Fundamentals of Remote Sensing SAR Polarimetry.pdf

24/06/13  

Fundamentals of Remote Sensing: SAR Polarimetry Gabriel VASILE, Chargé de Recherche, CNRS Nikola BESIC, Doctorant, Grenoble INP

GIPSA-lab Département Image Signal (DIS) Equipe SIGnal IMAge PHYsique (SIGMAPHY)

I Electromagnetic wave polarization (1/8) Electromagnetic wave:   •  electric field component e(r,  t) •  magnetic field component h(r, t)

characteristic impedance

     e(r, t) = ξ ⋅ h(r, t) × k direction vector

$  j (2 π ft− 2 π z) '    λ e(x, y, z, t) = ex ⋅ x + ey ⋅ y = ℜ % E0 ⋅ e ( & ) 1

Fundamentals of Remote Sensing: SAR Polarimetry

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I Electromagnetic wave polarization (2/8)

behavior of

  e(r, t)

EM wave polarization ~ in the plane perpendicular to the propagation direction ~ behavior of ex and ey

2π z + δx ) λ 2π ey = E0 y cos(2π ft − z + δy ) λ ex = E0 x cos(2π ft −

 e(z, t) ey (z, t)

ex (z, t) Phase difference between two components:

δ = δx − δy Fundamentals of Remote Sensing: SAR Polarimetry

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I Electromagnetic wave polarization (3/8)

δ = 0 ∨δ = π E0 x = E0 y

LINEAR 3

π 2 E0 x = E0 y

the rest…

CIRCULAR

ELIPTICAL

δ =±

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I Electromagnetic wave polarization (4/8) Fully polarized wave: Mathematical representation through the Jones vector:

! E0 x e jδx # J= # E e jδy " 0y

$ & & %

x axis – horizontal y axis – vertical

polarization

horizontal

vertical

circular (L)

circular (R)

Normalized Jones vector

! 1 $ # & " 0 %

! 0 $ # & " 1 %

1 ! 1 $ # & 2" i %

1 " 1 % $ ' 2 # −i &

Fundamentals of Remote Sensing: SAR Polarimetry

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I Electromagnetic wave polarization (5/8) Polarization ellipse:

χ =0 π ψ = (δ = 0 ) 2 3π ψ= (δ = π ) 2

LINEAR:

CIRCULAR:

χ ° [−45°, 45°]

- ellipticity

ψ ° [ 0°,180°]

- orientation angle

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χ =±

π 2

ELLIPTICAL: the rest…

Fundamentals of Remote Sensing: SAR Polarimetry

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I Electromagnetic wave polarization (6/8) Partly polarized wave: Mathematical representation through the Stokes vector:

! # I = ## # #"

S0 Q U V

S02 ≥ Q 2 +U 2 +V 2

d=

! $ # & # &=# & # & # &% # #"

2

2

2

2

Eh + Ev Eh − Ev

2ℜ {Eh Ev* } −2ℑ {Eh* Ev }

$ & & & & & & &%

Equality holds for fully polarized wave.

Q 2 +U 2 +V 2 S02

Degree of polarization

Fundamentals of Remote Sensing: SAR Polarimetry

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I Electromagnetic wave polarization (7/8) Poincaré sphere:

! # I = ## # #"

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! S0 S0 $ # & Q & = # S0 cos2ψ cos2 χ & # U & # S0 sin 2ψ cos2 χ V &% #" S0 sin 2ψ

equator

linear

poles

circular

the rest

elliptical

$ & & & & & %

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I Electromagnetic wave polarization (8/8) Polarimetric radar transmitted waves: (a)  Horizontally (b)  Vertically

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II SAR Polarimetry principle (1/12) SAR systems: (a) monostatic (b) bistatic

V

H

E

I

E

S

•  single pol (HH v VV v HV v VH) •  dual pol (HH & HV v VV & VH) •  full pol (HH & HV & VH & VV)

HH v VV – co-polarized channels HV v VH – cross-polarized channels

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Fundamentals of Remote Sensing: SAR Polarimetry

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II SAR Polarimetry principle (2/12) Agricultural fields in southern Manitoba

Full Pol: RADARSAT 2 •  Launched in 2007 •  Canadian Space Agency •  C band

Fundamentals of Remote Sensing: SAR Polarimetry

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II SAR Polarimetry principle (3/12) RH AH T

V H

AV

RV T H

V

H

V

RH RV

TRANSMITTER: RECEIVERS:

H&V H&V

SHH

SHV

SHH

SHV

SVH

SVV

SVH

SVV

(BACK)SCATTERING MATRIX 11

') ! S HH ([ S ] = # #" SVH )*

SHV $+) &, SVV &%) -

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II SAR Polarimetry principle (4/12) Scattering matrix:

Targets causing depolarization of the incident wave?

NO

12

YES

Coherent targets

Incoherent targets

Coherent backscattering

Incoherent backscattering

Backscattered wave described by the Jones vector

Backscattered wave described by the Stokes vector

Fundamentals of Remote Sensing: SAR Polarimetry

II SAR Polarimetry principle (5/12) Scattering matrix:

Backscattering coordinate system

Back Scatterer Alignment (BSA)

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Forward Scatterer Alignment (FSA)

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II SAR Polarimetry principle (6/12) Scattering matrix:

•  S and J – complex matrices •  K and M – real matrices •  Under reciprocity assumption: S, J, K and M – symmetric matrices Fundamentals of Remote Sensing: SAR Polarimetry

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II SAR Polarimetry principle (7/12) Sinclair matrix: SAR polarimetry SAR interferometry

! S HH

[S ] = #

#" SVH

! # k =# # #"

SHV $ & SVV &%

SHH 2SHV SVV

$ & & & &%

S

E =

Propagation

e − jkr [S ]E I r

Penetration depth

+

Backscattering mechanisms

target vector 15

Fundamentals of Remote Sensing: SAR Polarimetry

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II SAR Polarimetry principle (8/12) Target vector:

! S HH

SHV $ & SVV &%

[S ] = #

#" SVH

kTi = Trace ([ S ] [ψTi ])

Pauli matrices:

1 ! ψT 0 = # 2" 1 ! ψT1 = # 2" 1 ! ψT 2 = # 2"

1 0 1 0 0 1

0 $ &, 1 % 0 $ &, −1 % 1 $ & 0 %

" S +S HH VV 1 $ kT = $ SHH − SVV 2$ $# 2SHV

% ' ' ' '&

Frobenius norm:

kT

2

(

*

)

2

2

= Span([ S ]) = Trace [ S ] [ S ] = SHH + 2 SHV + Svv

2

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II SAR Polarimetry principle (9/12) Muller matrix: Incident Stokes vector d=1

I S = [M ] I I

Initially, 10 real parameters. Trace condition: Backscattered Stokes vector d