IEEE - Aerospace and Electronic Systems - May 2022 - Tutorial XV - 44

Tutorial:
DOI. No. 10.1109/MAES.2021.3100886
A Rationale for Backprojection in Spotlight Synthetic
Aperture Radar Image Formation
Jerald L. Bauck , Tempe, AZ 85283 USA
This note on backprojection for spotlight synthetic
aperture radar image formation is mainly pedagogic in
purpose and is intended to be accessible. The
presentation from first principles is elementary and
detailed, beginning with the wave equation and melding
wave notions with signal processing notions using a
compact and consistent notation throughout. A
reflection model is developed including a general
expression for the receiver signal, which does not depend
on a particular transmitted waveform. Then, the signal
is specialized to monochromatic waves to show how
waves and the Fourier transform fit together. In the end,
the signal is once again generalized so that the theory
works for any signal type. Backprojection is shown to
reconstruct the wave field that was lost by sampling it at
only one point, the receiving antenna. After specializing
some details to the synthetic aperture radar geometry,
the Projection Slice Theorem is introduced late, after an
understanding of the underlying principles is obtained.
Computational aspects are considered and it is seen that
backprojection and direct Fourier inversion, also known
as the polar format algorithm, are fundamentally the
same, differing only in some implementation details,
albeit significant ones, thus overturning the notion that
backprojection is not a Fourier process. Those who
might benefit from this article include people who have
worked in this field and who seek a somewhat different
point of view from the usual presentation, people in
other fields who are unfamiliar with some of the
engineering concepts involved, and signal processing
engineers who appreciate a bit ofwave theory.
INTRODUCTION
Similarities between spotlight-mode synthetic aperture
radar (SAR) and computerized tomography (CT) were
illuminated in 1983 [1]. With the parallels drawn
between the two fields, researchers in SAR were able
to borrow and adapt image reconstruction ideas from
CT and some existing SAR algorithms benefited from
the new perspective. Some of the closely related CT
algorithms that have been borrowed and used extensively
are called backprojection, convolution-backprojection,
filtered backprojection, or a related method
called filter of backprojections.
Figure 1 shows a typical basic setup and geometry of a
spotlight SAR. The radar transmitter-receiver is mounted
on a movable vehicle, typically an airplane or low Earth
orbiting satellite, which moves around a scene of interest
on the ground. The radar's antenna is pointed at the scene,
or dwelled, as the aircraft moves, allowing the scene to be
interrogated by a structured, designed, electromagnetic
pulse, which reflects from the ground patch and is then collected
and processed by the receiver; the interrogation is
repeated over a range of angles. An alternate and older
form ofSAR is stripmap mode whereby the antenna is not
dwelled and thus illuminates a strip of the ground as the
platform moves. While stripmap SARs image a larger area
than spotlight SAR, the resolution is worse given similar
system parameters. Variants include inverse SAR, where
the radar is considered to be stationary and the target rotates
and bistatic or multistatic spotlight SAR whereby the one
or more transmitters are in different locations than the one
or more receivers. Other SAR modes include scanSAR,
sliding spotlight, and interferometric SAR (InSAR). Some
radars are able to switch between multiple modes.
There are a number of classic and modern papers and
Author's current address: Jerald L. Bauck, Tempe, AZ
85283 USA (e-mail: other@bauck.net).
Manuscript received October 25, 2019, revised January
18, 2021; accepted July 6, 2021.
Review handled by Dale Blair.
0885-8985/21/$26.00 ß 2021 IEEE
44
books on SARbut most ofthem focus on stripmap mode and
mention spotlight mode little if at all, for example, [2]-[6].
Of those that do significantly mention spotlight mode, most
discuss mainly or only the polar format algorithm about
which we shall have more to say later [7]-[13], [14]. Works
with a significant orientation to backprojection are [1],
which apparently inspired [15], plus [16]-[18], [19]. Other
IEEE A&E SYSTEMS MAGAZINE
MAY 2022
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IEEE - Aerospace and Electronic Systems - May 2022 - Tutorial XV

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