IEEE - Aerospace and Electronic Systems - May 2022 - Tutorial XV - 64

A Rationale for Backprojection in Spotlight Synthetic Aperture Radar Image Formation
The idea of using backprojection in spotlight SAR is
nearly 40 years old but the polar format algorithm and its
variants still dominate. In light of the fact of much faster
hardware, fast algorithms, and the adaptivity of backprojection
to arbitrary amounts of wavefront curvature and
arbitrary flight paths in monostatic and multistatic modes,
a remark in a rather recent work [13] could be interpreted
to mean that it might be time to take another look at backprojection:
" The [polar format] algorithm was born in an
era when computing resources were scarce, and the limitations
of PFA were seen as a fair trade for its efficiency...
wide-beam imaging violates the tomographic [linear projections
leading to polar format algorithm] assumption...
we must be careful to approach new problems afresh, asking
which processing chain is best suited to the given
constraints. "
Many engineers have at one time or another found
themselves measuring the transfer function of an electronic
circuit, a mechanical structure, or a loudspeaker. To
find the response at a particular frequency, a sine wave is
injected and the response, real and imaginary or magnitude
and phase, is measured at some other point. If the
response is desired at multiple frequencies, the sine frequency
is varied and the results plotted. Some applications
use an exponential chirp with a matched filter [59]. Sometimes
these frequency data are inverse Fourier transformed
to get an impulse response estimate. Spotlight SAR is the
same, but in two dimensions, with the ground patch as the
system being measured and the image as the estimated
impulse response. In both cases, the measurement includes
the measuring equipment, which is hoped to have minimal
effect or is able to be deconvolved away, and in both cases
the inverse Fourier transform tends toward the impulse
response as the measurement bandwidth increases.
The presentation in this article has been focused on the
particular aspect of how backprojection arises in spotlight
SAR image reconstruction and to do that many aspects of
spotlight SAR and radar generally have been left out.
These aspects can be incorporated with the reader's previous
or future understanding.
REFERENCES
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64
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IEEE A&E SYSTEMS MAGAZINE
MAY 2022
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IEEE - Aerospace and Electronic Systems - May 2022 - Tutorial XV

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