Download ppt - 1 Interferometric Synthetic-Aperture Radar (InSAR) Basics

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Interferometric Synthetic-Aperture Radar (InSAR) Basics

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OutlineSAR limitations

Interferometry

SAR interferometry (InSAR)Single-pass InSAR

Multipass InSAR

InSAR geometry

InSAR processing steps

Phase unwrapping

Phase decorrelationBaseline decorrelation

Temporal decorrelation

Rotational decorrelation

Phase noise

Persistent scatterers

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SAR limitations

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SAR limitationsAll signals are mapped onto reference plane

This leads to foreshortening and layover

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Shadow, layover, and foreshortening distortion

Figure 5-4. Example of radar image layover. Seasat image of the Alaska Range showing the top of a mountain imaged onto the glacier at its foot (center). Shadows are also present on many of the backslopes of these steep mountains. Illumination is from the top [from Ford et al., 1989].

SEASAT Synthetic Aperture RadarLaunched: June 28, 1978Died: October 10, 1978orbit: 800 kmf: 1.3 GHz PTX: 1 kW: 33.8 s B: 19 MHz: 23 3 PRF: 1464 to 1647 Hzant: 10.7 m x 2.2 m x = 18 to 23 m y = 23 m

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SAR limitations – foreshorteningForeshortening: - < < ( is local slope).

Dilates or compresses the resolution cell (pixel) on the ground with respect to the planar case.

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SAR limitations – layoverLayover: ( is the local slope)

Causes an inversion of the image geometry. Peaks of hills or mountains with a steep slope commute with their bases in the slant range resulting in severe image distortion.

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SAR limitations – shadowShadow: - /2 ( is the local slope)

A region without any backscattered signal. This effect can extend over other areas regardless of the slope of those areas.

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Foreshortening and geocoding

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Interferometryinterferometry—The use of interference phenomena for purposes of measurement.

In radar, one use of interferometric techniques is to determine the angle of arrival of a wave by comparing the phases of the signals received at separate antennas or at separate points on the same antenna.

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SAR interferometry – how does it work?

Radar

Return could befrom anywhere on this circle

B

A1

A2

Antenna 1

Antenna 2

Return comes fromintersection

Single antenna SAR Interferometric SAR

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SAR interferometry – how is it done?

Single pass orSimultaneous baselineTwo radars acquire data from different vantage points at the same time

Repeat pass orRepeat trackTwo radars acquire data from different vantage points at different times

B is the interferometric baseline

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Single-pass interferometry

Single-pass interferometry. Two antennas offset by known baseline.

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Interferometric SAR – geometryThe key to InSAR is to collect complex SAR data from slightly offset perspectives, the separation between these two observation points is termed the baseline, B.

This baseline introduces for each point in the scene a slight range difference that results in a phase shift that can be used to determine the scatterer’s elevation.

From trigonometry (law of cosines)

Furthermore for R » B

[Note that B amplifies R]

For scatterers in the reference plane is known ( = o), otherwise is

unknown

Finding R enables determination of and z(x)

sinRB2BRRR 222

sinBR

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Law of cosines

2cosRB2BRRR

cosab2bac

222

222

sin

2cos

sinBRsinBR2

B

R2

RRsinBR2BRRR2

sinBR2BRRRR2RsinRB2BRRR22

22

2222222

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Interferometric SAR– radar phase

Radar phases

Since is measured, R can be determined

Example

Let = 10 cm (f = 3 GHz)measure to /100 (3.6º)equivalent to 0.1 mm or 0.3 ps resolution

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R

R4

jj1 eeE scatterer

RR4jj

2 eeE scatterer

jR

4j

*21

RRR4

j*21

eeEE

eEE

Multipass baselineTransmit and receive on antenna A1

Transmit and receive on antenna A2

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Interferometric SAR– radar phase

For single-pass InSAR where transmission is on antenna A1 and reception

uses both A1 and A2:

And

Simultaneous baselineTransmit on antenna A1

Receive on both A1 and A2

R4

jj1 eeE scatterer

RR22jj

2 eeE scatterer

jR

2j

*21

RR2R22

j*21

eeEE

eEE

2

R

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Radar interferometry – geometry

From geometry we know

but is undetermined if the scatterer is not on the reference plane.

To determine we use

where a = 1 for single-pass and a = 2 for multipass

So that

cosRhxz

sinBR

2a

R

sin

B2a

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Radar interferometry – geometry

From

we find

and

where a = 1 for single-passa = 2 for multipassa = 2 for single-pass, ping-pong mode

Precise estimates of z(x) require accurate knowledge of B, , and as well as R and h

B2asincosRhxz 1

B2asin 1

sin

B2a

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Interferometric SAR processing geometry

Range S phere

Doppler Cone

VelocityVector

Phase Cone

AircraftPosition

BaselineVector

S catterer is at intersection of RangeS phere, Doppler Cone and Phase

Cone

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SAR InterferometryInSAR provides additional information via phase measurements

This additional information enables a variety of new capabilities

Topography measurement

Vertical surface displacement (uplift or subsidence)

Lateral surface displacement (velocity)

Change detection (via phase decorrelation)

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SAR InterferometryMulti-pass interferometry

Two pass• Two scenes, one interferogram

topography, change detection surface velocity (along-track interferometry – temporal baseline)

Three pass• Three scenes, two interferograms

topography, change detection, surface deformation

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Differential interferometry – how does it work?

Three-pass repeat track

Two different baselines

Same incidence angle

Same absolute range

Parallel ray approximation used to detect changes

If the surface did not change between observations, then

),B(),B( 2211

0)sin(B

)sin(B

11

2212

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Interferometric SAR processingProduction of interferometric SAR images and data sets involves multiple processes.

Independent SAR data sets must be collected

Complex SAR images are produced

SAR images must be registered with one another

Interferometric phase information extracted pixel-by-pixel

Coherence is analyzed

Phase is unwrapped (removes modulo-2 ambiguity)

Phase is interpolated

Phase is converted into height

Interferometric image is geocoded

To produce surface velocity or displacement maps, successive pairs of InSAR images are processed to separate elevation effects from displacements.

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InSAR processing steps

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Phase history and magnitude image

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Phase image

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Illustrated InSAR processes (1 of 3)

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Phase coherenceLack of coherence caused by decorrelation

Baseline decorrelationSufficient change in incidence angle results in scatterer interference (fading effect)

Temporal decorrelationMotion of scatterers between observations produces random phase

– Windblown vegetation– Continual change of water surface– Precipitation effects– Atmospheric or ionospheric variations– Manmade effects

Rotational decorrelationData collected from nonparallel paths

Phase unwrapping to obtain absolute phase requires reference point

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SAR InterferometryThe radar does not measure the path length directly, rather it measures the interferometric phase difference, , that is related to the path length difference, R

The measured phase will vary across the radar swath width even for a surface without relief (i.e., a flat surface or smooth Earth)

increases as the sine of

If o is the incidence angle in the absence

of relief and z is the elevation of a pixel at the same Ro, then the change in incidence

angle induced by the relief is

sinB2a

R2a

oo sinR

z

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SAR InterferometryIt follows that

phase due to phase due tosmooth Earth relief

Removing the phase component due to the smooth Earth yields a “flattened interferogram”

ooo cosB

2asinB

2asinB

2a

oo

oflat sinR

zcosB

2a

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SAR Interferometry

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Ambiguity heightThe interferometric ambiguity height, e, which is the elevation for which the flattened interferogram changes by one cycle, is

The ambiguity height is like the sensitivity of the InSAR to relief.

From this relationship we know

• A large baseline B improves the InSAR’s sensitivity to height variations.

• However since the radar measures interferometric phase in a modulo 2 manner, to obtain a continuous relief profile over the whole scene the interferometric phase must be unwrapped.

• To unambiguously unwrap the phase, the interferometric phase must be adequately sampled.

• This sampling occurs at each pixel, thus if the interferometric phase changes by 2 or more across one pixel a random phase pattern results making unwrapping difficult if not impossible.

• The problem is aggravated for positive terrain slopes (sloping toward radar)

o

oo

cosBa

sinRe

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Phase unwrapping

z

x

ACTUAL ELEVATION PROFILE

x

Phase

0

2

WRAPPED PHASE

x

Phase

0

2

4

6

8

UNWRAPPED PHASE

Formerly phase unwrapping was an active research area, now Matlab has a built-in function (unwrap.m) that does this reliably for most cases.

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Baseline decorrelationTo illustrate this consider two adjacent pixels in the range dimension – pixel 1 & pixel 2 – on a surface with slope .

The interferometric phase for these two pixels is

For small r (small slant range pixel spacing)

and from geometry we know

so that

sinB2a

sinB2a

2

1

cosB

2acosB

2asinB

2a12

tanR o

r

tanRcosB

2a

o

r12

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Baseline decorrelationLimiting to 2 results in a critical baseline, Bc such that if

B > Bc the interferometric phases will be hopelessly

unwrappable.

This phenomenon is know as baseline decorrelation.

B denotes the perpendicular component of baseline B

where a = 1 for single-passa = 2 for multipassa = 2 for ping-pong mode

[i.e., Tx(A1)–Rx(A1 , A2); Tx(A2)–Rx(A1, A2); repeat]

r

occ a

tanRcosBB

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Perpendicular BaselinePerpendicular Baseline, B

Parallel-ray assumptionOrthogonal baseline component, B, is key parameter used in InSAR analysisB = B cos( - )

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Baseline decorrelationWhile Bc represents the theoretical maximum baseline that

will avoid decorrelation, experiments show that a more conservative baseline should be used.

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CorrelationThe degree of coherence between the two complex SAR images, s1 and s2, is defined as the cross-correlation

coefficient, , or simply the correlation

where

s2* is the complex conjugate of s2

E{ } is ensemble averaging

(incoherent) 0 < < 1 (coherent)

is a quality indicator of the interferometric phase,for precise information extraction, a high value is required.

}s{E}s{E

}ss{E2

22

1

*21

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Decorrelation effectsFactors contributing to decorrelation include:

Spatial baseline• Inadequate spatial phase sampling (a.k.a. baseline decorrelation)

• Fading effects

Rotation• Non-parallel data-collection trajectories

• Fading effects

Temporal baseline• Physical change in propagation path and/or scatterer between observations

Noise• Thermal noise

• Quantization effects

Processing imperfections• Misregistration

• Uncompensated range migration

• Phase artifacts

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Noise effectsRandom noise (thermal, external, or otherwise) contributes to interferometric phase decorrelation.

Analysis goes as follows:

Consider two complex SAR signals, s1 and s2, each of

which is modeled as

where c is a correlated part common to the signal from both

antennas and the thermal noise components are n1 and n2.

The correlation coefficient due to noise, N, of s1 and s2 is

2211 ncsandncs

}ss{E}ss{E

}ss{E*22

*11

*21

N

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Noise effectsSince the noise and signal components are uncorrelated, we get

Recall that the signal-to-noise ratio (SNR) is |c|2/|n|2 yields

For an SNR of , the expected correlation due to noise is 1

For an SNR of 10 (10 dB), N = 0.91

For an SNR of 4.5 (6.5 dB), the N = 0.81

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2

Nnc

c

122N SNR1

1

cn1

1

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Noise effectsNoise also increases the uncertainty in the phase measurement, i.e., the standard deviation of the phase,

SNR

1

signal

n

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Noise effects

Note that the slope as

1

A 6.5 dB SNR yields a 50 standard deviation and a correlation of about 0.8

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Noise with another decorrelation factor

Now consider two complex SAR signals, s1 and s2, each of

which is modeled as

where c is a correlated part common to the signal from both

antennas, di is the uncorrelated part due to spatial baseline

decorrelation (exclusive of noise), and the thermal noise

component is ni.

The correlation of s1 and s2 for an infinite SNR is

222111 ndcsandndcs

22

2

spatialdc

c

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Noise with another decorrelation factorNow re-introducing noise we get

and since SNR is (|c|2 + |d|2 )/|n|2

222

2

noisespatialndc

c

222

22

22

2

noisespatialndc

dc

dc

c

122

2

noisespatial SNR1

1

dc

c

Nspatialnoisespatial

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Decorrelation and phaseThe decorrelation effects from the various causes compound, i.e.,

where

scene denotes long-term scene coherence

N represents decorrelation due to noise

H includes system decorrelation sources

including baseline decorrelation, misregistration, etc.

The probability density function (pdf) reveals some statistical characteristics of the interferometric phase.

For strong correlations ( 1) the phase difference is very small and only a few outliers exist.

HNscene

Bamler, R. and D. Just, “Phase statistics and decorrelation in SAR interferograms,” IGARSS ’93, Toyko, pp. 980-984, 1993.

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Spatial baseline decorrelation

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Rotational decorrelation

Complete decorrelation results after rotation of 2.8 at L-band and 0.7

at C-band.

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Temporal decorrelation

~ 0.5 yields reasonably reliable topographic maps

Complete decorrelation results after rms motion of ~ /3

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Fading effects

Increasing the number of looks reduces the phase standard deviation, especially for N > 8

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Uncompensated range migration effects

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Misregistration effects

Residual misregistration of 1/8 resolution cell leads to a 42-standard deviation for a 10-dB SNR and a 23-standard deviation

for an SNR of .

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MisregistrationMisregistration leads to increased phase variance, not a phase offset (bias).

SAR imaging geometry variations contribute to misregistration.

Removing geometric distortion and shifts is called coregistration or registration.

A two-part process for achieving acceptable registration involves a coarse or rough registration followed by a fine or precise registration process.

The goal is to register the two complex SAR images to within 1/8 of a pixel.

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Rough registrationIn the rough registration process reference points (pass points) are identified in both images.

Transformations are determined that will align the pass points in both images.

The transformation and resampling is applied to one of the images so that the two images are registered at the pixel level.

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Rough registrationSpline interpolation is used to resample the image to provide the pixel-level registration.

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Precise registrationFollowing rough registration, a precise registration process is used to achieve the desired 1/8 pixel registration.

Again reference (pass) points are selected.

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Precise registrationAn image segment from the master image is selected and in the same location in the slave image a slightly smaller image segment is selected.

These image segments undergo 8:1 interpolation (to achieve a 1/8 pixel registration).

A search for the proper two-dimensional shift is conducted using the correlation coefficient as the measure of goodness.

Results from this search process are applied to the overall image.

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Precise registration

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Geometric correction

2

02 zHr_slr_gr

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The steep slope, as seen in the slant range axis, appears to have a negative slope. This phenomenon is used as a layover indicator.

The areas affected by layover are identified and undergo additional processing to remove the associated geometric distortion.

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Geometric correctionThe pixels affected by layover can then be resorted to correct for the geometric distortion resulting from the layover effect.

Uncorrected residual height (elevation) errors will prevent complete removal of layover effects.

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In regions of shadow, the low SNR results in large phase errors and, consequently, large height errors.

Height errors must be detected and corrected to produce valuable elevation maps.

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Temporal decorrelation and persistent scatterersMaterial taken from Ferretti, Prati, and Rocca, “Permanent scatterers in SAR interferometry,” IEEE Transactions on Geoscience and Remote Sensing, 39(1), pp. 8-20, 2001.

Multipass SAR interferometry involves phase comparison of SAR images gathered at different times with slightly different look angles.

Multipass InSAR enables production of digital elevation maps (DEMs) with meter accuracy as well as terrain deformations with millimetric accuracy.

Factors limiting the usefulness of multipass InSAR include:temporal decorrelation

geometric decorrelation

atmospheric inhomogeneities

Without these difficulties, very long term temporal baseline interferometric analyses would be possible revealing subtle trends.

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Temporal decorrelation and persistent scatterers

Temporal decorrelationScenes containing elements whose electromagnetic response (scattering) changes over time render multipass InSAR infeasible. Vegetated areas are prime examples.

Geometric decorrelationScenes containing scatterers whose scattering varies with incidence angle limits the number of image pairs suitable for interferometric applications.

Atmospheric inhomogeneityAtmospheric heterogeneity superimposes on each complex SAR image an atmospheric phase screen (APS) that compromises interferometric precision.

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Temporal decorrelation and persistent scatterersConventional InSAR processing relies on the correlation coefficient as a quality indicator of the interferometric phase.

These decorrelation factors all degrade the overall scene correlation.

However, studies have found that scenes frequently contain permanent or persistent scatterers (PS) that maintain phase coherence over long time intervals.

Often times the dimensions of the PS are smaller than the SAR’s spatial resolution. This feature enables the use of spatial baseline lengths greater than the critcal baseline.

Pixels containing PSs submeter DEM accuracy and millimetric terrain motion (in the line of sight direction) can be detected.

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The availability of multiple persistent scatterers widely distributed over the scene enables estimation of the atmospheric phase screen (APS)

With an estimate of the APS, these effects can be removed enabling production of reliable elevation and velocity measurements.

A network of persistent scatterers in a scene has been likened to a “natural” GPS network useful for monitoring sliding areas, urban subsidence, seismic faults, and volcanoes.

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Persistent scattererWhat makes a good persistent scatterer ?

Scatterers with a large RCS and a large scattering beamwidth.

For example, naturally occuring dihedrals and trihedrals.

These can often be found in urban areas and rocky terrrain.

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Taken from Warren, Sowter, and Bigley, “A DEM-free approach to persistent point scatterer interferometry,” FIG Symposium, 2006.

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Atmospheric phase screen estimated from analysis of two complex Atmospheric phase screen estimated from analysis of two complex SAR images separated over a 425 day period.SAR images separated over a 425 day period.

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