performance requirements for correction of ionospheric signals...

F. Meyer1), M. Eineder2), R. Brcic2), K. Papathanassiou3), J.-S. Kim3) , P. Rosen4)

1)Geophysical Institute, University of Alaska Fairbanks2)Remote Sensing Technology Institute, German Aerospace Center (DLR)

3)Microwaves and Radar Institute, German Aerospace Center (DLR)4)Jet Propulsion Laboratory, Pasadena

Performance Requirements for Correction of Ionospheric

Signals in L-band SAR Data

Collaborating Organizations:

F. MeyerAugust 2010, Zurich, CH 2

Table of Contents

• Ionospheric Phase Delay Influence on SAR and InSAR

• Proposed Methods for Ionospheric Correction

• Definition of Performance Requirements for Ionospheric Correction

– SAR Polarimetry

– SAR Imaging

– SAR Interferometry

• Performance of Ionospheric Correction Methods – First Results

• Conclusions and Recommendations

Signal Propagation through the Ionosphere

EUV radiation of

the sun ionizes

neutral atoms and

molecules

Typical vertical

profiles of the

plasma density

Refractive Index:

Two-way phase shift of frequency f due to

the ionosphere (nadir looking Radar):

TEC = Total Electron Content

@ L-band: ~ 2 phase cycles

@ C-band: ~ .5 phase cycles

@ X-band: ~ .3 phase cycles

F. Meyer 3August 2010, Zurich, CH


Taylor Expansion of Phase Delay

2

03

00

02

0000

28.40428.40428.404ffTEC

fcffTEC

fcTEC

fc

Advance of signal phase

Delay of signal envelope

ionospheric induced chirp rate

change

Ionospheric Phase ScreensPolar Irregularities

5

Ionospheric Phase ScreensEquatorial Irregularities

6


Faraday Rotation

• Faraday Rotation changes polarimetric angle with which a system observes the earth surface

• Currently -10º - 10º in L-band but increase to ~25º expected at solar max.

• In P-band, W may be subject to wrapping

Transmitted signal Signal at ground level

WTECB

f

KW seccos

2

Magnetic field intensity &

angle with observation direction


Methods for Ionospheric Correction

Faraday Rotation (FR) Based Correction

• FR estimation from quad-pol data – Freeman, 2004;

Quegan, 2010

• FR estimation from HH-HV correlation – Nicoll & Meyer, 2008

Range Split-Spectrum Based Correction

• Distributed targets in Repeat-pass InSAR →tsTEC – Rosen, 2009, 2010

• Coherent Targets in single image → sTEC – Papathanassiou, 2009

• Amplitude correlation of sub-looks → TEC – Meyer & Bamler, 2005

Transmitted ground levelW


Methods for Ionospheric Correction

Azimuth Autofocus Based Correction

• Contrast maximization for point targets – several authors

• Coherent AF: Phase Curvature analysis – Papathanassiou, 2008

• Incoherent AF: Sub-look co-registration (MLR) – Meyer & Nicoll, 2008

Hybrid Methods

• Combination of range and phase offsets in InSAR – Meyer, 2005

• Two dimensional phase signature of point targets – Papathanassiou

• …


Problem Statement

• Question to Answer:

How accurate does correction have to be?

• This paper defines requirements for ionospheric correction based on

calibration specifications

• Requirements will be derived for SAR Polarimetry, SAR Imaging, and SAR

Interferometry

• Notes:

• Given a set of calibration specs, the maximum allowable error in ionospheric

correction is calculated

• is calculated such that 95% of all corrected image pixels will fulfill

calibration specs (2 sigma law)

max,W

max,W


Requirements for SAR Polarimetry

• Relevant Polarimetric Calibration parameters:

– Channel amplitude imbalance

– Channel phase imbalance

– Cross talk

– Radiometry 0

• Calibration parameters vs. Faraday Rotation:

f

farg

arg( f ) vs. FR | f | vs. FR vs. FR 0 vs. FR


Requirements for SAR Polarimetry

• For calibrated SAR data:

• is calculated for ALOS PALSAR calibration specs

• Most stringent requirement caused by cross talk spec

WW

WW

WW

WW

cossin

sincos

cossin

sincos

vvhv

vhhh

vvhv

vhhh

SS

SS

MM

MM

max,W

All requirements

uncritical!


Requirements for SAR Based Imaging

• Quality parameters specified for imaging include:

– Geolocation accuracy

– Internal image geometry

– Specified image resolution (low sensitivity to ionosphere in L-band → not

studied here)

• Range mislocation caused by ionospheric range delay

• Azimuth mislocation caused by ionospheric gradients

– Phase gradient:

– Azimuth shifts:

T

TEC

cf

K

T

S

c

f

T

ionoiono

44

TECf

Kdhn

f

KTECfS eiono sec,

22

FM

v

Taz sationo


Requirements for SAR Based Imaging

• Assuming :

• For ALOS PALSAR parameters we get:

TT tionoTtionoiono 00 ,,

TECTECSf

Kfiono

sec, 2

TECsat

TECSTFMfc

vKf

az

2

4,

Can be reduced by

decreasing aperture time

used for processing


Requirements for SAR Interferometry

• Ionosphere induced interferometric phase component at pixel k

corresponds to:

• Main applications of InSAR:

– Topographic mapping

– Deformation monitoring

ktkionoktionok TECf

K

c

sec

4,,

kkk

ktopo H

R

B

sin

4 ,

kdefo r

4

TECk

k

kH

Bf

KRk

2tan

,2

TEC

k

rf

Kk

2cos2


Requirements for SAR Interferometry

• Simulation parameters for topographic mapping:

– B = 1500m

– Height accuracy set to DTED-2 (30m) and DTED-3 (10m)

• Simulation parameters for deformation monitoring:

– Required deformation accuracy set to

• For ALOS PALSAR parameters we get:

kH

cmkr

5.0

All requirements

below 1 TECU


• Requirements for a PALSAR-like system:

– Polarimetry:

– Image geolocation:

– Image geometry

– Topographic Mapping from InSAR:

– Deformation mapping from InSAR:

– Ionospheric mapping:

• Based on the developed parameters, existing ionospheric correction

methods can be tested for their applicability for operational

implementation

Summary of Requirements

TECUECT

1ˆ

2ˆ W

TECUECT

01.0ˆ

TECUECT

1.005.0ˆ

TECUECT

005.0ˆ

TECUECT

1.0ˆ

Faraday Rotation Based CorrectionW – Dependency on Number of Looks

• All estimators show decreasing trend

of W with higher number of Looks.

• Bickel & Bates estimator shows best

performance.

19

W

[º]

W

[º]

W

[º]

W

[º]

W

[º]


• Wide-bandwidth SAR & Image Pairs:

– Use frequency dependents of signal delay

• Transmit two sufficiently separated frequency bands and form

interferograms

• Phase difference between interferograms is proportional to

Split-Spectrum based Correction

cos

22

TEC

fc

Kf

f0flow fhigh

e.g. 80MHz

TECc

K

fc

ff topo

010

1

1

44

TEC

c

K

fc

ff topo

020

2

2

44

2

1

1

2

1

2

2

1

4

11

f

f

f

f

c

ff

ff

topo

2

2

2

1

1

1

2

2

114

11

ffc

K

ff

ff

TEC

2.1.

1. 2.

Split-Spectrum Based CorrectionTheoretically Achievable Performance

• Performance of k-InSAR for ionospheric correction as a function of

interferometric coherence and number of looks

– For the TerraSAR-L mission a σ of 0.1 TECU could be attained after averaging over

only 103 resolution cells.

– For ALOS-PALSAR low resolution (14 MHz) images, averaging over 104 resolution cells

is required.

22

ALOS PALSAR Parameters TanDEM-L / DESDynI Parameters

Number of samples in full-pol PALSAR scene: ~ 5*107

• Processing steps:– Extracted sub-looks:

– 2x10 multi-looking – Phase unwrapping using minimum cost flow algorithm

– Below: Comparison of TEC results from split-bandwidth InSAR and FR analysis

Split-Spectrum Based CorrectionExample: Frame 1400 – North Slope, AK

MHzBf SB 5;4

[TECU] [TECU]

TEC from FR TEC from k iono from FR measured

F. MeyerCEOS’10, Zurich, Switzerland 23


• Requirements for ionospheric correction were derived

• Requirements were defined such that corrected data meets calibration

specs and advertised system capabilities

• InSAR applications require strictest correction quality

• First analyzes and example show operational feasibility of correction

techniques

• Theoretically achievable performance parameters were derived

• Improved (integrated) correction methodology under development

Conclusions

Thanks for your attention!!

performance requirements for correction of ionospheric signals...

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