210 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 34, NO. 3, JULY 2009
220-kHz SAS on a Remus600 AUV, and delivered a 175-kHz
InSAS on a Seahorse AUV for Naval Oceanographic Office
(NAVOCEANO, Stennis Space Center, MS). Elsewhere com-
plete SAS hardware/software packages have been produced
by a number of firms. For example, Thales (Neuilly-sur-Seine,
France) produced a SAS on a Bluefin12 for NURC and QinetiQ
produced a SAS for the Swedish Navy 21-in AUV as well as
a dual frequency SAS for the U.S. Navy). Ultra Electronics
(Greenford, U.K.) and IXSEA (Marly-le-Roi, France) [135]
also have systems deployed by military customers but it is
unclear how many systems are in use by for-profit commercial
companies.
The most successful deployment of a commercial SAS
system has been achieved by the Norwegian Defence group FFI
(Horten, Norway). Initially, they deployed an Edgetech (Model
4400) with SAS capability on a HUGIN 1000 AUV [136],
[137]. More recently, they have deployed a Sensotek SAS on a
similar AUV [138]–[140] providing impressive imagery.
III. S
AMPLING REQUIREMENTS
Ideally the synthetic aperture should be sampled finer than
half a wavelength
since the maximum spatial frequency
for propagating waves is
[26]. For a single receiver
transducer, this constrains the maximum along-track speed to
where is the period between pings. In practice, a
higher speed is used where the sonar is moved a distance
between pings, since for a transducer of along-track dimension
most of the echo energy is within a spatial bandwidth of
. However, this results in aliasing of the synthetic aperture
since the energy in the sidelobes of the real beam pattern is
undersampled. The undersampling produces grating lobes in
the reconstructed image and these can mask weaker targets
[141]. More significantly, in interferometric applications, they
reduce the echo coherence and thus the height accuracy since
the autoambiguity sidelobe ratio (AASR) [8] is only
13 dB.
The undersampling can be mitigated by reducing the length of
the synthetic aperture (reduced aperture processing [24]) with a
corresponding loss of along-track resolution [20] (equivalent to
filtering in the wave-number domain [142], [143]). The AASR
can also be reduced to
23 dB by increasing the transmitter
along-track dimension to
1.6 times the dimension of the
receiver along-track dimension [144]. Otherwise, the sampling
interval should be at least
[104], [105] with a maximum
AASR of
24 dB.
For a high-resolution SAS where
may only be a few cen-
timeters, the sampling constraint imposes severe limits on the
potential forward velocity of the platform and so limits the area
mapping rate—loosely defined as the number of resolvable cells
imaged per second. Thus, we can have reasonable along-track
platform speeds (say 3–6 kn) or reasonable swath widths
(100–250 m) but not both. The workaround to this along-track
sampling limitation requires a multiplicity of hydrophones en-
gineered into an along-track receive array. Thus, a SAS, as now
commonly deployed, has a single transmitter/projector and an
array of
hydrophones and receivers. The along-track extent
of the hydrophone array is now
and thus the area
mapping rate has been increased by the number of hydrophones
. This workaround does not come without consequential
problems. Whereas the single-hydrophone SAS is relatively
insensitive to platform yaw errors, the multiple-hydrophone
SAS is sensitive to yaw errors (as well as still sensitive to any
slant-range displacement errors that is common to all synthetic
aperture systems).
With the shift to broadband multiple-hydrophone arrays,
sampling has become the accepted norm although sam-
pling is still feasible [79] by interleaving the phase centers from
adjacent pings.
IV. I
MAGE
RECONSTRUCTION ALGORITHMS
Synthetic aperture image reconstruction is an inverse problem
where the goal is to create an image of the seafloor reflectivity
from measurements of the echo signals along the synthetic aper-
ture [145]. Most algorithms try to invert the system model as-
suming that superposition applies, i.e., aspect-dependent scat-
tering and occlusions are negligible.
There is a plethora of similar SAS reconstruction algorithms.
Conceptually, the simplest SAS reconstruction algorithm is the
correlation algorithm (time-domain correlation). This algorithm
correlates the echo data against a simple model for the data that
would have been received for each image pixel and records the
peak value. In the temporal frequency domain, the algorithm
is called multifrequency holography [147]. When the SAS is
broadband, the correlation algorithm is mathematically identical
to delay-and-sum beamforming and backprojection.
While not pretty or elegant, these algorithms cope with all
array geometries and arbitrary platform histories; even wobbly,
circular, and spiral paths all with sway, surge, roll, and pitch;
none of that matters provided the path is known or measurable.
Clearly they can even cope with a nonlinear sound-speed profile
[148]. The downside is the computation time required to recon-
struct a typical scene.
Research soon began to concentrate on how to make
the image reconstruction algorithms work “better” than the
time-consuming pixel-by-pixel cross correlation. Usually, this
meant faster image reconstruction algorithms such as the block
processing algorithms developed from the single-antenna SAR
equivalent. If the seafloor is “flat,” all point reflector pixels
with the same offset from nadir produce the same data set in
the aperture plane but delayed by the appropriate number of
integral units of one ping period. Thus, only as many cross
correlations as across-track pixels are needed. This technique
is called fast correlation convolution beamforming [62], [120],
and range-stacking [149]. Still a certain amount of computation
is needed to get a reconstructed image. A variation on this tech-
nique is the famed, SAR developed, range-Doppler algorithm
[150], [151]. This starts by transforming the echo data into the
range-Doppler domain by taking a 1-D Fourier transform in the
along-track direction. A coordinate transformation and phase
correction is then applied to remove the curvature and thus
make the data point spread invariant. Finally, a 1-D along-track
inverse Fourier transform reveals the diffraction-limited image.
When beamwidths are wide, an additional secondary range
compression step is required [8].
As computers developed it became feasible to compute larger
2-D fast Fourier transforms (FFTs) and this spurred the develop-
ment of the wave-number algorithm [also called Stolt mapping,
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