1 Interferometric Synthetic-Aperture Radar (InSAR) Basics

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  • *Interferometric Synthetic-Aperture Radar (InSAR) Basics

  • *OutlineSAR limitationsInterferometrySAR interferometry (InSAR)Single-pass InSARMultipass InSARInSAR geometryInSAR processing stepsPhase unwrappingPhase decorrelationBaseline decorrelationTemporal decorrelationRotational decorrelationPhase noisePersistent scatterers

  • *SAR limitations

  • *SAR limitationsAll signals are mapped onto reference planeThis leads to foreshortening and layover

  • *Shadow, layover, and foreshortening distortionFigure 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 Radar Launched: June 28, 1978 Died: October 10, 1978 orbit: 800 km f: 1.3 GHz PTX: 1 kW : 33.8 sB: 19 MHz : 23 3PRF: 1464 to 1647 Hz ant: 10.7 m x 2.2 m x = 18 to 23 my = 23 m

  • *SAR limitations foreshorteningForeshortening: - < < ( is local slope).Dilates or compresses the resolution cell (pixel) on the ground with respect to the planar case.

  • *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.

  • *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.

  • *Foreshortening and geocoding

  • *InterferometryinterferometryThe 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.

  • *SAR interferometry how does it work?Single antenna SARInterferometric SAR

  • *SAR interferometry how is it done?Single pass orSimultaneous baselineTwo radars acquire data from different vantage points at the same timeRepeat pass orRepeat trackTwo radars acquire data from different vantage points at different timesB is the interferometric baseline

  • *Single-pass interferometrySingle-pass interferometry. Two antennas offset by known baseline.

  • *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 scatterers 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 unknownFinding R enables determination of and z(x)

  • *Law of cosines

  • *Interferometric SAR radar phaseRadar phases

    Since is measured, R can be determined

    ExampleLet = 10 cm (f = 3 GHz) measure to /100 (3.6) equivalent to 0.1 mm or 0.3 ps resolutionMultipass baselineTransmit and receive on antenna A1 Transmit and receive on antenna A2

  • *Interferometric SAR radar phaseFor single-pass InSAR where transmission is on antenna A1 and reception uses both A1 and A2:

    AndSimultaneous baselineTransmit on antenna A1 Receive on both A1 and A2

  • *Radar interferometry geometryFrom 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 multipassSo that

  • *Radar interferometry geometryFrom

    we find

    and

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

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

  • *Interferometric SAR processing geometry

    Scatterer is at intersection of Range

    Sphere, Doppler Cone and Phase

    Cone

    Baseline

    Vector

    Aircraft

    Position

    Phase Cone

    Velocity

    Vector

    Doppler Cone

    Range Sphere

  • *SAR InterferometryInSAR provides additional information via phase measurementsThis additional information enables a variety of new capabilitiesTopography measurementVertical surface displacement (uplift or subsidence) Lateral surface displacement (velocity)Change detection (via phase decorrelation)

  • *SAR InterferometryMulti-pass interferometryTwo passTwo scenes, one interferogram topography, change detection surface velocity (along-track interferometry temporal baseline)Three passThree scenes, two interferograms topography, change detection, surface deformation

  • *Differential interferometry how does it work?Three-pass repeat trackTwo different baselines

    Same incidence angleSame absolute range

    Parallel ray approximation used to detect changesIf the surface did not change between observations, then

  • *Interferometric SAR processingProduction of interferometric SAR images and data sets involves multiple processes.Independent SAR data sets must be collectedComplex SAR images are producedSAR images must be registered with one anotherInterferometric phase information extracted pixel-by-pixelCoherence is analyzedPhase is unwrapped (removes modulo-2 ambiguity) Phase is interpolatedPhase is converted into heightInterferometric image is geocodedTo produce surface velocity or displacement maps, successive pairs of InSAR images are processed to separate elevation effects from displacements.

  • *InSAR processing steps

  • *Phase history and magnitude image

  • *Phase image

  • *Illustrated InSAR processes (1 of 3)

  • *Illustrated InSAR processes (2 of 3)

  • *Illustrated InSAR processes (3 of 3)

  • *Phase coherenceLack of coherence caused by decorrelationBaseline decorrelationSufficient change in incidence angle results in scatterer interference (fading effect)Temporal decorrelationMotion of scatterers between observations produces random phaseWindblown vegetationContinual change of water surfacePrecipitation effectsAtmospheric or ionospheric variationsManmade effectsRotational decorrelationData collected from nonparallel paths

    Phase unwrapping to obtain absolute phase requires reference point

  • *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

  • *SAR InterferometryIt follows that

    phase due to phase due to smooth Earthrelief

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

  • *SAR Interferometry

  • *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 knowA large baseline B improves the InSARs 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)

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

  • *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

  • *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 Bwhere a = 1 for single-pass a = 2 for multipass a = 2 for ping-pong mode[i.e., Tx(A1)Rx(A1 , A2); Tx(A2)Rx(A1, A2); repeat]

  • *Perpendicular BaselinePerpendicular Baseline, BParallel-ray assumptionOrthogonal baseline component, B, is key parameter used in InSAR analysisB = B cos( - )

  • *Baseline decorrelationWhile Bc represents the theoretical maximum baseline that will avoid decorrelation, experiments show that a more conservative baseline should be used.

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

    wheres2* is the complex conjugate of s2E{ } is ensemble averaging

    (incoherent) 0 < < 1 (coherent) is a quality indicator of the interferometric phase, for precise information extraction, a high value is