SAR Polarimetrie und Pol-SAR-Interferometrie: Theorie und ... · Short History of Radar...
Transcript of SAR Polarimetrie und Pol-SAR-Interferometrie: Theorie und ... · Short History of Radar...
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Folie [email protected] - 05.02.2007
Arbeitsgruppe Pol-InSARIrena Hajnsek, Kostas Papathanssiou, Helmut Schön, Raffael Zandona Schneider, Luca Marotti, Florian Kugler, Jayanti Sharma, Seungkuk Lee, Thomas Jagdhuber, Angelo Coscia
Microwaves and Radar InstituteGerman Aerospace Center
HH HV
VH VV
SAR Polarimetrie und Pol-SAR-Interferometrie: Theorie und Praxis in der Radarfernerkundung
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Overview of the Lecture
Part 1Short introduction into SAR
Part 2Basics and principles of SAR polarimetryMain applications of SAR polarimetry
Part 3Basics and principles of SAR interferometryDerivation of forest heights
Every part will be illustrated with examples and exercises using PolSARPro !
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SAR
Part 1:
Short introduction into SAR
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Electromagnetic Spectrum including the attenuation caused by water vapor in the atmosphere
Electromagnetic Spectrum
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Radar vs Optic‘s of Oberpfaffenhofen
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Range distance ro
object
oc (velocity of light)
Tx
Rx
transmit
t (time)
Total time delay =o
o
cr . 2
• Received echo signal (back-scattered signal of imaged object):
receive
Radar Measurement Principle
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Transmitter
Receiver
Antenna
Circulator
Data Recording
Radar Pulse
• Transmitter generates a high power pulse• Circulator or Switch - switches transmitted pulse to antenna,
returned echoes to receiver• Antenna directs transmitted pulses towards the target area• Receiver amplifies the received signal and converts to base band
• Transmitter generates a high power pulse• Circulator or Switch - switches transmitted pulse to antenna,
returned echoes to receiver• Antenna directs transmitted pulses towards the target area• Receiver amplifies the received signal and converts to base band
Basic Radar Block Diagram
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• Pulsed radar system
• Two-dimensional imaging (azimuth x slant range)
Side-Looking Imaging Geometry
yx
Swath
Azimuth
Range
z
Illuminated area
Antenna
Tx TxRx Rx
T = 1/PRF
τ
PRF = Pulse Repetition Frequency
τ• Timing of the Radar:
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• Radar reflectivity (backscattered signal) of the target as a function of position.
• radar transmits a pulse (travelling velocity is equal to velocity of light)
• some of the energy in the radar pulse is reflected back towards the radar.
This is what the radar measures.
It is known as radar backscatter σo(sigma nought or sigma zero).
What does the Radar measure ?
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E-SAR X-band Real-time Image, 3 x 3 m Resolution, 6 Looks
Single Channel Radar Image
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X-Band SAR Image of Munich
E-SAR, Test Site Munich - 1m x 2m resolution
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• Normalized radar cross-section (backscattering coefficient) is given by:
σo (dB) = 10. Log10 (energy ratio)
whereby
received energy by the sensor“energy reflected in an isotropic way”
energy ratio =
i.e. The backscattered coefficient can be a positive number if there is a focussing of backscattered energy towards the radar
orThe backscattered coefficient can be a negative number if there is a focussing of backscattered energy way from the radar (e.g. smooth surface)
What does the Radar measure ?
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Backscattering Coefficient σo
Levels of Radar backscatter Typical scenario
• Very high backscatter (above -5 dB) Man-Made objects (urban)Terrain Slopes towards radarvery rough surfaceradar looking very steep
• High backscatter (-10 dB to 0 dB) rough surfacedense vegetation (forest)
• Moderate backscatter (-20 to -10 dB) medium level of vegetationagricultural cropsmoderately rough surfaces
• Low backscatter (below -20 dB) smooth surface calm water, roadvery dry terrain (sand)
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Polarimetric
SAR
Polarimetric SAR
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Overview of the Lecture
Scattering PolarimetryWave Polarimetry
• Polarisation Ellipse
• Stoke Vector
• Jones Vector
• Polarisation State
• Scattering Matrix andMeasurements
• Backscattering Vector
• Backscattering Matrices
• Interpretation of ScatteringMechanisms
Decomposition Theorems
HistoricalIntroduction
• Pauli Matrice Decomp.
• Sphere-Diplane-HelixDecomp.
• Model Based Decomp.
• Eigenvector Decomp.
Part 2
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Part 2
Application of Polarimetric Radar Remote Sensing
• Terrain correction for quantitative surface parameter inversion
• Segmentation / Classifications (Agricultural Area, Urban Area,Sea Ice, Forestry, Oceanography)
• Modeling and Inversion of Surface Parameters
Overview of the Lecture
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Surface Roughness
Soil MoistureScattering Amplitudes
Vegetation BiomassAmplitude ratios
Surface SlopesRelative Phase Angles
Vegetation HeightPolarimetric Coherence
Tree Species
Snow Hydrology
Ice Thickness
Physical Parameters
Motivation for Radar Polarimetry in Remote Sensing
Radar Parameters
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Single Polarised versus Quad-Polarised- Adding Information
L-HH L-Band R=HH-VV G=2HV B=HH+VV
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Lexicographic Image @ C-band
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ESAR / Alling, Germany L-band
March July
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Folie 21Microwaves and Radar InstituteRed=HH-VV, Green= 2HV, Blue=HH+VV
Dresden, Germany / HH Polarisation
ESAR / L-band
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Scattering Classification Freeman/Durden & Wishart Segmentation
ESAR / L-band
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SVALEX 2005 SVALBARD - Norway Sea Ice @ L-band
Lexicographic-RGB Image @ L-band Red=HH, Green= HV, Blue=VV)
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Test Area Plaatgat (Dutch Plaatgat) 2002
10 km
Ameland
Schiermonnikoogisland
SchiermonnikoogIsland
Pauli-RGB Image @ L-band Red=HH-VV, Green= 2HV, Blue=HH+VV
Ocean Topography
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Soil
Moisture [mv]Dielectric Constant0
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Soil Moisture Estimation Results: AQUIFEREX Campaign (Tunesia) Nov. 2005
0
90
ESAR / L-band
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What does polarisation means ?
For all vector waves polarisation refers to thebehaviour in time of the wave field vectors
observed at a fixed point in space. (AZZAM & BASHARA)
Direction of Wave Propagation ---> kDirection of Wave Propagation ---> k
Elliptical Polarisation Linear Polarisation
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Short History of Radar Polarisation Part I
Before the definition of the polarisation different polarisation effects has been observed in nature:
1. The Vikings (800 b.c.) used a dichromic mineral to navigate in the absence of light, so that the diffuse light could be bundled to determine the position of light
2. The first discovery of polarised light has been made by Christian Hygens(1677) and Erasmus Bertolinus (1669) looking through a crystal doublet, where the incident light has been split into ordinary and extraordinary rays;
3. Malus (1808) could prove that polarisation is a intrinsic property and not something added by a crystal
A transition from the early discovery of polarisation to the present-day has been made by introducing the Theory of Electromagnetism. In this domain numerous names can be added – Amper, Faraday, Stokes etc.
Finally, Maxwell tied the previous work together with a consistent formulation to the laws of macroscopic electromagnetics.
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G. Sinclair (1950)
Radar Polarisation
G.A. DESCHAMPS(1952)
J.R. HUYNEN(1960)
E. M. KENNAUGH(1951)
W.M. BOERNER(1970)
Optimal polarisation for radar target detection
Geomteric presentation of the Stokes parameters -
Poincare Sphere
First Target Decomposition Theorems
Distribution of multi-polarimetry and multi-
frequency for Application
Short History of Radar Polarisation Part IIThe first use of radio and microwave frequencies started in the 1930s and advanced considerably in the second world war. The first radars typically received a signal of the same polarisation and had no full polarisation capability.
The radar target acts as a polarisation transformer and expressed the properties of a coherent target by a 2x2 scattering matrix.
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• Polarisation Ellipse
• Stokes Vector (real wave descriptor)
• Jones Vector (complex wave descriptor)
• Polarisation state in the real and complexdomain
Wave
Polarimetry
Wave Polarimetry
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Plane Waves
Wave equation: 0rEt
rE 2
2
002 =
∂∂
+ )()( rrrr μμεεωΔ
)exp()( rkiErE rrrrr ⋅=
Linear, source-free, homogeneous, isotropic media:
)()(),( trkftrkftr ωωΨ +⋅+−⋅= −+
rrrrr
Er
… complex constant amplitude vector
Real electric field vector: })trk(iexpERe{})texp()r(ERe{)t,r(E ωω −⋅=−=rrrrrr
Complex electric field vector:
Constant phase front of : Plane orthogonal to !!!),( trE rr →=⋅→ .constrk rrkr
kr
… wave vector μμεεω 00k =||r
Solutions:
Light waves are electromagentic in nature, where the electric component is used to describe the polarisation state
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Wave Polarisation
)exp( hhh iaEhE δ=⋅=rr
)exp( vvv iaEvE δ=⋅=rr
)cos()}(expRe{)}(expRe{),( hhhhhh atrkiatrkiEtrE δτδωω +=+−⋅=−⋅= rrrrr
trk ωτ −⋅= rr)cos()}(expRe{)}(expRe{),( vvvvvv atrkiatrkiEtrE δτδωω +=+−⋅=−⋅= rrrrr
Real field representation:
Complex field representation:
Plane Wave Propagating in the kr
+ direction
Right Handed Orthonormal K.S. )( hvkrrr
vh EvEhEvvEhhE rrrrrrrrr+=⋅+⋅= )()(
),(),(),( trEvtrEhtrE vhrrrrrr +=
|| vv Ea =
|| hh Ea =
Real Amplitudes
Real Amplitudes
Planewave
Phase difference
Direction Projection (length of the vector)
The definition of polarisation requires a reference coordinate system and a directionof propagation
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Polarisation Ellipse
)cos(),( hhh atrE δτ +=r
hv δδδ −=
Electric Field Vector:
and where
The field-vector moves in time along an ellipse known as the polarisation ellipse),( trE rr
General representation of a rotated ellipse !!!
)cos(),( vvv atrE δτ +=r
),(),(),( trEvtrEhtrE vhrrrrrr +=
0aaa1aa
aaa12
vh
2
2vvh
vh2h ≥=
−−
)(sin
/)/(cos)/(cos/
det δδ
δ
δδ 2
vh
vh2
v
2v
2h
2h
aatrEtrE2
atrE
atrE sin),(),(cos),(),(
=−+rrrr
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Polarisation EllipseThe shape of the polarisation ellipse describes the polarisation state of the plane wave:
Orientation angle ψ : Major Axis Inclination Angle
Ellipticity angle χ : ±=χtan Minor Ellipse AxisMajor Ellipse Axis
Polarisation AnglesDeschamps Parameters
⎟⎟⎠
⎞⎜⎜⎝
⎛=
h
v
aaa arctan
hv δδδ −=
22πψπ
≤≤−44πχπ
≤≤−Range: and
Phasedifference:
Amplitude:
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Polarisation Ellipse
Orientation angle ψ :
Ellipticity angle χ :
Horizontal Vertical Linear at θº Left Circular Right Circular
0º 90º θº -90º - 90º -90º - 90º
0º 0º 0º -45º 45º
Elliptical Circular Linear
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Wave Polarisation and Polarisation Ellipse
Direction of Wave Propagation ---> k
Elliptical Polarisation
Circular Polarisation
Linear Polarisation
Linear Polarisation
h
v
h
v
h
v
h
v
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Orthogonal Polarisation States
Horizontal and Vertical
Left Elliptical and Right Elliptical Left Circular and Right Circular
Linear at y and Linear at y + π/2
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Polarisation HandednessThe rotation sense is defined by looking into the direction of wave propagation:
Left Handed Rotation
Ellipticity angle χ < 0
Right Handed Rotation
Change of propagation direction implies a permutation of polarisation handedness !
Ellipticity angle χ > 0
Deschamps angle δ > 0 Deschamps angle δ < 0
… clockwise in propagation direction… anti-clockwise in propagation direction
IPU Convention:
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Polarisation Handedness
“…Circularly polarized waves have either a right-handed or left –handed sense, which is defined by convention. The TELSTAR satellite sent out circularly polarized microwaves. When it first passed over the Atlantic,
the British station at Goonhilly and the French station at PleumeurBodou both tried to receive its signals. The French succeeded because
their definition of polarization agreed with the American definition. The British station was set up to receive the wrong (orthogonal) polarisationbecause their definition of sense…was contrary to ‘our’ definition…”
from J R Pierce “Almost Everything about Waves”, Cambridge MA, MIT Press, 1974, pp 130-131
“…Circularly polarized waves have either a right-handed or left –handed sense, which is defined by convention. The TELSTAR satellite sent out circularly polarized microwaves. When it first passed over the Atlantic,
the British station at Goonhilly and the French station at PleumeurBodou both tried to receive its signals. The French succeeded because
their definition of polarization agreed with the American definition. The British station was set up to receive the wrong (orthogonal) polarisationbecause their definition of sense…was contrary to ‘our’ definition…”
from J R Pierce “Almost Everything about Waves”, Cambridge MA, MIT Press, 1974, pp 130-131
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Wave Description
Monochromatic Plane Waves are completely described by four parameters:
- Two parameters for the description of the polarisation state of the wave
- The wave amplitude or the wave intensity
- A initial absolute phase reference
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Stokes Vector for Monochromatic Waves
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vh
vh
2v
2h
2v
2h
3
2
1
0
R
EE2EE2EEEE
qqqq
q ∈
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡−+
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
∗
∗
}Im{}Re{||||||||
:r
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡++
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
δδ
δ
sincos
),,(
vh
vh
2v
2h
2v
2h
3
2
1
0
vh
aa2aa2
aaaa
qqqq
aaqr
23
22
21
20 qqqq ++=
3210 qqqq ,,, are wave intensities:
0q total wave intensity321 qqq ,, polarised wave intensity
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
)sin()cos()sin()cos()cos(
),,(
χχψχψ
χψ
2a22a22a
a
qqqq
aq
2
2
2
2
3
2
1
0
r
Only three from the four Stokes elements are independent:
Stokes Vector:
Wave polarisation state estimation via intensities measurements only !!!
The total wave energy is polarised
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Poincaré Sphere
23
22
21
20 qqqq ++=
North Pole: Right Circular Polarisation
South Pole: Left Circular Polarisation
Southern Hemisphere: Left Handed Polarisations
Northern Hemisphere: Right Handed Polarisations
Aquator: Linear Polarisations
321 qqq ,, : Cartesian coordinates of a point on a sphere with radius 0q
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
3
2
1
0
qqqq
q :rStokes Vector: with Equation of Sphere in R3
Poincaré Sphere:
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Jones Vector
vh EvEhEvvEhhE rrrrrrrrr+=⋅+⋅= )()(
2vv
hh
v
h Ciaia
EE
E ∈⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡=
)exp()exp(
δδr
nnmmnnmm EEEEE εεεεεε rrrrrrrrr+=⋅+⋅= )()(
⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡=
)exp()exp(
nn
mm
n
m
iaia
EE
Eδδr
vh EE , are the complex projections onto vh rr,
Jones vector:
Jones vector:
nm EE , are the complex projections onto nm εε rr ,
The description may be considered as a component representation in the 2-dim complex vector space with basis },{ vh rr
referred to the orthonormal basis},{ nm εε rr
Generalisation: Projection of onto two arbitrary orthonormal polarisation states nm εε rr ,Er
The is represented as a linear combination of two orthogonal linear polarisation h and v.Er
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Jones Vector
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡ −−=⎥
⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡=
χχ
ψψψψ
φδδ
sincos
cossinsincos
)exp()exp()exp(
iiA
iaia
EE
E 0nn
mm
n
mrJones vector:
Thus, it describes completely the shape of the polarisation ellipse, the sense of rotation of the field vector and the wave intensity. But, it contains not the information about the direction of wave propagation and so about the polarisation handedness of the wave.
The Jones vector contains four parameters in terms of 2 complex scalars:
f( Polarisation Angles )f(Deschamps Parameters)
Important: The wave is a vector function with a physical meaning independently of any reference frame. But its representation depends on the chosen reference basis.
Wave intensity:= 2n
2m EEEE |||| +=⋅+
rr
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Directional Jones Vector
)}(expRe{),( trkiEtrE ω−⋅+= ++
rrrrr)}(expRe{),( trkiEtrE ω−⋅−= −−
rrrrr
∗± = m
rrEETime reversal = Complex conjugation:
Plane Wave Propagating in the kr
− directionPlane Wave Propagating in the kr
+ direction
⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡=
)exp()exp(
vv
hh
v
h
iaia
EE
Eδδr
Jones vector: ⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡=
)exp()exp(
vv
hh
v
h
iaia
EE
Eδδr
Jones vector:
Directional Jones vector (IPU Convention):
The Jones vector is insufficient to describe the direction of wave propagation !!!
and
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Complex Polarisation Ratio
Ciaiaa
EE
mnm
n
m
n ∈=−== )exp(tan)(exp: δδδρ
)cos()cos()sin()cos()sin(),(
χψχχψχψρ
212i22
++
=⎟⎠
⎞⎜⎝
⎛−
= ∗ρρρρψ
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21 }Re{arctan)(
⎟⎠
⎞⎜⎝
⎛−
= ∗ρρρρχ
12
21 }Im{arcsin)(
2n
m CEE
E ∈⎥⎦
⎤⎢⎣
⎡=
r
Jones vector:
Complex Polarisation Ratio:
where is a linear reference basis},{ nm εε rr
Complex Space Polarisation Description Real Space Polarisation Description
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Complex Polarisation Ratio: Geometrical Interpretation
)cos()cos()sin()cos()sin()(exp:
χψχχψδδρ
212i22i
aa
EE
mnm
n
m
n
++
=−==
Right Circular Polarisation
Positive Imaginary Part: Right Handed Polarisations
Real Axis: Linear Polarisations:
Negative Imaginary Part: Left Handed Polarisations
Left Circular Polarisation
i=:ρ
i−=:ρ
1
1−
Complex Polarisation Ratio:
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Partially Polarised Waves
Polarisation ellipse varies in time
Partially polarised waves
Wave coherency matrix (Complex domain)
Polarisation can be defined only in the sense of statistical average
Generalised Stokes vector (Real domain)Partially polarised wave descriptors:
Amplitude and phase of the electric field vector become random processes
Quasi-Monochromatic waves:
wave packets of incoherent waves with different frequencies over a narrow
frequency band
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Monochromatic vs. Partially Polarised Waves
Direction of Wave Propagation --->
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Partially Polarised Waves: Coherency Matrix
⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡=
)exp()exp(
nn
mm
n
m
iaia
EE
Eδδr
Jones vector: representation in the reference basis},{ nm εε rr
⎥⎦
⎤⎢⎣
⎡><><><><
=⎥⎦
⎤⎢⎣
⎡∗∗
∗∗
nnmn
nmmm
2221
1211
EEEEEEEE
JJJJ
:→>⋅=< +EEJrr
:][Coherency Matrix:
By definition: 2x2 hermitian positive semi-definite matrix
⎥⎦
⎤⎢⎣
⎡−+−+
=⎥⎦
⎤⎢⎣
⎡
1032
3210
2221
1211
qqiqqiqqqq
JJJJ
Diagonal Elements:
Off-Diagonal Elements: cross-correlation between nm EE and
intensities of =→ ])([JTraceEE nm and Total wave intensity
Coherency Matrix=f(Stokes Vector) Stokes Vector=f(Coherency Matrix)
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡−+
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
}Im{}Re{
:
12
12
2211
2211
3
2
1
0
J2J2JJJJ
qqqq
qr
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Partially Polarised Waves: Coherency Matrix
Completely polarised wave: … i.e. maximum correlation between
Completely unpolarised wave: … i.e. absence of any polarised structure in the wave
>>=<< ∗∗nnmm EEEE
0EEEE mnnm >=>=<< ∗∗1J
1001
IJ 0 =→⎥⎦
⎤⎢⎣
⎡=→ ])det([][
Partially polarised wave: … i.e. certain degree of correlation between
Coherency Matrix:
0JEEEEEEEE mnnmnnmm =→= ∗∗∗∗ ])det([))(())((
nm EE and
nm EE and
0JEEEEEEEE
Jnnmn
nmmm >→⎥⎦
⎤⎢⎣
⎡><><><><
=∗∗
∗∗
])det([][
Degree of Polarisation:
⎟⎠
⎞⎜⎝
⎛−= 2JTrace
J41m]))([(])det([⎥
⎦
⎤⎢⎣
⎡><><><><
=∗∗
∗∗
nnmn
nmmm
EEEEEEEE
J :][
1m =DoP:
1m0 <<DoP:
0m =DoP:
Polarised Wave PowerTotal Wave Power
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Wave Description
Monochromatic Plane Waves are completely described by four parameters:
- Two parameters for the description of its polarisation state
- The wave amplitude which defines the size of the polarisation ellipse
- A initial absolute phase reference
Partially Polarised Plane Waves are completely described by five parameters:
- Two parameters for the description of the polarisation state
- The degree of polarisation
- The wave amplitude which defines the size of the polarisation ellipse
- A initial absolute phase reference
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Wave and Polarisation Descriptors
Real Domain Complex Domain
Wave Descriptor:
Polarisation State Descriptor:
Wave Descriptor:
Polarisation State Descriptor:
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
3
2
1
0
qqqq
q :rStokes Vector:
⎥⎦
⎤⎢⎣
⎡=
n
m
EE
E :r
Jones vector:
Polarisation Angles
Deschamps Parameters
m
n
EE
=:ρComplex Polarisation Ratio:
I. Monochromatic Waves:
II. Partially Polarised Waves:
Monochromatic & Partially Polarised Waves:
>⋅=< +EEJrr
:][Wave Coherency Matrix:
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Scattering Polarimetry
• SCATTERING MATRIX AND MEASUREMENTS• Backscattering Vector
• Backscattering Matrices
• Interpretation of Scattering Mechanisms
Scattering
Polarimetry
Folie 54Microwaves and Radar Institute
The Scattering Problem: Matrix Representation
Scattering in the far-zone region:
Mapping of the 2-dim incident vector into the 2-dim scattered vector
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡)()(
)()()()()exp(
)()(
rErE
rSrSrSrS
rri
rErE
iv
ih
VVVH
HVHHsv
sh
r
r
rr
rr
r
rκ
⎥⎦
⎤⎢⎣
⎡=
)()(
)(rErE
rE iv
ihi
hv r
rrr
⎥⎦
⎤⎢⎣
⎡=
)()(
)(rErE
rE sv
shs
hv r
rrr
Incident Field Scattered Field
Jones Vector: Jones Vector:
2x2 Complex Scattering Matrix
)(rEihvrr
)(rEshvrr
28
Folie 55Microwaves and Radar Institute
Coherent Scattering Matrix
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡iv
ih
VVVH
HVHHsv
sh
EE
SSSS
rri
EE )exp(κ
⎥⎦
⎤⎢⎣
⎡=
)exp(||)exp(||)exp(||)exp(||)exp(][
VVVVVHVH
HVHVHHHH
iSiSiSiS
rriS
φφφφκ
[S] is independent on the polarisation of the incident wave !!!
… also known as the Jones Matrix in the Bistatic and Sinclair Matrix in the Monostatic case
IJS
Complex Scattering Amplitudes:
=f(Frequency,Scattering Geometry)
and depends only on the physical and geometrical properties of the scatterer
⎥⎦
⎤⎢⎣
⎡−
−−=
||)(exp||)(exp||)(exp||)exp()exp(][
VVVVVHVH
VVHVHVVVHHHHVV
SiSiSiS
ririS
φφφφφφφκ
Seven Parameters: 4 Amplitudes & 3 PhasesAbsolute PhaseFactor
Total Scattered Power: 2VV
2VH
2HV
2HH SSSSSSTraceSSpanTP ||||||||)]][([])([ +++=== +
Folie 56Microwaves and Radar Institute
Bistatic Measurement of the Scattering Matrix
⎥⎦
⎤⎢⎣
⎡
VVVH
HVHH
SSSS
⎥⎦
⎤⎢⎣
⎡
VVVH
HVHH
SSSS
VVHVVHHH SSSS VVHVVHHH SSSS
29
Folie 57Microwaves and Radar Institute
Monostatic Measurement of the Scattering Matrix
⎥⎦
⎤⎢⎣
⎡
VVVH
HVHH
SSSS
⎥⎦
⎤⎢⎣
⎡
VVVH
HVHH
SSSS
VVHVVHHH SSSS VVHVVHHH SSSS
Folie 58Microwaves and Radar Institute
VH VV
HH HV
Azim
ut
Range
E-SAR / Test Site: Oberpfafenhoffen
Scattering Amplitude Images
30
Folie 59Microwaves and Radar Institute
Polarimetric Airborne SAR Sensors
AIRSARNASA / JPL (USA)
DC8P, L, C-Band (Quad)
AES1AeroSensing (D)
GulfStream CommanderX-Band (HH), P-Band (Quad)
DOSAREADS / Dornier GmbH (D)
DO 228 (1989), C160 (1998), G222 (2000)S, C, X-Band (Quad), Ka-Band (VV)
EMISARDCRS (DK)G3 Aircraft
L, C-Band (Quad)
ESARDLR (D)DO 228
P, L, S-Band (Quad)C, X-Band (Sngl)
MEMPHIS / AER II-PAMIRFGAN (D)
Transal C160Ka, W-Band (Quad) / X-Band (Quad)
PISARNASDA / CRL (J)
GulfStreamL, X-Band (Quad)
PHARUSTNO - FEL (NL)
CESSNA – Citation IIC-Band (Quad)
RAMSESONERA (F)
Transal C160P, L, S, C, X, Ku, Ka, W-Band (Quad)
STORMUVSQ / CETP (F)
Merlin IVC-Band (Quad)
RENEUVSQ / CETP (F)Écureuil AS350
S, X-Band (Quad)
SAR580CCRS (CA)
Convair CV-580C, X-Band (Quad)
Folie 60Microwaves and Radar Institute
Experimental SyntheticAperture Radar System
E-SAR
P-Band (λ 68 cm)
L-Band (λ 23 cm)
X-Band (λ 3 cm)
C-Band (λ 5 cm)
System Engineer Ralf Horn
31
Folie 61Microwaves and Radar Institute
Single polarization channel
SRTM, February 2000
Receive
Transmit
Shuttle Polarimetric SAR Interferometry
SIR-C Mission: First Ever PolarimetricInterferometry L/C-Band Quad Pol - April 1994 10 days/October 1994 10 days
*last 3 day repeat pass interferometry (1 day repeatcycle) Time baseline of 1, 2, 3 days and 6 month
X-band6 m Receive AntennaC-band8 m Receive Antenna
X-band and C-band12m Transmit and Receive Antennas
Baseline:60 m long Mast, 45 deg off nadir
Orbit height: 233 kmInclination: 57 degX-band look angle: 52 degX-band swath: 50 km
Folie 62Microwaves and Radar Institute
2300 kgWeight
25 m x 25 mResolution100 kmSwath Width
10,74 m x 2,16 m
AntennaSize~ 23°Incident
Angle
19 MHz Bandwidth~780 kmAltitude
1,275 GHzFrequencyJune 26, 1978Launch
First Civilian SAR Satellite: SEASAT (1978)
32
Folie 63Microwaves and Radar Institute
• SEASAT 1978 L-Band (1.25 GHz) HH
• ERS 1/2 1991/95 C-Band (5 GHz) VV
• ALMAZ 1 1991/92 S Band (3 GHz) HH
• JERS-1 1992 L-Band HH
• RadarSat 1995 C-Band HH
• ENVISAT (ASAR) 2002 C Band HH,VV(VH)
• ALOS (PALSAR) 2006 L-Band QuadPol
• Radarsat II 2007 C-Band QuadPol
• TerraSAR 2006 X-Band QuadPol
Satellite SAR Systems
Folie 64Microwaves and Radar Institute
SEASATNASA/JPL (USA)
L-Band, 1978
ERS-1European Space Agency (ESA)
C-Band, 1991-2000
SIR-C/X-SARNASA/JPL, L- and C-Band (quad)
DLR / ASI, X-bandApril and October 1994
J-ERS-1Japanese Space Agency (NASDA)
L-Band, 1992-1998
RadarSAT-1Canadian Space Agency (CSA)
C-Band, 1995-today
ERS-2European Space Agency (ESA)
C-Band, 1995-today
Shuttle Radar Topography Mission (SRTM)NASA/JPL (C-Band), DLR (X-Band)
February 2000
ENVISAT / ASAREuropean Space Agency (ESA)
C-Band (dual), 2002-today
ALOS / PALSARJapanese Space Agency (NASDA)
L-Band (quad), 2005
TerraSAR-XGerman Aerospace Center (DLR) / Astirum
X-Band (quad), 2006
RadarSAT-IICanadian Space Agency (CSA)
C-Band (quad), 2006
SAR-LupeBWB, GermanyX-Band, 2005
Spaceborne SAR Systems
33
Folie 65Microwaves and Radar Institute
Wavelength 0.236 m
Chirp Bandwidth 14 MHz
Peak Transmit Power 2 kW
Duty Cycle 3,5 % (7 % / 2)
Noise Figure 4 dB
Antenna Size (Tx , Rx) 8.9 m x 3.1 m
Quantisation 5 bit (BAQ)
Launch date Januar 2006Weight 4000kgSolar Power ~7Kw@EOLOrbit Sun SynchronousAltitude 691.65 kmRevolution 14+27/46Yaw steering ONInclination 98.16 degreesAttitude error 0.4e-4°
Folie 66Microwaves and Radar Institute
Frequency Frequency range Application Example
band
• VHF 300 KHz - 300 MHz Foliage/Ground penetration, biomass
• P-Band 300 MHz - 1 GHz Biomass, penetration
• L-Band 1 GHz - 2 GHz Agriculture, forestry, soil moisture
• C-Band 4 GHz - 8 GHz Ocean, agriculture
• X-Band 8 GHz - 12 GHz Agriculture, ocean, high resolution radar
• Ku-Band 14 GHz - 18 GHz Glaciology (snow cover mapping)
• Ka-Band 27 GHz - 47 GHz High resolution radars
Commonly used Frequency Bands
34
Folie 67Microwaves and Radar Institute
X-SAR/SIR-C Mission, DLR/NASA, 199
Attenuation due to Clouds and Rain Cells at X-Band
Folie 68Microwaves and Radar Institute
Frequency and Polarisation Diversity
C-bandR: HH G: HV B: VV
L-bandR: HH G: HV B: VV
P-bandR: HH G: HV B: VV
35
Folie 69Microwaves and Radar Institute
C-bandR: HH G: HV B: VV
L-bandR: HH G: HV B: VV
P-bandR: HH G: HV B: VV
Environmantal Monitoring
LARSEN B collapse observed in 2002 by ERS /Envisat
Envisat Radar monitoring Antarctica Ice and Sea-Ice extent (April-to June 2004)
Folie 70Microwaves and Radar Institute
Oil Spil Monitoring / Detection
36
Folie 71Microwaves and Radar Institute
Flooding Monitoring - German Flood Event (Summer 2002)
ASAR Alternating Polarization mode - Swath IS2 - 19 August 2002 R: |HH| G: |HV| B: |HH|-|VV|
Folie 72Microwaves and Radar Institute
Scattering Polarimetry
• Scattering Matrix and Measurements
• BACKSCATTERING VECTOR• Backscattering Matrices
• Interpretation of Scattering Mechanisms
Scattering
Polarimetry
37
Folie 73Microwaves and Radar Institute
Scattering Vector
⎥⎦
⎤⎢⎣
⎡=
VVVH
HVHH
SSSS
S][Scattering Matrix:
Scattering Vector: 4T
43214 CkkkkSTrace21SVk ∈=== ][)]([])([: Ψ
r
.])?([.V … Matrix Vectorisation Operator
Ψ … Complete Set of 2x2 Basis Matrices
Vectorial formulation of the Scattering Problem in terms of system vectors
2VV
2VH
2HV
2HH44
24 SSSSSSpankkk ||||||||])([|||| +++==⋅= +
rrrFrobenious Norm of :4k
r
2VV
2VH
2HV
2HH SSSSSSpanTP ||||||||])([ +++==Frobenious Norm of :][S
Folie 74Microwaves and Radar Institute
Ψ … any complete set of four matrices leaving the norm of invariant4kr
Lexicographic & Pauli Scattering Vectors
⎭⎬⎫
⎩⎨⎧
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡=
1000
20100
20010
20001
2L ,,,Ψ
⎭⎬⎫
⎩⎨⎧
⎥⎦
⎤⎢⎣
⎡ −⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡−⎥
⎦
⎤⎢⎣
⎡=
0ii0
20110
21001
21001
2P ,,,Ψ
TVVVHHVHH4 SSSSk ][=
r
TVHHVVHHVVVHHVVHH4 SSiSSSSSS
21k ])([ −+−+=
r
)]([])([: ΨSTrace21SVk4 ==
r
Lexicographic Scattering Vector:
Pauli Scattering Vector:
Lexicographic Matrix Set:
Pauli Matrices Set:
Scattering Vector:
Advantage: Directly related to the system measurable
Advantage: Closer related to physical properties of the scatterer
38
Folie 75Microwaves and Radar Institute
4-dim Scattering Vector Transformations
L44P4 kDkvv
][= P41
4L4 kDkvv
−= ][
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
VV
VH
HV
HH
L4
SSSS
kr
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−+−+
=
)( VHHV
VHHV
VVHH
VVHH
P4
SSiSSSSSS
21k
r
Lexicographic Scattering Vector: Pauli Scattering Vector:
Unitary Transformation:
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−
−=
0ii0011010011001
21D4][
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−
−== +−
0011i100i1000011
21DD 4
14 ][][
and
and
where is a 4x4 special unitary matrix in order to preserve the norm of : ][ 4D 4kr
Folie 76Microwaves and Radar Institute
⎥⎦
⎤⎢⎣
⎡−
−−=
||)(exp||)(exp||)(exp||)exp()exp(][
VVVVXXXX
VVXXXXVVHHHHVV
SiSiSiS
ririS
φφφφφφφκ
Five Parameters: 3 Amplitudes & 2 PhasesAbsolute PhaseFactor
BackscatteringIn the case of monostatic backscattering from reciprocal scatterers:
BSAXX
BSAVH
BSAHV SSS == )( FSA
XXFSA
VHFSAHV SSS =−=Reciprocity Theorem
→⎥⎦
⎤⎢⎣
⎡=
VVXX
XXHH
SSSS
S][
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
VV
XX
XX
HH
L4
SSSS
kr
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡−+
=
0S2
SSSS
21k
XX
VVHH
VVHH
P4
r
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
VV
XX
HH
L3
SS2
Skr
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−+
=
XX
VVHH
VVHH
P3
S2SSSS
21k
r
3-dim Lexicographic and Pauli Scattering Vectors:
Note: The factor is required to keep the vector norm of invariant L3kr
2
The scattering problem can be addressed in the 3-dim complex space:
39
Folie 77Microwaves and Radar Institute
3-dim Scattering Vector Transformations
L33P3 kDkvv
][= P31
3L3 kDkvv
−= ][
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
VV
XX
HH
L3
SSS
kr
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−+
=
XX
VVHH
VVHH
P3
S2SSSS
21k
r
Lexicographic Scattering Vector: Pauli Scattering Vector:
Unitary Transformation:
and
and
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−=020101
101
21D3][
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−==−
011200
011
21DD T
31
3 ][][
where is a 4x4 special unitary matrix in order to preserve the norm of : ][ 3D 3kr
Folie 78Microwaves and Radar Institute
Scattering Polarimetry
• Scattering Matrix and Measurements
• Backscattering Vector
• BACKSCATTERING MATRICES• Interpretation of Scattering Mechanisms
Scattering
Polarimetry
40
Folie 79Microwaves and Radar Institute
Partial ScatterersDeterministic Scatterers Partial Scatterers
Completely described by [S] Cannot be described by a single [S]
• Change the polarisation state of the wave • Change the polarisation state of the wave
• Do not change the degree of polarisation and also change the degree of polarisation
Scatterers with Space or Time VariabilityPoint Scatterers
MonochromaticIncident Wave
MonochromaticScattered Wave
Depolarisationdescribed by second order statistics
Folie 80Microwaves and Radar Institute
Covariance and Coherency Matrices in BackscatteringCovariance Matrix [C]:
>⋅=< ∗L3L33 kkC
rr:][
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
><><><><><><
><><><=
∗∗
∗∗
∗∗
2
2
2
3
||22||22
2||:][
VVHVVVHHVV
VVHVHVHHHV
VVHHHVHHHH
SSSSSSSSSS
SSSSSC
Coherency Matrix [T]:
>⋅=< +P3P33 kkT
rr:][
Pauli Scattering Vector:
[ ]TXXVVHHVVHHP3 S2SSSS2
1k −+=r
Lexicographic Scattering Vector:
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
><>−<>+<>−<>−<>+−<>+<>−+<>+<
=∗∗
∗∗
∗∗
2HVVVHHHVVVHHHV
HVVVHH2
VVHHVVHHVVHH
HVVVHHVVHHVVHH2
VVHH
3
S4SSS2SSS2SSS2SSSSSSSSS2SSSSSS
T||)()()(|)(|))(()())((|)(|
:][
TVVXXHHL4 SS2Sk ][=
r
and are by definition 3x3 hermitian positive semi-definite matrices][][ 33 TCand contain in general 9 independent parameters
41
Folie 81Microwaves and Radar Institute
Covariance vs. Coherency Matrix
[T] and [C] are unitarily similar (i.e., they have the same eigenvalues)
• [T] allows a physical interpretation of the scattering process
• Mean scatterer orientation can be more easily obtained from [T]
• [T] is diagonal for azimuthally symmetric media while [C] is not
• [T] is fundamentally related to the Mueller matrix and Stokes vector
[T] is closer related to physical / geometrical properties of the scattering process than [C]
• Polarimetric Scattering Amplitudes
• Polarimetric Phase Angles
• Polarimetric Correlations
Both contain information about:
Folie 82Microwaves and Radar Institute
Covariance 2 Coherency Matrix Transformation
( )( )
( ) ( ) ⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−+−−−+−−++−+−+++
=
45225
5233616331
5263313361
c2cc2cc2cc2cccccccccc2cccccccc
21T
**
***
***
][
( )( ) ( )
( ) ⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−−+−−−−−+−+−++++
=
2241532241
53653
2241532241
tttttt2tttttt2t2tt2
tttttt2tttt
21C
****
****
**
][
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
653
542
321
ccccccccc
C**
*][
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
653
542
321
ttttttttt
T**
*][
Covariance 2 Coherency Matrix Transformation:
Coherency 2 Covariance Matrix Transformation:
133
13LL33LL3PP DCDDkkDDkkDkkT −−++++ =⋅=⋅=⋅= ]][][[][][][][][
vvvvvv
]][[][][][][][][ 31
33PP1
33PP1
3LL DCDDkkDDkkDkkC −+−+−+ =⋅=⋅=⋅=vvvvvv
L33P3 kDkvv
][= P31
3L3 kDkvv
−= ][⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−=020101
101
21D3 ][and where
42
Folie 83Microwaves and Radar Institute
Mueller Matrix
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡−+
=
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
=
}Im{}Re{||||||||
:
sv
sh
sv
sh
2sv
2sh
2sv
2sh
s3
s2
s1
s0
s
EE2EE2EEEE
qqqq
qr
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡−+
=
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
=
}Im{}Re{||||||||
:
iv
ih
iv
ih
2iv
2ih
2iv
2ih
i3
i2
i1
i0
i
EE2EE2EEEE
qqqq
qr
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
i3
i2
i1
i0
33323130
23222120
13121110
03020100
s3
s2
s1
s0
qqqq
mmmmmmmmmmmmmmmm
qqqq
is qMq rr ][=
… also known as Stokes Matrix or Kennaugh Matrix in the Monostatic case (BSA convention)
[M] is a 4x4 real matrix
Stokes vectorfor the incident field
Stokes vectorfor the scattered field
The absolute phase of the scattering matrix is not preserved in [M] :-(
RSSSSfm VVVHHVHHij ∈= )(
Folie 84Microwaves and Radar Institute
Mueller Matrix
Ti3
i2
i1
i0
i qqqqq ][:=r
Monochromatic incident wave Monochromatic scattered wave
Monochromatic incident wave Depolarised scattered wave
[M] contains the same information as [C] or [T]: 9 independent parameters
[M] contains the same information as [S]: 5 independent parameters
[M] is symmetric for backscattering problems in the BSA convention
Ti3
i2
i1
i0
i qqqqq ][:=r
Ts3
s2
s1
s0
s qqqqq ][:=r
Ts3
s2
s1
s0
s qqqqq ][:=r
is qMq rr ][=
is qMq rr ][=
1m= 1m0 <<DoP: DoP:
1m=DoP: 1m=DoP:
Non Depolarising Scattering
Depolarising Scattering
43
Folie 85Microwaves and Radar Institute
Scatterer Descriptors
Scattering Matrix
Mueller Matrix
Coherency Matrix Covariance Matrix
Folie 86Microwaves and Radar Institute
Scattering Polarimetry
• Scattering Matrix and Measurements
• Backscattering Vector
• Backscattering Matrices
• INTERPRETATION OF SCATTERING MECHANISMS• Directly from the Scattering Matrix
• Model based
Scattering
Polarimetry
44
Folie 87Microwaves and Radar Institute
Interpretation of Scattering Mechanisms
⎥⎦
⎤⎢⎣
⎡=
VVHV
HVHH
SSSS
S][ [ ]TxxVVHHVVHHP S2SSSS2
1k −+=v
PP
kk1ev
vv =
( )( )( ) ⎥
⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−+
=⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡==
XX
VVHH
VVHH
P3
2
1
PP S2
SSSS
k21
ii
ik
k1e vv
vv
φβαφβα
φα
expsinsinexpcossin
expcos
Scattering Matrix: Scattering Vector:
Unitary Representation:
Parameterisation of in terms of five angles:ev 321 φφφβα ,,,,
Folie 88Microwaves and Radar Institute
Interpretation of Scattering Mechanisms
e00
001e vv
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−=
βΔβΔβΔβΔ
cossinsincos' e
10000
e vv
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡ −= αΔαΔ
αΔαΔcossinsincos
'
( )( )
( ) ⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡ −
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
001
10000
00
001
i000i000i
e
3
2
1
αααα
ββββ
φφ
φcossinsincos
cossinsincos
expexp
expv
Point Reduction Theorem:
Change of Scattering Mechanism:
45
Folie 89Microwaves and Radar Institute
Interpretation of Scattering Mechanisms
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
010
001
100001010
100010001
e'v
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
=⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
02121
001
1000212102121
100010001
e'v
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡ −
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−=
001
10000
00
001e αα
αα
ββββ cossin
sincos
cossinsincos'v
H-DipolScatterer
Dihedral Scatterera=90º and β=0º
a=45º and β=0º
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−+
=⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
HV
VVHH
VVHH
P S2SSSS
k21
001
e vv
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−=⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−−=
02121
001
1000212102121
100010001
e'v V-DipolScatterer
a=45º and β=180º
where
Folie 90Microwaves and Radar Institute
Scattering Processes: Fresnel Scattering
θεθθεθ
2
2
HRsincossincos
−+−−
=θεθεθεθε
2
2
VRsincossincos
−+−−
=
⎥⎦
⎤⎢⎣
⎡=
V
H
R00R
S][
Fresnel Reflection Coefficients:
Scattering Matrix:
… where e is the dielectric constant of the surface
and
HH
VV
Incidence Angle [Degree]
Am
plitu
de
ε = 20.
46
Folie 91Microwaves and Radar Institute
Scattering Processes: Bragg Scattering
θεθεθεθε
2
22
V11Rsincos
)]sin()[sin(−++−−
=
Bragg Scattering Coefficients:
Scattering Matrix:
… where ε is the dielectric constant of the surface
⎥⎦
⎤⎢⎣
⎡=
V
H
R00R
S][
θεθθεθ
2
2
HRsincossincos
−+−−
= and
VV
HH
Incidence Angle [Degree]
Am
plitu
de
ε = 20.
Folie 92Microwaves and Radar Institute
Scattering Processes: Dihedral Scattering
⎥⎦
⎤⎢⎣
⎡−
=⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡−
= ϕϕ iPTPS
STSS
PT
ST
PS
SSi eRR0
0RRR0
0RR00R
e001
1001
S][
θεθθεθ
2S
2S
SSRsincossincos
−+
−−=
θεθεθεθε
2SS
2SS
PSRsincossincos
−+
−−=
θεθθεθ
2T
2T
STRsincossincos
−+−−
=θεθεθεθε
2SS
2SS
PSRsincossincos
−+
−−=
Fresnel Coefficients:
Scattering Matrix:
and
and
HH
VV
Incidence Angle [Degree]
Am
plitu
de
ε = 20.
47
Folie 93Microwaves and Radar Institute
→⎥⎦
⎤⎢⎣
⎡=
dbba
S][⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−+
=c2baba
21k
v
[ ]⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−=
10000
R3 αααα
α cossinsincos
:)(
kRRRk 333
vv)]([)]([)]([),,( γβαγβα =
[ ]⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡ −=
ββ
βββ
cossin
sincos:)(
001
0R3 [ ]
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−=
10000
R3 γγγγ
γ cossinsincos
:)(
Scattering Processes: Volume Scattering
πα 20 ≤≤
πβ ≤≤0
πγ 20 ≤≤
Rotation about x-axisRotation about y-axisRotation about z-axis
),,(),,(][ γβαγβα +⋅= kkTvv
Coherency Matrix:
Folie 94Microwaves and Radar Institute
Scattering Processes: Volume Scattering
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
z
y
x
000000
ρρ
ρΡ ][
11L4V
rii ))/(( −+=
επρ
∫∞
+++=
0
23z
23y
23x
zyxi ds
2ls2ls2ls2
8lllL /// )/()/()/(
/)(
zyxzyx l
1l1
l1LLL :::: =
1m
2m11L11LA
r
r
ry
rxP ++
+=
+−+−
=εε
εε
)()(:
ll
LLm
x
y
y
x ==:
1LLL zyx =++
2l
2l
2l
43V zyxπ=where is the particle volume and
with
Principal Polarisability Matrix:
Particle Anisotropy: Particle Shape Ratio:
∞≤≤m0
1m<
1m> oblate spheroids
prolate spheroids
48
Folie 95Microwaves and Radar Institute
Scattering Processes: Volume Scattering
T3
T3
T3333 RRRPRRRP )]([)]([)]([][)]([)]([)]([),,]([ αβγγβαγβα =
∫∫∫=α β γ
γβαγβαγβα dddpppPT )()()(),,]([][
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
b000b0001
aT][)(
)(2PP
2P
A7A6221Ab++
−= 50b0 .≤≤
Special Case:Random Volume
p(α )
-π π
p(γ )
-π π
p(β )
-π / 2 π / 2
where
Coherency Matrix:
where )(),(),( γβα ppp are the pdf’s for the corresponding angle distributions
Folie 96Microwaves and Radar Institute
Scattering Processes: Volume Scattering
A=0.01
A=0.20
A=0.40
A=0.60
A=0.80
A=1.00
H/a Loci for varying particle
shape and width of distribution
Prolate Particles
oriented volume random volume
dipole
sphere
49
Microwaves and Radar Institute
[S]
COHERENTDECOMPOSITION
E. KROGAGER(1990)
W.L. CAMERON(1990)
[K]
[T] [C]
TARGETDICHOTOMY
EIGENVECTORS BASEDDECOMPOSITION
MODEL BASEDDECOMPOSITION
EIGENVECTORS / EIGENVALUES ANALYSIS&
MODEL BASED DECOMPOSITION
EIGENVECTORS / EIGENVALUES ANALYSISENTROPY / ANISOTROPY
S.R. CLOUDE - E. POTTIER(1996-1997)
A.J. FREEMAN(1992)
W.A. HOLM(1988)
S.R. CLOUDE(1985)
J.J. VAN ZYL(1992)
AZIMUTHAL SYMMETRY
J.R. HUYNEN(1970)
R.M. BARNES(1988)
Decomposition Theorems
Folie 98Microwaves and Radar Institute
Decomposition Theorems
Decomposition
Theorems• PAULI MATRICES DECOMP.
• Sphere-Diplane-Helix Decomp.
• Model Based Decomp.
• Eigenvector Decomp.
50
Folie 99Microwaves and Radar Institute
Pauli Matrices Decomposition
⎥⎦
⎤⎢⎣
⎡ −+⎥
⎦
⎤⎢⎣
⎡+⎥
⎦
⎤⎢⎣
⎡−
+⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡−+−+
=⎥⎦
⎤⎢⎣
⎡=
0ii0
d0110
c1001
b1001
abaidcidcba
SSSS
SVVVH
HVHH][
⎥⎦
⎤⎢⎣
⎡=
1001
aSa][
⎥⎦
⎤⎢⎣
⎡−
=1001
bSb][
⎥⎦
⎤⎢⎣
⎡=
0110
cSc][
⎥⎦
⎤⎢⎣
⎡ −=
0ii0
dSd ][
Single Scattering:
Dihedral Scattering ( … rotated by π/2 about the LOS )
Dihedral Scattering:
Transforms all polarisation states into their orthogonal states (disappears in backscattering)
VVHH SS =
VVHH SS −=
Folie 100Microwaves and Radar Institute
Azi
mut
h
Range
Scattering Amplitude Images
HH
C-band
SIR-C / Test Site: Kudara,Russia
VV HV
51
Folie 101Microwaves and Radar Institute
Scattering Amplitude Images
HH
L-bandSIR-C / Test Site: Kudara,Russia
VV HV
Azi
mut
h
Range
Folie 102Microwaves and Radar Institute
Pauli Images
C-band L-band
SIR-C / Test Site: Kudara,Russia
HH+VV
HH-VV
2HV
RGB-Coding:
52
Folie 103Microwaves and Radar Institute
Decomposition Theorems
Decomposition
Theorems• Pauli Matrice Decomp.
• SPHERE-DIPLANE-HELIX DECOMP.
• Model Based Decomp.
• Eigenvector Decomp.
Folie 104Microwaves and Radar Institute
Sphere-Diplane-Helix Decomposition
⎥⎦
⎤⎢⎣
⎡=
1001
SS ][Single Scattering:
Helix Scattering :
Dihedral Scattering: ⎥⎦
⎤⎢⎣
⎡=
)2cos(-)2sin()2sin()2cos(
][θθθθ
DS
⎥⎦
⎤⎢⎣
⎡−
=1i
i1SH ε
ε][
|| aAS =
|}Im{||| cb2AH ′=
VVHH
HVHVVVHHVVHH SS
SbccScSSbSSa
−==′=−=+=where:
22D cc1bA |}Re{||)}Im{|(|| ′+′−=
( ){ }][][)exp(][)exp(][ HHDDRSSVVVH
HVHH SASAiSAibac
cbaSSSS
S ++=⎥⎦
⎤⎢⎣
⎡−
+=⎥
⎦
⎤⎢⎣
⎡= φφ
53
Folie 105Microwaves and Radar Institute
Sphere-Diplane-Helix Images
C-band L-band
SIR-C / Test Site: Kudara,Russia
Sphere
DiplaneHelix
RGB-Coding:
Folie 106Microwaves and Radar Institute
Decomposition Theorems
Decomposition
Theorems
• Pauli Matrice Decomp.
• Sphere-Diplane-Helix Decomp.
• Model Based Decomp.
• EIGENVECTOR DECOMP.
54
Folie 107Microwaves and Radar Institute
Eigenvector Decomposition
Dr. Shane R. CloudeAEL Consultants
Prof. Dr. Eric PottierUniversity of Rennes 1
Cloude S R "Uniqueness of Target Decomposition Theorems in Radar Polarimetry", in Direct and Inverse Methods in Radar Polarimetry, Part 1, NATO-ARW, Eds. W.M. Boerner et al, KluwerAcademic Publishers, ISBN 0-7923-1498-0, pp 267-296, 1992
Cloude S R , E. Pottier, "A Review of Target Decomposition Theorems in Radar Polarimetry", IEEE Transactions on Geoscienceand Remote Sensing, Vol. 34 No. 2 March 1996, pp 498-518
Folie 108Microwaves and Radar Institute
Eigenvector Decomposition
Coherence Matrix: >⋅=< +P3P33 kkT
rr:][
Diagonalisation: 1333 UUT −= ]][][[][ Λ
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
333231
232221
131211
3][eeeeeeeee
U⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=Λ
3
2
1
000000
][λ
λλ
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡==
∗∗∗
∗∗∗
∗∗∗
+−
332313
322212
312111
31
3 ][][eeeeeeeee
UU
][][][)()()()(][ 33
23
13333222111
3
1iiii3 TTTeeeeeeeeT ++=⋅+⋅+⋅=⋅= +++
=
+∑ rrrrrrrr λλλλ
0321 ≥≥≥ λλλ⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
33
23
13
3
32
22
12
2
31
21
11
1
eee
eeee
eeee
e rrr
where:
3 real positive eigenvalues 3 orthonormal eigenvectors
][][][ 321 SSS
55
Folie 109Microwaves and Radar Institute
Scattering Entropy / AnisotropyCoherency Matrix Diagonalisation:
][][][)()()()(][ 33
23
13333222111
3
1iiii3 TTTeeeeeeeeT ++=⋅+⋅+⋅=⋅= +++
=
+∑ rrrrrrrr λλλλ
32
32
32
32
PPPPA
+−
=+−
=λλλλ:
321
iiP
λλλλ++
=:i3
3
1ii PPH log: ∑
=
= with:Scattering Entropy:
Scattering Anisotropy:
Totally Polarised Scatterer
Totally Unpolarised Scatterer
→= 0H
→= 1H1H0 ≤≤ where:
→= 0A
→= 1A1A0 ≤≤
2 Equal Secondary Scattering Processes
Only 1 Secondary Scattering Processwhere:
Folie 110Microwaves and Radar Institute
Scattering Entropy Images
C-band L-band
H=0
H=1
SIR-C / Test Site: Kudara,Russia
56
Folie 111Microwaves and Radar Institute
Scattering Anisotropy ImagesSIR-C / Test Site: Kudara,Russia
C-band L-band
A=0
A=1
Folie 112Microwaves and Radar Institute
Eigenvector Decomposition: Scattering Mechanisms
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
|||
|||][ 3213 eeeU rrr
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
)exp()sin()sin()exp()sin()sin()exp()sin()sin()exp()cos()sin()exp()cos()sin()exp()cos()sin(
)exp()cos()exp()cos()exp()cos(][
333222111
333222111
332211
3
iiiiii
iiiU
εβαεβαεβαδβαδβαδβα
γαγαγα
][][][)()()(][][][][ 33
23
13333222111
1333 TTTeeeeeeUUT ++=⋅+⋅+⋅== +++− rrrrrr λλλΛ
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
)exp()sin()sin()exp()cos()sin(
)exp()cos(
εβαδβα
γα
ii
ier
1st Scattering Mechanism
2nd Scattering Mechanism
3rd Scattering Mechanism
57
Folie 113Microwaves and Radar Institute
Mean Scattering Parameters
Coherency Matrix Diagonalisation:
321
iiP
λλλλ++
=:
Mean α-Angle:
Mean β-Angle:
Mean γ-Angle:
Mean δ-Angle:
332211 PPP αααα ++=
332211 PPP ββββ ++=
332211 PPP γγγγ ++=
332211 PPP δδδδ ++=
)()()(][ +++ ⋅+⋅+⋅= 3332221113 eeeeeeT rrrrrr λλλ
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
)exp()sin()sin()exp()cos()sin(
)exp()cos(
εβαδβα
γα
ii
ier
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
)exp()sin()sin()exp()cos()sin(
)exp()cos(
iii
iii
ii
i
ii
ie
εβαδβα
γαr
Eigenvectors: Appearance Probabilities:
Mean Scattering Mechanism
Mean ε-Angle: 332211 PPP εεεε ++=
Folie 114Microwaves and Radar Institute
α-Angle Images
C-band L-band
a=0°
a=90°
a=45°
SIR-C / Test Site: Kudara,Russia
58
Folie 115Microwaves and Radar Institute
Alpha Parameter for Surface Scattering
Range of a with moisture content
Folie 116Microwaves and Radar Institute
ALOS-PalSAR: Quad-Pol @ 23.5° / Test Site: ALPSRP022952640 ALPSRP029662640
30.06.2006 15.08.2006
SNR
HHVV Phase
HHVV Phase
SNR
59
Folie 117Microwaves and Radar Institute
Decomposition Theorems
Decomposition
Theorems
• Pauli Matrice Decomp.
• Sphere-Diplane-Helix Decomp.
• Eigenvector Decomp.
• MODEL BASED DECOMP.
Microwaves and Radar Institute
Target Decomposition for Targets with Reflection Symmetry
JACOB J. VAN ZYL (1992)
ANTHONY FREEMAN (1992)
Model Based Decomposition
MODEL BASED DECOMPOSITION
EIGENVECTOR / MODEL BASEDDECOMPOSITION
60
Folie 119Microwaves and Radar Institute
Freeman Decomposition I.
][][][][ VDS TTTT ++=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
000010
fT
2
SS βββ
][⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−
−=
000010
fT
2
DD ααα
][⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
100010002
fT VV ][
Vegetation Scattering : Bragg-Scattering + Dihedral Scattering + Random Volume of Dipols
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡++−
−++=
V
VDSDS
DSV2
D2
S
f000ffffßf0fßff2fßf
T ααα
][4 Equations
for 5 Unknowns
where and
Re(HHVV)-fv/3 > 0 Single bounce is dominant alpha =1
Re(HHVV)-fv/3 < 0 Double bounce is dominant beta =1
Folie 120Microwaves and Radar Institute
Freeman Decomposition II.
][][][ / VDS TTT +=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−=
θθθθβ
ββ
θθθθ
220220
001
000010
220220
001fT
2
SDS
cossinsincos
cossinsincos][ /
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
m000m0001
fT VV ][
Oriented Bragg or Dihedral Scattering + Random Volume of Spheroids
5 Equations for 5 Unknowns
m - shape of particles in cloud (m = 0 spheres, m = 0.5 dipoles)
θ - ground azimuth slope
β -ground scattering amplitude(single or double bounce)
and
61
Folie 121Microwaves and Radar Institute
|HH-VV|, |HV|, |HH+VV| Freeman/Durden, PD, PV, PS
Freeman Decomposition
Folie 122Microwaves and Radar Institute
Modified three component model – adding the HELIX
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡±=10
10000
21][
jjT Helix
m
Reflection symmetry is not anymore assumed, as for the Freeman three component model
Y. Yamaguchi, et al., “Four-component scattering model for polariemtric SAR image decomposition,”IEEE TGRS, vol.43, no. 8, 2005
Four Component Model Based Decomposition
62
Folie 123Microwaves and Radar Institute
Pauli Vector, |HH-VV|, |HV|, |HH+VV|
POLARIMETRIC SIGNATURE
RAN
GE
FLIGHT
A MANMADE STRUCTURE - AN EXAMPLE
EMISAR C-Band Polarimetric SAR Image of Store Belt BridgeLee, J.-S.; Krogager, E.; Ainsworth, T.L.; Boerner, W.-M. ,‘Polarimetric Analysis of Radar Signature of a Manmade Structure ‘
IEEE, TGARS Letters, vol.3, issue 4, pp. 555- 559
Folie 124Microwaves and Radar Institute
Denmark Storebelt Bridge Signature
|HH|Flight Direction
|HV|
|VV|
63
Folie 125Microwaves and Radar Institute
1 32
d
Single Double
Triple
Double
Roundtrip distances:Single bounce return: Double bounce return: Triple bounce return:
θ is the local incidence angle.
)cos(2 θ− dL2L
)cos(2 θ+ dL
L
Independent of height
Multi Bounce Scattering
Folie 126Microwaves and Radar Institute
High-resolution POLSAR signature of a suspension bridge under construction - the deck was not installed.
Pauli Decomposition, |HH-VV|, |HV|, |HH+VV|
Aerial Photo Krogager SDH DecompositionBlue= Sphere Green = Helix Red = Diplane.
RAN
GE
FLIGHT
Polarimatric Target Decomposition
EMISAR C-Band Polarimetric SAR Image of StoreBelt Bridge
64
Folie 127Microwaves and Radar Institute
Bridge under construction - deck not installed
Aerial Photo Dominant scat. mech. are extracted by applying decomp.:Blue= Surface Green = Dipole Red = Double Bounce.
Cloude and Pottier Decomposition
Direct bounce from cables
Triple bounce from cables
Double bounce from cables
Entropy
Alpha(Rotational invariant)
EMISAR C-Band Polarimetric SAR Image of StoreBelt Bridge
Folie 128Microwaves and Radar Institute
|HH+VV|
|HH-VV|
|HV|
After Completion of Bridge Construction
Denmark Storebelt Bridge Signature
EMISAR C-Band Polarimetric SAR Image of StoreBelt Bridge
65
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|HV||HH-VV||HH+VV|
RAN
GE
FLIGHT
Polarimetric Target Decompisition – AFTER COMPLETION
SDH
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Entropy
Dominant scat. mech. are extracted by applying decomp: Blue= SurfaceGreen = DipoleRed = Double Bounce
Cloude & Pottier Decomposition – AFTER COMPLETION
Angle α
66
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Bridge & Buoy Radar Signatures
Polarimetric SAR Image ( |HH-VV|, |HV|, |HH+VV| )
Navigation Map of Storebelt, Denmark
(EMISAR C- Band)
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·Agriculture/Land-UseCrop Classification/Moisture Content EstimationUrban Area mappingUrban Topography for Mobile comms
·ForestryBiomass Estimation: (Saturates For High Biomass)
C-band saturation at 50 tons/hectareL-band saturation at 100 tons/hectareP band saturation at 200 tons/hectare
DeforestationForest Canopy Height EstimationTree Species DiscriminationForest Re-growth Monitoring
·GeologyPlayas :Smooth Natural Surfaces(rms = 1cm)Alluvial fans, Sand Dunes, MorainesSedimentary Rock formationsLava Flows (extreme in surface roughness)Weathering Erosion StudiesSurface Roughness Estimates
·HydrologyFlood mapping/Forest InundationSnow HydrologySoil Moisture
·Sea Ice/OceanographyIce Roughness/Thickness StudiesPolar Ice Cap StudiesExtra-Terrestrial Ice/Water Studies
·MeteorologyRain rate estimationWater/Ice particle studies
Severe Storm/Flood warning
·Topography/CartographyDirect Surface Slope EstimationAccurate DEM GenerationDifference of DEMS for Vegetation mapping
·Humanitarian DeminingSurface Penetrating Radar (SPR)SAR for Mine Field Detection
Applications of Radar Polarimetry
67
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Part II
Application of Polarimetric Radar Remote Sensing
• Terrain correction for quantitative surface parameter inversion
• Segmentation / Classifications (Agricultural Area, Urban Area,Sea Ice, Forestry, Oceanography)
• Modeling and Inversion of Surface Parameters
Overview of the Lecture
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Zeulenroda L-band fully polarimetric
Zeulenroda X-Band DEM
68
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Orientation Angle EstimationLee, J.-S., Schuler, D. L. & Ainsworth, T. L, » Polarimetric SAR Data Compensation for Terrain AzimuthSlope Variation » , IEEE Transactions on Geoscience and Remote Sensing, 1999
Q = orientation angle f = radar look angleN = tilted surface normal tan w, tan g = azimuthal/range slopex and y = horizontal plane V and H = polarisation plane
Using Circular Polarisation Method
[ ]⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=⋅= +
333231
232221
131211
33
TTTTTTTTT
kkTvv
⎪⎩
⎪⎨
⎧
≥+=
≤=+=
42
44 πθπθθ
πθθθπφθfor
for
{ }⎟⎟⎠
⎞⎜⎜⎝
⎛−
=2233
232arctan
TTTRE
φ
Coherencymatrix:
Orientation angle:
Where angle f is:
N
z
y
x
f
QH
V Radar-basis
Scattering-basis
( )φφγ
ωsincostan
tantan+
−=Θ
Folie 136Microwaves and Radar Institute
Zeulenroda Orientation Angle from the X-band DEM
Zeulenroda Orientation Angle from the polarimetric L-band
69
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SAR L-band, VV-pol Image
Ocean Internal Wave Detection - Orientation Angle (New York Bight Dataset)
Orientation Angle Image
AIRSAR Data: CM3474, 07/16/92Azimuth Direction
Ran
ge D
irect
ion
IW INDUCED CHANGES
NEWMETHOD
Courtesy of Dale Schuler
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Dihedrals
Oberpfaffenhofen Dihedral ExperimentOrientation difference:Position: 5.0°Measured: 4.03°
Orientation
Line of SightRotation
70
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Segmentation
/
Classification
Segmentation/ Unsupervised Classification
• H/a/A Unsupervised Classification
• Wishard Classifiction
• Freeman-Durden Classification
• L-band and X-band Classification
Prof. Eric Pottier - University of Rennes 1
Dr. Jong-Sen Lee – Naval Research Laboratory
Folie 140Microwaves and Radar Institute
POL-SAR PROCESSINGPHENOMENOLOGIC
QUALITATIVE ANALYSIS
BASIC THEORY
SPECKLE FILTERING
POLARIMETRICTARGET
DECOMPOSITION
POLARIMETRICCLASSIFICATIONMONO/DUAL FREQUENCY
ScatteringMatrix
Unsupervised Classification
(Preserving Scattering Mechanisms)
71
Microwaves and Radar Institute
0.5 1.00 0 45° 90°
ENTROPY (H) ALPHA ( α )
H / A / α DECOMPOSITION
2 0A B B0 + B B0 −
WEIHERBACHTALL-band 1998 ANISOTROPY (A)
0.5 1.0 0
Microwaves and Radar Institute
10n
0
1
2H
0.5 1.00
α
0
45° 90°
POLSAR DATA DISTRIBUTION
IN THEH / α PLANE
Alp
ha (
α)
0 0.2 0.4 0.6 0.8 10
102030405060708090
Entropy (H)
H / A / α DECOMPOSITION
72
Microwaves and Radar Institute
Alp
ha (
α)
0 0.2 0.4 0.6 0.8 10
102030405060708090
Entropy (H)
C1
C2
C3
C4
C5
C6
C7
C8
Alp
ha (
α)
0 0.2 0.4 0.6 0.8 10
102030405060708090
Entropy (H)
H / A / α DECOMPOSITION 10
n
00.20.40.60.8
11.21.41.61.82
LOW H MEDIUM H HIGH H
SURFACESCATTERING
VOLUMESCATTERING
MULTIPLESCATTERING
Microwaves and Radar Institute
H /α CLASSIFICATION
C1 C2 C3 C4 C5 C6 C7 C8
H / α Classification SpaceSub-divised into 9 basic zones
Location of the boundariesis arbitrary and generically
Degree of arbitrariness on thesetting of these boundaries
Segmentation is offered merelyto illustrate the unsupervisedclassification strategy and to emphasize the geometrical
segmentation of physical scatteringprocesses
73
Microwaves and Radar Institute
1994 LEE et al. PROPOSED A SUPERVISEDALGORITHM BASED ON THE COMPLEXWISHART DISTRIBUTION FOR THECOMPLEX COVARIANCE / COHERENCY MATRIX.
1998 LEE et al. DEVELOPED A COMBINED UNSUPERVISEDCLASSIFICATION METHOD THAT USES THE H / a PLANEWHICH INITIALLY CLASSIFIES THE POLSAR IMAGE. THISSEGMENTED IMAGE IS THEN USED AS TRAINING SETS FORTHE INITIALIZATION OF THE SUPERVISED WISHARTCLASSIFIER.
1999 INTRODUCTION OF THE ANISOTROPY (E. POTTIER - J.S.LEE)IMPROVEMENT OF THE CAPABILITY TO DISTINGUISHBETWEEN DIFFERENT CLASSES WHOS CENTERS END INTHE SAME ENTROPY (H) AND ALPHA (α) ZONE.
WISHART CLASSIFIER
Dr J.S. LEEN.R. L US -NAVY
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PROVIDE INITIAL [Tm](0)
FOR EACH CLASS
[ ]( ) [ ]∑=
=
=mNk
1kk
m
0m T
N1T
Cluster Center of the class m(Lee 1998)
CLASSIFY THE WHOLE IMAGEWITH THE DISTANCE PROCEDURE
[ ] [ ] [ ]( ) [ ]( ) mjTdTdifTT jmm ≠∀<∈
COMPUTE [Tm](k+1) FOR EACH CLASSUSING THE CLASSIFIED PIXELS OF STEP 2
[ ]( ) [ ]∑=
=
+ =mNj
jj
m
km T
NT
1
1 1
TERMINAISONCRITERION ?
Alp
ha (
α)
0 0.2 0.4 0.6 0.8 10
102030405060708090
Entropy (H)
H / α WISHART Segmentation
74
Microwaves and Radar Institute
During the classification,the clustercenters can move out their zones
or several clusters may end in the same zone
Identification of the terrain typemay cause some confusion due to
the color scheme
The combined Wishart classifier isextended and complemented with the
introduction of the Anisotropy (A)
H/α - WISHART CLASSIFIER
C1 C2 C3 C4 C5 C6 C7 C8
Microwaves and Radar Institute
Alp
ha (
α)
0
30
60
90
0 0
0.50.5
11
Entropy (H) Anisotropy (A)
POLSAR DATA DISTRIBUTIONIN THE
H / A / α CLASSIFICATION SPACE
75
Microwaves and Radar Institute
Alp
ha (
α)
0 0.2 0.4 0.6 0.8 10
102030405060708090
Entropy (H)
Alp
ha (
a)
0 0.2 0.4 0.6 0.8 10
102030405060708090
Entropy (H)
Alp
ha (
α)
0 0.2 0.4 0.6 0.8 10
102030405060708090
Entropy (H)
A > 0.5l2 >> l3
THE 2 COMPLEMENTED H / α PLANES10
n
0
2
3
1
10n
0
2
3
1
10n
0
2
3
1
1 SCATTERINGMECHANISM
3 SCATTERINGMECHANISMS
2 SCATTERING MECHANISMS(1+e) (e+e)
A < 0.5l2 == l3
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2 Successive k - mean Classification procedures
21>A
8 Training sets
16 New Training sets
Introduction of the Anisotropy (A)information once the first classification
procedure has met its termination criterion
21<A 2
1>A
H/A/α - WISHART CLASSIFIER
76
Microwaves and Radar Institute
C1 C2 C3 C4 C5 C6 C7 C8
C9 C10 C11 C12 C13 C14 C15 C16
4th ITERATION
H/A/α - WISHART CLASSIFIER
2 0A B B0 + B B0 −
WEIHERBACHTAL DLR - ESAR
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Unsupervised Classification Preserving Scattering Mechanisms
Polarimetric SAR (POLSAR) classificationComplex Wishart distribution (Lee et al., 1994)Wishart + Entropy/Alpha (Lee et al., 1999)Wishart + Entropy/Alpha/Anisotropy (Pottier and Lee, 2000)Deficiency: Wishart classifier is a statistic operator. Pixels in a class can be mixed in scattering mechanisms
A new approachPreserving scattering property of each pixel based on Freeman and Durden decomposition:
Double bounceSurfaceVolume (Canopy)
Better stability in convergenceAutomated color rendering
Dr J.S. LEEN.R. L US -NAVY
77
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Classification Based onFreeman and Durden Decomposition
Freeman and S.L. Durden, “A Three-Component Scattering Model for Polarimetric SAR Data”
IEEE TGRS, vol. 36, no. 3, May 1998
|HH-VV|, |HV|, |HH+VV| Freeman and Durden
Volume(Canopy)
Double-Bounce
RoughSurfaceSurface
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Freeman/Durden + Wishart
The proposed algorithm• Divide the image by Freeman/Durden decomposition into
three categories based on the• Merge clusters within each category by the Wishart between-
class-distance
• To preserve polarimetric scattering properties, • Double bounce
• Surface
• Volume (Canopy)
• Automatic color rendering by scattering characteristics
),,( SVD PPP
78
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• Initial ClusteringFiltering POLSAR Image (lee et al., 1999), if needed.1. Decompose each pixel by Freeman and Durden decomposition into one of
three categories by its dominant scattering mechanism D // V / S3. Divide pixels in each category into 30 groups (initial clusters) with equal
number of pixels.Cluster Merging4. Merge initial clusters within each category by the Wishart between-class-
distance (Lee et al., 1999)5. Merge small cluster first, and limit the size of each cluster by
M= total Number of Pixels and N is the desired number of clustersWishart Classification6. Compute averaged covariance matrices (class centers).7. Within each category, apply the Wishart classification for 2 to 4 iterations for
scattering mechanism preservation.• Automated Color Rendering
8. Assign color for each final class according to its category (D/V/S) 9. Within each category, color intensity of a class is proportional to its averaged
power.
Implementation
dNMN /2max =
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Procedure – Flow Chart PolSARCovariance
FREEMAN DECOM.
Pixels inSURFACECategory
Pixels inVOLUMECategory
Pixels inD. BounceCategory
Classify into Five Classes
Select pixels within 9x9
window
Apply Adaptive Speckle filtering
Classify into Five Classes
Select pixels within 9x9
window
Apply Adaptive Speckle filtering
Classify into Five Classes
Select pixels within 9x9
window
Apply Adaptive Speckle filtering
Unsupervised
Classification
Filtering
Pixels inMIXED
Category
Classify into Five Classes
Select pixels within 9x9
window
Apply Adaptive Speckle filtering
Alternatively
CPPPPPPMax
SVDBSVDB ≤
++),,(
79
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DLR E-SAR L-Band Data
Freeman/Durden Decomposition Classification Map
Experimental Results – Oberphaffenhofen
Image size : 1536 x 1280PolSAR Speckle Filtering Applied
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DLR E-SAR L-Band Data
Freeman Decomposition Classification Map
Experimental Results – Oberphaffenhofen
80
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X-Band PI-SAR Classification - Tsukuba
Unsupervised Classification H/α + Wishart (8 classes)
H/α/A + Wishart (16 classes)
|HH-VV| |HV| |HH+VV|
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X-Band PI-SAR ClassificationScattering Preserving Classification
Classification map – Original 4-look Classification map - speckle filtered (0.5)
81
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L-Band PI-SAR ClassificationScattering Preserving Classification
Freeman/Durden Decomposition Classification map – Original data (5 - look)
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Conclusion – Unsupervised Classification
PolSAR has great capability in terrain and land-use classification.For accurate classification, data correction are required:
CalibrationLook angle variationsOrientation angle variations – Azimuth slope
Incorporates interferometry (Pol-InSAR)
82
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flight
N look
sea ice 1sea ice 2sea ice 3sea ice 4
water 1water 2water 3
land 1land 2land 3land 4
Colour code (5 null classes)
Sea Ice Classification
Labrador Sea (west coast of Newfoundland)
HH
HV
HH
VV
SIR-C/X
L-band Data
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SURFACE PARAMETERS
Parameter inversion models:
I. Theoretical Models
II. Semi-/Empirical Extensions
III. Model Based Extensions
Modelling
and Inversion
Modelling and Inversion
83
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VOLUMETRIC MOISTURE CONTENT
mv [vol. %]
Surface Parameters Description
ModelTopp et al. (1980)
Dielectric Constant e
"' εεεε jr −==
SURFACE ROUGHNESS
rms - height s [cm]
autocorrelation length l [cm]
Wavenumber k =2p/λks
X =4.00C =2.26 L =0.54 P =0.18
X =3, C =6, L =23, P =68Wavelength λ [cm]
klX =16.10C =9.03L =2.17P =0.74
Material Properties Geometric Properties
RAD
AR M
easu
rem
ents
Nat
ural
Sur
face
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Models for the Estimation of Surface ParametersModeling and Inversion
EMPIRICALEXTENSIONS
THEORETICALMODELS
Geometrical-Optic 1963
Physical-Optic 1963
Oh et all. 1992
Dubois et all. 1995Integral Equation 1992
Shi et all. 1997
Ex-Bragg 1999
MODEL BASEDEXTENSIONS
SCATTERING DECOMPOSITION
APPROACHES
Eigen-DecompositionFreeman-Decomposition
Small Perturbation 1988
84
Folie 167Microwaves and Radar Institute
Small Perturbation Model
[ ] ( )( )
,00,
⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡=
rP
rS
VVVH
HVHH
RR
SSSS
Sεθ
εθ
22
22
)sincos(
))sin1()(sin1(
θεθε
θεθε
−+
+−−=
rr
rrPR
θεθ
θεθ2
2
sincos
sincos
−+
−−=
r
rSR
Bragg Scattering Matrix:
Ideal Surface
p
s
VV
HH
RR
SS
= is independent of roughness
Exact solution of Maxwell equation for s reaching 0
ZRkjSZRkjS
PVV
SHH
⋅⋅=⋅⋅=
θθ
cos2cos2 Z = F.T.(E(x, y))
q = Incidence angle
k = 2π/λ
60 degree
25 degree
Folie 168Microwaves and Radar Institute
Small Perturbation Model (Bragg-Model)
Measured versus estimated volumetric moisture content mv [vol. %] using SPM
0
0.2
0.4
0.6
0.8
1
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0m v [vol %]
ks
elbe0-4elbe4-8weih0-4weih4-8
Validity range of the SPM for the ground measurements - surface roughness against
volumetric soil moisture
SPM
0
10
20
30
40
0 10 20 30 40measured m v [vol. %]
estim
ated
mv
[vol
. %]
Weiherbach 0-4 cmWeiherbach 4-8 cmElbe 0-4 cmElbe 4-8 cm
85
Folie 169Microwaves and Radar Institute
Models for the Estimation of Surface ParametersModeling and Inversion
EMPIRICALEXTENSIONS
THEORETICALMODELS
Geometrical-Optic 1963
Physical-Optic 1963
Oh et all. 1992
Dubois et all. 1995Integral Equation 1992
Shi et all. 1997
Ex-Bragg 1999
MODEL BASEDEXTENSIONS
SCATTERING DECOMPOSITION
APPROACHES
Eigen-DecompositionFreeman-Decomposition
Small Perturbation 1988
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( )⎪⎩
⎪⎨⎧ ≤=
otherwise021
11ββββP
20 1
πβ ≤≤
Rotation SymmetricRoughness Term
Ideal Bragg Surface
Real Surface
zero cross-polarisation
and zerodepolarisation
non-zerocross-
polarisation
and non-zerodepolarisation
β
−β1
P(β)
+β1
β
k
SensorScattering Plane
AzimuthalOriented Surface
+ =
Polarimetric Surface Scattering Model ExtendedBragg Model (X-Bragg)
86
Folie 171Microwaves and Radar Institute
[ ] ))4(sinc1(00
0))4(sinc1( )2(sinc*0)2(sinc
13
1312
121
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−+=
βββ
β
CCC
CCT
23 2
1=C PS RR −( )( ) **2 PSPS RRRRC −+= 2
1 PS RRC +=2
0 1πβ ≤≤
I. Hajnsek, E. Pottier & S.R. Cloude, ‘Inversion of Surface Parameters in Polarimetric SAR’, IEEE Transactions on Geoscience and Remote Sensing, submitted 2000.
[ ]( )( )
( )( )⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−−+
+−+
== +
0000
02*
*2
PSPSPS
PSpSPS
PP RRRRRR
RRRRRR
kkTrrCoherency Matrix
for a Ideal Bragg Surface
Second Order Statistics - Coherency Matrix
Coherency Matrixfor a Real Surface
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Prediction of the Ex-Bragg Model I
(HH+VV)(HH-VV) coherence versus b1 for different local incidence angles
Cross polarised power versus b1 for different local incidence angles
87
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Decoupling Soil Moisture from Surface Roughness
2
2
11
3322
2 PS
PS
RR
RRT
TT−
−=
+
Function of ks Function of e‘ and AOI
ε‘ = 10-40AOI= 20°-
50°AOI= 35°
ε‘ = 10-40
)4(sin 13322
3322 β=+− c
TTTT
Folie 174Microwaves and Radar Institute
Scattering Entropy / Anisotropy / α-AngleCoherency Matrix Diagonalisation:
)()()(][ +++ ⋅+⋅+⋅= 3332221113 eeeeeeT rrrrrr λλλ
32
32
PPPPA
+−
=:
321
iiP
λλλλ++
=:
i3
3
1ii PPH log: ∑
=
=Scattering Entropy:
Scattering Anisotropy:
Totally Polarised ScattererTotally Unpolarised Scatterer
→=0H→=1H
1H0 ≤≤
2 Equal Secondary Scattering ProcessesOnly 1 Secondary Scattering Process
→=0A→=1A
1A0 ≤≤
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
)exp()sin()sin()exp()cos()sin(
)cos(
iii
iii
i
i
iieγβαδβα
αr
Mean α-Angle:
332211 PPP αααα ++=
Appearance Probabilities:
),,( 321i =
88
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Prediction of the Ex-Bragg Model II
Variation of Anisotropywith Roughness (Model Parameter ß1 )
Variation of Entropy/Alpha values with Dielectric Constant (45 degrees AOI)
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Frequency:1.5to18.5 GHz10°
20°
30°
40°
50°
Anisotropy versus frequency plot forthe EMSL data
Entropy/alpha angle plot for the EMSL data
Experimental Data from the Joint Laboratory Center (Ispra)Collected in European Mircowave Signature Laboratory (EMSL)
quad-pol scattering matrix(HH,VV,HV,VH); s = 0.4 cm; surface correlation lenght l = 6; dielectric constant e‘ = 8; frequency range = 1.5-18.5
89
Folie 177Microwaves and Radar Institute
LHH Image Alpha AngleEntropy
Eigenvector DecompositionTest Site Elbe River - August 1997
N N N
0 1.5 km
N
Anisotropy
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Inversion Procedure X-Bragg
X-Bragg ModelSLC Data
Eigenvector Decomposition
Entropy/Alpha
Eigenvector Decomposition
Entropy/Alpha
LUT-Comparison
Dielectric Constant
Universal Polynomial
INPUT DATA
Soil Moisture Content
90
Folie 179Microwaves and Radar Institute
Volumetric Moisture
N
N
0 500 m
Field 10
Field 13
Field 14
Field 16
Qualitative Presentation of the Estimated Surface Parameters
N
0 500 m
Field 10
Field 13
Field 14
Field 16
Surface Roughness
Folie 180Microwaves and Radar Institute
0
10
20
30
40
0 10 20 30 40measured m v [vol %]
estim
ated
mv [v
ol. %
]
Elbe 0-4 cmElbe 4-8 cmWeiherbach 0-4 cmWeiherbach 4-8 cm
Measured versus Estimated
Volumetric Moisture mv [%]
0-4 cm 4-8 cm corr.
Elbe RMSerror 8 3 0.7/0.8
Weih RMSerror 7 6 0.2/-
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1measured ks
estim
ated
ks
Elbe Weiherbach
ks corr.
Elbe RMSerror 0.14 0.6
Weih RMSerror 0.21 0.35
Surface Roughness ks
91
Folie 181Microwaves and Radar Institute
Main Problem
* The presence of vegetation cover limits drastically the performance of the algorithms
* Scattering decomposition techniques lead to an improved performance but do not solvethe problem
Outlook
Dual-Frequency Polarimetry (for example: L- and P-band)
Combination of Polarimetric and Interferometric Measurements
Combination of Mono- and Bi-Static Polarimetric Measurements
Main results for Quantitative - Surface Parameter Estimation
* The results of the investigation lead to the conclusion that moisture content and surface roughness of bare surfaces can be estimated with an accuracy of 10%, for
moisture content ranging from 0 up to 40 [vol. %] and roughness scales up to ks < 1.
Uncertainties during measuring the surface parameters leads to inaccurate measurements
which should be accounted.
Folie 182Microwaves and Radar Institute
References (Part I)Theory SAR-Polarimetry:
Boerner, W. M. et al., ‘Polarimetry in Radar Remote Sensing: Basic and Applied Concepts’, Chapter 5 in F. M. Henderson, and A.J. Lewis, (ed.), “Principles and Applications of Imaging Radar”, vol. 2 of Manual of Remote Sensing, (ed. R. A. Reyerson), Third Edition, John Willey & Sons, New York, 1998. Borgeaud, M., S. V. Nghiem, R. T. Shin & and J. A. Kong, ‘Theoretical Models for PolarimetricMicrowave Remote Sensing of Earth Terrain’, Journal of Electromagnetic Waves and Applications, vol. 3, no.1, pp. 61-81, 1989.Chen, H. C., ’Theory of Electromagnetic Waves: A Coordinate-Free Approach’, McGraw-Hill Book Company, New York, 1983. Cloude, S. R., ‘Group Theory and Polarisation Algebra’, OPTIK, vol.75, no. 1, pp. 26-36, 1986.Cloude, S. R., ‘Polarimetry: The Characterisation of Polarimetric Effects in EM Scattering’, PhD. Thesis, University of Birmingham, Faculty of Engineering, UK, October 1986Cloude, S. R. & E. Pottier, ’A Review of Target Decomposition Theorems in Radar Polarimetry’, IEEE Transactions on Geoscience and Remote Sensing, vol. 34, no. 2, pp. 498-518, 1996Cloude, S.R., ‘Symmetry, Zero Correlations and Target Decomposition Theorems’, Proceedings 4th Int. Workshop on Radar Polarimetry, PIERS, pp. 58-66, 1998.Collet, E., ‘Polarized Light: Fundamentals and Applications’, Marcel Dekker, Inc., New York, 1993.Graves, C. D., ’Radar Polarization Power Scattering Matrix’, Proceedings of the IRE, vol. 44, no. 5, pp. 248-252, 1956.Huynen, J. R., ‘Phenomenological Theory of Radar Targets’, Ph. D. thesis, University of Technology, Delft, The Netherlands, December 1970.Sinclair, G., ’The Transmission and Reception of Elliptically Polarized Waves’, Proceedings of the IRE, vol. 38, no. 2, pp. 148-151, 1950.Woodhouse, I., ’Introduction to Microwaves Remote Sensing’, CRC Taylor & Francis, p. 370, 2005.Van Zyl, J. J., ‘On the Importance of Polarization in Radar Scattering Problems’, Ph.D. thesis, California Institute of Technology, Pasadena, CA, December 1985.
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Application (Classification / Surface Parameter Inversion)Cloude, S. R. & E. Pottier, ‘An Entropy Based Classification Scheme for Land Applications of Polarimetric SAR’, IEEE Transactions on Geoscience and Remote Sensing, vol. 35, no.1, pp. 68-78, 1997.Hajnsek, I., Pottier, E. & Cloude, S.R., ‘Inversion of Surface Parameters from Polarimetric SAR’, IEEE Transactions on Geoscience and Remote Sensing, vol. 41, no. 4, pp. 727-745, 2003.Lee, J. S., M. R. Grunes, T. Ainsworth, D. Lu, D. L. Schuler, & S. R. Cloude, ‘Unsupervised Classification Scheme of Polarimetric SAR Images by Applying Target Decomposition Theorems and Complex WishardDistribution’, IEEE Transactions on Geoscience and Remote Sensing, vol. 34, no. 5, pp. 2249-2258, 1999.Lee, J. S., M. R. Grunes & G. De Grandi, ’Polarimetric SAR speckle filtering and its implication on classification’, IEEE Transactions on Geoscience and Remote Sensing, vol. 37, no. 5, pp.2363-2373, 1999.Nghiem, S. V., S. H. Yueh, R. Kwok, and F. K. Li, ‘Symmetry Properties in polarimetric Remote Sensing’, Radio Science, vol. 23, no. 4, pp. 713-720, 1988.Pottier, E., D. L. Schuler, J. S. Lee & T. L. Ainsworth, ‘Estimation of the Terrain Surface Azimuthal/Range Slopes Using Polarimetric Decomposition of Polsar Data’, Proceedings of IGARSS’99, Hamburg, Germany, 1999.Pottier, E., ‘Unsupervised Classification Scheme of POLSAR Images based on the Complex Wishard Distribution and the H/A/alpha Polarimetric Decomposition Theorem’, Proceedings 4th Int. Workshop on Radar Polarimetry, PIERS, pp. 535-547, 1998.Schuler, D. L., J.S. Lee & T. L. Ainsworth, ’Comparisation of Terrain Azimuthal Slope Effects in Geophysical Parameter Studies Using Polarimetric SAR Data’, Remote Sens. Environ, vol. 69, pp. 139-155, 1999. Ulaby, F. T. & Elachi, C., ’Radar Polarimetry for Geocience Applications’, Artech House, Inc., Norwood, MA, 1990.
References (Part II)