Constraining Coherence Optimisation in Polarimetric Interferometry of Layered Targets

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Constraining Coherence Optimisation in
Polarimetric Interferometry of Layered Targets

• José Luis Gómez-Dans
• University of Bristol (UK)
• Shaun Quegan
• University of Sheffield (UK)

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Objectives

• What are the fundamental issues with PolInSAR for
  height measurements?
• Are there any fundamental limitations?
• Physics
• Algorithms
• Test our hypotheses in a tightly controlled
  environment
• Present some results from vegetation measurements

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Layered targets and PolInSAR

• We can generate interferograms using different
  polarisations
• Can we identify individual layers using this
  approach?
• If so,then we can
• Separate layers using polarisation diversity
• Define layers in terms of a dominant scattering
  matrix

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An example target
VV

• Two layers
• Separation 0.15m
• VV and HH nails
• C band
• Easy to simulate
• Easy to measure
• More results available for discussion!!!!

HH
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Pol Synthesis Simulations and Experimental Results
Height as contours
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Coherence Optimisation

• Coherence extrema are associated with individual
  layers
• Choose the polarisation that results in the
  highest coherence
• Two approaches
• Unconstrained Different polarisation states for
  the two acquisitions
• Constrained Identical polarisation states for
  the two acquisitions
• How do we constrain optimisation?

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Constraining Optimisation

• Force polarisation states to be identical
• Straightforward derivation (Colin,
  Titin-Schneider et al., Gomez-Dans)
• Eigenvector problem

TP-1QQTw?w
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Constrained Optimisation(2)
TP-1QQTw?w
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Unconstrained
Constrained
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Mature Wheat Canopy

• Data gathered 18.06.1999
• C band results
• Crop density 441 shoots m-1
• Mean crop height 589 cm

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3D reconstruction of a wheat canopy
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Single Polarisation InSAR
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Polarisation Synthesis_at_45o
Height is shown as contours
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Coherence
Unconstrained
Constrained
Coherence values are essentially identical for
either approach
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Unconstrained Optimisation Retrieved Height
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Constrained Optimisation Retrieved Height
VV
LL
VH
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Conclusions (I)

• PolInSAR is useful for layered targets. It seems
  possible to
• Separate layers based on coherence extrema
• Estimate layer heights
• Estimate layer properties
• Polarimetry
• Depth
• Constrained optimisation was much more stable and
  provided much better inversions than
  unconstrained optimisation.

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Conclusions (II)

• GB-SAR measurements allow detailed analysis of
  what happens when retrieving crop height using
  PolInSAR techniques at C band.
• Successful height recovery was possible in the
  incidence angle range 38o - 45o where the canopy
  and soil were separated by different mechanisms.
• The best height retrievals came from the
  difference between LL-LL (soil) and VV-VV
  (canopy).

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InSAR Geometry
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Mean a angle
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Co-Polar Correlation Coefficient Magnitude
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Co-Polar Correlation Coefficient Phase
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Unconstrained Eigenvector 1
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Unconstrained Eigenvector 2
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Constrained Eigenvector 1
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Constrained Eigenvector 2