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An Overview of SAR Interferometry

Rocca F., Prati C., Ferretti A. Dipartimento di Elettronica e Informazione (DEI) Politecnico di Milano (POLIMI), Piazza Leonardo da Vinci 32, 20133 Milano, Italy
rocca elet.polimi.it prati elet.polimi.it
http://www.elet.polimi.it

Abstract

In this presentation we propose an overview of SAR interferometry discussing its possibilities and limits, making reference to the TANDEM experiments carried out with ERS 1 and 2. The coherence of the interferometric pair is an important parameter, that combined with the more usual backscatter amplitudes, leads to useful images segmentation. Due to the 1 day delay between passes of the two satellites, the coherence is high but on highly forested areas; very useful DEM's are obtainable from the fringes. The combination of several passes can reduce the dispersion due to atmospheric artifacts. Millimetric motion of large areas of the terrain or of corner reflectors can be measured with good reliability and therefore the possibility has been demonstrated to measure subsidence, landslides, volcanoes deflation, and coseismic motions.

Keywords: SAR-Interferometry, Phase Unwrapping, DEM reconstruction, Atmospheric Effects, Terrain Changes, Coherence Estimation

Introduction

  Synthetic Aperture Radar (SAR) systems record both amplitude and phase of the backscattered echoes. The phase of each pixel of a focused SAR image is the sum of three distinct contributions:

1 - the two-ways travel path (sensor-target-sensor: hundreds of kilometers in the satellite case) that, divided by the used wavelength (a few centimeters), corresponds to millions of cycles;

2 - the interaction between the incident e.m. waves and the scatterers within the ground resolution cell;

3 - the phase shift induced by the processing system used to focus the image.

Therefore, the phase of a single SAR image is of no practical use. On the contrary, if two SAR images from slightly different viewing angles are considered (interferometric pair) their phase difference (interferometric fringes) can be usefully exploited to generate Digital Elevation Maps (DEMs), to monitor terrain changes and to improve the range resolution. The interferometric fringes image is derived as the phase of the SAR interferogram, that is the complex image formed by cross-multiplying the two SAR images. The relation between the interferometric fringes and ground elevation is usually explained by means of the monochromatic approach [24, 14]. It is based on the assumption that the RF bandwidth is so small (and this is the case of most satellite systems including SEASAT, ERS-1, JERS-1, ERS-2 and RADARSAT) to be negligible. Thus the system is considered monochromatic. However, if the finite bandwidth of the system is considered (wavenumber shift approach), a relative shift of the ground wavenumber spectra dependent on the baseline and the local slope is found. A few important consequences come out from this result [16, 5]. Using the simpler monochromatic approach we show the relationship between the relative terrain elevation and the interferometric fringes. Then we will determine the quality of the Digital Elevation Model derived from interferometry. Two sections will be dedicated to the description of other applications of SAR interferometry: small terrain motion detection and uses of the coherence for image segmentation. Symbols that will be used through the text and the main parameters values of the ERS-1 SAR system (that will be assumed as typical parameters of SAR from satellites) are shown in Table 1.

The monochromatic approach

  Let us consider two complex SAR images taken from two slightly different viewing angles (see Figure 1), tex2html_wrap_inline3146 and tex2html_wrap_inline3148 . Even if non simultaneous acquisitions are considered, we shall suppose, for now, that the terrain backscatter did not change.

Figure 1: Interferometric SAR geometry in a plane orthogonal to the rectilinear platforms (tex2html_wrap_inline3310 and tex2html_wrap_inline3312) trajectory.

Let us now exploit the ''monochromatic approximation'': the relative system bandwidth is so small (i.e. in the ERS-1 case its value is tex2html_wrap_inline3150 ) to be neglected. The phase difference tex2html_wrap_inline3152 between correspondent complex pixels in tex2html_wrap_inline3146 and tex2html_wrap_inline3148 is proportional to the travel path difference tex2html_wrap_inline3158 (the factor 2 accounts for the two ways travel path):

  equation309

( tex2html_wrap_inline3216 is a constant). The interferometric phase tex2html_wrap_inline3218 of a single pixel is still of no practical use. The travel path difference tex2html_wrap_inline3158 is usually much greater than the wavelength tex2html_wrap_inline3222 (in most of the practical cases, the travel path difference from the satellite can be as large as a few hundred meters whereas the used wavelength is of the order of a few centimeters) and the measured phase tex2html_wrap_inline3224 shows an ambiguity of many cycles. On the other hand, passing from one pixel to its neighbor (only a few meters apart in the slant range direction), the variation of the travel path difference ( tex2html_wrap_inline3226 ) may be much smaller than tex2html_wrap_inline3228 and the variation of the interferometric phase tex2html_wrap_inline3230 is not ambiguous. Moreover, a simple relation between tex2html_wrap_inline3232 and the relative terrain elevation can be derived.

tex2html_wrap_inline3234

Symbol Meaning
tex2html_wrap_inline3236 wavelength
tex2html_wrap_inline3238 central frequency
W system bandwidth
tex2html_wrap_inline3242 sampling frequency
tex2html_wrap_inline3244 Nyquist frequency
tex2html_wrap_inline3246 off-nadir angle
tex2html_wrap_inline3248 local terrain slope (range)
H platform altitude
tex2html_wrap_inline3252 slant range resolution
tex2html_wrap_inline3254 slant range sampling interval
tex2html_wrap_inline3256 ground range resolution
B baseline
tex2html_wrap_inline3260 normal baseline
tex2html_wrap_inline3262 radial baseline
tex2html_wrap_inline3264 critical baseline
r slant range axis
tex2html_wrap_inline3268 sensor-target distance
y ground range axis
z elevation axis
tex2html_wrap_inline3274 ground range wave number
tex2html_wrap_inline3276 interferometric phase
Symbol ERS-1 value
tex2html_wrap_inline3278 5.66cm
tex2html_wrap_inline3282 5.3GHz
W 16MHz
tex2html_wrap_inline3242 18.96MHz
tex2html_wrap_inline3294 23deg.
H 780km
tex2html_wrap_inline3302 9 meters
tex2html_wrap_inline3264 1100 meters

In Figure 1 we have indicated the position of the two SAR sensors ( tex2html_wrap_inline3310 and tex2html_wrap_inline3312 ) and their relative displacements parallel ( tex2html_wrap_inline3262 ) and normal ( tex2html_wrap_inline3260 ) to the slant range direction. We have also indicated the position of two point scatterers and their relative displacements parallel ( tex2html_wrap_inline3318 ) and normal ( tex2html_wrap_inline3320 ) to the slant range direction. Let us assume as a reference the positions of tex2html_wrap_inline3310 and tex2html_wrap_inline3324 with their relative distance tex2html_wrap_inline3268 . By changing the sensor and target position by tex2html_wrap_inline3328 and tex2html_wrap_inline3330 respectively the sensor-target distance becomes:

equation332

  Since the distance between the two SAR sensors is generally much smaller than the sensor-target distance tex2html_wrap_inline3268 (a few hundred meters compared with 800 km, in the ERS-1 case), the following expression of the interferometric phase variation holds:

  equation338

This result shows that if we know the relative displacement of the two orbits normal to the slant range direction tex2html_wrap_inline3260 , the distance tex2html_wrap_inline3268 and the value of the SAR wavelength tex2html_wrap_inline3428 , then the phase difference tex2html_wrap_inline3430 depends only on the tex2html_wrap_inline3320 value, i.e. the elevation difference between the points displayed in Figure 1, measured in the direction normal to the slant range axis. Thus the interferometric phase image represents a map of the relative terrain elevation with respect to the slant range direction. A linear term can then be subtracted from the interferometric phase so that the phase corresponding to the flat horizontal terrain is a constant. After some algebra, the version of equation 0.3 that refers to the relative elevation tex2html_wrap_inline3434 with respect to a flat terrain becomes:

  equation348

where we have indicated with tex2html_wrap_inline3526 the altitude of ambiguity, i.e. the elevation change correspondent to a 2 tex2html_wrap_inline3528 phase shift.

Phase unwrapping

  Up to now it has been assumed that the phase difference tex2html_wrap_inline3530 of equation 0.4 would be directly obtained from the interferometric fringes. However such an assumption is in some way misleading. In fact, from the interferogram, the complex values tex2html_wrap_inline3532 can be determined but not the tex2html_wrap_inline3534 values themselves. What is measured is not the phase difference value tex2html_wrap_inline3536 , but its principal value tex2html_wrap_inline3538 , limited between tex2html_wrap_inline3540 and tex2html_wrap_inline3542 . The interferometrical fringes show typical discontinuities like those shown in Figure 2.

Figure 2: ERS-1 - Mt. Vesuvius (Italy) August 27th and September 5th, 1991. Interferometric fringes. The estimated baseline is 193 m.

Two adjacent discontinuities separated by a constant elevation increment, corresponding to a tex2html_wrap_inline3544 phase drop, represent the height contours of the terrain elevation map. However, since the real phase values are ``wrapped'' around a tex2html_wrap_inline3546 interval, to obtain the correct map (and, thus, the correct label of each contour line), a map of the multiples of tex2html_wrap_inline3548 to be added to the ''wrapped'' phase should be found (phase unwrapping).

At the beginning of the studies on SAR interferometry (1988-89), the phase unwrapping problem was investigated assuming that only two SAR images were available. That was the actual situation at that time since the only few interferometric SAR images were from the SEASAT and the JPL single pass airborne systems. Many techniques of phase unwrapping of interferometric SAR images have been proposed [7, 6, 19]. A summary of these techniques is out of the scope of this paper.

More recently, however, a different strategy to solve the phase unwrapping problem has been considered. With the huge amount of SAR images from the European satellites ERS-1 and ERS-2 together with the availability of Digital Elevation Models (typically from the optical stereo SPOT) the basic assumption changed: all the available information should be exploited to get a DEM [20]. Then, an available Digital Elevation Model (DEM) can be transformed into the SAR geometry and subtracted from the interferogram. Depending on the DEM accuracy and on the normal baseline tex2html_wrap_inline3260 the phase of the residue can be so small to show a single fringe with no need of phase unwrapping.

The multibaseline approach

An alternate approach to phase unwrapping comes from the comparison of images with different baselines [3]. Theoretically it would be enough to have three interferograms with baselines that are prime with respect to each other to remove ambiguities (Chinese remainder theorem). In a practical case, where data are noisy and baselines random, the use of multiple interferograms increases significantly the elevation ambiguity level. Precise location of the flight paths together with a good estimation of the standard deviation of the phase noise allows the use of Maximum Likelihood (ML) and Maximum A Posteriori (MAP) techniques to estimate the height difference of each pixel with respect to a reference one, taking into account a priori information.

The conditional density function of the elevation for each interferogram is periodic with a different period (the altitude of ambiguity) dependent on the baseline. In each period the higher is the quality of the fringes (the coherence) the sharper is the histogram. The product of the conditional densities shows a neat peak whenever the coherence is not close to zero and the baseline errors are not too high. The sharper is the global peak, the higher is the reliability of the results i.e. the probability that the correct value of the height variation lies inside a given interval.

The benefits of the multibaseline approach are twofold. First, combining all the information it is possible to limit the impact of the noise. Besides, there is minor risk of aliasing with respect to conventional single interferogram phase unwrapping: working simultaneously on more interferograms, phase unwrapping is possible even if the phase is undersampled. Of course the higher the noise, the worse the reliability and the more likely the phase unwrapping errors.

As a conclusion, even if a fully automatic phase unwrapper that works in all conditions is not available yet, phase unwrapping does not appear to represent a serious problem in SAR interferometry anymore.

Digital Elevation Map preparation

  The elevation map derived from SAR interferometry lies on a plane where the reference axes correspond to the azimuth and slant range directions.

Such a coordinates system is different from the reference systems in the azimuth-ground range plane used in the usual elevation maps. Thus it is necessary to transfer the unwrapped phase from the slant range coordinates system to the ground range system; the obtained values must be interpolated and resampled in terms of uniform ground range cells.

Rectification of the elevation map

  From Figure 3 it is evident that the horizontal position of a backscatterer depends on both the slant range coordinate and the elevation. Through simple geometrical expressions the relation between these three parameters can be found. The ground range coordinate with respect to the initial point, indicated by y, is the sum of two components: the first is the horizontal displacement in the case of flat terrain, the second caused by a non-zero elevation drop.

Figure 3: Cross-section of the SAR system geometry normal to the azimuth direction. The ground range coordinate depends on both the range position and the point elevation.

  equation373

Since the position of the points depends on its elevation, the correspondence between ground range and slant range is quite irregular. In fact, the well known foreshortening effect causes a compression of the areas with ascending slope and a spread of the descending areas. As a consequence the ground difference, corresponding to a constant slant range displacement, will be much larger in the case of ascending slopes. Furthermore, when layover effects occur several areas of the earth's surface can disappear from the SAR image.

In a ground range reference system the obtained elevation map will have a quite uneven sampling interval. Thus to obtain a regular sampled map the elevation values must be interpolated. For our purposes a linear interpolation is quite adequate. In fact, in flat or descending areas the interpolating points are fairly close, whereas with an ascending slope the foreshortening effect produces such a large slant range compression that the interpolating points lie much further away and no interpolator would operate correctly. The results of the rectification process, performed for the SAR image of the area near the Vesuvius is shown in Figure 4 .

Figure 4: A perspective view of Mt. Vesuvius obtained from ERS descending orbits interferograms.

Combination of ascending and descending orbits data

Any current DEM estimate is very useful for unwrapping. In fact, data from different takes and therefore with different baselines can be combined, but only if properly positioned in space; in the case of a flat region, uninteresting for the unwrapping problem, the coregistration can be carried out using ephemerides. Not so in complex topography situation, where the registration is DEM dependent. We arrive to an iterative procedure where the available data are combined in such a way to achieve a progressive improvement of the DEM. In this operation, the combination of data from ascending and descending orbits could be very helpful[13]. First, to unravel the layover areas, that, if not in shadow, may appear well behaved with the other orbit. Second, and equally relevant, the combination of the two views is only possible if the DEM is correct; hence, it is a powerful check of its quality, to remove blunders, reduce the elevation dispersion, etc.

Monitoring terrain changes

  If the SAR acquisitions are not simultaneous, the interferogram phases (fringes) are also affected by the possible terrain changes. Two types of temporal terrain evolution can be identified by means of multitemporal interferometric SAR images: decorrelation changes and small terrain motions; a very interesting report on the possibility of monitoring terrain changes can be found in [2].

Decorrelation changes. A random change of the position and physical properties of the scatterers within the resolution cell can be detected as low coherence of the images and will be dealt with in another section.

Small terrain motions. Local centimetric relative motions in slant range, generate large local phase shifts in the interferogram. The phase difference tex2html_wrap_inline3590 thus generated is governed by a mathematical relation completely different from that of the interferometric fringes (that, in order to avoid any confusion we shall indicate with tex2html_wrap_inline3592 ) described by equation 0.3. It is, in fact, proportional to the ratio between the relative motion tex2html_wrap_inline3594 along the slant range direction and the transmitted wavelength tex2html_wrap_inline3596 . Thus, if we have a non simultaneous interferometric SAR pair with a given baseline tex2html_wrap_inline3260 and a small terrain relative motion occurs between the two acquisitions, the following expression of the interferometric phase difference holds:

  equation392

From equation 0.6, it is clear that the two terms tex2html_wrap_inline3672 and tex2html_wrap_inline3674 should be separated in order to recover the terrain relative motion. The simplest way to estimate small motions consists of choosing an image pair with a very small baseline (zero or a few meters would be sufficient in the case of ERS-1) so that the first term is much smaller than the second. An interesting example of such a solution is shown in Figure 5.

Figure 5: ERS-1 SAR interferometry. Fringes generated from two images of the area of Nice on the border between France and Italy, with a time interval of 9 days and a baseline of 6 meters.

Two ERS-1 images of the area of Nice on the border between France and Italy, with a time interval of 9 days and a baseline tex2html_wrap_inline3676 m, have been used to generate an interferogram. In Figure 5 the interferometric fringes are shown. Due to the very small baseline the fringes do not show rapid variations (even if the topography of that area is not flat at all) but for a small area close to the center of the map. In that area a very active landslide has being monitored by the group of the Institute de Physique du Globe (IPG) in Paris[1]. From the ERS-1 interferometric data, an average landslide velocity of about 1cm per day has been estimated. The result is in good agreement with the data provided by the IPG group. Moreover, the ERS-1 interferometric SAR image provides a set of measurements of the landslide relative motion on a very dense grid ( tex2html_wrap_inline3680 meters) at a cost that is much smaller than that of any other traditional techniques. The accuracy of the motion measurement offered by such a technique has been tested with an ERS-1 experiment (the ''Bonn experiment''), where elevation change as small as 9 mm of a few artificial radar targets (corner reflectors) has been detected with no ambiguity [9, 15].

If a stereo SAR pair with a very small baseline is not available, the topography contribution to the interferometric phase ( tex2html_wrap_inline3684 ) must be subtracted from the fringes. It can be accomplished in two different ways. If a topographic map of the area of interest is available, it has to be transformed in the azimuth slant range coordinates and scaled proportionally to the baseline of the interferometric pair in order to have an estimate of the phase component tex2html_wrap_inline3686 . Then, it should be subtracted from the fringes (an impressive example of this technique has been shown by CNES [10] for the Landers earthquake). As an alternative, an additional SAR image can be exploited in order to have an interferometric SAR pair with no terrain changes [4]. For the sake of simplicity, let us label the three SAR images with 1, 2 and 3 with no regard to their time consecution. Let us also assume that during the first two images no terrain changes occur. Thus, the fringes generated from the first two images will be proportional to the phase tex2html_wrap_inline3694 to be subtracted from the fringes generated either from the couple 1-3 or 2-3. From equation 0.3, it is clear that the proportionality coefficient is given by the ratio of the two baselines tex2html_wrap_inline3702 and tex2html_wrap_inline3704 (or tex2html_wrap_inline3706 ). However, since the proportionality holds on the phases and not on their principal values (apart from the special case of an integer ratio between the baselines), the fringes obtained from the couple 1-2 must be first unwrapped and then scaled. Other very important results on the use of this technique for studies of volcano deflation (Etna) or glacier motion can be found in [11, 8].

Atmospheric Effects

In repeated pass SAR interferometry from satellite, different propagation velocities along the scene due to atmospheric changes (at the time of the two surveys) could be responsible of interferometric phase variations that cannot be related either to the topography or to relative terrain motions[25,20]. Multibaseline techniques can be usefully exploited to get a DEM that is less affected by artifacts by averaging the uncorrelated atmospheric contributions coming from the single interferograms [3]. When the ML DEM is generated it is possible to get the phase difference with respect to each interferogram. These phase residues are proportional to atmospheric changes.

Experimental results

Seven ERS-1/ERS-2 Tandem interferometric pairs have been used to generate a DEM of Mt. Vesuvius [3]. Orbits number, dates and normal baselines are summarized in Table 2.

tex2html_wrap_inline3716

SAT ORB DATE Bn
ERS-1 20794 07/07/95
ERS-2 1121 08/07/95 39
ERS-1 21295 11/08/95
ERS-2 1622 12/08/95 57
ERS-1 22297 20/10/95
ERS-2 2624 21/10/95 135
ERS-1 22798 24/11/95
ERS-2 3125 25/11/95 220
ERS-1 23299 29/12/95
ERS-2 3626 30/12/95 253
ERS-1 23800 02/02/96
ERS-2 4127 03/02/96 146
ERS-1 24802 12/04/96
ERS-2 5129 13/04/96 106

As an example the phase residues obtained by subtracting the combined DEM from the April, July and August interferograms of the Vesuvius data set are shown in Figure 6, Figure 7 and Figure 8.

Figure 6: Vesuvius. Differential interferogram generated subtracting the estimated DEM from the April 1996 Tandem interferogram. The normal baseline is 106 m.

Figure 7: Vesuvius. Differential interferogram generated subtracting the estimated DEM from the July 1995 Tandem interferogram. The normal baseline is 39 m.

Figure 8: Vesuvius. Differential interferogram generated subtracting the estimated DEM from the August 1995 Tandem interferogram. The normal baseline is 57 m.

The phase variations (about one fringe peak to peak) with very low spatial frequency (more than one kilometer in both directions) visible in the figure are generated by atmosphere changes within the surveys. These effects appear to be the major limitation to the use of SAR interferometry as a technique for generating highly accurate Digital Elevation Models and for detecting small surface deformations. However, the interferometric phase depends on the relative elevation through a coefficient that is directly proportional to the baseline (see equation 0.3): the higher the baseline, the higher the phase variation correspondent to the same topography. On the other hand, the phase variations due to atmospheric changes are independent of the baseline. Thus, the higher is the baseline of the interferometric pair the smaller is the topographic error due to parasitic effects. Moreover, if many interferometric pairs of the same area are available, ''outliers'' can be identified and eliminated from the database. The remaining results can be combined to ''filter out'' the effects of atmospheric changes.

An example of outliers identification is shown in Figure 9.

Figure 9: Example of atmospheric outliers.

Here seven elevation profiles (along a range line) generated with the tandem pairs of the Vesuvius data set are superposed. It can be clearly seen that for some range positions there is a good consensus of five profiles and two outliers coming from the small baseline (39 and 57 meters) interferograms. In a companion paper [3], it is shown that by eliminating the outliers from the database and by weighting properly the different DEMs, the rms difference found between SAR and SPOT DEMs is 10 meters.

It should be mentioned here that once an accurate DEM is available, also low coherence interferometric pairs (typically from the 35 days repeat cycle or its multiples) can be usefully exploited to get info on terrain deformations with low spatial frequency and/or atmospheric artifacts. Low-pass filtering the differential interferogram that contains low frequency signal plus white spectrum noise, allows us to extract useful information. An example is shown in Figure 10.

Figure 10: Etna 36 days interferogram. The topographic contribution has been compensated for and low frequency phase distortions are visible.

Here the phase of the low-pass filtered differential interferogram of the Valle del Bove (Mt. Etna) is shown. Low frequency phase variations that occurred in 36 days are clearly visible. More differential images could then be used to identify the time evolution of the phase variations. Possible terrain deformations might be separated from atmospheric artifacts by fitting a deformation model to the time evolution of the phase variations [11].

Coherence

  The quality of the interferometric phase depends on the amount of noise that, in general, comes from distinct sources [14, 18]: i- system noise; ii- terrain change (non simultaneous acquisitions); iii- images misregistration; iv- approximate and unequal focusing of the two passes; v- decorrelation due to the baseline (''geometric'' decorrelation). It is obvious that there is no way to avoid the first two sources of noise. On the other hand, as far as the last three sources are concerned, they can be taken under control. In other words, since in most cases the system noise is quite small compared with the usually sensed signals, and the processor noise is well under control if it is designed to be phase preserving [14], it can be seen that the fringes quality is degraded by scattering change in time and volumetric effects only. The coherence tex2html_wrap_inline3730 of two complex SAR images tex2html_wrap_inline3146 and tex2html_wrap_inline3148 , is defined as follows [16]:

  equation475

where E[.] means the expected value (that in practice will be approximated with a sampled average) and tex2html_wrap_inline3754 the complex conjugate. The absolute value of tex2html_wrap_inline3756 is a fundamental information on the exploitability of SAR interferograms. The signal (usable fringes) to noise ratio tex2html_wrap_inline3758 can be usefully expressed as a function of the coherence:

  equation481

Thus, it is clear that every effort should be dedicated to avoid coherence loss during the interferogram generation process.

The statistical confidence of the estimated coherence (sampled coherence) and of the derived measurements, depends on the number of independent samples (n) that can be combined for the computation. As a first approximation, the standard deviation of the estimator is proportional to tex2html_wrap_inline3798 . Thus, whenever uniform areas (in the statistical sense) are identified, the sampled coherence can be computed as:

  equation488

In fact, since the coherence is estimated from the combination of the phases of a few pixels at the very least, the topography effects on the interferometric phase tex2html_wrap_inline3836 proportional to the known terrain changes have to be removed from the result. Thus, in order to compensate this unwanted effect, the vectors at the numerator of equation 0.9 must be deskewed before summing.  It is also clear that, in order to generate an interferogram, the pixels of the images gathered in the two different images must be registered accurately, so that the random variates corresponding to the reflectivity are properly aligned. A single pixel shift, if the focusing processor is a good one, is enough to practically zero the correlation. In the following we will not consider the effects due to misregistration and system noise, since they can be avoided with a good system or with a proper processing. The elevation error tex2html_wrap_inline3838 of maps generated by means of SAR interferometry will follow the value of tex2html_wrap_inline3758 as:

displaymath3728

As an example, the coherence map of the area of Mt. Vesuvius in Italy observed from ERS-1 on August 27th and September 5th 1991 is shown in Figure 11.

Figure 11: Coherence map of Mt. Vesuvius.

(see also the fringes obtained with the same passes that are shown in Figure 2). The sampled coherence has been computed on small rectangles tex2html_wrap_inline3914 (azimuth, slant range) pixels large (n=64) that reasonably belong to uniform areas. The coherence map can be converted into an elevation error map (apart from systematic errors). As expected, areas covered by thick vegetation or in foreshortening or layover show an almost zero coherence and are not usable for SAR interferometric applications (e.g. DEM generation and super-resolution).

Multi-Interferogram Coherence Maps

A multi-interferogram approach can be usefully exploited to estimate the coherence using an ensemble average instead of a space one. When a good DEM is available with the same resolution of the SAR images, it is in fact possible to combine all the data to compute a multi-baseline coherence map tex2html_wrap_inline3918 of the area of interest on a fine spatial resolution: the increased number of freedom degrees (due to multiple interferograms) allows to get high resolution products (say 20 tex2html_wrap_inline3920 20 m).

First the topographic contribution on the phases of each interferogram is compensated for using the DEM. Then the phases are high-pass filtered to eliminate local distortions due to atmospheric effects. Finally the mean phase value is subtracted in each interferogram so that all the data can be considered phase aligned. The estimation is then straightforward:

  equation504

where tex2html_wrap_inline3940 is the standard space average on the i-th interferogram (this time using a small estimation window).

The achieved coherence map highlights what remains unchanged during the time interval between the first and the last acquisition and could be exploited for image segmentation and classification; it gives a measure of SNR on a fine spatial resolution.

Applications to image segmentation

SAR coherence is an additional source of information with noticeable diagnostic power. In the following we shall enumerate some of the most relevant applications. In [12] it was first observed that forests, that appeared with variable reflectivity in the ERS - 1 detected images, appeared almost black in the coherence images: this effect is due to the scarce penetration of C band radiation in the vegetated canopy, so that small variations of the positions of leaves and smaller branches were enough to change the disposition of the scatterers and therefore practically annihilate coherence; likewise happens for water bodies, that appear always with negligible coherence. In [17, 23, 22] it was also observed that cultivated field changed their coherence after plowing, harvesting etc., so that it was possible to detect anthropogenic effects in multitemporal sequences of takes of the same area, by looking at sudden coherence losses. In general, the combination of multitemporal observation both of detected images and coherence allows a very good segmentation of agricultural areas; it is thus possible to identify cultures (potatoes are harvested in that month, whereas corn matures in that other .. ). Other authors [21] observe that from the phase of the interferometric takes the height of the trees and therefore the biomass can be estimated.

Conclusions

  In this overview, we have seen that interferometry is speckle free, since its effect disappears from the differential phase. Further, we have seen that the fringes, given the short revisiting times of the TANDEM mission, may give a very good DEM, with a vertical resolution that could be in the tens of meters range, using the combination of several passes to combat atmospheric effects. Millimetric motion of large areas of the terrain or of corner reflectors have been measured with good reliability and therefore the possibility of using the system to measure subsidence, landslides, coseismic motion has been demonstrated. However, several conditions have to be met, the most important being the maintenance of some coherence of the scatterers during the entire experience. This is possible in the case of exposed rocks, but in other cases artificial reflectors may be needed to link together scattering structures that may change due to vegetation, floods, storms, etc. Coherence is an important clue, that combined with the more usual backscatter amplitude, leads to high quality images segmentation. The combination of multiple images will improve resolution.

References

1
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2
Dixon, T., Editor, SAR Interferometry and Surface Change Detection, 1994, Report of the Workshop in Boulder, February 3 and 4, 1994, http://southport.jpl.nasa.gov/scienceapps/dixon/index.html

3
Ferretti A., Prati C., Rocca F., Monti Guarnieri A. ''Multibaseline SAR Interferometry for automatic DEM reconstruction'' Proc. 3rd ERS Symposium - Florence 1997 - http://florence97.ers-symposium.org/

4
Gabriel A.K., Goldstein R.M., Zebker H.A., Mapping small elevation changes over large areas: differential radar interferometry , J.G.R., Vol.94, N.B7, July 1989, pp.9183-9191.

5
Gatelli F., Monti Guarnieri A., Parizzi F., Pasquali P., Prati C., Rocca F., 1994, Use of the spectral shift in SAR interferometry: applications to ERS-1, IEEE Trans. on GARS, Vol. 32 , No 4, July 1994, pp.855-865.

6
Giani M., Prati C., Rocca F., 1992, ''SAR interferometry and its applications'', ESA report N.8928/90/F/BZ.

7
Goldstein R.M., Zebker H.A., Werner C.L., 1988, Satellite radar interferometry: Two-dimensional phase unwrapping, Radio Science, Vol.23, N.4, pp. 713-720.

8
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Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry