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The lectures will begin with an overview of the idea of radar
imaging, including some beautiful images to provide motivation.
Next will be a discussion of radar system architecture, along
with a mathematical description of what each part of the system
does to the transmitted or received signal. The
processing of the received signal, in particular, involves some sophisticated mathematical
ideas to pull the signal out of the noise.
Next there will be a discussion of how the electromagnetic waves
propagate after they leave the antenna. The propagation of
electromagnetic waves is governed by Maxwell's equations; the audience
will learn why a scalar wave equation is appropriate for most
analysis of radar scattering. The analysis of radar signals will
be provided first
with a simple onedimensional wave propagation model.
The audience will learn from this that
radar can measure both target range and target velocity, but that
there is an uncertainty principle that both range and
velocity cannot be measured simultaneously with arbitrary accuracy.
The theory based on the onedimensional model is sufficient to
understand some of the basic ideas behind highresolution imaging,
and understanding this point of view is important for communicating
with radar engineers.
Next, a fully threedimensional scalar wave propagation model will be
introduced, and the basics of scattering theory will be discussed.
The threedimensional model leads to a formula for the radar signal that
includes the transmitted waveform, the reflectivity of the target,
and geometrical spreading factors. This model will be used to
explain ISAR (Inverse Synthetic Aperture Radar) imaging, which is
generally used for airborne targets. The audience will learn
that ISAR imaging commonly reduces to a multidimensional Fourier
transform. A movie will be shown of ISAR images.
For targets on the ground, it is important to analyze the radiation
from the antenna. The discussion of antennas will begin with a slide
show of the many different forms of antennas. For the analysis of
radiation from antennas, the full vector Maxwell's equations will be
used; in particular, the vector potential formulation will be
introduced and used to derive a formula relating the current density
on the antenna to the farfield radiation pattern. Examples will
be included to show how typical antenna beam patterns arise.
With threedimensional wave propagation and antenna beam patterns
now understood, the lectures will address spotlightmode SAR.
The audience will discover the similarity
between ISAR and spotlightmode SAR.
Next, stripmap mode SAR will be addressed. Here the imaging
process is more complicated and depends on the fact that the
map from target reflectivity to radar signal is a FIO (Fourier Integral
Operator). The audience will learn how to construct a parametrix
(approximate inverse) for the FIO; applying this parametrix to the
radar signal results in a stripmap mode SAR image. Properties of
this image follow from the properties of the FIO; the necessary
notions from microlocal analysis will be introduced.
The lectures will end with a survey of the state of the art and of
some of the areas of active research.
Tuncay Aktosun
aktosun@uta.edu
Last modified: May 23, 2008
