I.
INTRODUCTION
Phase Gradient Autofocus-A
Robust
Tool
for
High
Resolution
SAR
Phase Correction
D.
E
WAHL
I!
H.
EICHEL,
Member, IEEE
D.
C.
GHIGLIA
C.
V
JAKOWATZ, JR,
Member, IEEE
Sandia National Laboratories
The phase gradient autofocus (PGA) technique for phase
error correction of spotlight mde synthetic aperture radar
(SAR)
imagery
is
examined carefully
in
the context of four
fundamental
signal
processing steps that constitute the algorithm
We demnstrate
that
excellent results over a wide variety of scene
content, and phase error function structure are obtained
if
and
only
if
all
of these steps are included
in
the
processing. Finally, we
show that the computational demands of the full PGA algorithm
do not represent a large fraction of the total image formation
problem, when mid to large
size
images are involved.
Manuscript received June 18,
1992;
revised April
9,
1993.
IEEE
Log
NO.
T-AESBOBl16653.
Authors’ address: Sandia National Laboratories, P.O.
Box
5800,
Division 5912, Albuquerque,
NM
87185.
0018-9251/94/$4.00
@
1994 IEEE
The ability
of
a synthetic aperture radar
(SAR)
to form a high resolution image is dependent on
maintaining subwavelength knowledge
of
platform
position from pulse to pulse during the aperture
generation time.
As
imaging standoff distances and
aperture generation times increase, the need to
measure and accurately track the antenna phase
center puts an extreme burden on any motion
compensation system. In addition, phase perturbations
due to propagation effects can destroy the utility
of
high resolution imagery, even with perfect motion
compensation.
measurement system is used to sense platform motions
over some range of frequencies. These may then be
removed from the data prior to image formation
[l].
For motion errors beyond the measurement
capabilities
of
inertial measurement units or for
propagation induced errors, it is necessary to use
data-driven autofocus techniques
[2,
31.
It seems unlikely then, that any high resolution
SAR
system will fully meet its ultimate utility without
some means for automatically focusing the imagery,
independent
of
the source or the form
of
the phase
error. Simple automatic focusing methods have
been proposed and built since the early days
of
SAR
development. However, these techniques and
extensions thereof, that basically track low-order
polynomial-like motion errors, have not kept pace with
the requirements. High-order phase-error correction
has usually been relegated to postprocessing techniques
generally requiring human intervention.
In
addition,
it has been difficult to focus scenes containing these
errors without having strong isolated scatterers present.
Since the initial publication
of
phase gradient
autofocus
(PGA)
[4],
the algorithm has seen
widespread utilization throughout the
SAR
community.
PGA
has been demonstrated, by ourselves and
others in the
SAR
community, to provide near
diffraction-limited performance on a wide variety
of
real-world images.
SAR
designers now have a practical
tool by which phase-degraded imagery can be restored
to designed impulse response
(IPR)
specifications
in nearly all cases. It is important to note that this
performance is achieved with
PGA
independent
of
SAR
scene content. Specifically, bright isolated
point-like reflections are not needed. Therefore scenes
completely devoid
of
cultural features can be restored.
Some concern has been levied toward
PGA
in
terms
of
its purported computational burden.
A
natural
technical question now arises. Is it possible to shortcut
or circumvent any of the processing steps within
the
PGA
construct for the sake of computational
efficiency? Several autofocus methods have been
proposed that embody a subset
of
the algorithmic
steps
of
PGA
[5-71,
but in our opinion, they have
In a typical
SAR
application, an inertial
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS
VOL.
30,
NO.
3
JULY 1994
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