Geoscience Reference
In-Depth Information
pointing direction. This poses challenges for observing plasma irregularities with important
scale sizes of a kilometer or less, which is often the case in ionospheric research.
Aperture synthesis radar imaging utilizes spaced-antenna data to construct true images of
the scatterers versus bearing. Some approaches are adaptive, and some achieve “super
resolution” by incorporating the effects of diffraction in the analysis. All information about
range and Doppler shift can be retained, meaning that the images can be four dimensional,
not counting the time axis. As the techniques can synthesize large apertures from small,
sparsely-distributed sensors, they may be especially beneficial for small and medium-sized
radars, although some of the benefits can only be realized when high signal-to-noise ratios are
available.
In this paper, we review the formulation of the radar imaging problem, which is based on
concepts and language derived from radar interferometry and radio astronomy. As radar
imaging belongs to the class of problems known as inverse problems, some of the ideas from
that domain are also reviewed. The factors that govern the resolution achievable in practice
will be described, and optimal strategies for sensor placement will be discussed. Error analysis
in radar imaging is treated, and some extensions to the basic imaging procedure are outlined.
Finally, examples of radar imaging implementations are drawn from upper atmospheric and
ionospheric applications. Application in the lower atmosphere exist as well but will not be
covered here (Chau & Woodman, 2001; Hassenpflug et al., 2008; Palmer et al., 1998).
2. Imaging problem
The imaging problem has been formulated by (Thompson, 1986), and we follow his treatment
below. We consider the far-field problem only and regard the backscatter in a given range gate
as a random process constituted by plane waves with sources that are statistically uncorrelated
and distributed in space. Imaging data have the form of complex interferometric cross spectra
obtained from spaced antenna pairs separated by a vector distance
d
.
Such “visibility”
measurements
V
(
k
d
,
f
D
)
are related to the “brightness” distribution
B
(
σ
ˆ
,
f
D
)
, the scattered
power density as a function of bearing and Doppler frequency, by
A
N
(
e
jk
d
·σ
d
V
(
k
d
,
f
D
)=
σ
)
ˆ
B
(
σ
ˆ
,
f
D
)
Ω
(1)
where
k
is the wavenumber,
f
D
is the Doppler frequency, and ˆ
is a unit vector in the direction
of the bearing of interest and where the integration is over all solid angles in the upper half
space. As different Doppler spectral components of the data are treated independently, we
omit
f
D
in the formalism that follows.
In (1),
A
N
is the normalized two-way antenna effective area. In radar imaging, the antennas
used for reception are typically much smaller than the antennas used for transmission, and
A
N
is consequently dominated by the characteristics of the transmitting antenna array. Together,
the product
A
N
B
is the effective brightness distribution,
B
eff
, which represents the angular
distribution of the received signals. It is this quantity that are interested in recovering from
the data, the antenna radiation patterns being known. The radiation pattern need only be
treated explicitly when heterogeneous receiving antennas are used (see below).
σ
