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1 Télédétection radar – 3A SICOM SIM SN
INSIS Fundamentals of Remote Sensing: SAR Interferometry
Notions fondamentales de télédétection : l’interférométrie RSO
Gabriel VASILE Chargé de Recherche CNRS
gabriel.vasile@gipsa-lab.grenoble-inp.fr
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Range focusing
Azimuth focusing
range
azim
ut
SAR amplitude image ©SYTER, Telecom ParisTech
SAR focusing: ERS-1, Chamonix valley, 512 × 512 pixels
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Range focusing
Azimuth focusing
azim
ut
range
SAR focusing: ERS-1, Chamonix valley, 512 × 512 pixels
SAR phase image ©SYTER, Telecom ParisTech
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Emission: H and V Reception: H and V
Penetration depth
Backscattering mechanisms
+
Propagation
2 phenomena -> differential measurements
Sinclair formula & differential measurements
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Two SLC images: kM (master), kS (slave) Same target area Slightly different viewing angles Hermitian product -> complex cross-correlation
Internal coherence M&S intensities
Differential measurements – InSAR
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Two SLC images: kM (master), kS (slave) Same target area Slightly different viewing angles Hermitian product -> complex cross-correlation
Normalized complex cross-correlation
INTERFEROMETRIC PHASE: φ = arg{C} INTERFEROMETRIC COHERENCE: c = ABS{C}
Differential measurements – InSAR
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Fully polarimetric SAR data Cross-polar symmetrisation (monostatic case)
Vectorisation on the Pauli basis (target vector): k=[SHH+SVV SHH-SVV 2SHV]T
Hermitian product -> complex correlation Polarimetric coherency matrix
Differential measurements – POLSAR
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Polarimetric interferometric coherency matrix:
Polarimetric M&S coherency matrices:
Differential measurements – POL-InSAR
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Radar Interferometry Outlines
Overview of interferometry Satellite Interferometry Satellite InSAR geometry InSAR processing
measuring topography Satellite Differential InSAR D-InSAR processing
measuring motion on the Earth’s surface SAR examples
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Satellite Interferometry
For satellite interferometry of the repeat-pass type, one image is taken one day, and a second image is taken of the same scene one or more days later. More images can be taken at later intervals and used in the processing,
as long as the scene retains reasonable coherence over the longer time interval
Because there is always a time delay, and usually parallax as well, assumptions must be made or processing must be done to remove the unwanted component of motion or topography
In Feb. 2000, the Shuttle Radar Topography Mission obtained topographic (elevation) data of much of the Earth’s surface using single-pass interferometry, i.e., image pairs were acquired at the same time using two radar antennas separated physically to create a 60-m fixed baseline.
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Radar Interferometry from Space
SRTM
TANDEM ERS-1/2
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Radar Interferometry from Space
SRTM
TANDEM ERS-1/2
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Radar Interferometry from Space : SRTM mission
NASA / DLR
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Coverage of 11-day SRTM Mission (Feb. 2000)
NASA / DLR
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SRTM Perspective View with Landsat Overlay
NASA / DLR
Elevation data from C-band across-track interferometric radar, SRTM Acquired Feb. 16, 2000 Height exaggeration 2x Landsat overlay Acquired: Dec. 14, 1984 View toward the North 34.42°N 119.17°W
Santa Clara River Valley, California
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ERS –1 and ERS – 2 TANDEM Mission (1995-2000)
ESA • Repeat pass interferometric SAR uses two antenna positions to acquire two SAR images.
• Vertical height is determined by comparing phase measurements.
• Observable terrain shifts are on the order of the radar wavelength or smaller.
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Radar Interferometry from Space
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ERS –1 and ERS – 2 TANDEM Mission • Colour: Interferogram Phase, 16
steps from 0 to 2π radians • Intensity: Interferogram Magnitude • Saturation: Coherence • Interferogram Magnitude is the
background black-and-white image - similar to regular SAR image.
• Coherence (colour brightness) indicates the degree of phase correlation. Low coherence indicates greater change (lakes at upper left). High coherence indicates least change (exposed rocks at lower left).
• Colour-coded interferogram phase: a phase change of 2π radians corresponds to an altitude change of 232 m
Schefferville, Québec
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Satellite Repeat-pass InSAR Geometry
• A radar is essentially a distance or range measuring sensor
• It can measure range in 2 ways: • Time delay:
R=c/2B = 8 m • Phase:
R=λ/100 = 1 mm • Phase is much more accurate • but is a relative measurement only
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How a SAR Measures Phase
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Phase after Scattering from a Random Surface
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Interferometer Phase
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How Differential Phase Measures Topography
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Interferometric phase ambiguity
Wrapped phase φ = φ (mod 2π)
Nyquist criterion | φ(N) − φ(M)| < π
Unwrapped phase φ
φ
“Automatic’’ methods: local approach : cuts positioning, propagation global approach: least squares (phase or local frequencies)
Phase Unwrapping
€
φc (M,N) =
φ(N) −φ(M) if φ(N) −φ(M) < π
+2π if φ(N) −φ(M) ≤ −π−2π if φ(N) −φ(M) ≥ π
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
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2 images single look complex (SLC):
After co-registration:
Complex multi-looking: (m,n) (i,j)
SLC 1
Coh. Phase
Amp 1 Amp 2
SLC 2
Interferogram Estimation
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Distribution of the sample coherence d as function of theoretical coherence value D and the number of looks L>1:
Distribution function of L, D = 0.5 Bias function of L
Coherence Estimation
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Distribution of the sample phase φ as function of theoretical coherence value D and the number of looks L>1:
Distribution function of D β = 0, L = 4
Distribution function of L β = 0, D = 0.7
D
Phase Estimation
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Measuring Coherence
Coherence must always be measured to assess the suitability of the data set for InSAR processing
Coherence magnitude is closely related to the local standard deviation of differential phase
High coherence magnitude tells us: images have good SNR phase centres of scatterers are stable any motion is spatially “organized”
Coherence magnitude: 0.3 - 0.5 is useable, but noisy 0.5 - 0.7 is good 0.7 - 1.0 is excellent
Coherence has also been successfully used as a terrain classification parameter: water, vegetation, desert, city
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InSAR Processing
Process data to SLC images Register the two images to 1/10 pixel Over-sample by a factor of 2 in both dimensions Filter common bands in spectrum Conjugate multiply to form interferogram Smooth the interferogram Measure coherence Unwrap phase Estimate geometry parameters (especially baseline) Remove flat-earth fringes Convert unwrapped phase to height and/or motion
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InSAR Processing: Chitina River Valley, S.E. Alaska
ERS images acquired Feb. 1994
• B⊥ = 40 m • Flat-earth fringes were
removed. • Phase is still wrapped. • Each revolution of the colour
wheel represents an increase of 200 m in altitude.
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Topography Contours from Interferogram: ERS-1, 1991
Franklin Bluffs and Sagavanirktok River on the North Slope of Alaska Perspective view generated from an interferometrically derived DEM
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Radar Differential Interferometry from Space
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Radar Differential Interferometry from Space
The information contained in the D-InSAR phase can be decomposed in:
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Radar Differential Interferometry from Space
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D-InSAR: orbital compensation
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D-InSAR: topographic compensation (DTM)
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D-InSAR: adaptive filtering
38 Télédétection radar – 3A SICOM SIM SN LISTIC/LAPI 38
Glaciology: temperate glaciers Location
French Alps – “Chamonix Mont-Blanc” test site
Mer-de-Glace Argentière Location 45°55’15’’ N/ 6°55’45’’ E 45°56’15’’’N / 7°00’30’’ E
Area / Length 3,5 (km²) / 4.7 (km) 15 (km²) / 9 (km)
Mean slope ~ 9° (17%) ~14° (26%)
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ERS ascending (image panchromatic SPOT-1) ERS descending
ERS - 1/2: visibility assessment
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ERS-1/2 Interferogram (March 1996)
TANDEM ERS (Mer-de-glace)
(c) 100 km
5 km
SAR amplitude
InSAR coherence InSAR phase
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Mer-de-glace [660 × 361 pixels]
amplitude coherence phase
IDAN ML amplitude IDAN ML coherence IDAN ML phase
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Measuring Glacier Velocity by D-InSAR
filtered coherence
filtered phase
2D local frequencies
mesures In situ DTM
velocity field
TANDEM ERS, 10/11-March-1996 Chamonix Mont-Blanc
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IDAN ML unwrapped phase IDAN ML phase mod 2π
Mer-de-glace [618 × 405 pixels]: weighted least-square phase unwrapping
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From Slant Range to Ground Range DTM (Lat/Lon, WGS 1984):
separating relief / displacement geocoding
D-InSAR scalar measurement: slant range displacement
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Glacier Velocity Field: Argentière & Mer-de-glace “In situ” measurements:
unknown offset ablation sticks differential GPS
D-InSAR/DTM measurements: 3D displacement field glacier flow direction (SPF,MSF)
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TerraSAR-X StripMap Acquisition (3m res) of the Pyramids of Giza, Egypt Prel. Image recorded during calibration phase
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" South Nigeria, 3m res
TerraSAR-X Basic Image Products
City of Warri
Warri airport
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TerraSAR-X Basic Image Products
" Cape Town (South Africa) – 1m res
International airport
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TerraSAR-X Basic Image Products
Mombasa (Kenya) – 1m res
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TerraSAR-X Basic Image Products
" Addis Abeba (Ethiopia), 3m res
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Bibliography
H. Maître, Traitement des images de RSO, Hermes Sciences Publications, 2001
L. Lliboutry, Sciences Géométriques et Télédétection, Masson, 1992 C. Elachi, Introduction to the Physics and Techniques of Remote Sensing,
Wiley Series in Remote Sensing, 1987 Tutoriel du Centre Canadien de Télédétection (CCT):
http://www.ccrs.nrcan.gc.ca/resource/index_f.php#tutor Trouvé E., Imagerie Radar à Synthèse d’Ouverture, cours ETASM,
Université de Savoie, 2004 Faller N., TerraSAR-X: Surveying, Mapping & Infrastructure Development,
Map Africa 2007 Hajnsek I. at al., TerraSAR-X Mission: Application and Data Access,
Int. Summer School on Very High Resolution Remote Sensing, 2009
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