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Basics of Radar Polarimetry
Wolfgang Keydel
Vorlesung Erlangen
Literatur: Martin Hellmann, SAR Polarimetry, Tutorial http://epsilon.nought.deKeydel, W. (Editor) Radar Polarimetry and Interferometry; Lecture Series RTO-EN-SET-081Radar Interferometry and Polarimetryhttp://ftp.rta.nato.int/public//PubFullText/RTO/EN/RTO-EN-SET-081///EN-SET-081-$$TOC.pdf
Alle Kapitel als Downloads: http://www.rto.nato.int/pubs/rdp.asp?RDP=RTO-EN-SET-081
2Microwaves and Radar Institute, Wolfgang Keydel
Coherence
CE t E t
E t E t E t E t
( ( ) ( ))
( ) ( ) ( ) ( )
*
* *
1 2
1 1 2 2
E1 and E2 vary in conformity: C=1, E1 and E2 vary in opposition: C= -1
Coherence: = =CE t E t
E t E t E t E t
( ( ) ( ))
( ) ( ) ( ) ( )
*
* *
1 2
1 1 2 2
= 0 means incoherence, = 1 complete coherence
Continous transition from pure coherence to pure incoherence
Incoherent: Phases random & (directly or in effect) uniformly distributed
0 ≤ ≤ 2π.
Coherent: phase relations between waves are constant
0 ≤ ≤ 1
-1 ≤ C ≤ +1Correlation
3Microwaves and Radar Institute, Wolfgang Keydel
Polarisation Ellipse & Spatial Helixdecomposed
into orthogonal components x (horizontal H) and y (vertical V)
Courtesy Shane Cloude
4Microwaves and Radar Institute, Wolfgang Keydel
Polarisation Ellipse & Spatial Helixdecomposed
into orthogonal components x (horizontal H) and y (vertical V)
5Microwaves and Radar Institute, Wolfgang Keydel
Ausbreitung des Wellenvektors
Drehsinnbetrachtung
in Ausbreitungsrichtung
rechts
links
z
x
6Microwaves and Radar Institute, Wolfgang Keydel
EY
EX
Polarisation: Vektor Nature of Electromagnetic Waves
vertikal
horizontal
EY
EX
z
z
7Microwaves and Radar Institute, Wolfgang Keydel
Polarization Ellipse
χ = Ellipticity Angle: 0 ≤ χ ≤ π/4
Ψ= Orientation Angle: - π/2 ≤ ψ ≤ π/2
cos)2tan()2tan(andsin2sin2sin
a
a)tan(andcos
EE
EE2)2tan( 02
0y2
0x
0x0y
withsincosEE
EE2
E
E
E
Eyx000
0x0y
xy
2
0x
x
2
0y
y
y
jjkz0y
jkzyy eee)z(Ee)z(E)z(E y
xjjkz
0xjkz
xx eee)z(Ee)z(E)z(E x
yyxx e)z(Ee)z(E)z(E
ξ
χ
Ψ x
y
majoraxis
minor axis
η
αa ξ
aη
E
EX0
EY0
8Microwaves and Radar Institute, Wolfgang Keydel
x
χ
Ψ
y
x
η
Ψ
χ = 45°
x
y
Ψ
χ = 0°
y
Orthogonal Polarizations
Elliptical Circular Linear
Polarization Ratio:
For each Polarization State ρ exists an orthogonal Polarization State ρorth
)2cos()2cos(1
)2sin(j)2sin()2cos(e
E
E )(j
xO
yOyx
1*orth
9Microwaves and Radar Institute, Wolfgang Keydel
POLARIMETRIC DESCRIPTORSPOLARIMETRIC DESCRIPTORS
DIFFERENTTARGET POLARIMETRIC
DESCRIPTORS
X
Y
TRANSMITTER: X & YRECEIVER: X & Y
Courtesy Eric Poitier
Examples:k Target VectorE Jones Vektorg Stokes Vector[S] Streu -Matrix[K] Müller-Matrix
(KENNAUGH)[T] Coherency Matrix[C] Covariance Matrix
10Microwaves and Radar Institute, Wolfgang Keydel
Jones Vector for completely polarized Waves
yyxx e)z(Ee)z(E)z(E
Containes complete information about the Polarization Ellipse, except handleness.
Two plane waves propagating in opposite directiond have the same Jones Vector representation
Subscripts „+“ & „-“ compensate this lack using direction of Propagation Vektor k
Using the Polarisation Ratio the Jones Vector can be written as
1E
E
EE x
y
x
xy
sin
cos
cossin
sincos0
00
0
jeE
eE
eE
E
EE j
j
y
jx
y
x
y
x
11Microwaves and Radar Institute, Wolfgang Keydel
Different Polarization States
Courtesy Eric Pottier
x x
xx
y
yy
y
12Microwaves and Radar Institute, Wolfgang KeydelCourtesy Eric Poitier
x x
xx
y
y y
y
Jones Vector Descriptions for Characteristic Polarization States Propagation
Direction out of Page
13Microwaves and Radar Institute, Wolfgang Keydel
Change of Polarization Basis
0for
newbasistheofvectorstheareUofcolumnsThe
e,eande,e:basesonpolarizatilorthonormaTwo
1Y
y2y1x2x1
eEeEeEeEE:Field-E y2y2y1y1x2x2x1x1
1
1
1
1U
x
*x
*xx
ee
ee
1
1U
jjx
j*x
j
*xx
1Y1Y
1Y1Y
e,e y2y1
1
ρ
ρρ1
1eeand
ρ
1
ρρ1
1ee
*x
*xx
jy2
x*xx
jy1
Y2Y1
:e,ebasis-YforrsBasisvecto y2y1
e,ebasis-Xforratioonpolarizatiingcorrespondρ x2x1x
EUE
UMatrixvia 2x2EEvectorcomplexElement2oftionTransforma
2x,1x2y,1y
2y,1y2x,1x
E
EEand
E
EE:VectorsonesJ
2y
1y
2y,1y
2x
1x
2x,1x
14Microwaves and Radar Institute, Wolfgang Keydel
15Microwaves and Radar Institute, Wolfgang Keydel
The Stokes Vector
;g´ggg 23
22
21
20
g0 ~ total wave intensity,g1 ~ Difference between
hor. & vert. linear Parts,g2 & g3 ~ Phase difference between
hor. & vert. linear Parts
Absolute Phase lost!!
Completely polarized waves:
Incompletely polarized waves: ;g´ggg 23
22
21
20
>
Completely polarized waves:
sin2
cos2
)Im(2
Re2)(
00
00
2
0
2
0
2
0
2
0
*
*
22
22
3
2
1
0
yx
yx
yx
hv
yx
hx
yx
yx
EE
EE
EE
EE
EE
EE
EE
EE
g
g
g
g
Eg
)2sin(g
)2cos()2sin(g
)2cos()2cos(g
g
g
0
0
0
0
16Microwaves and Radar Institute, Wolfgang Keydel
Stokes Vektor Decomposition
Degree of Polarization:o
23
22
21
g
gggp
Decomposition into completly polarized & unpolarized Component
21
21
21
20 gggg General Case:
0
0
0
p1
g
g
g
g
3
2
1
0
)2sin(p
)2cos()2sin(p
)2cos()2cos(p
p
g0
g
All 4 Parameter derivable from intensity measurements
Orthogonal Polarization States located on diametrally oppositepositions on the Poincaré Sphere
17Microwaves and Radar Institute, Wolfgang Keydel
Poincare Sphere
18Microwaves and Radar Institute, Wolfgang Keydel
X
Y
T
RX
AX
RY
AY
YY
XY
YX
XX
S
S
S
SS
YXS
XXS
YYS
XYS
YXS
XXS
YYS
XYS
X Y X Y
T
RX
RY
SINCLAIR MATRICES
SCATTERING POLARIMETRY
SCATTERING POLARIMETRYSCATTERING POLARIMETRY
TRANSMITTER: X & YRECEIVERS: X & Y
19Microwaves and Radar Institute, Wolfgang Keydel
Radar Polarimetry
Full utilization of the vector nature of Electromagnetic Waves
via
Orientation of the Electric Vector in anElectro Scattering Matrix
EHr
EVr S
EHt
EVt
EHt
EVt
SHH SHVSVH SVV
Monostatic Radar Case: SHV= SVH
Relative Scattering Matrix
5 independent Parameter
4 complex coeffizients, 8 independent Parameter
Si, k
i ke
ji k
,
, ,=
0
… α = jk +E e-j(ωt +φ)kre -αr
E0
Radar Equation
20Microwaves and Radar Institute, Wolfgang Keydel
EMW Reflection
ISHHI ≥ ISHVI
ISVVI ≥ ISVHI
<Re(S*HHSVV)> ≥ < ISHVI2 >
Phase (S*HHSVV) ≈ 0
OddReflections
•
ISHHI ≥ ISHVI
ISVVI ≥ ISVHI
<Re(S*HHSVV)> ≥ < ISHVI2 >
Phase (S*HHSVV) ≈
•
•
EvenReflections
21Microwaves and Radar Institute, Wolfgang Keydel
Eigenschaften Streumatrix
|SHH |
|SHH |
|SHV |
|SHH |2
|SHH |2
|SHV |2 |φHV |
|φVV |
SHH SHVSVH SVV
Elemente
Invariante
1 0
0 2
Spur [S(HV)] = |SHH |2 +2 |SHV |2+ |SVV |2 = |1|2 + |2|
2
| Det [S(HV)] | = |SHHSVV – SHV2| = | 1 2 |
Si, k
i ke
ji k
,
, ,=
0
22Microwaves and Radar Institute, Wolfgang Keydel
BasismatrizenEine generische Matrix ist in Basismatrizen zerlegbar;
a S S b S S c S SHH VV HH VV HV VH ; ;
a b S a b SHH VV ;
Streuvektor k = (a,b,c) = (SHH + SVV ; SHH - SVV ; SHV)
SS S
S S
HH HV
VH VV
a b c
c a ba b c
1 0
0 1
1 0
0 1
0 1
1 0
Pauli Matrizen
23Microwaves and Radar Institute, Wolfgang Keydel
Depolarization Scheme
24Microwaves and Radar Institute, Wolfgang Keydel
Pauli Matrices
2
2
line
sin2sin2
1
2sin2
1cos
S
Sphere Statisical Volume
01
10Sdiff
,
10
01S
odd
Wire
cos2αsin2α
sin2αcos2αS
even
Diplane
1j
j1e
2
1S 2j
helix
Helix
25Microwaves and Radar Institute, Wolfgang Keydel
Pauli Matrices
RoughSurfacePlate,
Sphere, Dihedral;
TiltedDihedral;
Vegetation
01
10Sdiff
,
10
01S
odd
cos2αsin2α
sin2αcos2αS
even
Single Bounce,odd
Double Bounce,even
Volume Scattering,diffuse
Scattering Vector kscat = (kodd, keven, kdiff) = (SHH+ SHV, SHH- SHV; 2SHV)→
α
26Microwaves and Radar Institute, Wolfgang Keydel
01
10S,
cos2αsin2α
sin2αcos2αS,
10
01S dfiffus21
27Microwaves and Radar Institute, Wolfgang Keydel
28Microwaves and Radar Institute, Wolfgang Keydel
Dihedral with 45-degree tilt
Even-bounce, π/4-TiltDihedral
DihedralEven-bounce
Surface, sphere,Corner reflectors
Odd-bounce
Scatteringmechanism
Scattering typePauli matrix
1 0
0 1
1 0
0 1
0 1
1 0
Physical significance of elementary scatterers
D.G. Corr:Potential of Radar Polarimetry. QinetiQ, Cody Technology Park, A8/1008 Ively Road,Farnborough, Hampshire, GU14 0LX, United Kingdom
29Microwaves and Radar Institute, Wolfgang Keydel
Transformation from linear to circular Basis
VVHHRL
VVHHHVLL
VVHHHVRR
SS2
j´S
SS2
1jSS
SS2
1jSS
Circular Basis Radar Responses
NOYESNOLeft Helix
NONOYESRight Helix
NOYESYESDiplane
YESNONOSphere
LRRRLL
Microwaves and Radar Institute, Wolfgang Keydel
HERMITIAN MATRIX - RANK 1
COHERENCY MATRIXCOHERENCY MATRIX
TXYYYXXYYXX S2SSSS2
1k
A0, B0+B, B0-B : HUYNEN TARGET GENERATORS
MONOSTATIC CASE
COHERENCY MATRIX [T]
PAULI SCATTERING VECTOR k
[T] is closer related to Physical and Geometrical Properties of the Scattering
Process, and thus allows a better and direct physical interpretationCourtesy Eric Poitier
BBjFEjGH
jFEBBjDC
jGHjDCA2
kkT
0
0
0T*
Microwaves and Radar Institute, Wolfgang Keydel
PHYSICAL INTERPRETATION
SINGLE (odd) BOUNCESCATTERING
(ROUGH SURFACE)
DOUBLE (even) BOUNCESCATTERING
VOLUMESCATTERING
TARGET GENERATORSTARGET GENERATORS
Courtesy Eric Poitier
2
YYXX011 SSA2T
2
YYXX022 SSBBT
2
XY033 S2BBT
32Microwaves and Radar Institute, Wolfgang Keydel
Coherence & Covariance Matrices
CoherenceMatrix
CovarianceMatrix C k k
S S S S S S S
S S S S S S S
S S S S S S S
S S S S S S S
S S
T
HH HH HV HH VH HH VV
HV HH HV HV VH HV VV
VH HH VH HV VH VH VV
VV HH VV HV VV VH VV
* * *
* * *
* * *
* * *
2
2
2
2
k S S S Ss HH VV HV VH; ; ;
Todd odd even odd diff
odd even even even diff
odd diff even diff diff
odd HH VV even HH VV diff HV VH HV
*
* *
* *
* *
; ;
1
2
2
2
2
2
T kk
k k k k k
k k k k k
k k k k k
k S S k S S k S S S
33Microwaves and Radar Institute, Wolfgang Keydel
Zerlegung von [ T ] in 3 Kohärenzmatrizen [ Tn ],Gewichtung mit entsprechendem Eigenwert n.
0° ≤ αn ≤ 90° : Streumechanismus für jeden Vorgang
-180° ≤ n ≤ 180° : Objektorientierung gegen Sichtlinie
& γ : Phasenwinkel
Mittlerer - Winkel:
n nn 1
3
2 3
Entropie:
n nn
H 31
3
log
Anisotropie A 2 3:
T T e e e e
e
nn
n nn
n n
T
n
n
n nj n
n nj n
1
3
1
3
;
cos
sin cos
sin sin
mit
34Microwaves and Radar Institute, Wolfgang Keydel
Normalized Polarimetric Entropy, H ; Diversity of scattering mechanisms
H = -Σiλilog3 λi ….i = 1…3
mean α related to „Form“ scattering mechanismα = -Σiλi αi
simple
single (odd)bounce
Plate,Sphere
double (even)bounce
Diplane
multiple bounce
random
10H
α
45°0° 90°
anisotropic odd anisotropic even
isotropic evenisotropic odd Dipol
35Microwaves and Radar Institute, Wolfgang Keydel
H provides a measure of the diversity of the scattering mechanisms,degree of randomness statistical disorder
single mechanism H = 0, three mechanisms of equal power H = 1.
difficult mechanism discrimination when : H > 0.7
Eigenvalues Spectrum:
Related to scattering mechanisms, not an orientation.
Single (odd) bounce: α = 0; Diffuse scattering: α = 45; Double (even) bounce: α = 90°
Polarimetric Entropy:
i ii
H 31
3
log
- Angle:
n nn 1
3Mean
Anisotropy A 2 3:
36Microwaves and Radar Institute, Wolfgang Keydel
Measure for a targets homogeneity relative to the radar look direction.
Example: Amazon forest is a very homogeneous target ===> low anisotropy.
In contrast: row crops ===> high anisotrophy value.
Anisotropy A 2 3:
0 ≤ H ≤ 1Measure of the dominance of a given scattering mechanism within a resolution cell related
to amount of effective scattering mechanisms, normalized between 0 and 1.
H = 0: all scattering results from one mechanism (single bounce, double bounce),
H = 1 completely random scattering mechanisms ore 3 mechnisms of equal power resp.
Entropie:
n nn
H 31
3log
37Microwaves and Radar Institute, Wolfgang Keydel
DIFFICULT MECHANISM DISCRIMINATION WHEN : H > 0.7
ANISOTROPY(EIGENVALUES SPECTRUM)
32
32A
COMPLEMENTARY TO ENTROPY
DISCRIMINATION WHEN H > 0.7
ROLL INVARIANT
H / A /H / A / aa DECOMPOSITIONDECOMPOSITION
38Microwaves and Radar Institute, Wolfgang Keydel
H
C1 Urban -dihedral C4 Forestry C7 Forestry crown
C2 Dipolevolumetric scatterg
C5 Vegetation C8 Vegetation
C3 Surfacescattering
C6 Rough surfaceand vegetation
Single mechanism Two mechanisms Three mechanisms
Double bounce
Volumescattering
Surfacescattering
Not feasible
Scattering characteristics of regions in H-α plane
C8 Vegetation
C1 Urban dihedral
C2 Dipole volumetric scattering
C3 Surface scattering
C4 Forestry
C5 Vegetation
C6 Rough surface & vegetation
C7 Forestry crown
α°
0 0.2 0.4 0.6 0.8 10
10
20
30
40
50
60
70
80
90
39Microwaves and Radar Institute, Wolfgang Keydel
Comparision of unsuperwised classifications over a cultural & forested region
Left: Scattering vector. Right: Scattering mechanisms (H – α)
C8 Vegetation
C1 Urban dihedral
C2 Dipole volumetric scattering
C3 Surface scattering
C4 Forestry
C5 Vegetation
C6 Rough surface & vegetation
C7 Forestry crown
40Microwaves and Radar Institute, Wolfgang Keydel
Unsupervised image classification (left), initial scene (right)
C9 C10 C11 C12 C13 C14 C15 C16
C1 C2 C3 C4 C5 C6 C7 C8 Colour composite of 3 Pauli components(k vector elements are blue, red and green)
41Microwaves and Radar Institute, Wolfgang Keydel
The Combination of Polarimetry and Interferometry
SAR InterferometrySAR Polarimetry
Sensitive to scatterersshape, orientation and dielectric properties
Allows decomposition of differentscattering processes
occurring inside the resolution cell
Established technique forterrain topography estimation
allowsLocation of scattering centers
inside the resolution cell
Polarimetric SAR Interferometry
Potential to separate in height different scattering processesoccuring inside the resolution cell.
Sensitivity to the vertical distribution of the scattering mechanisms
Allows the investigation of 3D structure of volume scatterersrecovering co-registered textural plus spatial properties simultaneously
Phase sensitivity
Central Part: Coherence
42Microwaves and Radar Institute, Wolfgang Keydel
L-Band, SIR-C, Siberian Forest, Digital Elevation Image with cuts, Two Pass and Differential POLINT