Introduction to radar. interferometry

Transcription

1 Introduction to radar Introduction to Radar Interferometry interferometry Presenter: F.Sarti (ESA/ESRIN) With kind contribution by the Radar Department of CNES

2 All-weather observation system (active system) Potentialities of radar Penetration capabilities estimation of vegetal biomass Dielectric properties of medium Sensitivity to water content Sensitivity to geometrical structures with scales of the same order than the wavelength ENVISAT ASAR ERS SAR, Radarsat: C band 5,6 cm JERS, ALOS PalSAR: L band 23 cm λ

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4 Sea roughness Waves, wind, sea pollution, storms Topography, slope Cities Ships and military detection RADARSAT SCANSAR IMAGE (500 km SWATH)

5 Active instrument. Intensity and Phase. Coherent illumination. Speckle noise (consequence of a coherent illumination) I m R e Δ φ pixel n 1 pixel n 2 I m R e contribution of one pixel response scatterer

6 The speckle noise, consequence of a coherent illumination Large radiometry : large noise The speckle noise is a multiplicative noise Low radiometry : low noise Image SETHI, bande C, 3 m

7 Interferometry : content Principle of interferometry Products Digital Elevation Models (DEMs) Ground Movement mapping Coherence map Limitations Temporal Geometric Atmospheric propagation Signal-to-Noise Ratio Illustrations of Applications

8 Principle Products Digital Elevation Models Ground Movements Coherence map Limitations Temporal Geometric Atmospheric propagation Signal-to-Noise Ratio Illustrations of Applications

9 Principle 1/8 Each image pixel (of a single look complex LSC product) contains two terms: Amplitude : A Phase : pixel ϕ specific ϕ = ϕ + ϕ specific is not estimable dist Pixel = A. e jφ ϕ dist 2π Dist λ = Two Way = 4π Dist λ (Single) Phase cannot be used as an information

10 Principle 2/8 Δϕ = ϕ If we have two images and if the ground didn t change, ϕ = ϕ specific _ 1 im _ 2 ϕ im _1 specific _ 2 = ϕ dist _ 2 ϕ dist _1 Dist 1 Pixel 1 = A 1. e jφ1 Dist 2 Pixel 2 = A 2. e jφ2 Δϕ = 4π ( Dist2 Dist 1 ) λ Δϕ Image of is called an Interferogram Image of Distance differences (removal of unknown phase term, pixel-specific)

11 Principle 3/8 Co-registration of images 1 2 Master image Slave image Geometry image1 (Master) Geometry image 2 (slave) Terrain geometry The distance measurement principle relies on the same terrain pixel. Practically, the two images have (always) a (slightly) different geometry. In order to compute a phase difference pixel by pixel, the images must be first precisely co-registered (made superimposable) : resampling of the slave image into the master image geometry. Coregistration must be sub-pixel precise (better than 0.3 pixels) and can be achieved by means of complex correlation.

12 Principle 4/8 Geometric information included in the interferograms (1/5) 1 1. Ground displacement Master image (Day 1) 1 Slave image (Day 2) Only the component of the displacement in the radar viewing direction can be measured by interferometry

13 Principle 5/8 Geometric information included in the interferograms (2/5) 2. Atmospheric propagation effects Day 1 Day 2

14 Principle 6/8 Geometric information included in the interferograms (3/5) 3. topography : DEM Etna - simulation Iso Altitude Curves

15 Principle 7/8 Geometric information included in the interferograms (4/5) 4. orbital configuration (baseline) Borth R 2 R 1 i δi Dist2 Phases variations over a flat terrain (1D approach) contribution removed by the interferometric processing Dist1 xˆ Δϕ = 4π ( Dist2 Dist1 ) λ

16 Principle 8/8 Geometric information included in the interferograms (5/5) 4. orbital configuration (baseline) (Cntd) residual fringes Phases variations over a flat terrain (3D approach)

17 Principle Products (applications) Digital Elevation Models Ground Movements Coherence map Limitations Temporal Geometric Atmospheric propagation Signal-to-Noise Ratio Illustrations of Applications

18 B Elevation Ground Displacements i Borth Etna Etna Landers H.A. HA, Height of ambiguity = variation of altitude between two pixels induced by topography, giving one fringe on the interferogram (by stereoscopic effect). For ERS: H.A.~10,000 /Borth (m) Iso-altitude curves After elimination of orbital fringes, ground elevation is represented by iso- altitude curves.. Phase gives then a measure of elevation modulo the altitude of ambiguity (function of the orbital baseline, causing a stereoscopic effect). Iso-displacement curves (non simultaneous acquisitions) If a pixel was displaced between the two acquisitions, this generates a difference in distance and therefore a phase difference. The accuracy of the measurement is of the order of mm. Phase measurements are modulo 2π, 2 thus showing up as fringes (need of unwrapping)

19 Principle Products (applications) Digital Elevation Models Terrain Movements Coherence map Limitations Temporal Geometric Atmospheric propagation Signal-to-Noise Ratio Illustrations of Applications

20 Relief Slight stereo effect (B/H = 10-4!) But sufficient for small image distortions (only at phase level) few centimeters enough to produce phase shifts proportional to Elevation Precise measurement λ but known modulo creates fringes need to be unwrapped Etna - question : what variation of altitude corresponds to one fringe? By definition, it corresponds to the altitude of ambiguity simulation Iso Altitude Curves

21 Relief The altitude of ambiguity (1/3) S 2 B orth 4π d Δϕ = = λ 4π hδ i λsin( i) S 1 i δ i h λ.sin( i) =.Δϕ 4π. δ i Dist B d With : δ i = Borth Dist h A

22 Relief The altitude of ambiguity (2/3) Altitude of ambiguity : elevation that corresponds to a 2π phase shift λsin( i) Δϕ = 2π h = = 2δ i λ. Dist.sin( i) 2. B orth Ea = λ. Dist.sin( i) 2. B orth Ea Numerical example : B orth : 100 m, Dist=890 km, i=23, λ=5.6 cm Ea=97 m If Borth = 0, then Ea=infinite

23 Relief The altitude of ambiguity (3/3) Influence of the altitude of ambiguity on the fringe density (Ea=500m) (Ea=250m)

24 Relief Accuracy Vertical Accuracy a fraction of the Altitude of Ambiguity depends on the interferogram noise depends on the phase standard-deviation σ ϕ σ z =.Ea 2. π Examples ERS, ENVISAT : Ea/4 or Ea/5 50 down to 3 m SRTM : Ea/15 18 m in C Band ; 6 m in X Band Airborne : better than Ea/100 down to 10 cm

25 Relief : The SRTM mission 3D view X-SAR SRTM Cotopaxi altimetric resolution: 6 m

26 Principle Products (applications) Digital Elevation Models Ground Movements Coherence map Limitations Temporal Geometric Atmospheric propagation Signal-to-Noise Ratio Illustrations of Applications

27 Ground movements (1/6) Non-simultaneous acquisitions If we can eliminate fringes due to the relief (Diff. Interferometry) Direct measurement of displacement (movement) sub-centimetric accuracy: each fringe corresponds to a displacement equals to λ/2 (irrespective of the baseline) differential within the image (relative) movements towards the satellite Landers Magnitude ERS Iso Displacement Curves

28 Ground movements (2/6) 1 Master image (Day 1) 1 Slave image (Day 2) δϕ = 4. π. displ λ // Movement in the radar viewing direction displ // displ _ orth The visible displacement is of the same order of magnitude as a fraction of λ (a few mm) The interferometric measurement is insensitive to displ_orth (North-South slip not measurable by interferometry with polar orbiting SAR) Remark: Non-simultaneous observations Relief effect correction (by model or topographic interferogram substraction)

29 Ground movements (3/6) Effect of a DEM error on the differential interferometric processing 1 2 Dist2 Dist2_cor Dist1_cor Dist1 Corrupted DEM information Err_DEM Real terrain 4π/λ.[(Dist2_cor-Dist1_cor)-(Dist2-Dist1)] 2π. Err_DEM/Ea Numerical example : Err_DEM=30m, Ea=90m, Err_DEM/Ea=0.33 The DEM error creates 0.33 fringe on the differential interferogram, which is equivalent to an displacement error of 0.9 cm.

30 Ground movements (4/6) Measurement Accuracy a fraction of half the wavelenght depends on the interferogram noise ( coherency) depends on the phase standard-deviation Displacement measurement accuracy Examples σ displ. σ ϕ =. λ 2. π 2 ERS : One fringe = λ/2 = 28 mm few mm JERS : One fringe = λ/2 = 11,5 cm few cm

31 Ground movements (4/6) Izmit earthquake I : Mean Amplitude H: Phase (Interf.) S: Coherence Izmit 17/08/99

32 Ground Displacement Modelling Monitoring ground deformation : magmatic chamber variations, seismic deformation (reverse modelling) Pre, post-seismic deformation (millimeters) Fault monitoring Integration with GPS

33 Ground movements (1/6) Subsidences over Paris Paris ONERA97/CNES 99 1,6 cm ERS 1Km

34 Processing chain DIFSAR Co-registration Coherency Unwrapped phase interferogram Interferogram Geocoded displacement map DEM Phase model Orbital data

35 Interferometric processing n SLC images Co-registration of images Selection of M pairs Interferograms and coherence maps generation Steps: Coregister all the images Topography elimination Coherence maps Precise orbital data Topography (DEM or a tandem interferometric pair) Interferograms Flattening Flattening Flattened phase Unwrap the phase Combine the measures at the different times The output consists in sparse space-time displacement measurements (no model assumptions) Preliminary estimates of the displacement maps (optional input) Sparse unwrapping Sparse unwrapping Additionally steps to improve the results: Accurate estimation of orbital data GPS Data (optional) Temporal analysis Temporal analysis 3D-displacement map Filter, model and fit/interpolate the sparse space-time measurements

36 Principle Products (applications) Digital Elevation Models Terrain Movement Coherence map Limitations Temporal Geometric Atmospheric propagation Signal-to-Noise Ratio Illustrations of Applications

37 Coherency Map coherence = γ = M M i i 2. E. i * E i 2 ; 0 γ 1 Computed on a window (n = 5, 20, 80, ) Measures mainly the phase stability between the two acquisitions : quality and reliability index of interferometric measurement A low level of coherence reflects the fact that changes took place between the two acquisitions Very sensitive to temporal change and therefore to land cover (vegetation, flow & erosion, human activity, ) : thematic applications

38 Coherence Map (thematic mapping)

39 Forest damage 1) Cartographic reference 2) Forestry inventory 3) SPOT data 4) Coherence before storm 5) Coherence after storm 6) Damaged areas (pink)

40 Principle Products (applications) Digital Elevation Models Ground Movements Coherence map Limitations Temporal Geometric Atmospheric propagation Signal-to-Noise Ratio Illustrations of Applications

41 LIMITATIONS performances: precise measurement large surfaces temporal information Accuracy of a few mm S.Paul de Fenouillet limitations: geometrical constraints (baseline) coherency loss (noise on interferograms) atmospheric artifacts

42 Principle Products (applications) Digital Elevation Models Ground Movements Coherence map Limitations Temporal Geometric Atmospheric propagation Signal-to-Noise Ratio Illustrations of Applications

43 Temporal Limitations Liquid surfaces (always in movement) Vegetation (growth, wind, plough, harvest, ) Erosion Unstable surfaces Human activity Underground concealment Any change on the ground Remark: higher (multitemporal) coherency in L band on low vegetation (penetration: soil coherency). Better for deformation monitoring

44 Principle Products (applications) Digital Elevation Models Ground Movements Coherence map Limitations Temporal Geometric Atmospheric propagation Signal-to-Noise Ratio Illustrations of Applications

45 Geometric limitations 1/6 The specific phase comes from the physical mechanism of wave backscattering It is linked to the speckle (reconstruction phase) Speckle derives from the vectorial summation of response of each elementary reflector in one pixel (coherent illumination) A φ vectorial summation (amplitude and phase) 1 pixel

46 Geometric limitations 2/6 S 2 If the incidence angle changes, the reconstruction phase changes The larger the pixel, the more sensitive it is to a small variation of incidence angle (directivity, like antenna) Sensitive to incidence Sensitive to slope Sensitive to Baseline (δi) S 1 δi Apparent pixel size viewed from the radar 1 pixel High Incidence Geometric loss of coherence Low Incidence radar sampling Slope > 0

47 Geometric limitations 3/6 The same stands for volumic backscattering Apparent pixel size, viewed from the radar radar sampling surfacic backscattering volumic backscattering Remark: for simultaneous interferometric, X band (smaller penetration, smaller apparent pixel) is more coherent on forests than L band : better for surfacic DEM ERS1&2 tandem coherence Forest / Non Forest Coast lines

48 Geometric limitations 4/6 Equivalent Frequency shift : ΔF = F p. δi tg( i α) = c. Borth λ. Dist. tg( i α) R 1 Borth R 2 (.sin( i )) 1/ α F p T = 1/ F p i δi α ( sin( i α δ )) 1/ i F p Observing a surface under two slightly different point of view (R 1 and R 2 ) is equivalent to a two-frequencies observation from one given location (ex : R1)

49 Geometric limitations 5/6 If ΔF B, there is no coherence Image 1 B Range spectral domain Image 2 Δ f d High resolution is more resistant for interferometry B Range spectral domain B Range spectral domain Δ f d Δ f d

50 Geometric limitations 6/6 Comparison between ERS and a High Resolution SAR ERS / " HR Radar " (2m) comparison % common spectrum Local terrain slope (in )

51 Principle Products (applications) Digital Elevation Models Ground Movements Coherence map Limitations Temporal Geometric Atmospheric propagation Signal-to-Noise Ratio Illustrations of Applications

52 Propagation Effects 1/4 Interferometry is corrupted by atmospheric artifacts, creating a path difference between the two images. Two types: istandard atmosphere variation (time-varying but topography-related) ilocal heterogeneities (time-varying)

53 Propagation Effects 2/4 Troposphere The refactive index is function of the partial vapor content Not a function of the frequency dilatation of the distances creates heterogeneities strong limitation in case of non-simultaneous acquisitions Δl tropo 10 6 h. = h θ h= 0 0 cos max N( h). dh Δ N = 1,45. ΔT + 0,269. Δp + 4,51. Δe

54 Propagation Effects 3/4 Troposphere and Relief Even in case of global vapor content change Dilatation of distance depends on the relief Vapor content

55 Propagation Effects 4/4 Ionosphere The refactive index is function of the Total Electronic Content (TEC) Depends on the frequency band Strong effects in L Band (or P Band) Less effects in X or C Band 40,28 Δl iono =. TEC 2 f

56 Atmospheric artifacts Ionospheric hole Clouds - Cumulus Cloud chain (Etna)

57 LIMITATIONS : POSSIBLE SOLUTIONS Expert interpretation, on the basis of a-priori knowledge (topography, climate, displacement models and prediction, GPS...) Atmospheric modelling - limited application, need of dense vertical profiles, ionosphere... Stacking of interferograms for averaging Correlation of interferograms Permanent scatterers A mixed solution is possible. Compromise to be found as a function of required accuracy, auxiliary data available, number of images

58 Principle Products (applications) Digital Elevation Models Ground Movements Coherence map Limitations Temporal Geometric Atmospheric propagation Signal-to-Noise Ratio Illustrations of Applications

59 Signal-to-Noise ratio (1/3) σ ϕ as a function of the image Signal-to-Noise ratio and Window size: INTERFEROMETIC PHASE NOISE 120 Window size Standard deviation ( ) Noise Signal to Noise ratio Signal

60 Signal-to-Noise ratio (2/3) Interferometric Coherence as a function of the image Signal-to-Noise ratio and Window size: INTERFEROMETRIC COHERENCE Coherence 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 Window size Noise Signal to Noise ratio Signal

61 Signal-to-Noise ratio (3/3) distribution σ ϕ 1 0,8 0,6 0,4 0,2 Phase histogram in fonction of Standard Deviation Phase ( )

62 Principle Products (applications) Digital Elevation Models Ground Movements Coherence map Limitations Temporal Geometric Atmospheric propagation Signal-to-Noise Ratio Illustrations of Applications

63 June 28 th 1992 Landers Earthquake (California) Area : 90 km x 90 km (7.3 event) 0 2π One fringe = 28 mm displacement Post-sismic event Main rift Interferogram processed with a pair of ERS-1 images taken before (April 24, 92) and after (June 93) Earthquake

64 Gulf of Corinthe Greece (North- East Peloponese) 1995 (ERS imagery) Subsidence effect that contributes in enlarging the Gulf Loss of coherence (the interferometric measurement cannot be used locally. Various reasons : meteo, vegetation, relief,...

65 A sad recent application : Abbruzzo earthquake deformation field mapping with radar interferometry (April 2009) ENVISAR ASAR ascending geometry

66 Abbruzzo earthquake deformation field mapping with radar interferometry (April 2009) ENVISAR ASAR descending geometry

67 Abbruzzo earthquake deformation field mapping with radar interferometry COSMO-SkyMed interferogram Model (P.Briole, ENS Paris)

68 Monitoring of industrial risks : Impact of a geothermal power plant on the environment (MESA, USA) USA Power plant Mexico ERS radar image Interferogram processed with a pair of ERS images separated by 2 years

69 Mount Etna : Volcano deflation monitored by radar interferometry 30 ERS-1 images studied (May 1992 Oct. 1993) Map projection interferogram showing large scale deflation 2 orbits : days, +518 days Modelling of the deflation on the same period (Institut de Physique du Globe, Paris)

70 Piton de la Fournaise Réunion Island (June 1998) Interferogram processed with a pair of RADARSAT images (orbites 7753 et 14270)

71 Piton de la Fournaise Ile de la Réunion (Juin 1998) Radarsat1 Differential Interferogram : Mars 1998 Eruption 10/04/97-30/07/ m altitude of ambiguity

72 Principle Products (applications) Digital Elevation Models Ground Movements Coherence map Limitations Temporal Geometric Atmospheric propagation Signal-to-Noise Ratio Illustrations of Applications An alternative technique: Permanent scatterers

73 An alternative: Permanent scatterers

74 An alternative: Permanent scatterers not all backscatterers are PS! not uniform distribution needs many acquisitions (40-60)