Can. J. Remote Sensing, Vol. 33, No. 1, pp. 52–59, 2007
SAR processing in the temporal domain: application to direct interferogram generation and mountain glacier monitoring Jean-Marie Nicolas, Gabriel Vasile, Michel Gay, Florence Tupin, and Emmanuel Trouvé Abstract. Synthetic aperture radar (SAR) interferometry has the potential to measure temperate glacier displacement with a large coverage of the surface compared with pointwise terrestrial ground measurements. The significant topographic relief in mountainous areas, however, where most alpine glaciers are located, makes the use of SAR imagery rather difficult. Among the difficulties, when the resolution increases, the focusing of satellite SAR images, usually performed in the frequency domain with a constant-height hypothesis, becomes a critical issue. SAR processing in the temporal domain is a different approach that enables the use of information such as the local topography. In this paper, we present an original method to perform this temporal domain focusing by modeling the relative motion of the satellite and Earth points. The method allows production of SAR single look complex (SLC) images directly in ground geometry and reduces the need for resampling and phase correction to obtain interferograms. A tandem pair of European remote sensing (ERS) SAR images acquired over the Mont-Blanc area is used to illustrate the proposed approach. The results are presented with amplitude images and interferograms measuring glacier 1 day displacements and are compared with the results from the differential interferometric automated process applied to survey of nature (DIAPASON) and repeated orbit interferometry package (ROI–PAC) conventional SAR processors. Résumé. L’interférométrie en radar à synthèse d’ouverture (RSO) présente la propriété de pouvoir mesurer les déplacements des glaciers tempérés sur de grandes étendues, comparé aux mesures effectuées directement sur le terrain. Cependant, les zones fortement montagneuses où se trouvent la majorité des glaciers alpins rendent la pratique de l’imagerie RSO difficile. De plus, dans ce contexte, une étape critique est celle de la focalisation des images RSO satellitaires, généralement synthétisées par passage dans le domaine fréquentiel sous l’hypothèse de surface plane, et qui s’avère alors problématique, surtout dans le cadre de la haute résolution. Aussi la synthèse temporelle des images RSO semble une voie intéressante à explorer puisqu’elle permet d’introduire un certain nombre d’informations, comme la topographie locale. Dans cet article, nous présentons donc une méthode originale de synthèse temporelle prenant en compte la position et le mouvement relatif de chaque point au sol vis à vis du satellite. Elle permet de construire une image complexe (SLC) directement en géométrie sol, ce qui évite, lors de la construction d’un interférogramme, de rééchantillonner les données ainsi que de les corriger du terme de phase topographique. Cette approche est illustrée sur un jeu de données « ERS-tandem » acquis sur le massif du Mont-Blanc. Interférogramme et images d’amplitude permettent alors d’en. Les images (image d’amplitude et interférogramme permettant de déduire les déplacements du glacier sur un jour) sont comparés avec celles fournies par les logiciels DIAPASON (« differential interferometric automated process applied to survey of nature ») et ROI–PAC (« repeated orbit interferometry package »).
Introduction Nicolas et al.
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The use of synthetic aperture radar (SAR) interferometry to monitor temperate glaciers is promising: it should provide useful information such as glacier surface topography and, by differential interferometry, velocity fields with an accuracy that cannot be obtained using optical data. SAR processing and the following steps such as interferogram computation and phase unwrapping are still difficult to perform in mountainous areas with significant topographic relief. To improve the quality of SAR interferograms, it is recommended that the SAR processing start from the RAW data and focus on them with the same Doppler centroid so that the ground targets are seen with the same viewing angle (Massonnet and Feigl, 1998). Standard interferometric software, such as the open-source repeated orbit interferometry
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package (ROI–PAC) (Rosen et al., 2000) or the differential interferometric automated process applied to survey of nature (DIAPASON) (Massonnet, 1997), performs the focusing in the
Received 7 April 2006. Accepted 3 October 2006. J.-M. Nicolas and F. Tupin. Département Traitement du Signal et des Images GET, Télécom Paris, 46, rue Barrault, 75013 Paris, France. G. Vasile and E. Trouvé.1 Laboratoire d’Informatique, Systèmes, Traitement de l’Information et de la Connaissance, Université de Savoie, Polytech’Savoie, BP 80439, 74944 Annecy-le-Vieux CEDEX, France. M. Gay. Laboratoire des Images et des Signaux, INP Grenoble, BP 46, 38402 Saint-Martin-d’Hères, France. 1
Corresponding author (e-mail:
[email protected]). © 2007 CASI
Canadian Journal of Remote Sensing / Journal canadien de télédétection
Figure 1. (a) Motions of a satellite S and an Earth point P around the Earth. (b) Illustration of the closest point approach (CPA) between two moving points.
frequency domain to reduce the computation load, which was a critical issue at the time these SAR processors were developed. In both cases, the SAR focusing is performed with a meanaltitude hypothesis, which is valid with European remote sensing (ERS) data and slow height variations. This hypothesis tends to introduce focusing errors in areas with significant topographic relief, such as in mountainous areas where most temperate glaciers are located. In the Alps, for instance, there is a height difference of almost 4000 m between the Chamonix valley and the summit of Mont-Blanc, corresponding to a foreshortening that can be compared with the ERS field of view (some kilometres). For high-resolution data, this effect is more severe, and a digital elevation model (DEM) is usually required for SAR synthesis. In this paper, we propose an original approach useful for such specific areas and based on a coherent processing of RAW data in the temporal domain, as classically done in optics (Goodman, 1968) or acoustics (for example, in ultrasound imaging). Time-domain processing methods are rather well known in SAR processing and correspond to the famous backprojection algorithm (Soumekh, 1999). Compared to conventional SAR processing in the frequency domain, which requires nonlinear mapping to deal with migration (Hein, 2004), one of the main advantages of the time-domain approach is that it is “open” to introduce local ground information in the processing. More precisely, instead of using a constant-altitude hypothesis, we propose to introduce a DEM to take the local altitude into account in high mountain regions in the SAR processing step. The results obtained by the proposed approach are presented on parts of ERS images in the Mont-Blanc area in the Alps. Several interferometric pairs, including tandem data, have been processed over a selected area that includes two well-known glaciers, namely Argentière and Mer-de-Glace. The results are compared with those obtained by DIAPASON and ROI-PAC at © 2007 CASI
two levels: single look complex (SLC) images and multilook interferograms, where the phase measures the glacier displacement and the coherence reveals surface changes.
SYTER: a temporal-domain SAR processor Contrary to the conventional SAR processors that operate in the spectral domain, Synthèse temporelle radar (SYTER) processes RAW data only in the temporal domain. Even if timedomain methods are globally very precise (Barber, 1985), they are very slow and were almost never used. Today, this approach is possible thanks to the present speed and available memory of a basic PC (for example, on an XP2200+ Athlon-based computer with 768 MB RAM memory, SYTER requires less than 1 h for an ERS quarter scene without any code optimization). Using this approach, SAR processing is reduced to a coherent sum of delayed RAW data, corresponding to a filtering step rather well-known as “beam-forming” in other domains, such as with ultrasound imaging or sonar applications, which favour the antenna approach. Geometrical description Beam-forming requires good positioning of the data and good modeling by the sensors. In the case of ERS data, we know that the ERS satellite orbit is elliptical with a very small eccentricity (e = 0.001165). At a first level of approximation, a locally circular orbit can be used and matches rather well with processing devoted to a reduced area (some square kilometres, for example). At this level of approximation, the ERS antenna motion reduces to a plane rotation in an Earth-centred Cartesian coordinate system, defined by the inclination of the orbit i and the altitude of the satellite H. At time t, Kepler relations provide 53
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r the rotation vector ΩS and the position of the satellite S depending on the time by the following relation: r → OS = F (ΩS(H), H, i, t)
(1)
At the same time and in the same Earth-centred Cartesian coordinate system, a given Earth r point P rotates around the north axis with a rotation vector Ω E. The position P depends on the latitude Ψ, its altitude h, and the Earth radius RE by the following relation (Figure 1a): r → OP = G(Ω E, Ψ, RE, h, t)
(2)
yielding the relation between the antenna and a given Earth → point, satisfied by the vector PS: r r → PS = G(Ω Ε , Ψ, RE, h, t) − F (ΩS(H), H, i, t)
(3) SYTER SAR processor
The analytical relation of the distance between the antenna and a given Earth point becomes r r PS = D(ΩS(H), H, i, Ω Ε , Ψ, RE, h, t)
The distance |PS|, defined by Equation (4), is the keystone of any SAR processor. Indeed, when this distance is at a minimum (Figure 1b), this situation is called closest point approach (CPA), as done mainly in the sonar community. As the relative radial speed vanished at the CPA, there is no Doppler effect: this situation is also called “zero Doppler position” in the radar community. As ERS is operated in a yaw-steering mode, we can consider that the CPA belongs to the main side lobe of the physical antenna. For each specific element of the synthetic antenna, it is possible to know its position relative to the CPA and, accordingly, the distance between this element and the Earth point. The knowledge of this distance enables the determination of the delays δτj required by the beam-forming step for each position j of the antenna around the CPA (Figure 2). Therefore, even if there is a small squint effect, it is simply processed as a nonzero delay for the ground points belonging to the axis of the physical antenna.
(4)
Note that this approach is not reduced to the combination of two rotations: it is possible at this step to introduce the real motion of the satellite (which is an ellipse slightly twisted by the flatness of the Earth) and a reference ellipsoid for the Earth, but Equation (4), which is easy to deduce in the case of circular motions, becomes more complex.
In the case of two-dimensional (2D) arrays, such as phased arrays used in medical ultrasound imaging, the beam-forming considers all the positions of the elementary sensors with regard to a given point P inside their main side lobe. When the antenna is moving, the pulse repetition frequency (PRF) and the width of the elementary antenna (which defines this main side lobe) provide the set of positions of the moving antenna. As the distance between each elementary antenna and the point P is given by Equation (4), the time delay required for the beamforming can be directly deduced by assuming a constant light
Figure 2. (a) Beam-forming in a static configuration (P and S have no motion). (b) Modification of beam-forming with moving points. The delays (i.e., migrations) depend on the position of the target P and the relative motion. 54
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Figure 3. Several configurations for beam-forming: (a) full-aperture zero Doppler synthesis (no squint); (b) full-aperture negative Doppler synthesis (positive squint); (c) subaperture positive Doppler synthesis (negative squint); (d) subaperture negative Doppler synthesis (positive squint).
celerity. Actually, the distance variations correspond to the well-known range migration. SYTER is based on the following remarks: (1) If the analyzed scene is rather small (some square kilometres), these time delays only depend on the elementary sensors and on the position of the given point P along the swath (actually, they have a slight dependence on the latitude of the CPA). Thus, it is possible to tabulate these delays in a two-dimensional array not exceeding some megabytes. (2) As RAW data are band-limited (the bandwidth is 18.96 MHz and the central frequency is 5.300 GHz for ERS), the time delays have to be considered at two levels. The first level (“slow time”) consists of resampling a RAW base-band signal to delay the data. The second level (“fast time”) consists of a phase term, which is deduced from the time delay and from the central frequency: this phase term is simply multiplied by the RAW resampled data. In SYTER, each line is oversampled (slow time) with a given factor (32, 64, or 128) so that a piecewise approximation of each line is used in the next step. (3) A conventional SAR processing starts geometrically from the final image: for each point of the slant range image, the azimuthal filter deals with a lot of RAW lines that will generally be processed in the frequency domain. Instead of this classical approach, SYTER considers each point of a RAW line and tracks the positions in the final image for which this point will be required. SYTER reads each line in the RAW file, oversamples this line as previously described, and adds the contribution of this oversampled line in the final image with a phase term corresponding to the “fast time”. At each step, only one resampled line is required. © 2007 CASI
(4) Conventional SAR processing generally provides slant range images: because of the rotundity of the Earth, a nonregular resampling is required to obtain a ground range image. In the case of SYTER, as the target points P are chosen on the Earth’s surface, the resulting image is directly provided in ground range. This avoids a resampling step that may be tricky for the phase term. Moreover, for interferometric processing, if the baseline is introduced in SYTER, the two images can be considered as perfectly registered and no ancillary resampling is required between the master and the slave image. (5) Indeed, there is a very small squint angle during the acquisition (the main side lobe is not perfectly centred on the CPA) which is generally considered as a nonzero Doppler centroid value. In a temporal approach, this squint angle Ψ can be deduced from the Doppler centroid value (obtained, for example, by RAW data along-track spectrum analysis). Then, the beam-forming step takes into account only the elements of the phased array corresponding to the main side lobe of the synthetic antenna and illuminating the target point. Moreover, conventional sub-band coding can be processed directly with a subaperture synthesis by reducing the size of the final synthetic antenna as illustrated in Figures 3c–3d (instead of selecting sub-bands in the image spectrum). (6) The distance expression (Equation (4)) takes into account the altitude of the target point P. Moreover, if a DEM is available for the processed area, SYTER can introduce the local altitude (in the present version, only a mean local altitude is required). Therefore, better beamforming can be achieved in high mountainous areas where variations in height of several thousand metres are often encountered. In the conventional slant range geometry, the corresponding foreshortening is not 55
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negligible with regards to the field of view and might result in defocusing effects. (7) Due to the reference chosen for the phase in the beamforming step, there are no orbital fringes on SYTER interferograms. Indeed, the baseline is introduced in SYTER SAR processing so that an interferometric couple is directly coregistered with the same phase reference. Moreover, if a DEM is available, there are no elevation fringes on the interferogram; they would directly correspond to specific differences between the two acquisitions: local motion (for example, in an seism or on glaciers), atmospheric effects, or geometric errors on the satellite positioning. According to these remarks, the algorithm proposed in SYTER consists of two main steps illustrated in Figure 4: (1) tabulation of the delays and corresponding shifts using the simplified acquisition geometry described in the previous section (Equations (1)–(4)); and (2) computation of the final image by reading the RAW data row by row, projecting them on the corresponding pixels of the final image, and adding their contributions in a coherent summation.
Experimental results The feasibility of such SAR processing has been demonstrated over an area that includes two well-known glaciers in the Mont-Blanc massif: the Argentière and the Merde-Glace glaciers, separated by the Aiguille Verte, a famous 4000 m summit.
Temporal domain processing results As SYTER requires baseline values to process RAW data, the two resulting ground range images corresponding to two acquisitions are coregistered and can be compared directly without orbital fringes. In Figure 5, the same part of Argentière glacier has been processed from ERS tandem data (10 and 11 March 1996). Each squint angle of the two acquisitions can be deduced by azimuthal Fourier transform of the RAW data (this analysis is relevant, since ERS is operated in a yawsteering mode). By choosing a common subaperture, it is possible to process directly the two data with the same spectral content. For example, Figure 6 provides the spectra of the two images of Figure 5: we can verify that these two spectra share the same domain. Therefore, the interferogram phase noise is significantly reduced. Figure 7 provides the coherence and phase of the interferogram computed without coregistration directly from the two previous SLC images. Comparison with frequency domain processor At the present stage, a visual comparison with two conventional interferometric processing chains can be performed. The same ERS RAW data have been processed by ROI–PAC and DIAPASON software tools using precise orbit information from Delft University, The Netherlands, to remove orbital fringes. Such information is not yet used in the proposed temporal domain processor, where only the mean baseline is entered. Figure 8 presents the results obtained with the three SAR processors. The narrow fringe patterns due to the displacement of several glaciers are visible. The upper right part of Figure 8a shows the Tour glacier, which is quite large, and below, the long
Figure 4. Block diagram of SYTER algorithm. 56
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Figure 5. Tandem images on Argentière glacier: (a) 10 March 1996; (b) 11 March 1996.
Figure 6. Spectra of the SLC images of Argentière glacier.
Figure 7. Interferogram built from the tandem images of the Argentière glacier: (a) coherence; (b) phase. Fringes appear mainly on the Argentière glacier, but also on the Chardonnet glacier (right bank of the Argentière glacier). © 2007 CASI
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Argentière glacier (15 km), which appears with its tongue on the left side and its accumulation area on the right side in the image. A high coherence level can be observed, except where the phase information is lost, for instance in the icefall areas, because of the rapid changes in the ice blocks and the aliasing due to acceleration of the glacier. In the middle and lower parts of the image, there is a group of three glaciers made of the Merde-Glace (on the left) and Leschaux (on the right) glaciers, which are visible in ERS descending images, and the Tacul
glacier, which is connected to the Mer-de-Glace glacier but is not visible due to the foreshortening effect. The velocity, which can be derived from the fringe pattern, shows two areas with higher speeds in the middle of the Mer-de-Glace and Leschaux glaciers, whereas the speed decreases over the Leschaux glacier before its confluence with the Tacul. The global fringe patterns, coherence, and amplitude obtained by the different processors are very similar. The differences in shapes and orientations are due to the different
Figure 8. ERS-1 and ERS-2 tandem after orbital fringe correction (2 × 10 complex multilooking): (a–c) DIAPASON amplitude (a), coherence map (b), and interferogram (c); (d–f) ROI–PAC amplitude (d), coherence map (e), and interferogram (f); (g–i) SYTER amplitude (g), coherence map (h), and interferogram (i). 58
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sampling geometries: ROI–PAC and DIAPASON results are in radar geometry, whereas the temporal processor result is directly sampled in ground geometry. The temporal approach provides less noisy and apparently smoothed results: actually, a more precise tuning of SAR processing parameters can be achieved with SYTER. Indeed, if the two acquisitions have different squint values (i.e., Doppler centroid values), the processing takes into account the same common subaperture.
Conclusions and perspectives
Geoscience and Remote Sensing Symposium, Singapore, 3–8 August 1997. IEEE, New York. Vol. 3, pp. 1338–1340. Massonnet, D., and Feigl, K. 1998. Radar interferometry and its application to changes in the Earth’s surface. Reviews of Geophysics, Vol. 36, No. 4, pp. 441–500. Rosen, P.A., Hensley, S., Joughin, I.R., Li, F.K., Madsen, S.N., Rodriguez, E., and Goldstein, R.M. 2000. Synthetic aperture radar interferometry. Proceedings of the IEEE, Vol. 88, No. 3, pp. 333–382. Soumekh, M. 1999. Synthetic aperture radar signal processing. John Wiley & Sons, New York.
This paper presents a revisited approach to SAR processing in the temporal domain and provides an improved local SAR processor for use in mountainous regions where the significant topographic relief can lead to defocusing. This effect will become more important with the increased resolution of the new generation of SAR satellites, namely ALOS-PALSAR, TerraSAR-X, RADARSAT-2, and Cosmo-SkyMed. The principle of the proposed approach has been described. The results have been illustrated in ERS SAR interferograms over temperate glaciers located in the Alps and compared with the results from standard processors that operate in the frequency domain. It is important to notice that no specific computer is required at the present time: a standard PC (2 GHz, 256 MB RAM memory) can process 25 km2 in a few hundred seconds. By operating in the temporal domain, the proposed geometrical approach enables the introduction of local information in the imaged area, such as the elevation provided by a digital terrain model. The main steps in the proposed approach are as follows: compute a SYTER image on the geoid, as presented in the paper; simulate a SAR amplitude image (using a DTM and the same delay code); and register the image. The final SLC image is then processed by an enhanced version of SYTER using the altitude of each Earth point.
Acknowledgments This work has been supported by the French national project ACI Masse de données 2004–2007 “MEGATOR” (http://www.lis.inpg.fr/megator). The authors wish to thank the European Space Agency (ESA) category 1 projects 1088 and 3525 for the ERS images and would like to express their gratitude to the anonymous reviewers for providing precise comments and useful advice on the paper.
References Barber, B.C. 1985. Theory of digital imaging from orbital synthetic-aperture radar. International Journal of Remote Sensing, Vol. 6, No. 7, pp. 1009–1057. Goodman, J.W. 1968. Introduction to Fourier optics. McGraw-Hill. Hein, A. 2004. Processing of SAR data. Springer. Massonnet, D. 1997. Producing ground deformation maps automatically: the DIAPASON concept. In IGARSS’97, Proceedings of the International
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