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1 F. Rocca Spectral shift and differential interferometry

Spectral shift and differential interferometry

Fabio RoccaPolitecnico di Milano

e.mail [email protected]


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


)(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



B nα

f

RF on-board filter

Master

Slave

Frequency shift Δf

RBn=Δθ

)( tan αθ −−=Δ

RfBf n



-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

.


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


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)


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


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.


Common band filtering: an example


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


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)


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


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


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/


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


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


Fringes |γ| Quick-and-Dirty including amplitudes scaling

|γ| Complex

Quick-and-Dirty vs. complex coherence estimationEstimation window 11x11 points


Detected image

Effect of power equalization before Q&D estimation

Equalized detected image


Interferometric Quick Look over Japan (1)


IQL over Japan (2)


IQL over Japan (3)


IQL over Antarctic


DINSAR: Differential SAR Interferometry


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


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



Synthetic interferogram generation

SAR coordinates DEM Synthetic Interferogram


Inte

rfer

ogra

mm

a si

ntet

ico

Inte

rfer

ogra

mm

a re

ale

Differential Interferogram

_=

Synthetic interferogram generation


1 day Etna differential interferogram

30 F. Rocca Spectral shift and differential interferometryImage courtesy of S. Madsen,



Bam earthquake (Iran, 2003)• ENVISAT data, geocoded.

• Topographic fringes do not hide the ground motion


The landslide of St.Etienne de Tinee

Differential Interferometry


DEM used to remove baseline change

Bn = 200 mDt = 35 giorni (luglio-agosto 2001)

Differential interferogram

Etna 2001


Etna 2001

• ERS Interferogram

• Geocoded Differential


Differential InterferometryInterferogram Synthetic Interferogram Differential Interferogram


Estimated motion

Space-varying time-constant velocitieshave been hypothesized.

Color coded subsidence velocity inmillimeters per year is shown.


Differential phases along the Valle del Bove

Master: April 96

1 August 95 2 August 95


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


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


2

1

2

1

Subway excavations1

Bradiseismic phenomena2

Naples

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