Phase error assessment of MIRASSMOS by means of Redundant Space Calibration.pdf

•Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•Laboratory

Phase error assessment of
MIRAS/SMOS by means of Redundant
Space Calibration

Rubén Dávila(1), Francesc Torres(1), Nuria Duffo(1), Ignasi
Corbella(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

1/20

•Remote
•Laboratory

The Soil Moisture & Ocean Salinity Earth Explorer Mission (ESA)
Aperture Synthesis
Interferometric Radiometer
• 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

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):

Launched November 2009
 TB (ξ, η) − Tph 2

V(u, v) =< b1 (t)b (t) >= F 
*
2 F(ξ, η) 
(SMOS artist’s view, by EADS-CASA Space Division, Spain)
 1−ξ −η

2 2


IGARSS 2011 Vancouver 2

•Remote
•Laboratory

Simplified block diagram of a single baseline
MIRAS measures
normalized correlations:

antenna 1

Mkj
antenna 2

antenna planes

System temperatures measured by a power detector in each receiver

Visibility sample at A TsysAk TsysAj
V = M kj
the antenna plane kj jφkj
A
Fringe Wash function at the origin (τ=0):
Gkj (0) e • Modulus (≈1)
IGARSS 2011 Vancouver • FWF Phase at antenna plane 3

•Remote
•Laboratory

Framework of the activity
SMOS is producing images within expected performance. However, there is
some 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:

φkj = (φkant − φ jant ) + (φkrec − φ jrec ) + φkj
A FWF

Antenna phase terms Receiver phases Fringe-wash term


•Remote
•Laboratory

SMOS phase calibration strategy

• 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)
Antenna Receiver
plane φkant plane φkrec Antenna phase test set-up

A L receiver " k "
η
C M kj
Noise injection
Correlator
Switch

Front end phase model receiver " j "


•Remote
•Laboratory

Redundant Space Calibration (RSC)
Redundant baselines measure the same visibility using a different pair of antennas

Redundant baselines

Visibility phase measured by a baseline: φVkj = φk − φj + φscene,kj
RSC phase differences are independent of the phase of the scene

Baseline phase differences: φVkj − φVji =k − 2φj + φi
φ

•Remote
•Laboratory

RSC system of equations
A system of equations can be built using independent RSC equations

0 0 1 −2 1 0 … … 0 
 
0 0 0 1 −2 1 0 … 0  Applied on calibrated
… … … … … … … … …  visibilities the RSC
  method retrieves the
0 … … … … 0 1 −2 1 ·φreceivers = φphase differences
…  residual phase error
… −1 1 … −1 1 .. …
 
… −1 … 1 … … 1 −1 … 
… … … … … … … … … 
 
A matrix: 66 x 69 Underdetermined system
Receivers vector: 69 x 1 (three unknown phases, rank = 66)
Phase differences vector: 66 x 1
Moore-Penrose pseudoinverse matrix
66 equations, 69 unknowns

Averaging is required to reduce uncertainty due to thermal noise

•Remote
•Laboratory

Averaging: visibility measurements must be carefully selected
• Low visibility amplitude: produces unwanted variations and jumps
• Fast scene changes: phase bias in land-ocean transitions
• RFI: interferences that spoils the phase values

Land-ocean transition

Low visibility
amplitude

RFI


•Remote
•Laboratory

RSC: examples of good quality visibility samples

Averaging
area Averaging
area
Averaging
area

Arm A Arm B Arm C

Red line: Average snap-shots


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RSC: Impact of undetermination
The 3 unknown phases have a physical meaning:

Tilt angle
Steering angle

Pointing error

Common path delay Irrelevant

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•Laboratory

RSC: Pointing error in the phase retrievals
Simulations show that a pointing error yields a linear phase error directly
related to the antenna position in the arms.

φerror,bslN = a·u bslN + b·v bslN

 a b 
TBcalibrated (ξ, η) = TBideal  ξ − ,η− 
 2π 2π 
a
ξps ' = ξps −
2π
b
ηps ' = ps −
η
2π

Retrieval error linear in each arm
The pointing error can be corrected, if required, using a point source (e.g, an
interference at a known position ξps , ηps)


•Remote
•Laboratory

Assessment on the pointing error in RSC retrievals
Simulation: SMOS point source retrieval by the RSC method: random phase error

Ideal Phase corrupted Corrected

•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.
12
IGARSS 2011 Vancouver

•Remote
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RSC implementation (i): Good/bad estimations
Due to pointing error, the difference between two phase retrievals must be
linear. This property is used to discard bad estimations of the RSC phases
φretrieved = φIVT,error + φpoint ing error
1 1

φretrieved = φIVT,error + φpoint ing error
2 2

φretrieved − φretrieved = φpoint ing error − φpoint ing error
2 1 2 1
Linear

Bad estimations Good estimations

•Remote
•Laboratory

RSC retrieved phases
Final RSC phases retrieved by averaging RSC phases from 38 orbits over the ocean

Horizontal Phases Vertical Phases
RSC Phase Error
dispersion

σH =5.97º
σV =3.17º

• RSC gives a conservative
Horizontal Mean Phases Vertical Mean Phases
upper bound for SMOS

residual phase errors

• RSC phase dispersion very

much contributed by

pointing error


•Remote
•Laboratory

RSC: phase error impact of pointing error
Mean pointing error (H)

Horizontal Phases
Simulation

r
SMOS std

<r>
Horizontal Std
σphases (°)
Simulation: point source shift for 200 cases
with σph=20º. 95% of points within a radius σH =5.97º σV =3.17º
r=2mrayleigh centred at the point source real
position
rH = 0.00066 rV = 0.00037
∆L H = km
0.76 ∆L V = km
0.43

ΔLH and ΔLV below 2% of SMOS resolution (42 km)

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RSC peformance assesssment: RFI in the Caribbean Sea
Interference from a vessel (11/02/2010, 21:23 semi-orbit)


16

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RSC peformance assesssment: RFI in the Caribbean Sea
Horizontal


17

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RSC peformance assessment: RFI in the Caribbean Sea

– Primary to Secondary Lobe Ratio (H):
Case Primary to Secondary Lobe Ratio
Real Point Source 17,40 dB
Corrected Point Source 16,50 dB

– Primary to Secondary Lobe Ratio (V):
Case Primary to Secondary Lobe Ratio
Real Point Source 17,40 dB
Corrected Point Source 16,65 dB

– The uncorrected RFI presents a main-to-secondary lobe ratio very
close to an ideal point source.
– The RSC method uncertainty above SMOS phase error accuracy!!

18

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RSC implementation: Interference in Cáceres (Spain)
Vertical

19

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Conclusions
• The RSC method cannot be used to phase calibrate SMOS in a per snap
shot basis due to the need for long averaging and filtering

• SMOS orbital phase drift requires periodic (2-10 min) correlated noise
injection (LO phase track)

• The RSC is used to validate the consistency of SMOS phase calibrated
visibilities:

•RSC phase retrieval accuracy limited by undetermination (pointing
error)
•SMOS phase errors well below σH=5.97 º and σV=3.17º, probably very
close to the σ =1º target

•Assessment on point sources (RFI) shows that the impact of SMOS
residual phase errors on image distortion is probably negligible

Phase error assessment of MIRASSMOS by means of Redundant Space Calibration.pdf

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Phase error assessment of MIRASSMOS by means of Redundant Space Calibration.pdf