phase error assessment of miras/smos by means of redundant … · remote sensing laboratory...
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Remote Sensing LaboratoryUniversitat Politècnica de Catalunya
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Rubén Dávila(1), Francesc Torres(1), Nuria Duffo(1), IgnasiCorbella(1), Miriam Pablos(1) and Manuel Martín-Neira (2)
(1) Remote Sensing Laboratory. Universitat Politècnica de Catalunya, Barcelona.SMOS Barcelona Expert Centre
(2) European Space Agency (ESA-ESTEC). Noordwijk. The Netherlands
Phase error assessment of MIRAS/SMOS by means of Redundant
Space Calibration
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Aperture Synthesis Interferometric Radiometer
2D images formed by Fourier Synthesis (ideal case). Cross correlation of the signals collected by each antenna pair gives the so-called: Visibility samples V(u,v):
( )( )
ηξ
η−ξ−
−ηξ>==< 2
22
phB*21 ,F
1
T,T)t(b)t(b)v,u(V F
The Soil Moisture & Ocean Salinity Earth Explorer Mission (ESA)
• MIRAS instrument concept- Y-shaped array (arm length ~ 4.5 m)- 21 dual-pol. L-band antennas / arm - spacing 0.875 λ (~1400 MHz)-no scanning mechanisms,
2D imaging by Fourier synthesis-(u,v) antenna separation in wavelengths
(SMOS artist’s view, by EADS-CASA Space Division, Spain)
Launched November 2009
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Simplified block diagram of a single baseline
antenna 1
antenna 2
antenna planes
MIRAS measures normalized correlations:
(0)Ak Aj
Akj
sys sysAkj kj j
kj
T TV M
G e φ=
Fringe Wash function at the origin (τ=0):
• Modulus (≈1)
• FWF Phase at antenna plane
System temperatures measured by a power detector in each receiver
Mkj
Visibility sample at the antenna plane
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SMOS is producing images within expected performance. However, there issome degree of image distortion (spatial errors) due to a number of causes.
This research activity is devoted to assess the different contributions of spatial errors, with two objectives in mind:
• SMOS Improved performance• SMOS follow-on specifications
The RSC method is devoted to assess the peformance of phase calibration.
For calibration purposes, the phase calibration term (antenna plane) is modeled as:
Framework of the activity
( ) ( )A ant ant rec rec FWFkj k j k j kjφ φ φ φ φ φ= − + − +
Antenna phase terms Receiver phases Fringe-wash term
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• Receiver phase drift is calibrated by periodic (2-10 min) correlated noise injection (LO phase track)
• Antenna phase term (manufacturing tolerances): Measured on ground
• Fringe washing term due to filter response differences (negligible)
SMOS phase calibration strategy
Front end phase model
Antenna phase test set-up
SwitchCorrelator
η
C
A L " "receiver k
" "receiver j
kjM
reckφ
antkφ
Antennaplane
Receiverplane
Noise injection
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Redundant Space Calibration (RSC)
Visibility phase measured by a baseline:
Baseline phase differences:
scenVkj k j e,kj = − +φ φ φ φ
RSC phase differences are independent of the phase of the scene
k j iVkj Vji 2− = −φ φ φ +φ φ
Redundant baselines measure the same visibility using a different pair of antennas
Redundant baselines
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A system of equations can be built using independent RSC equations
RSC system of equations
receivers phase differences
0 0 1 2 1 0 00 0 0 1 2 1 0 0
·0 0 1 2 11 1 1 1 ..
1 1 1 1
− … … − … … … … … … … … … …
=… … … … − … … − … − … … − … … … − … … … … … … … … …
φ
…
φ
A matrix: 66 x 69Receivers vector: 69 x 1Phase differences vector: 66 x 1
Underdetermined system (three unknown phases, rank = 66)
Moore-Penrose pseudoinverse matrix66 equations, 69 unknowns
Applied on calibrated visibilities the RSC method retrieves the residual phase error
Averaging is required to reduce uncertainty due to thermal noiseIGARSS 2011 Vancouver
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• Low visibility amplitude: produces unwanted variations and jumps• Fast scene changes: phase bias in land-ocean transitions• RFI: interferences that spoils the phase values
Averaging: visibility measurements must be carefully selected
Land-ocean transition
RFI
Low visibilityamplitude
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RSC: examples of good quality visibility samples
Arm A Arm B Arm C
Red line: Average snap-shots
Averaging area Averaging
areaAveraging
area
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The 3 unknown phases have a physical meaning:
RSC: Impact of undetermination
Common path delay
Tilt angle Steering angle
Pointing error
Irrelevant
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Simulations show that a pointing error yields a linear phase error directlyrelated to the antenna position in the arms.
RSC: Pointing error in the phase retrievals
Retrieval error linear in each arm
error,bslN bslN bslN a·u b·v+φ =
calibrated idealB BaT T , b
2 2 = − − π π
(ξ,η) ξ
η
'ps ps
'ps ps
a2b
2
ξ ξ −π
η = η −
=
π
The pointing error can be corrected, if required, using a point source (e.g, aninterference at a known position ξps , ηps)
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Simulation: SMOS point source retrieval by the RSC method: random phase error
Assessment on the pointing error in RSC retrievals
•Image blurring (example, σphases = 25º)
• Secondary lobes increase
• Small pointing error: the maximum has been displaced.Once the point source is RSC calibrated, image blurring and secondary lobes are
corrected. However, the pointing error is not compensated.
Ideal Phase corrupted Corrected
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Due to pointing error, the difference between two phase retrievals must belinear. This property is used to discard bad estimations of the RSC phases
RSC implementation (i): Good/bad estimations
Bad estimations Good estimations
1 1retrieved IVT,error point ing error
2 2retrieved IVT,error point ing error
2 1 2 1retrieved retrieved point ing error point ing error
φ = φ + φ
φ = φ + φ
φ −φ = φ −φ Linear
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Final RSC phases retrieved by averaging RSC phases from 38 orbits over the ocean
RSC retrieved phases
RSC Phase Errordispersion
H
V
5.97º3.17º
σ =σ =
Horizontal Phases Vertical Phases
Horizontal Mean Phases Vertical Mean Phases• RSC gives a conservative
upper bound for SMOS
residual phase errors
• RSC phase dispersion very
much contributed by
pointing error
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RSC: phase error impact of pointing error
Horizontal Std
Horizontal Phases
H
H
H
5.97ºr 0.00066L 0.76 km
σ ==
∆ =
Mean pointing error (H)
V
V
V
3.17ºr 0.00037L 0.43 km
σ ==
∆ =
ΔLH and ΔLV below 2% of SMOS resolution (42 km)
σphases (°)<r>
Simulation
SMOS std
Simulation: point source shift for 200 cases with σph=20º. 95% of points within a radiusr=2mrayleigh centred at the point source real position
r
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RSC peformance assesssment: RFI in the Caribbean Sea
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Interference from a vessel (11/02/2010, 21:23 semi-orbit)
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Horizontal
RSC peformance assesssment: RFI in the Caribbean Sea
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– Primary to Secondary Lobe Ratio (H):
– Primary to Secondary Lobe Ratio (V):
– The uncorrected RFI presents a main-to-secondary lobe ratio veryclose to an ideal point source.
– The RSC method uncertainty above SMOS phase error accuracy!!
Case Primary to Secondary Lobe RatioReal Point Source 17,40 dB
Corrected Point Source 16,50 dB
Case Primary to Secondary Lobe RatioReal Point Source 17,40 dB
Corrected Point Source 16,65 dB
RSC peformance assessment: RFI in the Caribbean Sea
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RSC implementation: Interference in Cáceres (Spain)
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Vertical
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• The RSC method cannot be used to phase calibrate SMOS in a per snapshot basis due to the need for long averaging and filtering
• SMOS orbital phase drift requires periodic (2-10 min) correlated noiseinjection (LO phase track)
• The RSC is used to validate the consistency of SMOS phase calibratedvisibilities:
•RSC phase retrieval accuracy limited by undetermination (pointingerror)•SMOS phase errors well below σH=5.97 º and σV=3.17º, probably veryclose to the σ =1º target
•Assessment on point sources (RFI) shows that the impact of SMOSresidual phase errors on image distortion is probably negligible
Conclusions
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