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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008
In order to determine what bare-earth DEM accuracies are
achievable under various types of forest and terrain condition, a
fully polarimetrie, single-pass interferometric L-Band system
has been assembled, and tests have recently commenced. It has
the virtue that as a single-pass system, temporal decorrelation
and residual motion effects should not impact the results. In the
following sections we will summarize the system design,
describe the processing methodology, and provide some early
results from our preliminary data.
4.1.1 Design Philosophy: This system is intended to answer
the question posed above: what are the achievable bare-earth
DEM accuracies achievable under a range of forest and
topography conditions? The concept behind the design of this
system is that the experimental platform should be relatively
inexpensive, consistent with the experiment needs and be
deployable in as short a period as possible. Thus there is no
attempt to satisfy more operational considerations. In particular,
we allow ourselves the luxury of flying at a relatively low
altitude, at the expense of a narrow swath. The results of the
tests, if positive, would be used to develop a follow-on strategy
including, potentially, a more appropriate design for operational
use.
4.1.2 System Description: The L-Band system is an
adaptation of the TopoSAR system described in (Maune, 2007).
The TopoSAR system previously supported simultaneous X-
Band (HH, single-pass InSAR) and P-Band (quad-pol, repeat-
pass InSAR). For purposes of this work, the TopoSAR digital
infra-structure is used to support only the L-Band (22.6 cm
wavelength) channels. The antennas, located at the ends of a 3.5
meter rigid baseline, measure (HH,VV,HV,VH) in a pulse-
sequential fashion. The design test altitude (1000m) was chosen
to match the minimum S/N requirements (given the relatively
modest power and antenna gain specifications for the available
hardware).
4.2 Ground Extraction Methodology
4.2.1 The PolInSAR Model: We utilize the well-known
Random Volume Over Ground (RVoG) Model (Treuhaft and
Siqueira, 2000; Papathanassiou and Cloude, 2001) in which the
projection of the observed complex coherences onto the unit
circle represents the ground phase (Papathanassiou and Cloude,
2001). This is expressed in Equation (4) as
r (*) = exp(iA) ^ + m< ' W ^ (4)
1 + m(w)
in which (f)^ is the phase related to the ground topography, m is
the effective ground-to-volume amplitude ratio (accounting for
the attenuation through the volume) and W represents the
observed polarization state. y v denotes the complex coherence
for the volume alone (excluding the ground component), and is
a function of the extinction coefficient cr for the random
volume, its height h v and the vertical wavenumber Kz.
(m=0), the observed coherence is given by the volume
coherence, y v rotated through (f> 0 . These two limiting
situations therefore determine the line geometry as shown in
Figure 6.
Two approaches are available to estimate the straight line: in
the first, we create a number of W -dependent coherences based
on lexicographic, Pauli and magnitude optimized coherences
(Papathanassiou and Cloude, 2001) and find a regression line
amongst them. In the second method we use a phase
optimization approach (Tabb, et. al., 2002) which traces out the
boundary of the coherence region and from which, if well-
behaved, an ellipse is formed whose major axis represents the
straight line solution. Using simulated data, the ground phase
results for the two approaches are similar. However with repeat-
pass data differences can be significant. Although it is a
secondary objective in this work, the model is also inverted
(Papathanassiou and Cloude, 2001) to extract canopy height.
Figure 6. Phase optimization approach for topographic phase
estimation: The green ellipse is the estimated coherence region.
The straight line (blue dashed) passes through two ends of the
coherence region. The ground topographic phase centre is
estimated from one of the line-circle intersection points (red
circle).
4.2.2 Design Implications: A fundamental parameter of the
model is K 2 the vertical wavenumber, defined in Equation (5).
On the one hand it determines the sensitivity of the derived
height to changes in phase through h= (f) Q /K 2 . Secondly it
impacts y v through the relationship K v = K 2 hJ2 and hence the
overall coherence observed as well as the line length. From this
perspective an optimum K 2 can be defined (Hellmann and
Cloude, 2004) that is effectively ‘tuned’ to the canopy height.
Given the baseline limitations in this work, an appropriate
flying altitude, H is determined such that K v is optimized for
tree heights in the 10-30m region.
„ 47T B cos 6
Kz ~
k H tgO
(5)
The key point of interest for this application is the assumption
that m is polarization dependent while y v is not. In particular,
for large m, the straight line intersects the unit circle (Figure 6)
and the associated phase at this point relates directly to the
desired ground elevation. In the limit of no ground component
4.2.3 Calibration: Both polarimetrie and interferometric
calibration is required. The polarimetrie calibration uses a
modified Quegan (Quegan, 1994) approach with trihedrals and
forest data allowing for range-dependant imbalance and cross
talk corrections, respectively, to be applied to each antenna.
