1 F. Rocca Spectral shift and differential interferometry
Spectral shift and differential interferometry
Fabio RoccaPolitecnico di Milano
e.mail [email protected]
2 F. Rocca Spectral shift and differential interferometry
αθ
λ
)()(
αθλθλ
−=
sing
The wavelength λ transmitted from the radar changes when projected on the ground depending on the incidence angle.
The spectral shift principle (1)
θ − α
λg
3 F. Rocca Spectral shift and differential interferometry
)(sin αθ −= gf
f
Passing from wave-length to frequency it is easy to see that the measured reflectivity spectrum changes with the view angle θ :
The radar transmitted frequency should change in order to compensate for the frequency change on the ground due to an angle change:
)(sin αθλ
−== fcfg
g
)(tan)(sin)cos(
2 αθαθαθ
θ −−=
−−
−=∂∂ fff g
θαθ
Δ−
−=Δ)(tan
ff
The spectral shift principle (2)
4 F. Rocca Spectral shift and differential interferometry
B nα
f
RF on-board filter
Master
Slave
Frequency shift Δf
RBn=Δθ
)( tan αθ −−=Δ
RfBf n
The spectral shift principle (3)
5 F. Rocca Spectral shift and differential interferometry
-90 -50 0 50 100-20
-15
-10
-5
0
5
10
15
20
Spe
ctra
l shi
ft (M
Hz)
slope (deg)
shadow
-67
descending
Layover
+23
blind angles
Baseline = 200 m500 m
1000 m
2×Sy
stem
Ban
dwid
th
(±B
r)
Critical baseline
Ground slopes and spectral shift
fBandwidth Δ=
ascend
.
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Common band filtering (1)
The signal band-width common to both master and slave images is:
fWWc Δ−=
being W the SAR band-width.
The image SNR due to the spectral shift Δf is thus:
ffW
SNRΔ
Δ−=
f
RF on-board filter
Master
Slave
Frequency shift Δf
cW
cW
The coherence:
Wf
SNRSNR Δ
−=+
= 11
γ
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Band-pass filter
cW2fΔ
cW2fΔ
−
Slave
Frequency shift Δf
f
RF on-board filter
Master
The baseline decorrelation can be eliminated by filtering out the uncorrelated bands of master and slave images.
This can be done by filtering the master and the slave images with band-pass filters with bandwidth Wcand central frequencies Δf /2 and -Δf /2 respectively.
NOTE: critical baseline > fW Δ=
cBRf
W=− )( tan αθ
Common band filtering (2)
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SlaveSlave
Low pass filter(bandwidth BS)Low pass filter(bandwidth BS)MasterMaster
Synthetic Fringes
exp(jϕ(P))
Synthetic Fringes
exp(jϕ(P))Conj( )Conj( )
Low pass filter(bandwidth BM)Low pass filter(bandwidth BM)
Space-varying common band filtering
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θ1θ2
Doppler shiftMaster
Slave
fxCommon band
Azimuth common band filtering
A different Doppler Centroid in themaster and slave images generatesan azimuth spectral shift and a coherence loss that can be avoided by an azimuth common band filtering.
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Common band filtering: an example
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Wide-Spectrum=2W-Δf
f
RF on-board filter
Master
Slave
Getting a wider spectrum in slant-range (1)The spectral shift principle can be exploited to get a ground reflectivity spectrum wider than that achieved from a single SAR image by combining two (or more) interferometric images.
If, after slant-range oversampling, the image spectra (band-width W ) are shifted by ±Δf/2 and coherently summed, a ground spectrum of band-width 2W-Δf is generated.
A wider slant-range spectrum corresponds to a higher slant-range resolution:
( )fWc
Δ−=Δ
22ρ
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f
RF on-board filter
Master
Slave
Common bandwidth
Wide bandwidth
Spectral shiftf0
f0
f0 Δf
Super-resolution
Getting a wider spectrum in slant-range (2)
13 F. Rocca Spectral shift and differential interferometry
θ1θ2
A sort of non-simultaneous SPOT-LIGHT configuration is synthesized.
Doppler shiftMaster
Slave
fxCommon band
Wide-Spectrum=2W-Δf
The same idea used to enhance the slant-range spectrum can be exploited to enlarge the azimuth spectrum by combining two SAR images with different Doppler Centroid.
Getting a wider spectrum in azimuth
14 F. Rocca Spectral shift and differential interferometry
Slant-range
Super-resolution: an exampleCourtesy of M. Suess, Damler-Benz Aerospace Dornier
Harbor with oil storage in Amsterdam
9 ER
S im
ages: res. enhancement 2.7
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The IQL processor has been introduced as a tool for SAR interferometric data browsing.
The IQL processor
• exploits the spectral shift principle in order to half the data rate with only a moderate loss of quality.
• reduces the computing costs (time, memory,disk-space) by moving the common band filtering in range and azimuth at the level of raw data.
Range: half band filter and 2:1 subsampling.Azimuth: 8 looks presumming (Polyphase) of which only 5 are processed.
• uses several “tricks” to gain efficiency:small optimized kernels for images co-registration“quick and dirty” algorithm to compute coherence maps
The Interferometric Quick Look processor
http://earth.esa.int/INSI/
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State vectors processing
Raw data
Ancillary information decoding
Replica
Raw data
Doppler Centroids Estimate
Range & azimuth focusing
Range 2:1 presumming
azimuth looks
Image #1 resampling
Doppler Parameters
Registration param. estimate
Looks Interferogram generation and phasing
Range and azimuth flattening
for each look
Mosaicing
Coherence estimate
Mosaicing
Strip-map interferogram
Strip-map coherence
BaselineAzimuth presumming
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The IQL processor uses the so called quick-and-dirty coherence estimation that is based on the intensities of the two images, rather than on their complex values:
The Quick-and-Dirty coherence estimation
Advantage: no need of estimating and removing the spatially varying interferometric phase before averaging.
Disadvantage: higher bias and variance with respect to the complex estimator.
NOTE: whenever a SAR image contains non-stationary absolute values, the Q&D estimator is strongly affected by the envelope of the absolute values.This effect can be avoided by scaling amplitudes of both images by an estimate of the local signal power obtained by averaging the detected images on a small (3x3x2) window.
12
ˆ22
21
21 −=∑∑
∑i ii i
i ii
II
IIγ
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Fringes |γ| Quick-and-Dirty including amplitudes scaling
|γ| Complex
Quick-and-Dirty vs. complex coherence estimationEstimation window 11x11 points
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Detected image
Effect of power equalization before Q&D estimation
Equalized detected image
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Interferometric Quick Look over Japan (1)
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IQL over Japan (2)
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IQL over Japan (3)
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IQL over Antarctic
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DINSAR: Differential SAR Interferometry
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dntdisplaceme λπϕ 4=Δ
If a scatterer on the ground slightly changes its relative position in the time interval between two SAR acquisitions (e.g. subsidence,landslide, earthquake …), an additive phase term, independent of the baseline, appears.
Here, d is the relative scatterer displacement projected on the slant-range direction
P P’
S 1
S 2
r
d
SAR interferometric phase: ground motion contribution
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The sensitivity of the interferometric phase to the ground motion is much larger than that to the elevation difference.
In the ERS case assuming a perpendicular baseline of 150m the following expression of the interferometric phase (after interferogram flattening) holds:
dq
ntdisplacemeelevation
22510 +
ΔΔΔ
−=
=+= ϕϕϕ
SAR interferometric phase: ground motion contribution
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Synthetic interferogram generation
SAR coordinates DEM Synthetic Interferogram
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Inte
rfer
ogra
mm
a si
ntet
ico
Inte
rfer
ogra
mm
a re
ale
Differential Interferogram
_=
Synthetic interferogram generation
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1 day Etna differential interferogram
30 F. Rocca Spectral shift and differential interferometryImage courtesy of S. Madsen,
SAR interferometric phase: ground motion contribution
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SAR interferometric phase: ground motion contribution
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Bam earthquake (Iran, 2003)• ENVISAT data, geocoded.
• Topographic fringes do not hide the ground motion
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The landslide of St.Etienne de Tinee
Differential Interferometry
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DEM used to remove baseline change
Bn = 200 mDt = 35 giorni (luglio-agosto 2001)
Differential interferogram
Etna 2001
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Etna 2001
• ERS Interferogram
• Geocoded Differential
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Differential InterferometryInterferogram Synthetic Interferogram Differential Interferogram
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SAR interferometric phase: ground motion contribution
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Estimated motion
Space-varying time-constant velocitieshave been hypothesized.
Color coded subsidence velocity inmillimeters per year is shown.
39 F. Rocca Spectral shift and differential interferometry
Differential phases along the Valle del Bove
Master: April 96
1 August 95 2 August 95
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ϕΔ atmosphere
If the propagation medium changes the time interval between two SAR acquisitions (e.g. humidity, temperature, pressure …), an additive phase term, independent of the baseline, appears.
SAR interferometric phase: atmospheric contribution
41 F. Rocca Spectral shift and differential interferometry
ϕϕϕϕϕϕ ΔΔΔΔΔΔ ++++=noiseatmospherentdisplacemeelevationflat
λπ
θ4
0
⋅⋅Δ
−RB
sinq n dλ
π4+θλ
πtan
4R
sBn−
Summary of the SAR interferometric phase contributions
42 F. Rocca Spectral shift and differential interferometryLOS 1
d
LOS 2
Ovest Est
Verticale
Measuring horizontal and vertical motion components
• The same area is observed in ascending and descendng passes. • The two motion projections allow the estimation of the UD and
EW motion components
43 F. Rocca Spectral shift and differential interferometry
2
1
2
1
Subway excavations1
Bradiseismic phenomena2
Naples