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