Geoscience Reference
In-Depth Information
(triple-product) analysis, is bias free. If the baseline of the triad are suitably arranged, this can
afford some information about sensor phase bias.
A promising class of calibration techniques involves finding the phase biases on the basis
of image characteristics through optimization. Uncompensated sensor phase biases tend
to degrade images and introduce artifacts that increase the image variance (decrease the
smoothness) as well as the overall image entropy. Holding the phase biases of three
non-collinear sensors to be arbitrary, the remaining phases could be adjusted to minimize
the image entropy, global variance, or some other cost function. Afterward, the phase offsets
could be readjusted to “rotate” the artifact-free image into its proper place, taking into account
known characteristics of the radar and the target. This optimization can take place outside
of the main imaging computation or possibly within it, adopting some of the principles
followed by Sharif & Kamalabadi (2008) for optimizing sensor placement. Their smoothness
and support metrics, respectively, could be imposed to accomplish the first and second steps
of the aforementioned calibration, respectively, only within a unified imaging framework.
Since the brightness/visibility mapping is not linear in the phase biases, the procedure would
necessarily be iterative.
5. Examples from the upper atmosphere
Here, we present examples of ionospheric phenomena that have been revealed or clarified
using aperture synthesis radar imaging. The examples are taken from observations of the
Jicamarca Radio Observatory, a 50-MHz phased array radar operated outside Lima, Peru.
Aperture synthesis radar imaging was introduced to upper atmospheric research at Jicamarca
in 1991 (Kudeki & Sürücü, 1991), and MaxEnt was applied there first five years later (Hysell,
1996). The number of sensors sampled has grown from four to eight in the intervening years.
Twelve-sensor experiments are being planned. The longest interferometry baseline available
is nearly 100 wavelengths long in the direction perpendicular to the geomagnetic field. A
subset of the main antenna array is used for transmission, and a phase taper is applied to
broaden the main beam and reduce the sidelobe level. Images are normally computed over a
≈
13
◦
-wide azimuth sector. In practice, only the central part of the sector contains echoes and
need be plotted.
At Jicamarca, imaging has mainly been applied to coherent scatter from field-aligned plasma
density irregularities. Different varieties of irregularities occupy altitudes between about
95-2500 km at the geomagnetic equator and can be detected by the strong, spectrally narrow
radar echoes that arise from them. While imaging is generally performed in two dimensions,
the echoes arrive from bearings very close to the locus of perpendicularity to the geomagnetic
field, and the images in each range gate can consequently be collapsed into a single dimension.
Alternatively, the imaging problem can be formulated in one dimension from the start. Two
dimensional images in range and azimuth are produced finally. Sequences of sequential
images can also be animated. Imaging in three dimensions has been applied in lower
atmospheric applications (Palmer et al., 1998).
We have plans to apply it to mesospheric
echoes as well.
Images are formed for each Doppler bin, and each image pixel or voxel consequently
represents a complete Doppler spectrum. Spectral information is conveyed through color
according to the example legend shown in Figure 1. Pixel colors represent the first
three moments of the spectrum, with the brightness, hue, and saturation specifying the
