Interferometric Synthetic-Aperture Radar (InSAR) Basics

Outline SAR limitations Interferometry SAR interferometry (InSAR) Single-pass InSAR Multipass InSAR InSAR geometry InSAR processing steps Phase unwrapping Phase decorrelation Baseline decorrelation Temporal decorrelation Rotational decorrelation Phase noise Persistent scatterers

SAR limitations

SAR limitations All signals are mapped onto reference plane This leads to foreshortening and layover

Shadow, layover, and foreshortening distortion SEASAT Synthetic Aperture Radar Launched: June 28, 1978 Died: October 10, 1978 orbit: 800 km f: 1.3 GHz PTX: 1 kW : 33.8 s B: 19 MHz : 23  3 PRF: 1464 to 1647 Hz ant: 10.7 m x 2.2 m x = 18 to 23 m y = 23 m 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].

SAR limitations – foreshortening Foreshortening: - <  <  ( is local slope). Dilates or compresses the resolution cell (pixel) on the ground with respect to the planar case.

SAR limitations – layover Layover:    ( 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 – shadow Shadow:    - /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

Interferometry interferometry—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.

SAR interferometry – how does it work? B A1 A2 Antenna 1 Antenna 2 Return comes from intersection Radar Return could be from anywhere on this circle Single antenna SAR Interferometric SAR

SAR interferometry – how is it done? B is the interferometric baseline Single pass or Simultaneous baseline Two radars acquire data from different vantage points at the same time Repeat pass or Repeat track Two radars acquire data from different vantage points at different times

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

Interferometric SAR – geometry The 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)

Law of cosines

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 Multipass baseline Transmit and receive on antenna A1 Transmit and receive on antenna A2

Interferometric SAR– radar phase For single-pass InSAR where transmission is on antenna A1 and reception uses both A1 and A2: And Simultaneous baseline Transmit on antenna A1 Receive on both A1 and A2

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

Radar interferometry – geometry From 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

SAR Interferometry InSAR 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)

SAR Interferometry Multi-pass interferometry Two pass Three 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

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

Interferometric SAR processing Production 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.

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 coherence Lack of coherence caused by decorrelation Baseline decorrelation Sufficient change in incidence angle results in scatterer interference (fading effect) Temporal decorrelation Motion of scatterers between observations produces random phase Windblown vegetation Continual change of water surface Precipitation effects Atmospheric or ionospheric variations Manmade effects Rotational decorrelation Data collected from nonparallel paths Phase unwrapping to obtain absolute phase requires reference point

SAR Interferometry The 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 Interferometry It follows that phase due to phase due to smooth Earth relief Removing the phase component due to the smooth Earth yields a “flattened interferogram”

SAR Interferometry

Ambiguity height The 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)

Phase unwrapping z x ACTUAL ELEVATION PROFILE Phase WRAPPED PHASE 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.

Baseline decorrelation To 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 decorrelation Limiting  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-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 Baseline Perpendicular Baseline, B Parallel-ray assumption Orthogonal baseline component, B, is key parameter used in InSAR analysis B = B cos( - )

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

(incoherent) 0 <  < 1 (coherent) Correlation The 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.

Decorrelation effects Factors contributing to decorrelation include: Spatial baseline Inadequate spatial phase sampling (a.k.a. baseline decorrelation) Fading effects Rotation Non-parallel data-collection trajectories 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

Noise effects Random 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

Noise effects Since 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

Noise effects Noise also increases the uncertainty in the phase measurement, i.e., the standard deviation of the phase, 

Note that the slope   as   1 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

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

Noise with another decorrelation factor Now re-introducing noise we get and since SNR is (|c|2 + |d|2 )/|n|2

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

Spatial baseline decorrelation

Rotational decorrelation Complete decorrelation results after rotation of 2.8 at L-band and 0.7  at C-band.

Temporal decorrelation Complete decorrelation results after rms motion of ~ /3  ~ 0.5 yields reasonably reliable topographic maps

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

Uncompensated range migration effects

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 .

Misregistration Misregistration 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.

Rough registration In 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.

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

Precise registration Following rough registration, a precise registration process is used to achieve the desired 1/8 pixel registration. Again reference (pass) points are selected.

Precise registration An 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.

Precise registration

Geometric correction

Geometric correction 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.

Geometric correction The 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.

Geometric correction 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.

Geometric correction

Geometric correction

Temporal decorrelation and persistent scatterers Material 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.

Temporal decorrelation and persistent scatterers Scenes containing elements whose electromagnetic response (scattering) changes over time render multipass InSAR infeasible. Vegetated areas are prime examples. Geometric decorrelation Scenes containing scatterers whose scattering varies with incidence angle limits the number of image pairs suitable for interferometric applications. Atmospheric inhomogeneity Atmospheric heterogeneity superimposes on each complex SAR image an atmospheric phase screen (APS) that compromises interferometric precision.

Temporal decorrelation and persistent scatterers Conventional 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.

Temporal decorrelation and persistent scatterers 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.

Persistent scatterer What 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.

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

Temporal decorrelation and persistent scatterers Atmospheric phase screen estimated from analysis of two complex SAR images separated over a 425 day period.

Temporal decorrelation and persistent scatterers

Temporal decorrelation and persistent scatterers

Temporal decorrelation and persistent scatterers

Temporal decorrelation and persistent scatterers

Temporal decorrelation and persistent scatterers