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

Remote Sensing LaboratoryUniversitat Politècnica de Catalunya

•Remote•Sensing•Laboratory

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

IGARSS 2011 Vancouver



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

3IGARSS 2011 Vancouver



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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




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



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


Technology

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