<s>
Synthetic-aperture	B-Application
radar	I-Application
(	O
SAR	O
)	O
is	O
a	O
form	O
of	O
radar	B-Application
that	O
is	O
used	O
to	O
create	O
two-dimensional	O
images	O
or	O
three-dimensional	O
reconstructions	O
of	O
objects	O
,	O
such	O
as	O
landscapes	O
.	O
</s>
<s>
SAR	O
uses	O
the	O
motion	O
of	O
the	O
radar	B-Application
antenna	O
over	O
a	O
target	O
region	O
to	O
provide	O
finer	O
spatial	O
resolution	O
than	O
conventional	O
stationary	O
beam-scanning	O
radars	B-Application
.	O
</s>
<s>
SAR	O
is	O
typically	O
mounted	O
on	O
a	O
moving	O
platform	O
,	O
such	O
as	O
an	O
aircraft	O
or	O
spacecraft	O
,	O
and	O
has	O
its	O
origins	O
in	O
an	O
advanced	O
form	O
of	O
side	B-Algorithm
looking	I-Algorithm
airborne	I-Algorithm
radar	I-Algorithm
(	O
SLAR	B-Algorithm
)	O
.	O
</s>
<s>
To	O
create	O
a	O
SAR	O
image	O
,	O
successive	O
pulses	O
of	O
radio	O
waves	O
are	O
transmitted	O
to	O
"	O
illuminate	O
"	O
a	O
target	O
scene	O
,	O
and	O
the	O
echo	B-Protocol
of	O
each	O
pulse	O
is	O
received	O
and	O
recorded	O
.	O
</s>
<s>
The	O
pulses	O
are	O
transmitted	O
and	O
the	O
echoes	B-Protocol
received	O
using	O
a	O
single	O
beam-forming	B-Algorithm
antenna	O
,	O
with	O
wavelengths	O
of	O
a	O
meter	O
down	O
to	O
several	O
millimeters	O
.	O
</s>
<s>
Signal	O
processing	O
of	O
the	O
successive	O
recorded	O
radar	B-Application
echoes	B-Protocol
allows	O
the	O
combining	O
of	O
the	O
recordings	O
from	O
these	O
multiple	O
antenna	O
positions	O
.	O
</s>
<s>
SAR	O
is	O
capable	O
of	O
high-resolution	O
remote	B-Application
sensing	I-Application
,	O
independent	O
of	O
flight	O
altitude	O
,	O
and	O
independent	O
of	O
weather	O
,	O
as	O
SAR	O
can	O
select	O
frequencies	O
to	O
avoid	O
weather-caused	O
signal	O
attenuation	O
.	O
</s>
<s>
SAR	O
images	O
have	O
wide	O
applications	O
in	O
remote	B-Application
sensing	I-Application
and	O
mapping	O
of	O
surfaces	O
of	O
the	O
Earth	O
and	O
other	O
planets	O
.	O
</s>
<s>
SAR	O
can	O
be	O
implemented	O
as	O
inverse	B-Algorithm
SAR	I-Algorithm
by	O
observing	O
a	O
moving	O
target	O
over	O
a	O
substantial	O
time	O
with	O
a	O
stationary	O
antenna	O
.	O
</s>
<s>
A	O
synthetic-aperture	B-Application
radar	I-Application
is	O
an	O
imaging	B-Algorithm
radar	I-Algorithm
mounted	O
on	O
a	O
moving	O
platform	O
.	O
</s>
<s>
Electromagnetic	O
waves	O
are	O
transmitted	O
sequentially	O
,	O
the	O
echoes	B-Protocol
are	O
collected	O
and	O
the	O
system	O
electronics	O
digitizes	O
and	O
stores	O
the	O
data	O
for	O
subsequent	O
processing	O
.	O
</s>
<s>
That	O
is	O
the	O
source	O
of	O
the	O
term	O
"	O
synthetic	O
aperture	O
,	O
"	O
giving	O
it	O
the	O
property	O
of	O
an	O
imaging	B-Algorithm
radar	I-Algorithm
.	O
</s>
<s>
The	O
azimuth	O
and	O
range	O
direction	O
are	O
focused	O
for	O
the	O
generation	O
of	O
2D	O
(	O
azimuth-range	O
)	O
high-resolution	O
images	O
,	O
after	O
which	O
a	O
digital	B-Application
elevation	I-Application
model	I-Application
(	O
DEM	O
)	O
is	O
used	O
to	O
measure	O
the	O
phase	O
differences	O
between	O
complex	O
images	O
,	O
which	O
is	O
determined	O
from	O
different	O
look	O
angles	O
to	O
recover	O
the	O
height	O
information	O
.	O
</s>
<s>
In	O
addition	O
,	O
multiple	O
baselines	O
can	O
be	O
used	O
to	O
extend	O
3D	B-Algorithm
imaging	I-Algorithm
to	O
the	O
time	O
dimension	O
.	O
</s>
<s>
Synthetic-aperture	B-Application
radar	I-Application
determines	O
the	O
3D	O
reflectivity	O
from	O
measured	O
SAR	O
data	O
.	O
</s>
<s>
It	O
is	O
basically	O
a	O
spectrum	O
estimation	O
,	O
because	O
for	O
a	O
specific	O
cell	O
of	O
an	O
image	O
,	O
the	O
complex-value	O
SAR	O
measurements	O
of	O
the	O
SAR	O
image	O
stack	O
are	O
a	O
sampled	O
version	O
of	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
of	O
reflectivity	O
in	O
elevation	O
direction	O
,	O
but	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
is	O
irregular	O
.	O
</s>
<s>
Thus	O
the	O
spectral	O
estimation	O
techniques	O
are	O
used	O
to	O
improve	O
the	O
resolution	O
and	O
reduce	O
speckle	B-Algorithm
compared	O
to	O
the	O
results	O
of	O
conventional	O
Fourier	B-Algorithm
transform	I-Algorithm
SAR	O
imaging	O
techniques	O
.	O
</s>
<s>
FFT	O
(	O
Fast	O
Fourier	B-Algorithm
Transform	I-Algorithm
i.e.	O
,	O
periodogram	O
or	O
matched	O
filter	O
)	O
is	O
one	O
such	O
method	O
,	O
which	O
is	O
used	O
in	O
majority	O
of	O
the	O
spectral	O
estimation	O
algorithms	O
,	O
and	O
there	O
are	O
many	O
fast	O
algorithms	O
for	O
computing	O
the	O
multidimensional	O
discrete	O
Fourier	B-Algorithm
transform	I-Algorithm
.	O
</s>
<s>
Computational	O
Kronecker-core	O
array	O
algebra	O
is	O
a	O
popular	O
algorithm	O
used	O
as	O
new	O
variant	O
of	O
FFT	O
algorithms	O
for	O
the	O
processing	O
in	O
multidimensional	O
synthetic-aperture	B-Application
radar	I-Application
(	O
SAR	O
)	O
systems	O
.	O
</s>
<s>
Capon	O
can	O
yield	O
more	O
accurate	O
spectral	O
estimates	O
with	O
much	O
lower	O
sidelobes	O
and	O
narrower	O
spectral	O
peaks	O
than	O
the	O
fast	O
Fourier	B-Algorithm
transform	I-Algorithm
(	O
FFT	O
)	O
method	O
.	O
</s>
<s>
SAMV	B-Algorithm
method	O
is	O
a	O
parameter-free	O
sparse	O
signal	O
reconstruction	O
based	O
algorithm	O
.	O
</s>
<s>
It	O
achieves	O
super-resolution	B-Algorithm
and	O
is	O
robust	O
to	O
highly	O
correlated	O
signals	O
.	O
</s>
<s>
Applications	O
include	O
synthetic-aperture	B-Application
radar	I-Application
imaging	O
and	O
various	O
source	O
localization	O
.	O
</s>
<s>
SAMV	B-Algorithm
method	O
is	O
capable	O
of	O
achieving	O
resolution	O
higher	O
than	O
some	O
established	O
parametric	O
methods	O
,	O
e.g.	O
,	O
MUSIC	O
,	O
especially	O
with	O
highly	O
correlated	O
signals	O
.	O
</s>
<s>
Computational	O
complexity	O
of	O
the	O
SAMV	B-Algorithm
method	O
is	O
higher	O
due	O
to	O
its	O
iterative	O
procedure	O
.	O
</s>
<s>
The	O
time-domain	O
Backprojection	O
forms	O
images	O
or	O
spectrums	O
by	O
matching	O
the	O
data	O
acquired	O
from	O
the	O
radar	B-Application
and	O
as	O
per	O
what	O
it	O
expects	O
to	O
receive	O
.	O
</s>
<s>
It	O
can	O
be	O
considered	O
as	O
an	O
ideal	O
matched-filter	O
for	O
synthetic-aperture	B-Application
radar	I-Application
.	O
</s>
<s>
Capon	O
and	O
APES	O
can	O
yield	O
more	O
accurate	O
spectral	O
estimates	O
with	O
much	O
lower	O
sidelobes	O
and	O
more	O
narrow	O
spectral	O
peaks	O
than	O
the	O
fast	O
Fourier	B-Algorithm
transform	I-Algorithm
(	O
FFT	O
)	O
method	O
,	O
which	O
is	O
also	O
a	O
special	O
case	O
of	O
the	O
FIR	O
filtering	O
approaches	O
.	O
</s>
<s>
But	O
it	O
offers	O
higher	O
frequency	O
resolution	O
in	O
the	O
resulting	O
power	O
spectral	O
density	O
(	O
PSD	O
)	O
than	O
the	O
fast	O
Fourier	B-Algorithm
transform	I-Algorithm
(	O
FFT	O
)	O
-based	O
methods	O
.	O
</s>
<s>
SAR	O
requires	O
that	O
echo	B-Protocol
captures	O
be	O
taken	O
at	O
multiple	O
antenna	O
positions	O
.	O
</s>
<s>
For	O
multiple	O
static	O
antennas	O
,	O
all	O
combinations	O
of	O
monostatic	O
and	O
multistatic	B-Algorithm
radar	I-Algorithm
waveform	O
captures	O
are	O
possible	O
.	O
</s>
<s>
The	O
lower	O
boundary	O
of	O
the	O
PRF	O
is	O
determined	O
by	O
the	O
Doppler	O
bandwidth	O
of	O
the	O
radar	B-Application
.	O
</s>
<s>
The	O
backscatter	O
of	O
each	O
of	O
these	O
signals	O
is	O
commutatively	O
added	O
on	O
a	O
pixel-by-pixel	O
basis	O
to	O
attain	O
the	O
fine	O
azimuth	O
resolution	O
desired	O
in	O
radar	B-Algorithm
imagery	I-Algorithm
.	O
</s>
<s>
In	O
this	O
mode	O
,	O
the	O
illuminating	O
radar	B-Application
beam	O
is	O
steered	O
continually	O
as	O
the	O
aircraft	O
moves	O
,	O
so	O
that	O
it	O
illuminates	O
the	O
same	O
patch	O
over	O
a	O
longer	O
period	O
of	O
time	O
.	O
</s>
<s>
Radar	B-Application
waves	O
have	O
a	O
polarization	O
.	O
</s>
<s>
Different	O
materials	O
reflect	O
radar	B-Application
waves	O
with	O
different	O
intensities	O
,	O
but	O
anisotropic	O
materials	O
such	O
as	O
grass	O
often	O
reflect	O
different	O
polarizations	O
with	O
different	O
intensities	O
.	O
</s>
<s>
Terrain	O
and	O
land	O
use	O
classification	O
is	O
one	O
of	O
the	O
most	O
important	O
applications	O
of	O
polarimetric	O
synthetic-aperture	B-Application
radar	I-Application
(	O
PolSAR	O
)	O
.	O
</s>
<s>
In	O
those	O
cases	O
a	O
four-component	O
scattering	O
model	O
can	O
be	O
used	O
to	O
decompose	O
polarimetric	O
synthetic-aperture	B-Application
radar	I-Application
(	O
SAR	O
)	O
images	O
.	O
</s>
<s>
The	O
SAR	O
data	O
is	O
first	O
filtered	O
which	O
is	O
known	O
as	O
speckle	B-Algorithm
reduction	O
,	O
then	O
each	O
pixel	O
is	O
decomposed	O
by	O
four-component	O
model	O
to	O
determine	O
the	O
surface	O
scattering	O
power	O
(	O
)	O
,	O
double-bounce	O
scattering	O
power	O
(	O
)	O
,	O
volume	O
scattering	O
power	O
(	O
)	O
,	O
and	O
helix	O
scattering	O
power	O
(	O
)	O
.	O
</s>
<s>
If	O
two	O
observations	O
of	O
the	O
same	O
terrain	O
from	O
very	O
similar	O
positions	O
are	O
available	O
,	O
aperture	O
synthesis	O
can	O
be	O
performed	O
to	O
provide	O
the	O
resolution	O
performance	O
which	O
would	O
be	O
given	O
by	O
a	O
radar	B-Application
system	I-Application
with	O
dimensions	O
equal	O
to	O
the	O
separation	O
of	O
the	O
two	O
measurements	O
.	O
</s>
<s>
If	O
the	O
two	O
samples	O
are	O
obtained	O
simultaneously	O
(	O
perhaps	O
by	O
placing	O
two	O
antennas	O
on	O
the	O
same	O
aircraft	O
,	O
some	O
distance	O
apart	O
)	O
,	O
then	O
any	O
phase	O
difference	O
will	O
contain	O
information	O
about	O
the	O
angle	O
from	O
which	O
the	O
radar	B-Application
echo	B-Protocol
returned	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
one	O
can	O
extract	O
terrain	O
altitude	O
as	O
well	O
as	O
radar	B-Application
reflectivity	O
,	O
producing	O
a	O
digital	B-Application
elevation	I-Application
model	I-Application
(	O
DEM	O
)	O
with	O
a	O
single	O
airplane	O
pass	O
.	O
</s>
<s>
One	O
aircraft	O
application	O
at	O
the	O
Canada	O
Centre	O
for	O
Remote	B-Application
Sensing	I-Application
produced	O
digital	B-Application
elevation	I-Application
maps	I-Application
with	O
a	O
resolution	O
of	O
5m	O
and	O
altitude	O
errors	O
also	O
about	O
5m	O
.	O
</s>
<s>
Interferometry	O
was	O
used	O
to	O
map	O
many	O
regions	O
of	O
the	O
Earth	O
's	O
surface	O
with	O
unprecedented	O
accuracy	O
using	O
data	O
from	O
the	O
Shuttle	B-Algorithm
Radar	I-Algorithm
Topography	I-Algorithm
Mission	I-Algorithm
.	O
</s>
<s>
This	O
means	O
that	O
if	O
the	O
terrain	O
shifts	O
by	O
centimeters	O
,	O
it	O
can	O
be	O
seen	O
in	O
the	O
resulting	O
image	O
(	O
a	O
digital	B-Application
elevation	I-Application
map	I-Application
must	O
be	O
available	O
to	O
separate	O
the	O
two	O
kinds	O
of	O
phase	O
difference	O
;	O
a	O
third	O
pass	O
may	O
be	O
necessary	O
to	O
produce	O
one	O
)	O
.	O
</s>
<s>
Tomo-SAR	O
has	O
an	O
application	O
based	O
on	O
radar	B-Algorithm
imaging	I-Algorithm
,	O
which	O
is	O
the	O
depiction	O
of	O
Ice	O
Volume	O
and	O
Forest	O
Temporal	O
Coherence	O
(	O
Temporal	O
coherence	O
describes	O
the	O
correlation	O
between	O
waves	O
observed	O
at	O
different	O
moments	O
in	O
time	O
)	O
.	O
</s>
<s>
Conventional	O
radar	B-Application
systems	I-Application
emit	O
bursts	O
of	O
radio	O
energy	O
with	O
a	O
fairly	O
narrow	O
range	O
of	O
frequencies	O
.	O
</s>
<s>
The	O
two	O
most	O
common	O
methods	O
to	O
increase	O
signal	O
bandwidth	O
used	O
in	O
UWB	O
radar	B-Application
,	O
including	O
SAR	O
,	O
are	O
very	O
short	O
pulses	O
and	O
high-bandwidth	O
chirping	O
.	O
</s>
<s>
Pulse-based	O
UWB	O
systems	O
,	O
being	O
the	O
more	O
common	O
method	O
associated	O
with	O
the	O
term	O
"	O
UWB	O
radar	B-Application
"	O
,	O
are	O
described	O
here	O
.	O
</s>
<s>
A	O
pulse-based	O
radar	B-Application
system	I-Application
transmits	O
very	O
short	O
pulses	O
of	O
electromagnetic	O
energy	O
,	O
typically	O
only	O
a	O
few	O
waves	O
or	O
less	O
.	O
</s>
<s>
Specifically	O
,	O
the	O
transmit	O
duty	O
cycle	O
is	O
so	O
exceptionally	O
low	O
and	O
pulse	O
time	O
so	O
exceptionally	O
short	O
,	O
that	O
the	O
electronics	O
must	O
be	O
capable	O
of	O
extremely	O
high	O
instantaneous	O
power	O
to	O
rival	O
the	O
average	O
power	O
of	O
conventional	O
radars	B-Application
.	O
</s>
<s>
(	O
Although	O
it	O
is	O
true	O
that	O
UWB	O
provides	O
a	O
notable	O
gain	O
in	O
channel	O
capacity	O
over	O
a	O
narrow	O
band	O
signal	O
because	O
of	O
the	O
relationship	O
of	O
bandwidth	O
in	O
the	O
Shannon	O
–	O
Hartley	O
theorem	O
and	O
because	O
the	O
low	O
receive	O
duty	O
cycle	O
receives	O
less	O
noise	O
,	O
increasing	O
the	O
signal-to-noise	O
ratio	O
,	O
there	O
is	O
still	O
a	O
notable	O
disparity	O
in	O
link	O
budget	O
because	O
conventional	O
radar	B-Application
might	O
be	O
several	O
orders	O
of	O
magnitude	O
more	O
powerful	O
than	O
a	O
typical	O
pulse-based	O
radar	B-Application
.	O
)	O
</s>
<s>
However	O
,	O
that	O
this	O
limitation	O
is	O
solved	O
in	O
chirped	O
UWB	O
radar	B-Application
systems	I-Application
.	O
</s>
<s>
The	O
principal	O
advantages	O
of	O
UWB	O
radar	B-Application
are	O
better	O
resolution	O
(	O
a	O
few	O
millimeters	O
using	O
commercial	O
off-the-shelf	O
electronics	O
)	O
and	O
more	O
spectral	O
information	O
of	O
target	O
reflectivity	O
.	O
</s>
<s>
Because	O
the	O
real	O
aperture	O
of	O
the	O
radar	B-Application
antenna	O
is	O
so	O
small	O
(	O
compared	O
to	O
the	O
wavelength	O
in	O
use	O
)	O
,	O
the	O
radar	B-Application
energy	O
spreads	O
over	O
a	O
wide	O
area	O
(	O
usually	O
many	O
degrees	O
wide	O
in	O
a	O
direction	O
orthogonal	O
(	O
at	O
right	O
angles	O
)	O
to	O
the	O
direction	O
of	O
the	O
platform	O
(	O
aircraft	O
)	O
)	O
.	O
</s>
<s>
Signals	O
are	O
integrated	O
over	O
time	O
and	O
thus	O
the	O
radar	B-Application
"	O
beam	O
"	O
is	O
synthetically	O
reduced	O
to	O
a	O
much	O
smaller	O
aperture	O
–	O
or	O
more	O
accurately	O
(	O
and	O
based	O
on	O
the	O
ability	O
to	O
distinguish	O
smaller	O
Doppler	O
shifts	O
)	O
the	O
system	O
can	O
have	O
hundreds	O
of	O
very	O
"	O
tight	O
"	O
beams	O
concurrently	O
.	O
</s>
<s>
(	O
See	O
pulse-doppler	B-Algorithm
radar	I-Algorithm
)	O
.	O
</s>
<s>
A	O
common	O
technique	O
for	O
many	O
radar	B-Application
systems	I-Application
(	O
usually	O
also	O
found	O
in	O
SAR	O
systems	O
)	O
is	O
to	O
"	O
chirp	B-Algorithm
"	O
the	O
signal	O
.	O
</s>
<s>
In	O
a	O
"	O
chirped	O
"	O
radar	B-Application
,	O
the	O
pulse	O
is	O
allowed	O
to	O
be	O
much	O
longer	O
.	O
</s>
<s>
But	O
in	O
a	O
chirped	B-Algorithm
radar	I-Algorithm
,	O
this	O
longer	O
pulse	O
also	O
has	O
a	O
frequency	O
shift	O
during	O
the	O
pulse	O
(	O
hence	O
the	O
chirp	B-Algorithm
or	O
frequency	O
shift	O
)	O
.	O
</s>
<s>
In	O
a	O
typical	O
SAR	O
application	O
,	O
a	O
single	O
radar	B-Application
antenna	O
is	O
attached	O
to	O
an	O
aircraft	O
or	O
spacecraft	O
such	O
that	O
a	O
substantial	O
component	O
of	O
the	O
antenna	O
's	O
radiated	O
beam	O
has	O
a	O
wave-propagation	O
direction	O
perpendicular	O
to	O
the	O
flight-path	O
direction	O
.	O
</s>
<s>
Resolution	O
in	O
the	O
range	O
dimension	O
of	O
the	O
image	O
is	O
accomplished	O
by	O
creating	O
pulses	O
which	O
define	O
very	O
short	O
time	O
intervals	O
,	O
either	O
by	O
emitting	O
short	O
pulses	O
consisting	O
of	O
a	O
carrier	O
frequency	O
and	O
the	O
necessary	O
sidebands	O
,	O
all	O
within	O
a	O
certain	O
bandwidth	O
,	O
or	O
by	O
using	O
longer	O
"	O
chirp	B-Algorithm
pulses	I-Algorithm
"	O
in	O
which	O
frequency	O
varies	O
(	O
often	O
linearly	O
)	O
with	O
time	O
within	O
that	O
bandwidth	O
.	O
</s>
<s>
The	O
differing	O
times	O
at	O
which	O
echoes	B-Protocol
return	O
allow	O
points	O
at	O
different	O
distances	O
to	O
be	O
distinguished	O
.	O
</s>
<s>
The	O
"	O
synthetic	O
aperture	O
"	O
simulated	O
at	O
maximum	O
system	O
range	O
by	O
this	O
process	O
not	O
only	O
is	O
longer	O
than	O
the	O
real	O
antenna	O
,	O
but	O
,	O
in	O
practical	O
applications	O
,	O
it	O
is	O
much	O
longer	O
than	O
the	O
radar	B-Application
aircraft	O
,	O
and	O
tremendously	O
longer	O
than	O
the	O
radar	B-Application
spacecraft	O
.	O
</s>
<s>
Although	O
some	O
references	O
to	O
SARs	O
have	O
characterized	O
them	O
as	O
"	O
radar	B-Application
telescopes	O
"	O
,	O
their	O
actual	O
optical	O
analogy	O
is	O
the	O
microscope	O
,	O
the	O
detail	O
in	O
their	O
images	O
being	O
smaller	O
than	O
the	O
length	O
of	O
the	O
synthetic	O
aperture	O
.	O
</s>
<s>
In	O
radar-engineering	O
terms	O
,	O
while	O
the	O
target	O
area	O
is	O
in	O
the	O
"	O
far	B-Algorithm
field	I-Algorithm
"	O
of	O
the	O
illuminating	O
antenna	O
,	O
it	O
is	O
in	O
the	O
"	O
near	O
field	O
"	O
of	O
the	O
simulated	O
one	O
.	O
</s>
<s>
When	O
the	O
radar	B-Application
is	O
to	O
be	O
carried	O
by	O
a	O
high-speed	O
vehicle	O
and	O
is	O
to	O
image	O
a	O
large	O
area	O
at	O
fine	O
resolution	O
,	O
those	O
conditions	O
may	O
clash	O
,	O
leading	O
to	O
what	O
has	O
been	O
called	O
SAR	O
's	O
ambiguity	O
problem	O
.	O
</s>
<s>
The	O
same	O
considerations	O
apply	O
to	O
"	O
conventional	O
"	O
radars	B-Application
also	O
,	O
but	O
this	O
problem	O
occurs	O
significantly	O
only	O
when	O
resolution	O
is	O
so	O
fine	O
as	O
to	O
be	O
available	O
only	O
through	O
SAR	O
processes	O
.	O
</s>
<s>
Combining	O
the	O
series	O
of	O
observations	O
requires	O
significant	O
computational	O
resources	O
,	O
usually	O
using	O
Fourier	B-Algorithm
transform	I-Algorithm
techniques	O
.	O
</s>
<s>
The	O
result	O
is	O
a	O
map	O
of	O
radar	B-Application
reflectivity	O
,	O
including	O
both	O
amplitude	O
and	O
phase	O
.	O
</s>
<s>
Unfortunately	O
,	O
the	O
phase	O
differences	O
between	O
adjacent	O
image	O
picture	O
elements	O
(	O
"	O
pixels	O
"	O
)	O
also	O
produce	O
random	O
interference	O
effects	O
called	O
"	O
coherence	O
speckle	B-Algorithm
"	O
,	O
which	O
is	O
a	O
sort	O
of	O
graininess	O
with	O
dimensions	O
on	O
the	O
order	O
of	O
the	O
resolution	O
,	O
causing	O
the	O
concept	O
of	O
resolution	O
to	O
take	O
on	O
a	O
subtly	O
different	O
meaning	O
.	O
</s>
<s>
The	O
scale	O
of	O
that	O
random	O
speckle	B-Algorithm
structure	O
is	O
governed	O
by	O
the	O
size	O
of	O
the	O
synthetic	O
aperture	O
in	O
wavelengths	O
,	O
and	O
cannot	O
be	O
finer	O
than	O
the	O
system	O
's	O
resolution	O
.	O
</s>
<s>
Speckle	B-Algorithm
structure	O
can	O
be	O
subdued	O
at	O
the	O
expense	O
of	O
resolution	O
.	O
</s>
<s>
Before	O
rapid	O
digital	O
computers	O
were	O
available	O
,	O
the	O
data	O
processing	O
was	O
done	O
using	O
an	O
optical	O
holography	B-Algorithm
technique	O
.	O
</s>
<s>
The	O
analog	O
radar	B-Application
data	O
were	O
recorded	O
as	O
a	O
holographic	B-Algorithm
interference	O
pattern	O
on	O
photographic	O
film	O
at	O
a	O
scale	O
permitting	O
the	O
film	O
to	O
preserve	O
the	O
signal	O
bandwidths	O
(	O
for	O
example	O
,	O
1:1	O
,	O
000,000	O
for	O
a	O
radar	B-Application
using	O
a	O
0.6-meter	O
wavelength	O
)	O
.	O
</s>
<s>
Then	O
light	O
using	O
,	O
for	O
example	O
,	O
0.6-micrometer	O
waves	O
(	O
as	O
from	O
a	O
helium	O
–	O
neon	O
laser	O
)	O
passing	O
through	O
the	O
hologram	B-Algorithm
could	O
project	O
a	O
terrain	O
image	O
at	O
a	O
scale	O
recordable	O
on	O
another	O
film	O
at	O
reasonable	O
processor	O
focal	O
distances	O
of	O
around	O
a	O
meter	O
.	O
</s>
<s>
This	O
worked	O
because	O
both	O
SAR	O
and	O
phased	O
arrays	O
are	O
fundamentally	O
similar	O
to	O
optical	O
holography	B-Algorithm
,	O
but	O
using	O
microwaves	O
instead	O
of	O
light	O
waves	O
.	O
</s>
<s>
The	O
"	O
optical	O
data-processors	O
"	O
developed	O
for	O
this	O
radar	B-Application
purpose	O
were	O
the	O
first	O
effective	O
analog	O
optical	O
computer	O
systems	O
,	O
and	O
were	O
,	O
in	O
fact	O
,	O
devised	O
before	O
the	O
holographic	B-Algorithm
technique	O
was	O
fully	O
adapted	O
to	O
optical	O
imaging	O
.	O
</s>
<s>
Because	O
of	O
the	O
different	O
sources	O
of	O
range	O
and	O
across-range	O
signal	O
structures	O
in	O
the	O
radar	B-Application
signals	O
,	O
optical	O
data-processors	O
for	O
SAR	O
included	O
not	O
only	O
both	O
spherical	O
and	O
cylindrical	O
lenses	O
,	O
but	O
sometimes	O
conical	O
ones	O
.	O
</s>
<s>
The	O
two	O
dimensions	O
of	O
a	O
radar	B-Algorithm
image	I-Algorithm
are	O
range	O
and	O
cross-range	O
.	O
</s>
<s>
Radar	B-Algorithm
images	I-Algorithm
of	O
limited	O
patches	O
of	O
terrain	O
can	O
resemble	O
oblique	O
photographs	O
,	O
but	O
not	O
ones	O
taken	O
from	O
the	O
location	O
of	O
the	O
radar	B-Application
.	O
</s>
<s>
This	O
is	O
because	O
the	O
range	O
coordinate	O
in	O
a	O
radar	B-Algorithm
image	I-Algorithm
is	O
perpendicular	O
to	O
the	O
vertical-angle	O
coordinate	O
of	O
an	O
oblique	O
photo	O
.	O
</s>
<s>
The	O
apparent	O
entrance-pupil	O
position	O
(	O
or	O
camera	O
center	O
)	O
for	O
viewing	O
such	O
an	O
image	O
is	O
therefore	O
not	O
as	O
if	O
at	O
the	O
radar	B-Application
,	O
but	O
as	O
if	O
at	O
a	O
point	O
from	O
which	O
the	O
viewer	O
's	O
line	O
of	O
sight	O
is	O
perpendicular	O
to	O
the	O
slant-range	O
direction	O
connecting	O
radar	B-Application
and	O
target	O
,	O
with	O
slant-range	O
increasing	O
from	O
top	O
to	O
bottom	O
of	O
the	O
image	O
.	O
</s>
<s>
Items	O
directly	O
beneath	O
the	O
radar	B-Application
appear	O
as	O
if	O
optically	O
viewed	O
horizontally	O
(	O
i.e.	O
,	O
from	O
the	O
side	O
)	O
and	O
those	O
at	O
far	O
ranges	O
as	O
if	O
optically	O
viewed	O
from	O
directly	O
above	O
.	O
</s>
<s>
When	O
viewed	O
as	O
specified	O
above	O
,	O
fine-resolution	O
radar	B-Algorithm
images	I-Algorithm
of	O
small	O
areas	O
can	O
appear	O
most	O
nearly	O
like	O
familiar	O
optical	O
ones	O
,	O
for	O
two	O
reasons	O
.	O
</s>
<s>
Secondly	O
,	O
the	O
radar	B-Application
illumination	O
then	O
being	O
downward	O
,	O
shadows	O
are	O
seen	O
in	O
their	O
most-familiar	O
"	O
overhead-lighting	O
"	O
direction	O
.	O
</s>
<s>
However	O
,	O
slopes	O
facing	O
the	O
radar	B-Application
will	O
be	O
foreshortened	O
and	O
ones	O
facing	O
away	O
from	O
it	O
will	O
be	O
lengthened	O
from	O
their	O
horizontal	O
(	O
map	O
)	O
dimensions	O
.	O
</s>
<s>
Then	O
one	O
"	O
sees	O
"	O
,	O
for	O
example	O
,	O
the	O
radar-facing	O
wall	O
of	O
a	O
building	O
as	O
if	O
from	O
the	O
inside	O
,	O
while	O
the	O
building	O
's	O
interior	O
and	O
the	O
rear	O
wall	O
(	O
that	O
nearest	O
to	O
,	O
hence	O
expected	O
to	O
be	O
optically	O
visible	O
to	O
,	O
the	O
viewer	O
)	O
have	O
vanished	O
,	O
since	O
they	O
lack	O
illumination	O
,	O
being	O
in	O
the	O
shadow	O
of	O
the	O
front	O
wall	O
and	O
the	O
roof	O
.	O
</s>
<s>
Surfaces	O
that	O
we	O
usually	O
consider	O
rough	O
will	O
,	O
if	O
that	O
roughness	O
consists	O
of	O
relief	O
less	O
than	O
the	O
radar	B-Application
wavelength	O
,	O
behave	O
as	O
smooth	O
mirrors	O
,	O
showing	O
,	O
beyond	O
such	O
a	O
surface	O
,	O
additional	O
images	O
of	O
items	O
in	O
front	O
of	O
it	O
.	O
</s>
<s>
The	O
direction	O
of	O
overlay	O
of	O
any	O
scene	O
point	O
is	O
not	O
directly	O
toward	O
the	O
radar	B-Application
,	O
but	O
toward	O
that	O
point	O
of	O
the	O
SAR	O
's	O
current	O
path	O
direction	O
that	O
is	O
nearest	O
to	O
the	O
target	O
point	O
.	O
</s>
<s>
These	O
considerations	O
,	O
along	O
with	O
the	O
speckle	B-Algorithm
structure	O
due	O
to	O
coherence	O
,	O
take	O
some	O
getting	O
used	O
to	O
in	O
order	O
to	O
correctly	O
interpret	O
SAR	O
images	O
.	O
</s>
<s>
A	O
technique	O
closely	O
related	O
to	O
SAR	O
uses	O
an	O
array	O
(	O
referred	O
to	O
as	O
a	O
"	O
phased	O
array	O
"	O
)	O
of	O
real	O
antenna	O
elements	O
spatially	O
distributed	O
over	O
either	O
one	O
or	O
two	O
dimensions	O
perpendicular	O
to	O
the	O
radar-range	O
dimension	O
.	O
</s>
<s>
When	O
the	O
radar	B-Application
is	O
carried	O
by	O
an	O
aircraft	O
or	O
an	O
orbiting	O
vehicle	O
,	O
those	O
positions	O
are	O
functions	O
of	O
a	O
single	O
variable	O
,	O
distance	O
along	O
the	O
vehicle	O
's	O
path	O
,	O
which	O
is	O
a	O
single	O
mathematical	O
dimension	O
(	O
not	O
necessarily	O
the	O
same	O
as	O
a	O
linear	O
geometric	O
dimension	O
)	O
.	O
</s>
<s>
Temporal	O
frequencies	O
being	O
the	O
variables	O
commonly	O
used	O
by	O
radar	B-Application
engineers	O
,	O
their	O
analyses	O
of	O
SAR	O
systems	O
are	O
usually	O
(	O
and	O
very	O
productively	O
)	O
couched	O
in	O
such	O
terms	O
.	O
</s>
<s>
The	O
core	O
of	O
both	O
the	O
SAR	O
and	O
the	O
phased	O
array	O
techniques	O
is	O
that	O
the	O
distances	O
that	O
radar	B-Application
waves	O
travel	O
to	O
and	O
back	O
from	O
each	O
scene	O
element	O
consist	O
of	O
some	O
integer	O
number	O
of	O
wavelengths	O
plus	O
some	O
fraction	O
of	O
a	O
"	O
final	O
"	O
wavelength	O
.	O
</s>
