1. •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

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

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

4. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•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
IGARSS 2011 Vancouver 4

5. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•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 "
IGARSS 2011 Vancouver 5

6. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•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
IGARSS 2011 Vancouver 6

7. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•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
IGARSS 2011 Vancouver 7

8. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•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
IGARSS 2011 Vancouver 8

9. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•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
IGARSS 2011 Vancouver 9

10. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•Laboratory
RSC: Impact of undetermination
The 3 unknown phases have a physical meaning:
Tilt angle
Steering angle
Pointing error
Common path delay Irrelevant
IGARSS 2011 Vancouver 10

11. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•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)
IGARSS 2011 Vancouver 11

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

13. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•Laboratory
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
IGARSS 2011 Vancouver 13

14. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•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
IGARSS 2011 Vancouver 14

15. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•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)
IGARSS 2011 Vancouver 15

16. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•Laboratory
RSC peformance assesssment: RFI in the Caribbean Sea
Interference from a vessel (11/02/2010, 21:23 semi-orbit)
IGARSS 2011 Vancouver
16

17. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•Laboratory
RSC peformance assesssment: RFI in the Caribbean Sea
Horizontal
IGARSS 2011 Vancouver
17

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

19. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•Laboratory
RSC implementation: Interference in Cáceres (Spain)
Vertical
19

20. •Remote
Remote Sensing Laboratory •Sensing
Universitat Politècnica de Catalunya
•Laboratory
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
IGARSS 2011 Vancouver 20