Imaging Radiometer with Aperture Synthesis(MIRAS),which will become the first ever two-dimensional(2-D)aperture sythesis L-band microwave ra-diometer for earth observation from space.
MIRAS consists of an array of72small receivers,arranged along three coplanar arms at120
,which gives an arm length of4.1m,capable of a2angular resolution.The mul-tiple narrow synthesized beams can resolve pixels ranging from 30–50km as seen from750-km orbit altitude.Each antenna element has one pair of balanced probes for each of the two polarizations,horizontal and vertical.The beamwidth for both polarizations is of the order of70Manuscript received Decembe The authors are
with the E
Centre of the European Sp Netherlands(e-mail:manue arturo.martin.polegre@esa.int). Publisher Item Identifier10.11
II.C ROSS C ORRELATION OF A NTENNA V OLTAGES
Consider one antenna element of MIRAS with its two sets of
balanced probes for the two polarizations.The antenna voltage
at the output of the vertical probe due to the whole scene is found
by summing the elemental voltages induced by all elementary
areas of the scene
,
,
,and the voltages should be understood as
normalized to the square root of the characteristic impedance
.
It is noted here that in(1)the vertical(or horizontal)effective
length unit vector is taken according to Ludwig’s third definition
[6],i.e.,
(2)
and for the horizontal polarization
(3)
where the term represents a sign ambiguity,
and and
(5)
where(
(9)
If and denote the distances from a particular far
source point to the two antenna elements under considera-
tion,then the path difference
has been neglected.The
average inside the integral in(9)becomes then equal to the auto-
correlation function of the electric field
,written in terms of the pixel polariza-
tion unit vectors,is
-
-
MARTÍN-NEIRA et al.:POLARIMETRIC MODE OF MIRAS1757 From(7)and(8),the vertical and horizontal components of
the electric field in the polarization of the antenna can be ex-
pressed
by
(14)
(15)
where the following simplified notation has been
used
(18)
where
(21)
(22)
and the equivalent relations for the pixel
fields
(23)
(24)
giving
is the angle from to,positive clockwise as seen
from behind the wave propagating toward the antenna.The
pixel-to-antenna field transformation matrix is,thus,a simple
rotation matrix.
The antenna and pixel polarization unit vectors are depicted
on the right-hand side of Fig.2together with and.In Fig.2,
it is easy to verify that the following arbitrary
choice
(27)
has been made.The angles that and form with respect to
the direction are
(),respectively.
The left-hand side of Fig.2shows that if the pixel wave is
affected by Faraday rotation and the incident field arrives rotated
by an
angle
(28)
Fig.  2.Pixel-to-antenna polarization transformation,including Faraday
rotation.
where
and
(33)
where all elements of all matrices depend implicitly on
(
);
1758IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.40,NO.8,AUGUST2002 mentioned above is irrelevant,as it is invariant to the sign of the
rotation
matrix
(37)
where
medium
impedance is given by
[9]
is the physical
temperature,is its
distance to the
radiometer,is the analytic delta function,
and is the polarimetric spectral emissivity
matrix
(43)
is the matrix of polarimetric spectral emissivities in the antenna
polarization frame,defined
by
(47)
The polarimetric cross correlation of the antenna voltages in
the domain of direction cosine coordinates
is
(49)
being the direction cosines
and
and are real num-
bers representing the brightness temperature in the vertical
and horizontal polarizations of the
antenna.
are the complex cross polarization brightness temperatures,
also in the antenna polarization reference.The matrix of
polarimetric brightness temperatures is Hermitian,and as
happened with the definition of the polarimetric emissivities,
the antenna-polarimetric brightness temperatures include the
effect of the Faraday rotation.
MARTÍN-NEIRA et al.:POLARIMETRIC MODE OF MIRAS1759 Inserting the antenna-polarimetric brightness temperatures
into(48)provides the final expression of the polarimetric cross
correlation of the antenna
voltages
(53)
One of the steps in the data processing of an aperture syn-
thesis radiometer is the recovery of the antenna-polarimetric
brightness temperatures.This is achieved by some inversion
method applied to the previous equation.The last step consists,
then,in their transformation into polarimetric brightness tem-
peratures referenced to the pixel frame.
Denoting the polarizations at the pixel by the
superscripts
,the polarimetric brightness temperatures in the pixel frame
are defined
by
(55)
where the dependence with
()is implicit.
Equation(55)shows that once the four elements of the polari-
metric brightness temperature matrix in the antenna frame have
been measured,then the pixel-polarimetric brightness tempera-
tures can be found through the inversemodulate
equation
-
-
.An
aperture synthesis radiometer will generally perform the cross
correlations at the origin of time
(

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