Operational process interferometric for the generation of a digital model of ground Applied to the couple of images ERS-1 ERS-2 to the area of Algiers F. Hocine, M.Ouarzeddine, A. elhadj-aissa,, M. elhadj-aissa,, Y. Smara Faculty of Electronics and Computer Science Houari oumediene University of Sciences and Technology, Image Processing and Radiation Laboratory, Algiers Faiza_ho@yahoo.fr, m.ouarzeddine@lycos.com, h.belhadj@lycos.com, mbelhadjaissa@yahoo.com, y.smara@lycos.com, ASTRACT The data used is a couple of SLC (Single Look Complexe) images acquired in the Tandem mission of the ERS1 (3 January 1996 ), ERS2 ( 4 January 1996 ) satellites. The area is a part of Algiers. Three basic steps in the interferometric procedure are necessary: the coo-registration using the orbital parameters, the interferometric product and the correction of the interferogram from the flat earth effect and the third step is the phase unwrapping which has been realised using the least square method. In parallel the coherence map has been generated to assess the interferogram quality. 1 INTRODUCTION Radar interferometry is a technique which allow the evaluation of the altitude of a point in the ground and detect the small displacement of the ground. This technique is based on the use of two radar images of the same scene acquired by two antennas separated by a distance named the baseline [1]. We present the interferometric process we have developed to obtain a Digital Terrain Model (DTM). 2 FORMULATION The phase of SAR image is rich of information but difficult to be explored. The phase difference φ( p) measured between the two acquisitions is given by Eq.1. 4π φ ( p ) = φ A ( p ) φ ( p ) = ( RA R ) (1) λ The phase difference between the two signals is directly related to the elevation h: RA R h = H - R A cos arcsin (2) Where: Component of the baseline λ Wavelength θ Incidence angle (23 To the centre of the scene) R : R range difference R A Proc. of FRINGE 2003 Workshop, Frascati, Italy, 1 5 December 2003 (ESA SP-550, June 2004) 90_smara
A θ R H p h Fig. 1. Principle of interferometric acquisition 3 INTERFEROMETRIC STEPS The interferometric data processing chain is composed on four basic parts given on fig. 2: Slave Image Master Image Coregistration Geocoding Control points Coherence Interferogram Flat earth removal Topographic Interferogram Phase Unwrapping Amplitude Orbital data and flat earth file generation DTM Fig. 2. Interferometric data processing chain to obtain a DTM composed on four
3.1 Coregistration To calculate the interferogram we must first overlap the two SLC images in order to manipulate them in the same geometry. One of them is taken as a reference. We define it then as the master image. In contrary the other one is called slave image. We used for the coregistration step, the est software developed by ESRIN (ESA). The method is based on the automated correlation where the principle is an automated research for control point and the application of a polynomial model of correction. Coregistration precision is to the 1/10 pixel [2]. 3.2 Geocoding For the geocoding we used the geographic coordinates of the four corners of each image. These are given in the descriptor file image provided with the data. 3.3 Spatial resampling The result of this resampling is to obtain an image where the pixel has a squared size. We reduced the resolution in azimuth from 3.9 m to 20.4 meters with a window of 1*5 dimension. The result is then a 5 looks image in azimuth with a resolution of 20*20m. Using this transformation, we could identify the objects shapes and attenuate the speckel effect. 3.4 Coherence map This image is mainly important to evaluate the correlation between the two acquisitions. The complex number η attributed to each pixel is given by Eq. 3 jφ A jφ( i, ρ e ρ i j e i j F (, ) (, ) A η = (3) ρ 2 2 ρ i j F A F (, ) The argument of η is a measure of complex correlation between the two images. The coherence value varies between 0 and 1. The better is the correlation, the more the coherence is approaching the 1 value. The coherence map can be seen as a confidence image regarding the interferogram. Results are given is fig. 3b. (a) (b) Fig.3. Intensity of the ERS1 Image of the 3 January 1996 (a), 5849*6589 pixel size, resampled by a 5 factor in azimuth direction, coherence map (b)
3.5 Phase difference image Phase difference image or interferometric phase is calculated using the argument of η φ = arg( η( i, ) = φ A φ (4) The phase φ is known just in the interval [0, 2pi); The ambiguous altitude is the separation between two fringes lines due just to the altitude effect. This altitude is denoted as: h a λr tanθ = (5) 2 efore retrieving this altitude we must correct the phase difference from the flat earth effect due to the baseline. 3.6 Flat earth correction When there is no topography and the ground is flat; there are fringes which result from the linear variation of the phase on the range direction. In the case of parallel orbits, these phase variations are not dependant on the azimuth; the fringes are then parallel to the satellite moving orbit. This phase difference is given by Eq.6 [3] : φ flat 4π ) r j = λr tan( θ α) (6) The application of this formula results in an image where fringes are aligned. Correcting the interferogram from this phase give as a result a topographic interferogram where the phase difference represents the correct information related directly to the height of the objet on the ground. Hence we can see the interferogram as an image of isolevel curves. Fig. 4 give the interferograms of the two selected regions and the corresponding interferograms corrected from flat earth effect.
(a.1) (a.2) (b.1) (b.2) Fig.4. Algiers region: Two windows images (500*500 pixels) of the two scenes ERS1/ERS2 (3 and 4 January 1996) Interferogram (a) Interferogram corrected from flat earth effect (b) 3.7. Phase unwrapping Phase difference φ after correction from flat earth effect presents for every pixel the phase related directly to the height of the object. Nevertheless, the information given by the phase do not represent directly the principal value of the phase but the phase in the interval [0,2pi), So we have to find the integer k number that must be added to find the real value phase. This step is referred to as the unwrapping phase. The absolute unwrapped phase ϕ is then: ϕ = 2πk + φ (7) In this step we tested the least squared method [3], which is a global method, with this method we look to minimise the squared difference in the whole image between the unwrapped phase and the discrete gradient of the wrapped phase in the point of interest. Results are given in Fig.5. Other method of unwrapping is being implemented. The method is based on the regularisation hypothesis and uses the Markovian [4],[5] segmentation.
(a) (b) Fig. 5. Unwrapped interferogram of the two test regions (500*500 pixels size) from the couple ERS1/ERS2 scenes (3 and 4 January 1996) 4. CONCLUSIONS The interferometric chain exposed in this paper, has shown the principle of the interferometry technique, the difficulties encountered, the methods implements and the results obtained. Results obtained promise a good continuation. We attempt for the future to implement better methods of phase unwrapping and comparison of DTM results with ground points measurement to assess how far our results are precise. 5. ACKNOWLEDGEMENT The Authors wish to thank the ESA (European Space Agency) for supplying them with the couple of ERS data in the frame of the ERS Envisat project CAT703. REFERENCES [1] Curlander J.C. & McDonough R.N.: Synthetic aperture radar: systems and signal processing. Wiley series in remote sensing, a Wiley interscience publication, New-York, 647p, 1991. [2] Emmanuel Trouvé : Imagerie interférentielle en radar à ouverture synthétique. Thèse de doctorat. École nationale supérieure des télécommunications, Paris, 19 juillet 1996. [3] David T. Sandwell and Price E. J.: Phase gradient approach to stacking interferograms. Institute of Geophysics and Planetary Physics Scripps Institution of Oceanography, La Jolla, 1998. [4] Labrousse D. : modélisation markovienne pour le déroulement de phases interférometriques sar. Thèse de doctorat. Université de Nice Sophia Antipolis [5] Huot E.: Etude de l évaluation temporelle de phénomènes terrestres au moyen de l imagerie radar. Thèse de doctorat 2000. Université de CAEN, Sciences Ecole doctorale SIMEN, France.