The Ionosphere and Interferometric/Polarimetric SAR

1
The Ionosphere and Interferometric/Polarimetric
SAR

• Tony Freeman
• Earth Science Research and Advanced Concepts
  Manager

2
(No Transcript)
3
Surface Clutter Problem

• Repeat-pass Interferometry
• Subsurface return has phase difference ?1 due to
  ionosphere propagation (same as surface return
  from location O)
• Surface clutter return (from location P) has
  phase difference ?2 due to ionosphere propagation
• So ?1 - ?2 is unknown - could be zero - depends
  on correlation length of ionosphere
• Is ?1 - ?2 variable within a data acquisition?
  (Probably)

Radar
Ionosphere
r2?r?2
r1
r2 ?1
r1?r
?i
O
P
?r
?r
z
Q
4
Ionospheric Effects Two-way propagation of the
radar wave through the ionosphere causes several
disturbances in the received signal, the most
significant of which are degraded resolution and
distorted polarization signatures because of
Faraday rotation. Except at the highest TEC
levels, the 100 m spatial resolution of CARISMA
should be readily achievable Ishimura et al,
1999. Faraday rotation in circular polarization
measurements is manifested as a phase difference
between the R-L and L-R backscatter measurements.
If this phase difference is left uncorrected, it
is not possible to successfully convert from a
circular into a linear polarization basis the
resulting linear polarization measurements will
still exhibit the characteristics of Faraday
rotation. The need to transform to a linear basis
stems from CARISMAs secondary science objectives
and the requirement to use HV backscatter
measurements, which have exhibited the strongest
correlation with forest biomass in multiple
studies. As shown in Bickel and Bates ,1965,
Freeman and Saatchi, 2004 and Freeman, 2004
it is, in theory, relatively straightforward to
estimate the Faraday rotation angle from fully
polarimetric data in circularly polarized form,
and to correct the R-L to L-R phase difference.
Performing this correction will then allow
transformation to a distortion-free linear
polarization basis.
5
Calibration/Validation Calibration of the
near-nadir radar measurements to achieve the
primary science objectives of ice sheet sounding
is relatively straightforward. The required 20 m
height resolution matches the capability offered
by the bandwidth available, and is easily
verified for surface returns by comparison with
existing DEMs. For the subsurface returns CARISMA
measurements will be compared with GPR data, ice
cores and airborne radar underflight data. The
required radiometric accuracy of 1 dB is well
within current radar system capabilities and can
be verified using transponders and or targets
with known (and stable) reflectivity. Radiometric
errors introduced by external factors such as
ionospheric fading and interference require
further study. Calibration of the side-looking
measurements over the ice is a little more
challenging but the primary science objectives
can still be met. Validation that the
differentiation between surface and subsurface
returns has been successful, will be carried out
by simulating the surface clutter using DEMs
and backscatter models. Calibration of the
side-looking measurements over forested areas
will be yet more challenging. The techniques
described in Freeman, 2004 will be used to
generate calibrated linear polarization
measurements. Data acquired over targets of
known, stable RCS, such as corner reflectors and
dense tropical forest will be used to verify the
calibration performance. Validation of biomass
estimates and permafrost maps generated from
CARISMA data will be carried out by comparison
with data acquired in the field.
6
Introduction and Scope

• Faraday rotation is a problem that needs to be
  taken into consideration for longer wavelength
  SARs
• Worst-case predictions for Faraday rotation for
  three common wavebands

7
Effects on Polarimetric Measurements
8
Effects on Interferometric Measurements
9
(No Transcript)
10
Summary of Model Results

• Spread of relative errors introduced into
  backscatter measurements across a wide range of
  measures for a diverse set of scatterer types
• Effects considered negligible (i.e. less than
  desired calibration uncertainty) are shaded

• Radiometric uncertainty - 0.5 dB
• Phase error - 10 degrees
• Correlation error - 6
• A Noise-equivalent sigma-naught of - 30dB is
  assumed

11
Estimating the Faraday Rotation Angle, W
12
Estimating the Faraday Rotation Angle, W

• Sensitivity to Residual System Calibration Errors
  (shaded cells represent errors in W gt 3 degrees)

13
Estimating the Faraday Rotation Angle, W

• Combining effects for a typical set of system
  errors, we see that a cross-talk level lt -30 dB
  is necessary to keep the error in W lt 3 degrees
  using measure (2)

For Measure (1) error is dominated by additive
noise

• P-Band case has channel amplitude imbalance of
  0.5 dB, phase imbalance of 10 degrees and NE so
  -30 dB
• L-Band case has channel amplitude imbalance of
  0.5 dB, phase imbalance of 10 degrees and NE so
  -24 dB

14
Correcting for Faraday Rotation
15

• Calibration Procedure for Polarimetric SAR data
• (Cannot estimate cross-talk from data)
• (Use any target with reflection symmetry to
  symmetrize data)
• (Trihedral signature or known channel imbalance)
• Taking Faraday rotation and typical system
  errors into account

16
Polarimetric Scattering ModelDistributed
scatterers

• Take a cross-product

• Take an ensemble average over a distributed area

• For uncorrelated surface and subsurface
  scatterers

No interdependence between surface and subsurface
returns

• Which leaves

• Similar arguments hold for other cross-products

17
Polarimetric Scattering ModelSurface-Subsurface
correlation

• Why should the scattering from the surface and
  subsurface layers be uncorrelated?

• 3 reasons
• The scattering originates from different
  surfaces, with different roughness and dielectric
  properties
• The incidence angles are very different (due to
  refraction)
• The wavelength of the EM wave incident on each
  surface is also quite different, since

18
Geometry
Radar
mv(?r), s, l, ?, ?i
loss tangent, tan ?
mv(?r), s, l, ?, ?i
19
Inversion?
Empirical Surface Scattering Model

• For each layer we have 5 unknowns mv(?r), s, l,
  ?, ?i
• For the surface return we know ?, and can
  estimate ?i if we know the local topography and
  the imaging geometry
• For the subsurface scattering, the wavelength ?
  is a function of the dielectric constant for the
  layer, i.e.
• In addition the attenuation of the subsurface
  return is governed by tan ?, ?r
• - This still leaves a total of 9 unknowns
• Under the assumptions of reciprocity (HV VH),
  and that like- and cross-pol returns are
  uncorrelated, we can extract just 5 measurements
  from the cross-products formed from the
  scattering matrix
• gt Inversion is not possible

20
Interferometric Formulation

• Correlation coeff

?

1. ?? 2.5
2. ?? 4.0

21
Interferometric Formulation

• Correlation coeff

invariant, as are
,

1. ?? 2.5
2. ?? 4.0

22
Surface Clutter Problem
Subsurface scattering from ?i 2.9 deg Surface
clutter from ?i 20 deg
Radar
r2?r
r1
r2
r1?r
?i
O
P
?r
?r
z
Q
23
2-Layer Scattering ModelConclusions

• Polarimetry
• Model derived from scattering matrix formulation
  indicates that there is no depth-dependent
  information contained in the polarimetric phase
  difference (or any cross-product)
• Unless - surface and subsurface returns are
  correlated
• Inversion of polarimetric data does not seem
  possible
• Stick with circular polarization for a spaceborne
  system?
• gt Only problem is resolution, position shifts
  due to ray bending
• Interferometry
• Behavior of the correlation coefficients for
  surface clutter and subsurface returns as a
  function of baseline length are different
  (assuming flat surfaces)