Geoscience Reference
In-Depth Information
Sharif & Kamalabadi (2008) studies the optimal placement of sensors for different remote
sensing applications, including aperture synthesis imaging. They considered data inversion
through Tikhonov regularization, which is similar to the methodology discussed here except
with Gaussian model statistics replacing model entropy as the prior probability. This
permitted an entirely linear formulation of the problem. Included in the imaging problem
were allowances for constraints on image smoothness and support. Optimization was in
terms of minimizing different variations on the model prediction error as well as some
detection performance metrics and the informativeness of the sensors with respect to the
image (mutual information). Computationally expedient means of performing the different
optimizations were also found. Sharif & Kamalabadi (2008) demonstrated that rather different
results could be obtained depending on the criteria for which the array was optimized.
There are generally good reasons, however, for confining all of the sensors to a plane if
possible. If the antennas are above imperfect earth, then their vertical phase centers may
not be well known, but at least they will be identical if the antennas are at the same
height and the dielectric constant of the earth is homogeneous. Moreover, with
d
z
= 0 for
all interferometry baselines and with the radical in the denominator incorporated into the
effective brightness, (2) becomes a two-dimensional Fourier transform. Translations in the
brightness consequently map to phase shifts in the visibilities which further map to linear
phase progressions of received signals across the aperture plane. This simple relationship can
be useful in establishing the absolute phases of signals from different sensors.
4.5 Phase calibration
Sensor phase biases associated with differential cable lengths and other systemic issues must
be removed through calibration in order for visibilities to be estimated and inverted. While a
number of calibration methods exist, calibration remains one of the most challenging aspects
of aperture synthesis imaging in practice (see for example Chau et al. (2008)). The “gold
standard” for calibration involves observing point targets with known bearings, i.e. radio
stars, and adjusting the complex gains of the receiver channels until the measured visibilities
match a model based on the known source locations. However, this is only possible for
large-aperture radars with adequate sensitivity, and the infrequency of radio star conjunctions
may pose practical problems. Feeding common signals through the entire signal chain is
another effective calibration strategy, but this too may be possible only infrequently.
Specular meteor echoes are quasi point-targets that can be observed frequently, even by small
radars. While their bearings are not known individually, they can be estimated collectively. If
the antenna array lies in a plane, phase biases can be estimated such that the bearings of all
meteor echoes are consistent across all interferometry baselines (e.g. Holdsworth et al. (2004)).
Corrections to the phase bias estimated can then be made such that the center of gravity of
the echoes is aligned with the effective two-way radar radiation pattern, with allowances
made for the expected anticipated altitude distribution of the specular meteor echoes. Other
radar targets may be used to fine-tune the calibration. For example, that echoes from plasma
irregularities arise from the locus of magnetic perpendicularity affords accurate knowledge of
their elevation along a given azimuth.
While not widely used in upper atmospheric research, closure phase measurements offer
additional information for phase calibration (Cornwall, 1989; Jennison, 1958). The idea is that
the sum of the visibility phases from a triad of sensors, calculated for instance using bispectral
