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3/12/08
1
Satellite Radar Interferometry and its applicationsPart 1, Radar fundamentals
Guest lecture Remote Sensing (GRS-20306)Wageningen UniversityRamon Hanssen
Delft Institute of Earth Observation and Space Systems
December 3, 2008 2 December 3, 2008 3
Contents Part 1 & 2Part 1• Radar background and fundamentals• Imaging radar, SAR• Physics and geometry• ResolutionPart 2• Interferometry, principles• Topography and deformation• Accuracy• Error sources• New processing methodologies: PSI
December 3, 2008 4
Radar background/history
December 3, 2008 5 December 3, 2008 6
Early ground based radar
RAdio Detection and Ranging
December 3, 2008 7
Bistatic – monostatic radar
• Monostatic: same antenna for transmitting and receiving
• Bistatic: different antennas for transmitting and receiving
December 3, 2008 8
Radar Types• Continuous Wave (CW) Radar. Transmits and receives
continuously. Usually bistatic. Velocity measurements.
• Pulse Radar. The common radar type. It sends the signal in pulses. Measures range and velocities
December 3, 2008 9
Radar mapping of the Moon, Venus, Mars(1946) (1961) (1963)
Main parameters:
•Distance
•Velocity
•Intensity
Retrograde rotation Venus
Improvement of Astronomical unit
December 3, 2008 10
Magellan Synthetic Aperture Radar Mosaic of Venus
December 3, 2008 11
Maat Mons, Venus
Magellan Synthetic Aperture Radar
Radar clinometry, altimeter, and backscatter
December 3, 2008 12
Towards imaging radar
December 3, 2008 13
Optical imagery (false color) versus radar imagery
Delft University, AE
Resolution: 4x20 m December 3, 2008 14
Physics
December 3, 2008 15
Radio waves, active sensor
Wavelength range is cm-m
24 cm 3 cm5 cm
December 3, 2008 16
Penetration (weather independent)
C b
and
Radar waves penetrate the atmosphere and clouds
Radar Images at Different Frequencies
X-band L-band P-band
December 3, 2008 18
• Landsat optical• Shuttle L-band radar• What do we see?
Sahara desert
Radar penetrates material with a low dielectric constant (dep. on wavelength)
Here about 3 m.
Sahara, NW Sudan (SIR-A)
Physics
December 3, 2008 19
Physics - Scattering
• Scattering is dominated by wavelength-scale structures
• Wavelength shorter: image brighter• Specular and Bragg scattering• Speckle
December 3, 2008 20
SPECULAR
Radar signal return depends on:
•Slope
•Roughness
•Dielectric constant
Scattering
Smooth Rough
December 3, 2008 21 December 3, 2008 22
Physics – scattering phase
Imag
inar
y
Real
Radar pixel phase is superposition of near-random scattering elements:
Unpredictable!
December 3, 2008 23
Geometry
Terminology • Foreshortening, layover, shadow• Why side-looking?• Incidence angle, • Coordinates range, azimuth
December 3, 2008 24
Fore
short
ening
Layo
ver
Shado
w
Geometry Slant range
Ground range
December 3, 2008 25
Geometry
Fore
short
ening
Layo
ver
Shado
w
JERS-1 data (M.Shimada)
December 3, 2008 26
Resolution, Pixel size, Posting
• Range• Azimuth
December 3, 2008 27
Pulsed versus CW radar
• Continuous wave radars need to receive while transmitting normally no range measurements
• Pulsed radars: Pulse repetition frequency (PRF): 1680 Hz
Pulse period: 1/PRF=0.6 ms
Skolnik,2001
τ=37 μs
0.6 ms
Time
Powe
r
Target echo
10-9 W
Peak power 103 W
Range measurement:
R = 0.5 c tp
Rule of thumb:
R [km] = 0.15 tp [μs]
(150 m = 1 μs)
tp
tpRange ambiguity!!
December 3, 2008 28
Relation pulse length – range resolution
• Pulse length: τ [s]=37 μs• Corresponds with distance:
c τ [m] = 3e8 ·37e-6 = 11.100 [m]• What is the smallest distance between two targets
to be separated?• Two targets can be recognized if separated
½c τ [m] = 5.5 [km]2-way travel
37 μs = 11.1 km
½cτ
December 3, 2008 29
Synthetic shortening pulse length• Transmit a ‘chirp’: signal with increasing frequency
over pulse interval
• Effective pulse interval:τ=1/bandwidth = 1/15.5 MHz = 64 ·10-9 [sec]
64 ns• Range resolution : ½cτ [m] = 9.6 [m] = c / (2 BR)
FM: frequency modulation
December 3, 2008 30
Matched filter
December 3, 2008 31
Antenna beam: Fraunhofer diffraction
December 3, 2008 32
Wave front concept
December 3, 2008 33
Fraunhofer Diffraction
Limits spatial resolution
Optical, 0.5 μm, lens 5 cm,1000 km 10 m
Microwave, 3cm, antenna 1m, 1000 km 30 km !!
•Monochromatic radiation•Far-field approximation and L >> w:
• θ = θ’• Plane wave at slit
Condition for minimum:
δ =w sin θ = m λ
y ≈ m λ L / w
tan θ = y / L
tan θ ≈ sin θ ≈ θ ≈ y/L
Lw
First minimum:
δ θ = λ / wDecember 3, 2008 34
Fraunhofer single slit(additive interferometry)
• Slit openings about wavelength size• Consider elements of wavefront in
slit, and treat as point sources
Constructive interference
Destructive interference
Sinc-pattern
December 3, 2008 35
Resolution I: RAR•Real Aperture Radar
•Resolution dependent on antenna dimension/pulse length
•Beam width (half power width) is ratio wavelength over antenna size:
December 3, 2008 36
Antenna dimensions
1.3 m
10 m
Calculate Ground Resolution
C-band λ= ~0.05 m
D=10 m antenna
Beam angle = 5.10-2/10 = 5.10-3 rad
R=850 km
times 8.5.105 = 42.102[m] = 4.2 km
Dλθ =
December 3, 2008 37
antenna
pulse
December 3, 2008 38
antenna
pulse length
pulse repetition
frequency (PRF)
swath
ground range
Slant range
December 3, 2008 39
Improvement in Resolution (Crimea, Ukraine)
Real Aperture Radar
5x14 km pixels
Massonnet and Feigl, 1998
December 3, 2008 40
Improvement of along-track resolution
Synthetic antenna
Physical antenna
Resolution cell
December 3, 2008 41
Improvement in Resolution (Crimea, Ukraine)
Real Aperture Radar Synthetic Aperture Radar
5x14 km pixels 4x20 m pixels
Massonnet and Feigl, 1998
December 3, 2008 42
Azimuth resolution SAR•Similar to range direction: dependent on bandwidth
Dopp
CSa B
v /=Δ
• Doppler frequency
λvfD
2=
λφ
λsCS
Dvvf sin22 /==
Lλβ = ββ sin≈
• Doppler frequency SAR
• Beam width:
December 3, 2008 43
LvLvvB
vvvf
vvvf
CSCSCSDopp
CSCSCS
D
CSCSCS
D
///
///
max,
///
min,
2/22
22
2sin2
22
2sin2
===
+=
+
≈
+
=
−=
−
≈
−
=
λλ
λβ
λβ
λ
β
λ
βλ
βλ
β
λ
β
22 /
// L
Lv
vBv
CS
CS
Dopp
CSa ===Δ• SAR resolution:
• Minimum Doppler:
• Maximum Doppler:
•Doppler bandwidth:
December 3, 2008 44
ERS, the values
• Az_res = v_s/c / B_Dop = 7100/ 1380= 5.14 m
• Az_pix = v_s/c / PRF = 7100/ 1680 = 4.22 m• Ra_res = c / (2 B_R) = 3e8 / (2x1.55e7) = 9.68 m• Ra_pix = c / (2 RSF) = 3e8/(2x1.86e7) = 7.91 m
Oversampling factor:
1.22
1.22
Samples:
Samples:
“Posting”
“Resolution”
“Pixel size”
December 3, 2008 45
Resolution II (SAR)
• Resolution SAR is inversely proportional with bandwidth
• Azimuth resolution SAR: Half antenna size!
• No influence of satellite height on azimuth resolution SAR image
• Range resolution improvement using chirp waveform
December 3, 2008 46
SAR SLC observationsSLC: Single-Look Complex data
•Single-look: no averaging, finest spatial resolution
•Complex: both real and imaginary (In-phase and quadrature phase) stored
Amplitude PhaseUninterpretable, due to scattering mechanism
Coherent imaging
December 3, 2008 47
End of part 1
3/12/08
48
Satellite Radar InterferometryPart 2, InSAR, fundamentals and applications
Guest lecture Remote Sensing, Wageningen University
Ramon Hanssen
Delft Institute of Earth Observation and Space Systems
December 3, 2008 49
Interferometric radar (InSAR)
December 3, 2008 50
Radar Interferometry
December 3, 2008 51 December 3, 2008 52
December 3, 2008 53 December 3, 2008 54 December 3, 2008 55 December 3, 2008 56
December 3, 2008 57
Example in 2D: interferogram
December 3, 2008 58
Range
Expressed as phase (radians)
December 3, 2008 59
Range
Expressed as integer cycles + fractional phase
December 3, 2008 60
Reference phase (flat earth phase)
Ellipsoid
-π
+π
Topography will add variation to the “flat earth phase”
December 3, 2008 61
Amplitude
Reference phase
RADAR INTERFEROMETRIC OBSERVATIONS
December 3, 2008 62
Phase-range relationship
December 3, 2008 63
Phase-height relationship(Far-field approximation)
Ellipsoid
Topographic phase is (inversely) scaled by the perpendicular baseline!
December 3, 2008 64
Amplitude
Reference phase
Topographic phase
RADAR INTERFEROMETRIC OBSERVATIONS
December 3, 2008 65
Height ambiguity
Height difference related to 1 phase cycle:
0
100
200
300
400
500
20 100
180
260
340
420
500
580
660
740
820
900
Perpendicular baseline [m]
Hei
ght a
mbi
guity
[m]
December 3, 2008 66
Phase and topography
December 3, 2008 67 December 3, 2008 68
Baseline dependency, height ambiguity
Bperp 173 m, Bt= 1day Bperp 531 m, Bt= 1 day
H2pi=45m H2pi=16m
December 3, 2008 69
Deformation measurements
December 3, 2008 70
Conventional Interferometry: Bam earthquake 26/12/2003
December 3, 2008 71
Conventional Interferometry: Glacier Dynamics (Svalbard, Spitsbergen)
5 KM
LOS
12 day interferogram
December 3, 2008 72
Satellite radar interferometry• Coseismic interferogram, showing deformation Izmit earthquake
• Every color cycle 7.5 cm horizontal motion
• Showing which segment of fault ruptured
December 3, 2008 73
Mauna Loa, Hawaii• Deformation
(inflation) of the Mauna Loa summit
• Position of the magma chamber better determined
December 3, 2008 74
…Very sensitive to deformation
Subsidence Las Vegas due to ground water extraction
December 3, 2008 75
Phase-deformation relationship
Subsidence ∆z
1 cycle LOS deformation is equal to half the physical wavelength
December 3, 2008 76
Topography and deformation
Ellipsoid
Sensitivity to deformation 1000x higher than for topography
December 3, 2008 77
Conditions for interferometry
• coherence
December 3, 2008 78
Model of observation equations (1)
Rank deficiency! Often treated opportunistically
Observation Unknowns
Functional model:
Stochastic model:Based on thermal (instrumental) noise
This is too much simplified, let’s make it more realistic!
December 3, 2008 79
Model of observation equations (2)• Add unknown parameter:
• Phase ambiguity
• Add error signal to stochastic model:• Atmosphere (troposphere, ionosphere)• Orbit errors• Decorrelation
• Geometric• Temporal
Integer valued unknown
Spatial varying disturbance~trend
Pixel-based noise
Spatially ~constant
Spatially varyingDecember 3, 2008 80
Atmospheric disturbance
• Spatially varying disturbance signal
• Can be ~5 cm over 20 km• Spatially correlated but
temporally uncorrelated (∆t>1 day)
• Introduces covariances in stochastic model
December 3, 2008 81
Example Interferometric Radar Meteorology
December 3, 2008 82
Geometric decorrelation• Baselines vary• Relative scattering
mechanisms change• Images become
uncomparable• Function of baseline,
Doppler centroid, and terrain slope
Note the trade-off between height sensitivity (large baseline) and noise reduction (small baseline)!
December 3, 2008 83
Spectral shift
• On the blackboard:• 1. explain that coherent differences can only be
obtained using overlapping spectra• 2. explain that a spectral shift of 1 data sample will
introduce a phase ramp of one cycle• Continue with geometric explanation spectral shift
(ground range-slant range)
December 3, 2008 84
Interferometric product is convolution of spectra
December 3, 2008 85
Wavenumber (spectral) shift
December 3, 2008 86
Temporal decorrelation
29
1 day
16618593112Perpendicular baseline (m)
6 years3 years2 years1 yearTemporal baseline
December 3, 2008 87
Coherence
December 3, 2008 88
Coherence loss as function of time1 day interval 3.5 year interval
Anthropogenic features remain coherent over long time intervals
December 3, 2008 89
Phase variance estimation:Coherence
•Optics equivalent to correlation:
•Estimation of coherence:
}|{|}|{|}{
22
21
*21
yEyEyyE⋅
=γ
∑ ∑∑
= =
==N
n
N
nnn
N
nnn
yy
yy
1 12)(
22)(
1
1)(
2)(
1
||||
|||ˆ| γ
complex number!
December 3, 2008 90
Coherence corrected for interferometric phase
•Optics equivalent to correlation:
•Estimation of coherence:
}|{|}|{|)exp(|}{|
}|{|}|{|}{
22
21
*21
22
21
*21
yEyEjyyE
yEyEyyE
⋅=
⋅=
φγ
∑ ∑∑
= =
=−
=N
n
N
nnn
N
nnnn
yy
jyy
1 12)(
22)(
1
1)()(
2)(
1
||||
|)exp(||ˆ|
φγ
Interferometricphase
Removal of the (non-ergodic) interferometricphase
Biased estimate! (over-estimation)
December 3, 2008 91
Coherence, multilooks, and phase PDF
1 look 10 looks 20 looksγ=0.9 γ=0.7 γ=0.5 γ=0.3 γ=0.1
γ=0.9 γ=0.7 γ=0.5 γ=0.3 γ=0.1
γ=0.9 γ=0.7 γ=0.5 γ=0.3 γ=0.1
December 3, 2008 92
Coherence vs SNR
NSS
SNRSNRSNR
+=
+=
+= −11
11
|| γ
The absolute value of the coherence can be related to the signal-to-noise ratio:
Signal to clutter ratio
December 3, 2008 93
Envisat interferograms (single master)
December 3, 2008 94
ERS-2 interferograms (single master)
December 3, 2008 95
Problems Conventional InSAR• Close satellite orbits required• Sensitive to changing surface backscatter behavior• Sensitive to atmospheric water vapor
29
1 day
16618593112Perpendicular baseline (m)
6 years3 years2 years1 yearTemporal baseline
Conclusion:
Conventional InSAR does not work for
•slow deformation, over
•vegetated/wet/changing surfaces,
•in non-arid climate regions
December 3, 2008 96
New processing methodologies
• To resolve the ambiguities• Separate topography and deformation• To detect information in the noise• To estimate/mitigate atmospheric signal• To estimate orbit errors