Satellite Radar Interferometry and its applications

Contents Part 1 & 2

Radar background/history

Part 1 • Radar background and fundamentals • Imaging radar, SAR • Physics and geometry • Resolution Part 2 • Interferometry, principles • Topography and deformation • Accuracy • Error sources • New processing methodologies: PSI

Part 1, Radar fundamentals

Guest lecture Remote Sensing (GRS-20306) Wageningen University Ramon Hanssen

3/12/08 1 December 3, 2008

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Delft Institute of Earth Observation and Space Systems

Early ground based radar

Bistatic – monostatic radar

RAdio Detection and Ranging

Radar Types

• Continuous Wave (CW) Radar. Transmits and receives continuously. Usually bistatic. Velocity measurements.

• Monostatic: same antenna for transmitting and receiving • Bistatic: different antennas for transmitting and receiving

• Pulse Radar. The common radar type. It sends the signal in pulses. Measures range and velocities

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Magellan Synthetic Aperture Radar Mosaic of Venus

Radar mapping of the Moon, Venus, Mars (1946) (1961) (1963)

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Maat Mons, Venus

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Towards imaging radar

Magellan Synthetic Aperture Radar Radar clinometry, altimeter, and backscatter

Main parameters: •Distance •Velocity •Intensity Retrograde rotation Venus Improvement of Astronomical unit December 3, 2008

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Optical imagery (false color) versus radar imagery

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Physics

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Radio waves, active sensor

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Penetration (weather independent)

Radar waves penetrate the atmosphere and clouds Delft University, AE

Resolution: 4x20 m

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24 cm

5 cm

3 cm

C band

Wavelength range is cm-m

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Physics Sahara desert

Radar Images at Different Frequencies X-band

Scattering

Physics - Scattering

Sahara, NW Sudan (SIR-A) L-band

• Landsat optical • Shuttle L-band radar • What do we see?

Radar signal return depends on:

Smooth

• Scattering is dominated by wavelength-scale structures • Wavelength shorter: image brighter • Specular and Bragg scattering • Speckle

P-band

Rough

•Slope •Roughness

SPECULAR

•Dielectric constant

Radar penetrates material with a low dielectric constant (dep. on wavelength)

Here about 3 m. December 3, 2008

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Imaginary

Physics – scattering phase

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Geometry

Radar pixel phase is superposition of near-random scattering elements:

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Geometry

Sl an t

Terminology • Foreshortening, layover, shadow • Why side-looking? • Incidence angle, • Coordinates range, azimuth

Unpredictable!

ra ng e

i en er rt ov ho y s La re Fo ow ad Sh

ng

Real Ground range December 3, 2008

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Geometry

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Resolution, Pixel size, Posting

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Pulsed versus CW radar

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Relation pulse length – range resolution 37 μs = 11.1 km

• Range • Azimuth

• 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 2-way travel ½c τ [m] = 5.5 [km]

• Continuous wave radars need to receive while transmitting Æ normally no range measurements • Pulsed radars: Pulse repetition frequency (PRF): 1680 Hz Pulse period: 1/PRF=0.6 ms

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g in en r ow ort ove d a sh y Sh ore La F

Range measurement: R = 0.5 c tp

τ=37 μs

Rule of thumb:

Peak power 103 W

Power

JERS-1 data (M.Shimada)

0.6 ms

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R [km] = 0.15 tp [μs]

Target echo December 3, 200810

-9

W

Time

tp Skolnik,2001

Synthetic shortening pulse length

Matched filter

(150 m = 1 μs) 27

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½cτ

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tp

Range ambiguity!!

Antenna beam: Fraunhofer diffraction

Wave front concept

• Transmit a ‘chirp’: signal with increasing frequency over pulse interval FM: frequency modulation

• 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) December 3, 2008

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•Monochromatic radiation •Far-field approximation and L >> w: • θ = θ’ • Plane wave at slit

tan θ = y / L tan θ ≈ sin θ ≈ θ ≈ y/L

Resolution I: RAR

Fraunhofer single slit

Fraunhofer Diffraction

(additive interferometry)

Destructive interference

C-band

•Resolution dependent on antenna dimension/pulse length Slit openings about wavelength size Consider elements of wavefront in slit, and treat as point sources

Constructive interference

Limits spatial resolution

L Condition for minimum:

θ=

•Real Aperture Radar

• •

w

Calculate Ground Resolution

•Beam width (half power width) is ratio wavelength over antenna size:

Sinc-pattern

λ

Antenna dimensions

D

λ= ~0.05 m

D=10 m antenna Beam angle = 5.10-2/10 = 5.10-3 rad 1.3 m R=850 km 2[m] 10 m = 4.2 km times 8.5.105 = 42.10

Optical, 0.5 μm, lens 5 cm, 1000 km Æ10 m

δ =w sin θ = m λ y≈mλL/w

Microwave, 3cm, antenna 1m, 1000 km Æ 30 km !!

First minimum:

δθ = λ / w December 3, 2008

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Improvement in Resolution Real Aperture Radar

pu fr lse eq r ue ep nc e t y iti (P on RF )

pulse

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Improvement of along-track resolution

(Crimea, Ukraine)

antenna antenna

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Synthetic antenna

Physical antenna

pulse length

S ra l an ng t e

swat h

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Resolution cell

ground range

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5x14 km pixels

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Massonnet and Feigl, 1998

Improvement in Resolution

Azimuth resolution SAR

(Crimea, Ukraine) Real Aperture Radar

Synthetic Aperture Radar

•Similar to range direction: dependent on bandwidth

• Doppler frequency

• Doppler frequency SAR

• Beam width: December 3, 2008

5x14 km pixels

4x20 m pixels

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• Minimum Doppler:

v Δa = S /C BDopp

fD = fD =

2v

λ 2v

λ λ β= L

f D ,min =

• Maximum Doppler:

f D ,max

•Doppler bandwidth:

BDopp

2vS / C sin

λ

−β −β 2v 2 ≈ S / C 2 = − vS / C β

λ

λ

+β +β 2vS / C sin 2vS / C 2 ≈ 2 = + vS / C β =

λ λ 2v β 2v λ / L 2vS / C = S / C = S /C = λ λ L

λ

ERS, the values Oversampling factor:

• 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“Resolution = c ” / (2 RSF) = 3e8/(2x1.86e7) = 7.91 m “Posting”

=

2vS / C sin φs

λ

• SAR resolution:

Δa =

β ≈ sin β 42

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1.22 1.22

“Pixel size”

Samples:

vS / C v L = S /C = BDopp 2vS / C 2 L

Samples:

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Massonnet and Feigl, 1998

Resolution II (SAR)

SAR SLC observations

Satellite Radar Interferometry

End of part 1

Part 2, InSAR, fundamentals and applications

SLC: Single-Look Complex data

• Resolution SAR is inversely proportional with bandwidth

•Single-look: no averaging, finest spatial resolution

• Azimuth resolution SAR: Half antenna size!

•Complex: both real and imaginary (In-phase and quadrature phase) stored Coherent imaging

• No influence of satellite height on azimuth resolution SAR image

Amplitude

• Range resolution improvement using chirp waveform

Guest lecture Remote Sensing, Wageningen University

Ramon Hanssen

Phase Uninterpretable, due to scattering mechanism

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3/12/08 48 December 3, 2008

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Delft Institute of Earth Observation and Space Systems

Radar Interferometry

Interferometric radar (InSAR)

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Example in 2D: interferogram

Range

Range Expressed as phase (radians)

Reference phase

(flat earth phase)

Expressed as integer cycles + fractional phase Topography will add variation to the “flat earth phase”

Ellipsoid +π December 3, 2008

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-π

RADAR INTERFEROMETRIC OBSERVATIONS Amplitude

Phase-range relationship

RADAR INTERFEROMETRIC OBSERVATIONS Amplitude

Phase-height relationship (Far-field approximation) Topographic phase is (inversely) scaled by the perpendicular baseline!

Reference phase

Reference phase

Ellipsoid December 3, 2008

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Topographic phase December 3, 2008

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Baseline dependency, height ambiguity

Phase and topography

Height ambiguity

Bperp 173 m, Bt= 1day H2pi=45m

Bperp 531 m, Bt= 1 day H2pi=16m

400 300 200

820

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740

660

580

500

420

340

260

180

0

900

100 100

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500

20

Height ambiguity [m]

Height difference related to 1 phase cycle:

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Perpendicular baseline [m]

Deformation measurements

Conventional Interferometry: Bam earthquake 26/12/2003

Conventional Interferometry: Glacier Dynamics (Svalbard, Spitsbergen)

radar interferometry •Satellite Coseismic interferogram, showing deformation Izmit earthquake

5 KM

• Every color cycle 7.5 cm horizontal motion • Showing which segment of fault ruptured

LOS

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12 day interferogram

…Very sensitive to deformation

Mauna Loa, Hawaii

Phase-deformation relationship

Subsidence Las Vegas due to ground water extraction

• Deformation (inflation) of the Mauna Loa summit • Position of the magma chamber better determined

Topography and deformation

1 cycle LOS deformation is equal to half the physical wavelength

Sensitivity to deformation 1000x higher than for topography Ellipsoid

Subsidence ∆z December 3, 2008

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Conditions for interferometry

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Model of observation equations (1)

Model of observation equations (2) • Add unknown parameter: • Phase ambiguity

Observation Rank deficiency!

Unknowns Often treated opportunistically

Stochastic model: Based on thermal (instrumental) noise

This is too much simplified, let’s make it more realistic! 77

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Functional model:

• coherence

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Integer valued unknown

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Spatially varying

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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

• Add error signal to stochastic model: • Atmosphere (troposphere, ionosphere) Spatial varying • Orbit errors ~trend disturbance • Decorrelation Pixel-based noise • Geometric • Temporal Spatially ~constant December 3, 2008

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Example Interferometric Radar Meteorology

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Wavenumber (spectral) shift

Geometric decorrelation

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1 day

1 year

2 years

3 years

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Perpendicular 29 baseline (m) December 3, 2008

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December 3, 2008

Coherence corrected for interferometric phase

•Optics equivalent to correlation:

•Optics equivalent to correlation:

γ=

E{ y1 y2* } E{| y1 |2 } ⋅ E{| y2 |2 }

complex number!

γ=

•Estimation of coherence:

| ∑n =1 y y

∑

N n =1

E{| y1 |2 } ⋅ E{| y2 |2 }

=

| y1( n ) |2

( n) 1

∑

( n) 2

N n =1

| γˆ |=

| y2( n ) |2

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Coherence loss as function of time 1 day interval

Interferometric phase

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3.5 year interval

10 looks

1 look

E{| y1 |2 } ⋅ E{| y2 |2 }

Anthropogenic features remain coherent over long time intervals

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The absolute value of the coherence can be related to the signal-to-noise ratio:

20 looks

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

Removal of the (nonergodic) interferometric phase

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Coherence vs SNR

Coherence, multilooks, and phase PDF

γ=0.9 γ=0.7 γ=0.5 γ=0.3 γ=0.1

| ∑n =1 y1( n ) y2( n ) exp(− jφ ( n ) ) |

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∑

N n =1

| y1( n ) |2

∑

N n =1

| y2( n ) |2

| γ |=

SNR 1 S = = SNR + 1 1 + SNR −1 S + N

Signal to clutter ratio

Biased estimate! (over-estimation) 90

ERS-2 interferograms (single master)

(single master)

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Problems Conventional InSAR

Conventional InSAR does not work for •slow deformation, over

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Temporal baseline

1 day

Perpendicular baseline (m)

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1 year 112

•vegetated/wet/changing surfaces, 2 years 3 years 6 years •in non-arid climate regions 93

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New processing methodologies

• Close satellite orbits required • Sensitive to changing surface backscatter behavior • Sensitive to atmospheric water vapor Conclusion:

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N

|

Envisat interferograms

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| E{ y1 y2* } | exp( jφ )

•Estimation of coherence: N

| γˆ |=

E{ y1 y2*}

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6 years

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Phase variance estimation: Coherence

• 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)

Coherence

Temporal decorrelation

Temporal baseline

Interferometric product is convolution of spectra

Spectral shift

• Baselines vary • Relative scattering mechanisms change • Images become uncomparable Note the trade-off between height• Function of baseline, sensitivity (large baseline) and noise Doppler centroid, reduction (small baseline)! and terrain slope

• • • • •

To resolve the ambiguities Separate topography and deformation To detect information in the noise To estimate/mitigate atmospheric signal To estimate orbit errors

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