IEEE Geoscience and Remote Sensing Magazine - March 2013 - 31

mr
d n = 2L0 , (47)
el

where n represents the elevation axis, and a repeat-pass
scenario is implicitly assumed. Concerning the sampling requirements of the tomographic aperture, i.e.,
the distance between passes, one needs to consider the
maximum spectral contributions of the received signal
in order to accomplish Nyquist and avoid high sidelobes
and ambiguities. Such frequency excursion in elevation
depends on the total height of the volume in the direction
perpendicular to LOS, h V , as follows [19]

mr
n # 2h0 , (48)
V

where n is the minimum required distance between
passes. In the frame of SAR tomography better resolution implies more passes, hence increasing the complexity of the whole acquisition geometry if resolutions in the
same order of magnitude as the range and azimuth resolutions are to be obtained without undesired artifacts. As
an example, the first experimental demonstration of SAR
tomography [19] used 13 passes with an equidistant separation of 20 m, reaching a resolution in elevation of 2.9 m at
mid-range.
Figure 23 shows a tomogram over a forested area
obtained with data acquired in 2006 by DLR's E-SAR airborne system in Dornstetten, Germany. The campaign
was performed at L-band in quad-pol mode and a total of
21 tracks with an average baseline of 20 m were recorded.
The tomogram clearly shows the different contributions
and their polarimetric signatures, where the color coding
corresponds to the elements of the Pauli vector (see (11)),
namely, blue for the surface scattering (S HH + S VV ), red for
the dihedral ground-trunk interaction (S HH - S VV ), and
green for the volume of the canopy (2S XX).
In opposition to airborne SAR sensors, spaceborne
sensors can only reach a certain maximum separation
between repeated acquisitions, especially with current
march 2013

ieee Geoscience and remote sensing magazine

FIGURE 22. Acquisition geometry for tomographic imaging with a

SAR sensor. L el is the synthetic aperture in elevation and n represents the elevation axis.

Height (m)

Lel

20
10
0
(a)
600

Slant Range (m)

Pol-InSAR, which however relies on a model in order to
retrieve the vertical scattering distribution (see Section
V). Finally, in order to retrieve the whole vertical distribution of the scatterers in imaging terms, it is necessary
to further exploit the synthetic aperture concept, which
requires the use of multiple passes of the SAR sensor over
the same area but at different positions, as depicted in
Fig. 22. Such a concept is known as SAR tomography [19],
[147]. One interesting application of SAR tomography is
the imaging of vegetated areas. The resulting tomograms
can be used, among other things, for the estimation of the
ground-topography beneath the foliage, for the estimation of structural parameters, as well as for the detection
of objects hidden beneath the foliage [19], [148], [149].
Similar as conventional SAR, the resolution in elevation
is given by the length of the synthetic aperture in elevation,
L el,

400

200
0

500
Azimuth (m)

1000

(b)
FIGURE 23. (a) Polarimetric tomographic profile over a forested

area using DLR's E-SAR system at L-band [21]. The profile corresponds to the yellow line shown on the SAR in (b). A total
of 21 tracks were acquired with an average baseline of 20 m.
Conventional beamforming, i.e., matched filtering, was used to
focus the data. The color coding corresponds to the elements of
the Pauli vector (see (11)), namely, blue for the surface scattering
(S HH + S VV ), red for the dihedral ground-trunk interaction
(S HH - S VV ), and green for the volume of the canopy (2S XX ).
single-satellite missions, since they are steered to follow
small orbital tubes (250 m in the case of TerraSAR-X). Furthermore, the distribution of the acquisition geometry is in
general non-uniform, hence resulting in an increase of the
sidelobe level if conventional beamforming approaches
are used to process the tomogram. The limited number of available samples together with the non-uniform
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Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - March 2013