POLINSAR AT LOW FREQUENCY AND IONOSPHERIC EFFECTS

Pascale Dubois-Fernandez, Sébastien Angelliaume, My-Linh Truong-Loi, ONERAAnthony Freeman, JPL

Eric Pottier, IETR CNRS 6164, Université de Rennes

SAPHIR

SAPHIR

Ionopheric Effect

• Dispersive effect• Propagation time depends on the TEC and on the

frequency. This creates a distortion of the chirp.

• Spatial variation of the TEC• Effect similar to trajectory disturbances ⇒ extensive

experience on very high resolution processing• Needs to be validated with representative 2-D phase

screens

• Faraday rotation

SAPHIR

Faraday rotation

⎟⎟⎠

⎞⎜⎜⎝

⎛ΩΩ−ΩΩ

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ΩΩ−ΩΩ

=Ω cossinsincos

cossinsincos

VVHV

HVHH

SSSS

M

Ω−Ω= 22 sincos VVHHHH SSM

Ω−Ω= 22 sincos HHVVVV SSM

ΩΩ++= cossin)( VVHHHVHV SSSM

ΩΩ+−= cossin)( VVHHHVVH SSSM

HVHVVH SMM 2=+

SAPHIR

Standard RVoG inversion (*)

dze

dzeee

v x

z

v x

h z

zikh z

iV

∫

∫=

0

cos2

0

cos2

0

θσ

θσ

ϕγ

h σx

* Cloude and Papathanassiou

*22

*11

*21

SSSS

SSS =γ

vγ

gγ

SAPHIR

Standard RVoG inversion + ionosphere

*22

*11

*21

MMMM

MMM =γ

?TEC 1 TEC 2

M1 M2

SAPHIRSAPHIR

SAPHIR

The set of interferometric coherences

TTRRT kSkE 11 = T

TRRT kSkE 22 =

*22

*11

*21

RTRTRTTRT

RTRTRT

EEEE

EE=γ

{ }TRRT kandkallforγ=Ζ?{ }TRRT kandkallfor),( 2121

ΩΩ=Ζ ΩΩ γ

= {the set of all interferometric coherences}

SAPHIR

Two cases

{ }TRRT kandkallfor),( 2121ΩΩ=Ζ ΩΩ γ

{ }),( 1121ΩΩ=Ζ ΩΩ RTγ { }),( 2121

ΩΩ=Ζ ΩΩ RTγ21 Ω=Ω 21 Ω≠Ω

Full Pol/ Compact Pol Full Pol/ Compact Pol

SAPHIR

Assuming identical ionospheres

TTRRT kRSRkE ΩΩ= 11 T

TRRT kRSRkE ΩΩ= 22

Ω=Ω=Ω 21

For exemple

⎟⎟⎠

⎞⎜⎜⎝

⎛==

01

TR kk °=Ω 0

°≠Ω 0

HHS

Ω−Ω= 22 sincos VVHHHH SSM

),(),( 0 TRTR kkkk γγ ≠Ω

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

Full polarimetry

SAPHIR

Assuming identical ionospheres

TTRRT kRSRkE ΩΩ= 11 T

TRRT kRSRkE ΩΩ= 22

TTRRT hShE 11 = T

TRRT hShE 22 =

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

Full polarimetry

Faraday rotation

TT hRk Ω−=

RR hRk Ω=TT kRh Ω=

RR kRh Ω−=

No Faraday rotation

Same measured signal

SAPHIR

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

such thatThe interferometric coherence set is invariant

No effect of ionosphere

),(),( 0 TRTR kkkk γγ ≠Ω

),(),( 0 TRTR hhkk γγ =Ω),(),,( TRTR hhkk ∃∀

0ZΩZ

Full polarimetry

No Faraday Rotation Faraday Rotation

One-to-one relation

SAPHIR

Assuming identical ionospheres

Z=ΖΩThe set of interferometric coherences is invariant

such thatThe interferometric coherence set is invariant

No effect of ionosphere

),(),( 0 TRTR kkkk γγ ≠Ω

),(),(0 TRTR hhkk Ω= γγ),(),,( TRTR hhkk ∃∀

21 Ω=Ω

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

The inversion can proceed without any adjustement except the selection of the ground. For that, use HVHVVH SMM 2=+

Full polarimetry

SAPHIR

Compact PolInSAR & same ionosphere

• The compact polarimetry mode:• π/2 mode: 1 circular transmit and 2 independent receive

polarizations: (RR,RL) or (RH, RV)

• Circular on transmit at lower frequency is essential• The single polarization on receive will be rotated through

the ionosphere; To insure the invariance of polarization at the surface level, circular polarization is the only choice

• Synthesis can be done on receive:

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=j

SkE TRR

12

111 ⎟⎟

⎠

⎞⎜⎜⎝

⎛−

= Ω

Ω−

jSRkeE T

R

j

R

12 11

Without ionosphere With ionosphere

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

Compact polarimetry

SAPHIR

Assuming identical ionospheres

⎟⎟⎠

⎞⎜⎜⎝

⎛−

= ΩΩ−

jSRkeE T

Rj

RC

111

*22

*11

*21

RCRCRCTC

RCRC

EEEE

EE=Ωγ

{ }RRT kallforγ=ΖΩ

Rj

RRj

R hRekkReh ΩΩ

Ω−Ω− == ;

Z=ΖΩThe set of interferometric coherence is invariant

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=j

ShE TRRC

111

⎟⎟⎠

⎞⎜⎜⎝

⎛−

= ΩΩ−

jSRkeE T

Rj

RC

122

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

Compact polarimetry

This is not the case if the transmit polarisation is not circular!!!

SAPHIR

Identical Faraday rotation

• Full polarimetry• The set of interferometric coherences is globally invariant• No effect on the inversion

• Compact polarimetry• If the transmit polarization is circular, the set of

interferometric coherence is globally invariant• no effect on the inversion

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

SAPHIR

Different ionospheres { }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

• Differential Faraday rotation• Correction of the data prior to PolInSAR inversion

• Full polarimetric case: Bickell and Bates, Freeman

• Compact pol: more later• What is the required accuracy of the correction?

Full polarimetry

SAPHIR

Assuming a different ionosphere on co-pol

• Notion of differential ionosphere• Assume no FR on acquisition 1

*22

*11

*21

EEEE

EE=Ωγ

Ω−Ω= 222 sincos VVHH SSE

HHSE =1

02cos γγ Ω>Ω

VVHHHH SSSEE *222*21 sincos Ω−Ω=

• Ω < 2°, • Small loss of coherence = 2%• Small error on the interf. phase < 2°

HH or VV

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

Full polarimetry

SAPHIR

Assuming a different ionosphere

• Assume no FR on acquisition 1

*22

*11

*21

EEEE

EE=Ωγ

RRSE =2

RRSE =1

0γγ =Ω

RR or LL

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

Full polarimetry

Invariant with FR

SAPHIR

Assuming a different ionosphere

• Notion of differential ionosphere• Assume no FR on acquisition 1

*22

*11

*21

EEEE

EE=Ωγ

RLj SeE Ω−= 2

2

RLSE =1

02 γγ Ω

Ω = je

VVHHHH SSSEE *222*21 sincos Ω−Ω=

• Ω < 2°, • no loss of coherence

RL

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

Full polarimetry

SAPHIR

Different ionospheres for PolInSAR

• Correction of the differential Faraday rot. to within 2°• Bickell and Bates, Freeman…

• Apply PolInSAR inversion on corrected data

• Make good use of 3 FR invariant coherences

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

HVHVVH SMM 2=+

RRRR SM =

LLLL SM =

Full polarimetry

SAPHIR

Assuming different ionospheres

• Compact PolInSAR

• Only one Faraday rotation invariant coherence

• We know that Faraday rotation will lower the coherence: The two polarisation states are not matched

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛jSS

SSSS

VVVH

HVHH

RV

RH 12

1

RRRR SM =

Compact polarimetry

SAPHIR

Assuming a different ionophere

Therefore, the correct correction of FR will maximize the interferometric coherence

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

Compact polarimetry

*22

*11

*21

ΩΩ

Ω

Ω =CCMM

CM

RHRH

RHγ

RHM1

RHM 2 ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛= Ω−

ΩΩ

RV

RHT

j

MM

ReC2

22 0

1FR correction

Faraday rotation of 100°

SAPHIR

Inte

rfer

omet

ric c

oher

ence RV

RH

PolInSAR and ionophere: Large differential FR?

Different areas: ionospheric differences of 100°RVRH

180°

ΔΩ within 5°

Simulation over Airborne dataΩ = 0° on Day 1Ω =100° on Day 2

We maximize the coherence by correcting the second acquisition with a varying FRYes with an accuracy better than 5°

Can we estimate the differential FR and correct for it?

Variation of the coherence with respect to a FR correction on the second acquisition

Compact polarimetry

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

Dubois-Fernandez et al. “The compact polarimetry alternative … ”, IEEE TGRS October 2008

SAPHIR

Compact PolInSAR inversion

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140

Angular extension with FP data [°]

Angu

lar

exte

nsio

n w

ith C

P da

ta [°

]

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30

Measured Height [m]

Estim

ated

Hei

ght [

m]

FPCP

Mode π/2

Mode FP

Angular sector

Inversion results

Compact polarimetry

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

SAPHIR

Compact PolInSAR inversion

0

0,5

1

1,5

2

2,5

3

3,5

0 5 10 15 20

Faraday Angle [°]

RM

S he

ight

err

or [m

]

CP pi/2CP pi/4

Compact polarimetry

{ }),( 2121ΩΩ=Ζ ΩΩ RTγ

21 Ω=Ω21 Ω≠Ω

SAPHIR

Conclusions

• Identical ionospheres• Invariance of the set of interferometric coherences when the

ionospheres are identical on both measurements• Full polarimetry and compact polarimetry (Circular transmit)

• Different ionospheres• 3 invariant coherences with Faraday rotation for FP• 1 invariant coherence with CP• Full polarimetry

• Correct the two datasets prior to data analysis• Compact polarimetry

• Correct for the differential FR by maximizing the interferometric coherences over all linear polarisations