Azimuthal SAR Interferogram(azisar)
Sylvain Barbot,Institute of Geophysics and Planetary Sciences,
Scripps Institution of Oceanography,University of California at San Diego
forward look interferogram
θ
α
ϕΔ
)sin(4
1 θαλπϕ −Δ=Δ r
r
backward look interferogram
rr
Δθ
αϕΔ
)sin(4
2 θαλπϕ +Δ−=Δ r
r
range d
irecti
on
range direction
))sin()(sin(4
21 θαθαλπϕϕϕ ++−Δ=−=Δ r
r αθλπϕ sincos
8rr
Δ=Δ
double difference interferogram
double difference suppresses topography and most of troposphere delays.measurement is still ambiguous, but no more relative (Δ0 ||Δr||.cos θ= 0)
rr
Δ
Geometry
L
efficient look direction
L3
λα =
antenna width
wavelength L
r θπϕcos
38
rΔ
=Δ
first fringe Δπ occurs for ||Δr||= 3L/8=3.75m (no wavelength dependence)
Lrπϕθ
83
cosΔ
=Δr
α is the efficient look angle
α
angular energy distribution
βα
L
λ LdL
dL
L
L
λ
θθλ
π
θθλ
πθα
λ
λ
31
)(sinc
)(sinc
/
0
/
0 ≈=
∫
∫
angle first moment from energy distributionReal Aperture Radar
)ˆ(ˆˆ)ˆ.( ιιιι ××+= rrrrrr
insar dbldiffstill not measured
ι a
plane of sight
rr
azimuth (satellite track)incidence
quake slip
arr ˆ.cosrr
=Δ θ
aararar ˆ).ˆ.()ˆ(ˆrrr
+××=
Azimuth View Angle
azimuth
emitted pulse
h=800 km
S=5 km
L=10 m
fo=5.3 GHz
range
Synthetic Aperture Radar
dt
df dop
π⋅
⋅=
21
€
=0 + 2 ⋅2π
λ⋅ R + v ⋅ t( )
1/ 2
€
f dop = 2 ⋅v ⋅ t
λ ⋅R
€
Bdop = 2 ⋅v ⋅T int
λ ⋅R
vLRT
1int ⋅⋅≈λ
L
vB dop ⋅=2
Doppler frequency
Instantaneous phase
Total Dopplerbandwidth
2
Lresolutionspatial =
R
aziθ
L vr
nearest range
Illumination duration Tint
Azimuth Compression
Fd > 0
Fd = 0
Fd < 0
sensor
target
How to filter for look directions ?
Range and look direction variation with time
Look Direction
Doppler analysis
lines of equi-Doppler
lines of equidistanceflight line
illuminated area
Range/Doppler reference system
How to filter for look direction ?
θλ
sin2v
fD =
Local ground incidence angle
Doppler analysis
case of a zero Doppler centroid
2/intT
dopBt
dopf
2/intT−lookcentral
lookbackward
vr
lookforward
intT
Doppler frequency varies linearly with time
Doppler analysis
Doppler frequency variation with time/space
Frequency spectrum in azimuth
(antenna pattern modulation)
f
azifS )(
dopB
2/intTt
dopf
2/intT−
intT
Doppler centroid
vr
Doppler analysis
Image spectrum=Doppler frequency *antenna spectrum * scene impulse response
zero Doppler centroid
vr
dopf
vr
dopf
2/intT− 2/intT
dopB
intT
dopB
intT
2/intT− 2/intT
Doppler analysis
Non-zero Doppler centroid case
non-zero Doppler centroid
forward look forward lookbackward lookbackward look
Doppler Power Spectrum
Doppler frequency / PRF
Aliasing Limit (DFT)
Doppler centroid ~ 0.75
Doppler analysis
back
war
d lo
ok
forward look
back
war
d lo
ok
Doppler analysis
Doppler shift (freq. domain) = azimuth modulation (time domain)
Doppler with range
fd(r)/f0=a2r2+a1r+a0
Dopplerat acquisition
Doppler centroid modulation
IeI
IeIlffi
tlfi
d
d
)/(2
2
0~
~
π
π
=
= Δ
Now easy to take backward and forward look
shifted to center
DFT
back
war
d
backward
forward
forw
ard
no need forDoppler
compensation
Hector Mine azimuth interferogram