interferometric error sources

J Synthetic Aperture Radar Interferometry

INTERFEROMETRIC ERROR SOURCESINTERFEROMETRIC ERROR SOURCES

In addition to the decorrelation contributions, several other sources of error exist in interferometry. These include

Layover and shadow in radar imagery from slant range geometry Multiple scattering within and among resolution cells Range and Azimuth sidelobes due to bandwidth/resolution

constraints Range and azimuth ambiguities due to design constraints Multipath and channel cross-talk noise as low-level interference Calibration errors Propagation delay errors from atmosphere and ionosphere

Interferometric Decorrelation


r

Radar Antenna

LAYOVER AND SHADOW IN RADAR IMAGINGLAYOVER AND SHADOW IN RADAR IMAGING

Ground Range

Slant Range

TERRAIN

RADAR IMAGE

Mapping of Earth’s surface into slant rangedistorts highly sloped areas

Layover Shadow


LAYOVER EFFECTS IN INTERFEROMETRYLAYOVER EFFECTS IN INTERFEROMETRY

As slopes increase and approach the look direction, the resolution element size normal to the look direction increases toward infinity. This has the following consequences:

– Radar backscatter return becomes very bright, giving high interferometric correlation (high SNR)

– Effective critical baseline decreases toward zero, with interferometric fringe rate approaching one cycle of phase per pixel

r

Local Slope

r

No surface slope Surface slope


LAYOVER EFFECTS IN INTERFEROMETRYLAYOVER EFFECTS IN INTERFEROMETRY

The distortion of terrain into slant range coordinates has consequences for the inference of terrain height from interferometric phase

– Widely spaced points on the sloping ground, well outside a particular ground resolution element, can contribute to the complex backscatter in a range resolution element, particularly when the slope exceeds the look angle, leading to incorrect heights.

– The close proximity in slant range of widely space ground elements at very different heights leads to phase shears that confound phase unwrapping algorithms.

Water

Bridge

l

r1

r12 r1

2r1 l

Two scatterers with range



MULTIPLE SCATTERING EFFECTSMULTIPLE SCATTERING EFFECTS

Layover illustration is also an example of multiple scattering effects that occur among resolution cells. In this case, the bridge return will dominate the water return. There will be multiple images of the bridge in the radar image at different ranges. Each range element in an interferogram will have its own interpretation of the height, depending on the scattering phase function of the bridge and water

Water

Bridge

l

r1

r12 r1

2r1 l



Similar effects occur within the volumeof a resolution element in forming the coherent backscatter. The aggregateheight is not necessarily the uniformlyweighted average of the scatter heights


SHADOW EFFECTS IN INTERFEROMETRYSHADOW EFFECTS IN INTERFEROMETRY As slopes approach being parallel to the look direction, the

resolution element size normal to the look direction decreases toward zero. This has the following consequences:

– Radar backscatter return becomes very dim, giving low interferometric correlation (low SNR), adding difficulty to phase unwrapping

– Effective critical baseline increases toward infinity, with interferometric fringe rate slowing down, easing phase unwrapping

No surface slope Surface slope

rr


LAYOVER AND SHADOW MITIGATIONLAYOVER AND SHADOW MITIGATION

For wide-swath interferometric systems that span a large range of incidence angles, the effects of layover and shadow can be mitigated through parallel track imaging:

– Layover more likely in near swath where look angle is shallow

– Shadow more likely in far swath where look angle is steep

– By flying parallel tracks with partial swath overlap, near swath layover regions are likely to be intact in far swath of parallel track, and shadow regions in far swath are likely to be intact in near swath of a different parallel track

For narrow swath systems, orthogonal imaging geometries are probably best

– Opposite side imaging (anti-parallel tracks) not optimal because near swath layover of one track corresponds to far swath shadow of anti-parallel track


EXAMPLE OF LAYOVER/SHADOW MITIGATIONEXAMPLE OF LAYOVER/SHADOW MITIGATION

Figure of Northridge Mosaic here.


RANGE SIDELOBES IN RADAR IMAGINGRANGE SIDELOBES IN RADAR IMAGING

Range sidelobes arise in extended time-bandwidth implement-ations of linear FM pulsed systems. For a pulse of duration with chirp rate , observing a target located at temporal position , the impulse response is:

W(t0) rectt tT p

e jK( t tT )

2

e jK( t t0 )2

dt

e jK ( tT t0 )2

e j2 K( t 0 t T )tdttT

tT p

pe jKt0

2 / 4 sinK(t0 tT) pK(t0 tT ) p

pK tT


RANGE SIDELOBES IN INTERFEROMETRYRANGE SIDELOBES IN INTERFEROMETRY The interferometric phase associated with the main lobe of a

resolution element contributes to the surrounding resolution elements weighted by the range impulse response

Phase noise contributed by range sidelobes usually modeled as additive noise term at the level NSR = ISLR. NSR is multiplied by expected signal level to compute noise power to add.

Range sidelobes actually contribute multiplicative noise: consider the case when the peak side lobe is brighter than the ambient backscatter

Main lobe withinterferometric phase

peak side lobeside lobes withinterferometric phase


AZIMUTH SIDELOBES IN RADAR IMAGINGAZIMUTH SIDELOBES IN RADAR IMAGING

Azimuth sidelobes arise in the naturally extended time-bandwidth environment of synthetic aperture systems. For a system with Fresnel zone , azimuth antenna length , observing a targe at azimuth location , the azimuth impulse response is:

F LxT

W(x0 ) rectx xT xp / 2

xp

e j(x xT )

2 /F2e j(x x 0 )2 / F2

dx

e jK (x T x0 )2

e j 2(x 0 xT )x / F2

dxxT x p / 2

xT x p / 2

, x p 2F2

L

x pe jKx02 / 4 sin (x0 xT )x p / F

2 (x0 xT )x p / F

2

In interferometry, treatment of azimuth sidelobes is similar to rangesidelobes


SIDELOBE MITIGATION STRATEGIESSIDELOBE MITIGATION STRATEGIES

In regions of high contrast, where sidelobes can lie above the ambient backscatter, or in regions that are are very dark and cannot tolerate a significant additional noise contribution, sidelobes must be reduced

Weighting of the matched filter function in range or azimuth compression can effectively reduce sidelobes in a controlled fashion

Cost of weighting is reduction in processing bandwidth, leading to reduction in resolution.

Design of an interferometer should consider bandwidth and weighting functions suited to the mapping problem of interest: e.g. urban mapping requires very fine resolution and very low sidelobes because the scenes are highly contrasted.


RANGE AMBIGUITIES IN INTERFEROMETRYRANGE AMBIGUITIES IN INTERFEROMETRY

Range ambiguities arise in spaceborne systems primarily, because the radar must pulse faster than the round-trip light time for a single pulse event.

Because multiple pulses are in the air, it is possible for the tail end of energy from a preceding pulse or leading end of energy from a succeeding pulse to contribute to a pulse of interest.

Though multiplicative noise, range ambiguities are modeled as additive thermal noise at a level NSR = total power integrated in ambiguous pulses within the swath. This noise ratio multiplied by the expected mean signal power sets the additive noise level. This roughly determines the interferometric phase noise contributed to the system.

Through adjustment of the pulse width and the pulse repetition frequency, it is possible to control range ambiguities.


ILLUSTRATION OF RANGE AMBIGUITIESILLUSTRATION OF RANGE AMBIGUITIES

Range ambiguity figure here


AZIMUTH AMBIGUITIES IN RADAR IMAGINGAZIMUTH AMBIGUITIES IN RADAR IMAGING

Azimuth ambiguities arise in radar imaging because the pulse repetition frequency is insufficient to satisfy the Nyquist criterion for adequate sampling of the Doppler spectrum.

Spaceborne systems are typically designed for low PRF, near the 3dB spectral width, to reduce data rate. As a result, energy in the tails of the azimuth spectrum aliases.

Azimuth ambiguities are again multiplicative, but are modeled in the usual additive way.

fPRF

Limiting the processingbandwidth to a fractionof the PRF reducesambiguity level


AMBIGUITY MITIGATION STRATEGYAMBIGUITY MITIGATION STRATEGY

Range and azimuth ambiguities contribute to the random phase noise in interferometry multiplicatively.

Both range and azimuth ambiguities rising above the ambient backscatter significantly corrupt the interferometric phase.

To reduce azimuth ambiguities, PRF should be increased to properly sample azimuth spectrum.

To reduce range ambiguities, PRF should be decreased (in general) to separate pulses in time as much as possible.

Trade-off must consider the required azimuth resolution, desired look angles, swath width, and noise level.


INTERFEROMETRIC RADAR SCHEMATICINTERFEROMETRIC RADAR SCHEMATIC

B

B

B

Target Pixel

Antenna a

Antenna b

ra

r b

Transmitter

Receiver a

Receiver b

a

b

STALO

Receiver Chain:

0

f0

i

fi

0,0 i , i

In addition to baseline andposition, time and phase delays in the radar requirecalibration.


RELATIONSHIP BETWEEN PARAMETERS AND RELATIONSHIP BETWEEN PARAMETERS AND INTERFEROMETER ELEMENTSINTERFEROMETER ELEMENTS

Parameter Element AccuracyB aseline vector , B , includinglength and att itude, forreduction of interferometricphase to height

Locations of the phasecenters of both antennas

a few millimeters

A bsolute radar range from oneantenna to targets, forgeolocation

Time delay through thecomposite transmitter /receiver

a few nanoseconds

D ifferential radar rangebetween channels, for imagealignment in interferogramformation

Time delays through thereceiver chains (but not thetransmitter chain)

few er nanoseconds

D ifferential phase betw eenchannels, for determination ofthe topography

Phase delays through thereceiver chains (but not thetransmitter chain)

a few degrees


CALIBRATION PARAMETER EQUATIONSCALIBRATION PARAMETER EQUATIONS

a (t) BB (t ra ) i

a kki1

N 1 i0

N 2

a ii0

N 1

ia

i0

N 1

4ra t

b (t) BB (t rb ) i

b kki1

N 1 i0

N 2

b ii0

N 1

ib

i0

N 1

2(ra rb )t

The phase at the receiver outputs is given by

Baseband frequency: BB c ii0

N 1

rx x i

x

i0

N 1

, x a,bReceiver time delay:

tTransmitter phase delay:


CALIBRATION PARAMETER EQUATIONS IICALIBRATION PARAMETER EQUATIONS II

a b

BB (ra r

b ) (ra r

b ) 2(ra rb )

The phase difference between the channels is

rx i

x kki1

N 1 i0

N 2

x ii0

N 1

ix

i0

N 1

, x a,b

Channel phase constant:

If total time and phase delay differences can be measured, then range difference proportional to topography (final term in equation)can be known. Note: this term is also dependent on baseline know-ledge accuracy.


CALIBRATION STRATEGIESCALIBRATION STRATEGIES

To determine the channel time and phase delays, assume that the interferometer is stable over time and baseline is known.

– Total time delay (range) can be determined by comparing location of known target to inferred location

– Differential time delay can be determined by scene matching over a flat surface

– Differential phase delay can be determined by inserting a calibration tone near the receiving antennas

a,caltone(t) BB ,cal( t ra) r

a

b,caltone(t) BB ,cal( t rb ) r

b

caltone BB ,cal ( ra r

b ) (ra r

b )


CALIBRATION STRATEGIES IICALIBRATION STRATEGIES II

It is also possible to calibrate the radar interferometer through simultaneous least squares adjustment, utilizing the sensitivity equations described earlier and reference data, such as a DEM

– Requires radar receiver time and phase stability over all time, which is difficult to achieve

– Requires baseline stability over all time

– Least squares adjustment and calibration tone is generally needed

One solution to potentially remove receiver delays without calibration tone: operate the interferometer in “ping-pong” mode.

– By using a single transmitter and receiver, differential time and phase delays are zero.

– Cost: double pulse repetition frequency for the one receiver required to properly sample azimuth spectrum.


CHANNEL ISOLATION IN RADAR CHANNEL ISOLATION IN RADAR INTERFEROMETRYINTERFEROMETRY

In some single-pass dual-aperture systems, energy can leak between receiver channels

– Standard mode: radiation from other antenna or platform scatterers entering the antenna (multipath)

– Ping-pong mode: switch between receiving antennas has some leakage, and multipath

Switch leakage and multipath from other antenna appear in interferometric phase signature as phase modulation at the interferometric fringe frequency.

Multipath from other platform scattering sources appears as phase modulation at a frequency proportional to the scatterer-antenna separation.

Repeat-pass single-aperture systems do not suffer from channel isolation problems.


SWITCH ISOLATION SWITCH ISOLATION

B

Antenna a

Antenna b

Transmitter

Receiver

STALO

Switch

Abejbe

j 4ra

Abejbe

j4rbta : Abe

jbe j 4

ra

Abej be

j4rb

tb : Abejbe

j 4r b

Abej be

j4ra

ab* : Ab2 e

j 4( ra rb ) 2 2e

j4(r a rb )

with leakage

In ping-pong operation,switch alternates antennasetting for transmit/receive.


SWITCH ISOLATION IISWITCH ISOLATION II

First term ofExpression

First two terms All three terms

Ab2 e

j 4(ra rb )

2 2ej4(ra rb )

Near Swath

Far Swath

j4(ra rb )

Near Swath

Far Swath

2

Near Swath

Far Swath

2

2

2


ANTENNA MULTIPATH IN INTERFEROMETRYANTENNA MULTIPATH IN INTERFEROMETRY

B

Antenna a

Antenna b

Transmitter

Receiver

STALO

Pure Switch

Abejb e

j 4ra

Abejbe

j 4( rb B)

Abejbe

j4rbAbe

jbe j 4

(ra B)

ab* : Ab2 e

j4(ra rb)

2cos4B2e

j4(ra rb)

Scatter to a

Scatter to b

Backscatter from target


Baseline B is constant. Multipath off antennas has sameeffect as switch leakage.


PLATFORM MULTIPATH PLATFORM MULTIPATH

B

Antenna a

Antenna b

Transmitter

Receiver

STALO

Pure Switch



AIRCRAFT WING


Scatter to a and b

rw

Bwb

Bwa

ab* : Ab2 e

j4(ra rb )

e j4

(ra rw Bwb)

ej4(rb rw Bwb )

2e j 4

(Bwa Bwb)

Multipath cross terms depend on “baseline” from platform scatterer


EXAMPLES OF MULTIPATHEXAMPLES OF MULTIPATH


ATMOSPHERIC PROPAGATION EFFECTS IN ATMOSPHERIC PROPAGATION EFFECTS IN RADAR INTERFEROMETRYRADAR INTERFEROMETRY

Due to turbulent mixing in the troposphere, particularly in the wet layers, the refractive index along the radar ray path varies within the scene.

Wet tropospheric variations of refractivity are typically an order of magnitude smaller than the dry troposphere total path refractivity because the wet troposphere is concentrated in a layer near the earth’s surface.

For single-pass two-aperture systems, the difference in path delay variations cancels to first order because the ray path sensed is nearly identical. The total path delay does affect the absolute range, as seen previously, but not significantly the differential range or phase.

For repeat-pass single-aperture systems, the difference in path delay is a substantial limiting factor.


IONOSPHERIC PROPAGATION EFFECTS IN RADAR IONOSPHERIC PROPAGATION EFFECTS IN RADAR INTERFEROMETRYINTERFEROMETRY

Due to turbulent mixing in the ionosphere, and diurnal variations of earth’s response to the solar wind, the refractive index along the radar ray path varies within the scene.

For airborne systems, the ionosphere is not a concern. For spaceborne platforms, the scale size of ionospheric anomalies

is large in the radar scene because the ionosphere is relatively close to the sensor.

For single-pass two-aperture systems, the difference in path delay variations cancels to first order because the ray path sensed is nearly identical.

For repeat-pass single-aperture systems, the difference in path delay is a substantial limiting factor.

interferometric error sources

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