lecture09LowRes

ρλ tan θ 2δρ
slant range resolution
Phase noise
•
InSAR phase standard deviation σφ asymptotically approaches Cramer-Rao bound as number of looks NL increases [Rodriguez and Martin, 1992]
σφ =
γ
−2
−1
2N L
→
γ =
1
2 +1 2 N Lσ φ
resolution element at slant range ρ
N
δρ ε i
elemental scatterers
Radar Imagery – Phoenix
N
illumination
flight path
Lake Pleasant
20 km
McDowell Mountains Sky Harbor Airport
ψ 1,ψ 2 , ρ , λ → δρ + α + µ ; δρ , ρ , B, β → θ ; θ , ρ , h → z
The Raw Interferogram
InSAR complex image
* s1s2 = Ab1 Ab 2 exp j (ψ b1 − ψ b 2 + φ )
Microwave – “all-weather” Coherent
• aperture synthesis, InSAR • complex-valued samples
C = I + jQ = Ae jψ
, ψ ∈ [0,2π )
images from earth.esa.int/applications/data_util/SARDOCS/spaceborne/Radar_Courses
Relevant Spaceborne SAR Missions
Satellite Seasat ERS-1 JERS-1 ERS-2 Radarsat-1 SRTM Envisat ALOS TerraSAR-X Radarsat-2 TerraSAR-L Dates 1978 1991-2000 1992-1998 19951995Feb 2000 2002-2007+ 2004-2009+ 2006-2011+ 2005-2012+ 2007? Sponsor US Europe Japan Europe Canada US/Italy/Germany Europe Japan Germany/Astrium Canada Europe Band L C L C C C/X C L X C L Comments Failure ended mission after 100 days Several mission phases with different orbits 44-day repeat orbit ERS-1/2 cross-platform InSAR possible; 35-day repeat Several modes; 24-day repeat orbit Shuttle Radar Topography Mission; SIR-C/X-SAR legacy Several modes; same orbit as ERS-1/2; 35-day repeat 46-day repeat orbit; ScanSAR possible Govt/commercial venture; 11-day repeat orbit 2003 launch slip increases dedication to Radarsat-1 16-day repeat orbit or same orbit as TerraSAR-X?
h
β
lˆ2
θ
ˆ l 1
ρ + δρ , α 2 , µ
ρ ,α1
ˆ lˆ 1 , l2 ≡ unit look vectors ! d
P z
0
2π
Linearization - The Flattened Interferogram
Reference surface interferometric phase
resolution element
Coherent sum of elemental scatterer returns 4πδρε i Ab exp ( jψ b ) = ∑ Aε i exp j ψ ε i − λ i =1
elemental scatterer backscatter amplitude, phase & one-way differential range
Parameters Affecting Surface Backscatter
Frequency/wavelength Look / incidence angle
Surface roughness
Polarization
images from NASA/JPL SIR-C Education Program and earth.esa.int/applications/data_util/SARDOCS/spaceborne/Radar_Courses
A1
θ0 δθ ρ ρ
θ = θ 0 + δθ
P z
− B sin (θ 0 − β ) + B 2 2 ρ φ0 = ( 4π λ )
Topography induces look angle variation
z = h − ρ cosθ ≅ ρ sin θ 0δθ
Flattened interferometric phase
SAR Resolution Element
Complex radar return s for a given resolution element
look angle θ
slant range ρ
4πρ s = Ab exp ( jψ b ) exp − j λ
resolution element backscatter amplitude & phase and propagation phase
Cannot perform InSAR across satellites unless otherwise noted Shorter repeat orbit period results in less overlap between adjacent tracks ERS-2 imaged one day after ERS-1 and images 1/2-hour after Envisat ERS-1/2 have better orbit control & SAR data 2-4x less expensive than Radarsat-1 L-band penetrates vegetation, C/X-band do not TerraSAR-X to provide higher resolution imagery as compared with other missions
Lecture 9
SAR Interferometry (InSAR) Overview InSAR + ScanSAR = Shuttle Radar Topography Mission Differential InSAR Applications
Characteristics of Synthetic Aperture Radar

White Tank Mountains
downtown Phoenix South Mountains
Luke AFB
Sierra Estrella Mountains
Phoenix, Arizona – incoherent sum of 32 ERS-1/2 SAR images ~ 100 x 100 km image
Phoenix Flattened Interferogram
19960218 / 19960219 / 1
mid-swath ambiguity height ~ 164 m
0
2π
Interferometric Correlation
Complex cross-correlation
• at each pixel in ref. image s1 and coregistered slave image s2
Repeat-Pass Interferometry Geometry
Propagation phases
A1
B
A2 B⊥
ψ p1 = − ψ p2 = −
where
4π
β
ˆ l 2
λ
4π
( ρ + α1 )
( ρ + δρ + α 2 + µ )
h
θ
ˆ l 1
ρ + δρ , α 2 , µ
ρ ,α1
φflat = φ − φ0 = ( 4π λ ) − B sin (θ − β ) + µ + α + B sin (θ 0 − β ) ≅ ( 4π λ ) [ − B⊥0δθ + µ + α ] = 2π ( z ha ) + 4π ( µ + α ) λ
" # $# %
where ha = − λρ sin θ 0 2 B⊥0 ≡ ambiguity height , B⊥0 = B cos (θ 0 − β )