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Imaging Polarimetric Interferometry: (POLInSAR) :
From SIR-C to Tandem-X
S. R. Cloude,
AEL Consultants, Scotland, UK E-mail : [email protected]
Web :http://web.mac.com/aelc
Polarization in Remote Sensing Group: http://www.linkedin.com/
1
Acknowledgement : All Terrasar/Tandem-X data provided courtesy of DLR under Research Contracts LAN 0638 and LAN 0943
1994 ……….. 2011
2
Overview
1. Introduction : Two missions and one story…
2. The Motivation : why polarimetry with interferometry?
3. Coherence Set Theory and Signal Processing Developments
4. Products : Forest Height +…
5. POLInSAR with Tandem-X : Can we do it?
6. Conclusions and Session Overview…
Cloude S.R., Papathanassiou K.P.,“Polarimetric SAR Interferometry”, IEEE Transactions on Geoscience and Remote Sensing, Vol. GRS-36. No. 5, pp. 1551-1565, September 1998
First publication of POLInSAR results from this mission:
Shuttle Radar Heritage.. not just SRTM…
..To Tandem-X : A Space-borne single pass Polarimetric Interferometer
… launched June 21st 2010…
..two potential POLInSAR modes
• Dual Polarization (inc. HH/VV)
• Quad Polarization (only experimental)
2 satellites in close formation orbit..
250 -500m separation…
The Motivation…
6
€
pi =λiλ∑
→ HN = − pi logN pi 0 ≤HN ≤1∑ 0 1
€
[J] = I1 00 1⎡
⎣ ⎢
⎤
⎦ ⎥ ⇒ H2 =1
€
[J] = I1 00 0⎡
⎣ ⎢
⎤
⎦ ⎥ ⇒ H2 = 0
Murphy’s Law : Can go wrong….will go wrong Cloude-Murphy : Can increase H…will increase H
N = 2 Wave Polarimetry …..but how about N = 3,4,5,6,7….??
Wave entropy
N = 3 POLSAR N = 4 Bistatic POLSAR/Compact POLInSAR N = 6 POLInSAR N = 8 Bistatic POLInSAR N = 9 Dual Baseline POLInSAR :
Low Entropy: The key to success in Remote Sensing
The entropy line
Microwave Scattering as an Entropy Source/Sink
€
[TRV ] = mv
0.5 0 00 0.25 00 0 0.25
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
⇒ H3 = 0.947POLSAR Forest
Scattering: An Entropy Source
How to lower the entropy of vegetation scatter?
..Mathematical solution is to zero fill €
€
TD[ ] =
0.5 0 0 00 0.25 0 00 0 0.25 0 0 0 0 0 0
⎡
⎣
⎢ ⎢ ⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥ ⎥ ⎥
Entropy vs dimension D
…but how can we realise this solution?
€
Tv[ ] =mv
1+ f p
1 0 00 cos2θ sin2θ
0 −sin2θ cos2θ
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
1 τ 0τ * f pδ 00 0 f p (1−δ)
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ .1 0 00 cos2θ −sin2θ
0 sin2θ cos2θ
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
Cloude 1999 Yamaguchi 2005 Neumann 2009 Arii 2010
..even for more recent volume models
8
€
[T6] = mv
TRV eiφTRVe−iφTRV TRV
⎡
⎣ ⎢
⎤
⎦ ⎥ ⇒ p =
0.50.250.25000
⎛
⎝
⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟
⇒ H6 = 0.5803
POLInSAR : The perfect solution? Probing vegetation at low entropy
s1
s2
α
P z
y
€
⇒ kz =4πΔθλ sinθ
≈4πB⊥
λR0 sinθ=4πBcos θ −α( )
λR0 sinθ
€
φ = kzho
…not quite…coherence loss (Cloude-Murphy in action)
€
[T6] =T11 Ω12
Ω12*T T22
⎡
⎣ ⎢
⎤
⎦ ⎥ mv
TRV γeiφTRVγe−iφTRV TRV
⎡
⎣ ⎢
⎤
⎦ ⎥ ⇒ p =
0.5 − 2δ0.25 −δ0.25 −δ2δδ
δ
⎛
⎝
⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟
⇒ H6 > 0.5803
9
Coherence Decomposition
€
˜ γ = γeiφ = ˜ γ v (γ procγ snrγ geom ˜ γ t ) 0 ≤ γ ≤1
€
f (z') = anPnn∑ (z')
an =2n +12
f (z')Pn (z')dz'−1
1
∫
€
f (z) = exp(−z −δ( )2
2χ 2)0
hv
Fourier-Legendre**
Gaussian-in-a-box*
*F. Garestier, P. Dubois-Fernandez and I. Champion, ”Forest height inversion using high resolution P-band Pol-InSAR data,” IEEE Trans. GRS, Vol. 46, No. 10, pp. 3544-3559, November 2008
**S. R. Cloude, ”Polarization coherence tomography,” Radio Sci., 41, RS4017, doi:10.1029/2005RS003436, September 2006
10
Coherence Tomography: First Results
H/α image
Red=hh-vv Green=2hv Blue=hh+vv
Dihedral trihedral forest
Coherence Set Theory…
Equal Scattering Mechanisms (ESM) or not?
w1 w2
€
[T6] =T11 Ω12
Ω12*T T22
⎡
⎣ ⎢
⎤
⎦ ⎥
ESM⎯ → ⎯ ⎯ T11 = T22 ?€
d =T11 T22
12 (T11 +T22)
≈1?
€
γ c =1
1+ RtS
*T ⋅ t S
t S*T ⋅ ˆ t M
2 −1⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
≈1?
€
T11 = Tmaster ⇒ tMT22 = Tslave ⇒ t S
w1 = w2?
Baseline B
ML ratio test
Generalized Coherence test
13
φ1
Constrained Coherence Region
€
[T ]−1[ΩH ]w = λw [ΩH ] =
12Ω12e
iφ1 +Ω12*Te−iφ1( )
[T ] =12T11 +T22( )
⎧
⎨ ⎪
⎩ ⎪
Max and min coherence for each φ1 are found from max/min eigenvalues of above.. By connecting the set of extreme coherences The shape of the boundary can be obtained
..to find the region inside of which the coherence variation with polarisation w is entirely contained
…(under the assumption w1 = w2) solve the following eigenvalue problem for all φ1
The size and shape of the coherence region/loci is important. ..It is often elliptical, with circular and linear as special cases.. LINKED TO SCATTERING MODELS..
Flynn T., Tabb M., Carande R., “Coherence Region Shape Estimation for Vegetation Parameter Estimation in POLINSAR”, Proceedings of IGARSS 2002, Toronto, Canada, pp V 2596-2598, 2002
14
€
˜ γ iNTX = eiφ (zo )
fiNTX (z ')eikzzdz '
−hv
hv
∫
fiNTX (z ')dz '
−hv
hv
∫
2-Layer Coherence estimation
There are then five components to the coherence
X X Ignore these two by a) using a dual TX system and b) no specular 3rd order scattering
15
Linear Coherence Loci of 2-layer Random-Volume-Over-Ground (RVOG)
µmax and µmin determine the ‘visible’ line length
The mu-spectrum….
Surface only
Volume only
€
˜ γ (w) = eiφ (zo )( ˜ γ vo + F(w) 1− ˜ γ vo( ))
µmax
µmin
2. L Ferro-Famil,. M Neumann, Y Huang, “Multi-Baseline Statistical Techniques for the Characterization of Distributed Media”, Paper WE4.06.5, Proceedings of IGARSS 09, Cape Town, SA, July 2009
The Products…
17
SIR-C / Test Site: Kudara,Russia Azimut
h
Range Pauli RGB Image
Temporal Baseline: 48 Hours
L-band
From SIR-C : Forest Height Estimation
18
…and new products : Biomass from height @ L band
Biomass Estimation from Forest Vertical Structure: Potentials and Challenges for Multi‐Baseline Pol‐InSAR Techniques, Pardini, Matteo ; Kugler, Florian ; Lee, Seung‐Kuk ; Sauer, Stefan ; Torano Caicoya, Astor ; Papathanassiou Konstantinos,, Proc. ESA-POLInSAR 2011, Frascati, Italy, January 2011
19
…improved by adding low frequency vertical structure information
Biomass Estimation from Forest Vertical Structure: Potentials and Challenges for Multi‐Baseline Pol‐InSAR Techniques, Pardini, Matteo ; Kugler, Florian ; Lee, Seung‐Kuk ; Sauer, Stefan ; Torano Caicoya, Astor ; Papathanassiou Konstantinos,, Proc. ESA-POLInSAR 2011, Frascati, January 2011
20
And not just forestry… The theory scales with baseline/height ratio
for problems in agriculture
6 x6 maize plants (2m x 2m)
hv = 1.8m
1.5 - 9.5 GHz (10MHz steps)
θ = 44:0.25:45 degrees
φ= 0:5:360 degrees
Data courtesy of (EMSL), Ispra, Italy
Single,dual and triple baseline
S R Cloude, “Dual Baseline Coherence Tomography”, IEEE Geoscience and Remote Sensing Letters, Vol4, No. 1, January 2007, pp 127-131
21
What are the opportunities and limitations for POLInSAR?
3 important issues:
• Do we have significant X-Band forest penetration? • Do we see a polarized ground at X-Band in dualpol mode (mu-spectrum)? • Is the entropy low enough for forest height estimation?
(SNR as a major entropy source)
Tandem-X
22
• Central Kalimantan (540 000 ha) • Vegetation: Tropical peat swamp forest types • Topography: Almost perfectly flat (slopes < 0.1%) • Biomass range: 50-400 ton/ha (high at edge and lower in centre). • Height range: 5-25 m. • Location centre: 114° 36’E, 2° 12’S
INDREX-II Campaign November 2004 onesian Radar EXperiment
23
X -Band Tomography: Single-Pass-Single-POL Coherence
Antenna pattern
Use: - This VV coherence - Tree height from P-band data - Surface topography phase
..to generate vertical X-band profiles through the canopy…
..using Coherence Tomography
24
X-Band Vertical Tomogram
25
Low entropy source
High entropy diffuser
observer
Low entropy source observer Target
Decomposition Theory
..but POLInSAR also needs a good mu-spectrum: An Optical Analog
Terrasar-X Data : Vancouver 25/04/2010
High Entropy Image
Low Entropy Image
Alp
ha A
ngle
of
sour
ce
Amplitude ms(w)
© DLR 2010
A useful physical model: Checking the mu-spectrum..
POLSAR
RV
G Single or dihedral scattering
€
T2 =t11 t12t12* t22
⎡
⎣ ⎢
⎤
⎦ ⎥ = ms
cos2α cosα sinαeiδ
cosα sinαe− iδ sin2α
⎡
⎣ ⎢
⎤
⎦ ⎥ +mv
2 00 1⎡
⎣ ⎢
⎤
⎦ ⎥ + n
1 00 1⎡
⎣ ⎢
⎤
⎦ ⎥
POLInSAR
€
w =cosα
sinαeiδ⎡
⎣ ⎢
⎤
⎦ ⎥ ⇒ ˆ γ s =
w*TΩ12ww*TT11ww
*TT22w
w⊥ =−sinα
cosαeiδ⎡
⎣ ⎢
⎤
⎦ ⎥ ⇒ ˆ γ v =
w⊥*TΩ12w⊥
w⊥*TT11w⊥w⊥
*TT22w⊥
€
w⊥*T w = 0
φ
φ = phase centre separation
RVOG
ALOS-PALSAR : Borneo, 10/05/2010 L-band satellite radar
Dual POL HH,VV
Total Scattering
Alpha color code
Dual POL HH,VV
Zero Entropy Scattering
ALOS-PALSAR : Borneo, 10/05/2010 L-band satellite radar
29
Terrasar-X : Borneo, 16/04/2010 X-band Satellite Radar
Dual POL HH,VV
Total Scattering
30
Dual POL HH,VV
Zero Entropy Scattering
Terrasar-X : Borneo, 16/04/2010 X-band Satellite Radar
Tandem-X : POLInSAR HH/VV Data sets Bistatic Mode
North Munich, Germany
12/04/2011
Kryckland, Sweden
21/02/2011
Mixed urban agriculture
and forestry
Boreal Forest
AOI=34o Perp Baseline =39m ambiguity height=134m kz =0.047
Tandem-X, North Munich, 12/04/2011
Total signal… ….zero entropy component
€
w⊥ w
Tandem-X, North Munich, 12/04/2011 POLInSAR Coherence Pair
Coherence of zero entropy component
φ
POLInSAR Phase difference φ
Tandem-X, North Munich, 12/04/2011 POLInSAR phase difference
..an idea of what to expect..
.for 20m high trees and kz = 0.05
..expect around 30 degrees phase difference
Δ
γ
Mean width
POLInSAR Mean Speckle Phase
Tandem-X, North Munich, 12/04/2011 Speckle model using mean coherence
River
Surface
Forest
X-band Coherence Regions
Conclusions and Session Summary
• POLInSAR products depend on the variation of interferometric coherence with polarization - low entropy probing of random scatterers like forests
• SIR-C was the first driver… - C and L bands quadpol with short repeat pass (days) and good SNR
• Followed by maturation of coherence set theory and algorithms/models (RVOG). …validation using airborne quadpol sensors
- again with good SNR and short repeat times (minutes)
• Satellite developments hindered by 2 issues ..lack of polarization diversity and/or long repeat times (e.g. 46 days ALOS –PALSAR)..
Now with Tandem-X we have a new generation: single-pass polarimetric interferometers in space… But…limited polarization (dual or compact) and limited SNR… Plus…we need better models for high frequency volume scattering…
High entropy diffuser +
distributed low entropy source
observer
X-band POLInSAR : a new model Vegetation as a distributed low-entropy source
Some important future issues:
- RVOG is invalid…smaller coherence region than expected…line fit will not give φ0 - Key to using coherence for vegetation products will then be good ground φ0 estimates - SNR as an important limiting entropy source for Tandem-X POLInSAR..