calibration of palsar polarimetric sar...

PolInSAR 2009National Aeronautics and Space Administration

Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California

11

CALIBRATION OF PALSAR POLARIMETRIC SAR DATA

Tony FreemanXiaoqing Pi

Bruce Chapman

Jet Propulsion Laboratory



22

OverviewOverview

• In this presentation, we will:– Describe a new approach to estimate Faraday rotation from

Polarimetric SAR data– Method takes full account of all system distortions and is based

on analysis of cross-talk terms – Show results are comparable with other techniques, incl. GPS– Confirm using PalSAR data that with enough FR, new approach

allows for full polarimetric calibration without corner reflectors– Establish the system cross-talk for PalSAR to be ~ -40 dB– Compare FR estimates using the new approach with ground-

based GPS measurements, including a correction for vertical TEC variations using the International Reference Ionosphere

– Introduce a 3-D model of the ionosphere that assimilates ground-based and space-based GPS measurements (e.g COSMIC, CHAMP, GRACE)



33

Wright, et al, IEEE TGRS 2003, Wright, et al, IEEE TGRS 2003,

-10 -5 -2.5 -1 0 1052.51 25Faraday Rotation in degrees

(x10 for P-band)

Mean Faraday Rotation at L-Band, April, GMT = 12:00Moderate Sunspot activity

R=20High Sunspot activity

R=160

• Model predictions of FR based on TEC, magnetic field

dhNBfK h

002 seccos θψ∫=Ω

• Proposed pre-rotation of transmitted wave to adjust for expected FR• Note Ω=0 crossing at Equator



44

• Introduced at ASAR 2003• System Model:

• Assume cross-talk is negligible or stable enough to allow routine correction using pre-determined values ==>

• Balance channels using approach described in (Freeman, 2004) andestimate Faraday Rotation (FR) using (e.g. Bickel and Bates, 1965):

• Use any target with non-zero HV to resolve ambiguities in FR

‘‘Freeman MethodFreeman Method’’ : Any : Any Ω, Ω, knownknown δ δ

Mhh Mvh

Mhv Mvv

⎛

⎝ ⎜

⎞

⎠ ⎟ = A(r,θ) e jφ 1 δ2

δ1 f1

⎛

⎝ ⎜

⎞

⎠ ⎟

cosΩ sinΩ−sinΩ cosΩ

⎛

⎝ ⎜

⎞

⎠ ⎟

Shh Svh

Shv Svv

⎛

⎝ ⎜

⎞

⎠ ⎟


⎛

⎝ ⎜

⎞

⎠ ⎟

1 δ3

δ4 f2

⎛

⎝ ⎜

⎞

⎠ ⎟ +

Nhh Nvh

Nhv Nvv

⎛

⎝ ⎜

⎞

⎠ ⎟

M = Ae jφ RTRFSRFT + N

Z 11 Z12Z 21 Z22

= 1 jj 1

Mhh MvhMhv Mvv

1 jj 1

Ω = 14 arg Z12 Z21

*

′ M hh ′ M vh

′ M hv ′ M vv

⎛

⎝ ⎜

⎞

⎠ ⎟ = A(r,θ) e jφ 1 0

0 f1

⎛

⎝ ⎜

⎞

⎠ ⎟


⎛

⎝ ⎜

⎞

⎠ ⎟

Shh Svh

Shv Svv

⎛

⎝ ⎜

⎞

⎠ ⎟


⎛

⎝ ⎜

⎞

⎠ ⎟

1 00 f2

⎛

⎝ ⎜

⎞

⎠ ⎟ +

Nhh Nvh

Nhv Nvv

⎛

⎝ ⎜

⎞

⎠ ⎟



55

‘‘Quegan methodQuegan method’’: : Ω=0, δΩ=0, δ's are small's are small

• System Model (no Faraday Rotation):

• Assumptions are*:

• Solve for five system parameters:

• Additional information is needed to solve for f1 and f2 to complete the relative calibration by defining each term in the distortion matrix

• This is often obtained from the signature of an external target with known HH/VV ratio such as a corner reflector (but it can also be obtained from receive channel cal-signals)

Mhh Mvh

Mhv Mvv

⎛

⎝ ⎜

⎞

⎠ ⎟ = A(r,θ) e jφ 1 δ2 / f1

δ1 1⎛

⎝ ⎜

⎞

⎠ ⎟

1 00 f1

⎛

⎝ ⎜

⎞

⎠ ⎟

Shh Svh

Shv Svv

⎛

⎝ ⎜

⎞

⎠ ⎟

1 00 f1

⎛

⎝ ⎜

⎞

⎠ ⎟

1 δ3

δ4 / f1 f2 / f1

⎛

⎝ ⎜

⎞

⎠ ⎟ +

Nhh Nvh

Nhv Nvv

⎛

⎝ ⎜

⎞

⎠ ⎟

f1 / f2, δ1, δ2 / f1, δ3, δ4 / f1

δi2 <<1, for i =1 to 4; f1 ~ 1; f2 ~ 1;

Shv = Svh; ShhShv* = SvvShv

* = 0; ρhhvv* ≠1; ShvShv* ≠ 0

*Similar approaches are described in Klein and Freeman (1991) and Freeman et al (1992)



66

Moriyama et alMoriyama et al’’s PalSAR resultss PalSAR results

Courtesy Prof. T. Moriyama, Nagasaki U.

Significance: System cross-talk is established to be < -35 dB (evaluated when/where Ω~0)



77

Moriyama et alMoriyama et al’’s PalSAR resultss PalSAR results

Courtesy Prof. T. Moriyama, Nagasaki U.

Significance: i) FR is close to zero near equator (as predicted); ii) Even small (1-2 deg) variations in Ω can be detected



88

Case I: Case I: Ω, δΩ, δ's are small's are small

• Start with the full System Model:

• When Ω is small,• So

• If δ’s are also small, we can neglect (δΩ) product terms, so:

• So system model for case when Ω and δ's are small is:

• This is identical in form to Quegan’s method which should yield:

• There are 7 unknowns, with only five equations, so additional information is needed to complete the calibration

cosΩ ≅1, sinΩ ≅ Ω1 δ2

δ1 f1

⎛

⎝ ⎜

⎞

⎠ ⎟


⎛

⎝ ⎜

⎞

⎠ ⎟ ≅

1 δ2

δ1 f1

⎛

⎝ ⎜

⎞

⎠ ⎟

1 Ω−Ω 1

⎛

⎝ ⎜

⎞

⎠ ⎟ =

1−δ2Ω Ω + δ2

δ1 − Ωf1 δ1Ω + f1

⎛

⎝ ⎜

⎞

⎠ ⎟

[Similarly for the right-hand side]

Mhh Mvh

Mhv Mvv

⎛

⎝ ⎜

⎞

⎠ ⎟ = A(r,θ) e jφ 1 δ2

δ1 f1

⎛

⎝ ⎜

⎞

⎠ ⎟


⎛

⎝ ⎜

⎞

⎠ ⎟

Shh Svh

Shv Svv

⎛

⎝ ⎜

⎞

⎠ ⎟


⎛

⎝ ⎜

⎞

⎠ ⎟

1 δ3

δ4 f2

⎛

⎝ ⎜

⎞

⎠ ⎟ +

Nhh Nvh

Nhv Nvv

⎛

⎝ ⎜

⎞

⎠ ⎟

1 δ2

δ1 f1

⎛

⎝ ⎜

⎞

⎠ ⎟


⎛

⎝ ⎜

⎞

⎠ ⎟ ≅

1 Ω + δ2

δ1 − Ωf1 f1

⎛

⎝ ⎜

⎞

⎠ ⎟


⎛

⎝ ⎜

⎞

⎠ ⎟

1 δ3

δ4 f2

⎛

⎝ ⎜

⎞

⎠ ⎟ ≅

1 δ3 + Ωf2

δ4 − Ω f2

⎛

⎝ ⎜

⎞

⎠ ⎟ and

Mhh Mvh

Mhv Mvv

⎛

⎝ ⎜

⎞

⎠ ⎟ = A(r,θ) e jφ 1 Ω + δ2( )/ f1

δ1 − Ωf1 1

⎛

⎝ ⎜

⎞

⎠ ⎟

1 00 f1

⎛

⎝ ⎜

⎞

⎠ ⎟

Shh Svh

Shv Svv

⎛

⎝ ⎜

⎞

⎠ ⎟

1 00 f1

⎛

⎝ ⎜

⎞

⎠ ⎟

1 δ3 + Ωf2

δ4 − Ω( )/ f1 f2 / f1

⎛

⎝ ⎜

⎞

⎠ ⎟ +

Nhh Nvh

Nhv Nvv

⎛

⎝ ⎜

⎞

⎠ ⎟

F = f1 / f2; ′ δ 1 = δ1 − Ωf1 ; ′ δ 2 = Ω + δ2( )/ f1

′ δ 3 = δ3 + Ωf2; ′ δ 4 = δ4 − Ω( )/f2



99

• For small Ω, δ’s system model can be expressed as:

• Now let δ’s ==> 0:

• Identical in form to Quegan’s method with:

• Therefore, for small Ω, and zero δ’s, the ‘Freeman’ and Quegan methods are equivalent- explains Moriyama et al’s results- Quegan approach confuses Ω with δ’s- can solve these expressions for f1, f2, Ω

• This will not be the case near solar max, when Ω is expected to increase

Mhh Mvh

Mhv Mvv

⎛

⎝ ⎜

⎞

⎠ ⎟ = A(r,θ) e jφ 1 Ω + δ2

δ1 − Ωf1 f1

⎛

⎝ ⎜

⎞

⎠ ⎟

Shh Svh

Shv Svv

⎛

⎝ ⎜

⎞

⎠ ⎟

1 δ3 + Ωf2

δ4 − Ω f2

⎛

⎝ ⎜

⎞

⎠ ⎟ +

Nhh Nvh

Nhv Nvv

⎛

⎝ ⎜

⎞

⎠ ⎟

Case Ia: Case Ia: ΩΩ is small and is small and δδ’’s ==> 0s ==> 0

Mhh Mvh

Mhv Mvv

⎛

⎝ ⎜

⎞

⎠ ⎟ = A(r,θ) e jφ 1 Ω / f1

−Ωf1 1⎛

⎝ ⎜

⎞

⎠ ⎟

1 00 f1

⎛

⎝ ⎜

⎞

⎠ ⎟

Shh Svh

Shv Svv

⎛

⎝ ⎜

⎞

⎠ ⎟

1 00 f1

⎛

⎝ ⎜

⎞

⎠ ⎟

1 Ωf2

−Ω / f1 f2 / f1

⎛

⎝ ⎜

⎞

⎠ ⎟ +

Nhh Nvh

Nhv Nvv

⎛

⎝ ⎜

⎞

⎠ ⎟

Ω δ Equivalent

0.5o -41 dB

1o -35 dB

2o -29 dB

3o -25 dB

6o -20 dB

10o -15 dB

′ δ 1 = −Ωf1; ′ δ 2 = Ω / f1; ′ δ 3 = Ωf2; ′ δ 4 = −Ω / f2



1010

Case II: Case II: Ω, δΩ, δ's are small 's are small andand crosscross--talk is symmetric talk is symmetric


• which is identical in form to Quegan’s method, an application of which should yield:

• For radar antennas whose cross-talk is symmetric on transmit and receive*, i.e.

• Thus

• Only restriction is that

δ1 = δ3 and δ2 = δ4

==> Can solve for all five system distortion terms f1, f2, Ω, δ1 and δ2, without additional information without additional information from an external target!from an external target!

Ω ≠ 0 and f2 ≠ − f1

*In monostatic radar systems, all passive and most active antennas are reciprocal

Mhh Mvh

Mhv Mvv

⎛

⎝ ⎜

⎞

⎠ ⎟ = A(r,θ) e jφ 1 Ω + δ2( )/ f1

δ1 − Ωf1 1

⎛

⎝ ⎜

⎞

⎠ ⎟

1 00 f1

⎛

⎝ ⎜

⎞

⎠ ⎟

Shh Svh

Shv Svv

⎛

⎝ ⎜

⎞

⎠ ⎟

1 00 f1

⎛

⎝ ⎜

⎞

⎠ ⎟

1 δ3 + Ωf2

δ4 − Ω( )/ f1 f2 / f1

⎛

⎝ ⎜

⎞

⎠ ⎟ +

Nhh Nvh

Nhv Nvv

⎛

⎝ ⎜

⎞

⎠ ⎟

F = f1 / f2; ′ δ 1 = δ1 − Ωf1 ; ′ δ 2 = Ω + δ2( )/ f1

′ δ 3 = δ3 + Ωf2; ′ δ 4 = δ4 − Ω( )/f1

F = f1 / f2; ′ δ 1 = δ1 − Ωf1 ; ′ δ 2 = Ω + δ2( )/ f1

′ δ 3 = δ1 + Ωf2; ′ δ 4 = δ2 − Ω( )/f2

f1 = 2′ δ 3 − ′ δ 1( )

′ δ 2 − ′ δ 4 /F( )F

F +1⎛ ⎝ ⎜

⎞ ⎠ ⎟ ; Ω = f1

2′ δ 2 − ′ δ 4 /F( ); f2 = f1 /F;

δ1 = ′ δ 1 + ′ δ 3( )− Ω f2 − f1( )[ ]/2; δ2 = f1 ′ δ 2 + ′ δ 4 /F( )/2



1111May14, 2008 Pi: Ionospheric Specifications Using SAR and GPS

ALOS PalSAR Polarimetric DataALOS PalSAR Polarimetric Data01/06/2007, 15:51:48 UT, over Washington D.C.

HH mag. FR FR: histogram (top) and mean values vs. range (middle) and azimuth (bottom) distance(Note that the sign of derived FR is flipped to compare with the result from another group.)



1212

Case II: Case II: Ω, δΩ, δ's are small 's are small andand crosscross--talk is symmetric talk is symmetric

• Results - from PalSAR data

Washington, DC (01/06/07)

Comparison ([1] and [2])

|f1| .98 .72Arg(f1) 24.2o -1.9o

|f2| .62 1.03Arg(f2) 0.9o 21.8o

Ω 2.6o 4.0o

|δ1| -43 dB <-35 dB|δ2| -41 dB <-35 dB

Atacama Desert (02/07/07)

Comparison ([1] and [2])

|f1| 1.02 .72Arg(f1) 6.5o -1.9o

|f2| .68 1.03Arg(f2) -16o 21.8o

Ω -0.9o -0.8o

|δ1| -38 dB <-35 dB|δ2| -43 dB <-35 dB

[1] Moriyama, T. et al, Initial Polarimetric Calibration of PalSAR, PolinSAR Workshop, Frascati, Italy January 2007

[2] Ω-values Derived from GPS estimates of TEC, corrected for PalSAR altitude/viewing geometry



13

Results

• Results for |f1|/ |f2| are consistent with an average value of 1.5

• Results for arg(f1/f2) are consistent with expected value (23o)



14

Results

• Results for |f1|, |f2| are consistent with expected values for |FR|>1

• Results for smaller FR angles are noisy (small signal problem)

• Results for arg(f1) and arg(f2) are consistent with expected values when |FR|>1

• Results for smaller FR angles are noisier



15

Results

• Results for cross-talk are < -35 dB and are on average closer to -40 dB

• Results suggest consistent cross-talk phase for |FR|>1

• Spread is relatively small

(+/- 30o and +/- 50o)



1616


• To calibrate (ignoring additive noise and system-level amplitude and phase A(r, θ) and ejφ):

• If cross-talk can be considered negligible:

Mhh Mvh

Mhv Mvv

⎛

⎝ ⎜

⎞

⎠ ⎟ = A(r,θ) e jφ 1 Ω + δ2

δ1 − Ωf1 f1

⎛

⎝ ⎜

⎞

⎠ ⎟

Shh Svh

Shv Svv

⎛

⎝ ⎜

⎞

⎠ ⎟

1 δ3 + Ωf2

δ4 − Ω f2

⎛

⎝ ⎜

⎞

⎠ ⎟ +

Nhh Nvh

Nhv Nvv

⎛

⎝ ⎜

⎞

⎠ ⎟

Calibrating Calibrating the systemthe system

ˆ S hhˆ S vh

ˆ S hvˆ S vv

⎛

⎝ ⎜

⎞

⎠ ⎟ =

1β

f1 − Ω + δ2( )− δ1 − Ωf1( ) 1

⎛

⎝ ⎜

⎞

⎠ ⎟

Mhh Mvh

Mhv Mvv

⎛

⎝ ⎜

⎞

⎠ ⎟

f2 − δ1 + Ωf2( )− δ2 − Ω( ) 1

⎛

⎝ ⎜

⎞

⎠ ⎟

where β = f1 − δ1 − Ωf1( ) Ω + δ2( )[ ]. f2 − δ1 + Ωf2( ) δ2 − Ω( )[ ]

ˆ S hhˆ S vh

ˆ S hvˆ S vv

⎛

⎝ ⎜

⎞

⎠ ⎟ ≅

1′ β

f1 −ΩΩf1 1

⎛

⎝ ⎜

⎞

⎠ ⎟

Mhh Mvh

Mhv Mvv

⎛

⎝ ⎜

⎞

⎠ ⎟

f2 −Ωf2

Ω 1⎛

⎝ ⎜

⎞

⎠ ⎟

where ′ β = f1 f2 1+ Ω2( )2



December 19, 2008 XPI@JPL: Imaging the Ionosphere Using SAR & GPS

IonosphericIonospheric MeasurementsMeasurementsUsing Radio SignalsUsing Radio Signals

TEC1045.8

3.402

7

f

dsnfc

r

t

e

−×=

⋅= ∫r

r

πφ

dsBnfK

r

t

e θcos02 ∫=Ωr

r

Phase Advance or Time Delay:

Faraday Rotation:

ne ─ electron densityB0 ─ ambien mag. fieldθ ─ angle between k and B0K = 2.365×104 (in MKS units)

Dual-Freq. Phase Combination

Rate of TEC (ROT) Change:Line-of-sight TEC

(Φ in units of length)

Rate of TEC Index (ROTI):



ALOS Scene over AlaskaALOS Scene over Alaska

December 19, 2008 Pi et al.: Imaging the Ionosphere Using SAR & GPS



Faraday Rotation Image Measured Using Faraday Rotation Image Measured Using PolarimetricPolarimetric SARSAR

• Faraday rotation is derived from polarimetric measurements made using ALOS L‐band PALSAR over Alaska at 07:28 UT on 4/1/2007

• The size of the Image scene is about ~28 x 62 km2

• 1D FR in the azimuth dir: mean FR in the range dimension is shown as a function of latitude. Noise of about 0.5 degrees is seen in the data before smoothing.

• 2D image: Features at scales < 110 x 197 m2 are smoothed or removed to reduce noise.

• The tilted strip seems aligned with the ambient magnetic inclination contour

• The FR image shows not only ionospheric gradient but also curvature within the radar scene in both azimuth and range directions.

(220.243°, 61.959°) (220.796°, 62.027°)



Magnetic InclinationMagnetic Inclination

Pi et al.: Imaging the Ionosphere Using SAR & GPS (Fall AGU)

SARObs.



A Series of ALOS Scenes over AlaskaA Series of ALOS Scenes over Alaska

December 19, 2008 Pi et al.: Imaging the Ionosphere Using SAR & GPS



Polar Polar IonosphericIonospheric Features Captured Features Captured in in PolarimetricPolarimetric SAR imagesSAR images

• Multiple strips of enhanced Faraday rotation aligned with magnetic inclination contours are observed in a single path over polar region by PALSAR in a polarimetric mode.

• FR structures as small as 0.1~0.2 degrees are identified after smoothing to reduce noise. • FR Discontinuity between the images raise possible calibration (by JAXA) or processing

issues. Pi et al.: Imaging the Ionosphere Using SAR & GPS (Fall AGU)

EUSAR 2008National Aeronautics and Space Administration


January, 2006

Global Assimilative Ionospheric ModelGlobal Assimilative Ionospheric Model

• Time dependent• 3D grid in a

magnetic frame

• Global and regional modelingby solving plasma hydrodynamic equations

- Numerically solving plasma continuity and momentum equations

- Finite volume on a fixed Eulerian grid

- Hybrid explicit-implicit time integration scheme

• Multiple ions:O+, H+, He+,

NO+,O2+, N+

DrivingForces

PhysicsModel

Obs. Operator

Kalman Filter4DVAR

Assimilative ModelingPi et al.: GAIM Global TEC

EUSAR 2008National Aeronautics and Space Administration


Faraday Rotation Faraday Rotation Retrieved from PalSAR and GPS DataRetrieved from PalSAR and GPS Data

• Faraday rotation is retrieved from ALOS/PalSAR data and using the GPS-based techniques , respectively, along the ALOS orbit track

• SAR-FR (blue) is obtained using the new calibration technique

• GPS-FR is obtained using GIM (2D) (red)

– IRI is used to estimate the suborbital to total TEC ratio

– IGRF is used to specify magnetic field

• GIM-TEC (black) used in FR estimation is also plotted as a reference

• GAIM-FR (3D) estimation is also being processed.

GPS-GIM TEC is rescaled and shifted to fit in the plot.

03/28/2007



2525

ConclusionsConclusions

• New approach to estimate FR gives results that are comparable with other techniques

• Technique takes full account of system distortions• With enough FR, full polarimetric calibration without

corner reflectors is possible• Exception when Ω < 1o (equivalent to a x-talk of ~-

35dB), new algorithm for full calibration appears SNR-limited

• PalSAR system cross-talk is < -35 dB and probably~ -40dB

• FR estimates from new algorithm and GPS-based estimates corrected for vertical profile are consistent==> GPS-based FR estimates can be used as a first

order correction for future spaceborne SARs

calibration of palsar polarimetric sar...

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