GENERATION OF DEM WITH SUB-METRIC VERTICAL ACCURACY FROM 30 ERS-ENVISAT PAIRS

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1 GEERATIO OF DEM WITH SUB-METRIC VERTICAL ACCURACY FROM 30 ERS-EVISAT PAIRS C. Colesanti (), F. De Zan (), A. Ferretti (), C. Prati (), F. Rocca () () Dipartimento di Elettronica e Inormazione, Politecnico di Milano, Piazza L. da Vinci, Milano, Italy, Phone: , Fax: , prati@elet.polimi.it () Tele-Rilevamento Europa - T.R.E. S.r.l., Via V. Colonna, Milano, Italy ABSTRACT According to the spectral shit principle, distributed scatterers can be coherently observed by ERS and EVISAT SAR systems despite o their carrier requencies 3 MHz requency shit. A km normal baseline should be set in order to compensate such a carrier requency dierence or almost horizontal terrain. This type o SAR intererometry coniguration can be useully exploited to get DEMs o rolling topographic eatures with very high vertical accuracy. This experiment has been carried out using an ERS-EVISAT intererometric pair with a normal baseline o about.5km (the 3MHz requency shit is partially compensated on cross-track terrain slopes ranging rom 0 to 7 degrees) and a very short (30 minutes) temporal separation, thus containing the temporal decorrelation to acceptable values.. THE THEORETICAL BACKGROUD The 3MHz requency dierence between SAR-ERS and ASAR-EVISAT introduces an additional term to the usual intererometric phase. The eect o this phase term deserves a separate analysis or point and distributed scatterers. In case o point scatterers a pure geometric analysis can be carried out with reerence to igure. S S θ r P P o q y r y Fig. Geometry o the intererometer in case o point scatterers. Setting to zero the phase dierence o the SAR images taken by the two satellites in correspondence to a reerence point, the ollowing expression o the intererometric phase holds: 4π = φ φ = c ( r r ) φ () where and are the SAR-ERS and ASAR-EVISAT central requencies (5.3GHz and 5.33GHz). The basic expression o the intererometric phase in () can be transormed ater some trivial substitution: Proc. o FRIGE 003 Workshop, Frascati, Italy, 5 December 003 (ESA SP-550, June 004) _prati

2 4π φ = r c [ ] 0 B + q Rsinθ e () where the ollowing deinition o the eective requency or horizontal terrain has been adopted: B + R tanθ = 0 e (3) It should be noted rom () that the intererometric phase depends on the point scatterers relative elevation as in the usual single requency intererometry and that a slant range dependent phase term appears. This new phase term introduces a sort o location phase screen on the intererogram that depends upon the actual point target position within resolution cell. However, the location phase screen disappears when e0 =, that in correspondence to the compensation baseline: B 7 5 o ( ) R tanθ ( 3 0 ) ( ) tan 3 km comp = (4) In any case it is clear that in presence o point targets the 3MHz central requency shit does not introduce any random phase noise on the intererogram. ot so in case o distributed scatterers. For the sake o simplicity let us reer to the igure. Here a inite number o elementary scatterers with random relectivity v n are located within a resolution cell ρ with a given slope α. The ollowing expressions o the signals recorded by the two SAR systems hold: 4π s = exp j r v c n 4π exp j c nρ + n = 4π 4 B π e α nρ s = exp j r e0 + q vn exp j c Rsinθ n= c + In (6) the ollowing deinition o the eective requency or ground slope α has been adopted: (5) (6) B e = α + (7) R tan ( θ α ) In (5) and (6), or the sake o simplicity, a boxcar resolution cell and uniormly spaced scatterers have been assumed. The intererogram is then ormed by cross-multiplying the two signals s and s complex conjugate: E * 4π nρ [ s s ] exp{ j } E[ v ] exp j ( ) = φ n eα (8) n= c + In (8) is still present the same deterministic phase term () ound or point targets, but now an additive random phase term comes rom the coherent combination o the elementary scatterers. It is also clear rom (8) that this random phase contribution disappears as eα =, that is when: ( ) R ( θ α ) B comp = (9) tan

3 In conclusion, the 3MHz requency gap introduces a random phase noise when the ground slope is not correctly compensated by the baseline (9). This random phase noise can be expressed in term o coherence as ollows: * [ s ] E s 4π nρ γ = = exp j ( e α ) E + = + (0) n c [ s ] E[ s ] It is interesting to note that, in general, the absolute value o the coherence takes the orm o the Fourier Transorm o the cross-product o the impulse responses o the SAR systems as a unction o ( eα - ). The absolute value o the coherence is when eα =. Moreover, both eα and can be slightly changed by means o the so called common band iltering. In the SAR-ERS case the signal bandwidth is W~5MHz and the central requency is. I a bandwidth is iltered out starting rom the lower bound o the signal spectrum, the actual signal bandwidth is reduced to W- and the central requency becomes + /. Clearly the central requency becomes - / i a bandwidth is iltered out starting rom the upper bound o the signal spectrum. The same can be done or the ASAR-EVISAT signal thus changing eα. With the common band iltering a unitary coherence can be recovered at the expense o a slant range resolution reduction until the required spectral shit is smaller than the signal bandwidth W. The same technique can be applied to the azimuth direction as the Doppler Centroid o the two signals is dierent S S θ r P P slope α P o q y r y Fig. Geometry o the intererometer in case o distributed scatterers.. THE PARIS EXPERIMET According to the spectral shit principle [], a irst experimental evidence o the possibility to generate a SAR- ERS/ASAR-EVISAT intererogram has already been provided [], [3]. The main goal o this new experiment is to quantiy the actual vertical accuracy o an ERS-EVISAT intererometric DEM o a rural area along the rivers Réveillon and Yerres (tributaries o Seine) in the immediate neighborhood o Paris. Then to show that with a 30 temporal baseline and.5km geometric baseline neat ringes can be obtained on vegetated areas whereas a random location phase screen is obtained on urban areas. Following the spectral shit theory, it should be pointed out that with a normal baseline o about.5km the 3MHz requency shit can be practically compensated on cross-track terrain slopes ranging rom - to 8 degrees. Moreover, in our data the DC dierence was ound to be about 800Hz thus leaving a common band in azimuth slightly greater than 0% o the ERS Pulse Repetition Frequency (see igure 3). The uniltered intererogram obtained ater an accurate images registration and its azimuth common band iltered version are shown in igure 4. The slant range common band iltered intererogram is shown in igure 5. Due to the.5km baseline, the altitude o ambiguity is about 6m. The map o the ground range slope shown in igure 5 has been derived rom the value o eα (changed by means o the common band iltering described above) that maximizes the local complex coherence.

4 Fig. 3 SAR-ERS and ASAR-EVISAT azimuth spectra. The resulting azimuth common band is about 0% o the ERS pulse repetition requency. Fig. 4 Let: uniltered intererogam obtained ater an accurate ERS-EVISAT images registration. Right: The intererometric ringes ater the azimuth common band iltering. In igure 6 a detail o the ERS-EVISAT intererometric ringes o the rural area including the rivers Reveillon and Yerres is shown. On this area the coherence and the relative elevation standard deviation histogram have been computed. The two histograms are shown in igure 7. Here the very high vertical accuracy that can be obtained by combining ERS- and EVISAT SAR images can be appreciated.

5 Fig. 5 Let: The ERS-EVISAT intererometric ringes ater the slant-range common band iltering. Right: local ground range slope estimated rom the local spectral shit that maximizes the local coherence. Réveillon Yerres Fig. 6 Detail o the ERS-EVISAT intererometric ringes o the rural area including the rivers Reveillon and Yerres. Finally the ERS-EVISAT intererogram o Paris is shown on igure 8. Here it is interesting to note that neat ringes are clearly visible on the city parks (the 30 temporal baseline avoids temporal decorrelation) whereas on the urbanized areas an almost random phase ield (the location phase screen o point scatterers) is present. This is exactly the opposite to what we are amiliar with ERS/ERS intererograms (small geometric and large temporal baselines). 3. COCLUSIOS From the achieved results it can be hypothesized that in case o lood plains where ground slopes are very modest, almost no temporal (30 time baseline) and volumetric decorrelation is expected, the main intererometric phase noise contribution comes rom the system SR. Assuming a conservative SR=0dB or both ERS and EVISAT, an intererometric phase noise standard deviation o about /0 radians (less than 6 degrees) holds. Assuming a -km

6 compensation baseline or horizontal terrain (9), an altitude o ambiguity o 5 meters is obtained and an elevation standard deviation o less than 0cm is expected. This possibility is very attractive and should be taken into consideration or planning the ERS- mission during the last part o its successul lie. For example the ERS- /EVISAT geometric baseline could be planned to be close to the compensation baseline (9) so to greatly increase the probability to get an useul ERS- Doppler Centroid ~ 5 cm. ~ 30 cm 3. ~ 40 cm Figure 7 - Let: coherence histogram o the area shown in igure 6. Right: Histogram o the elevation accuracy derived rom the coherence map shown on the let. Fig. 8 The let part o the image is centered on Paris. Here neat ringes are clearly visible on the city parks whereas on the urbanized areas an almost random phase ield is present. Reerences: [.] F. Gatelli, A. M. Guarnieri, F. Parizzi, P. Pasquali, C. Prati, F. Rocca. "The Wavenumber Shit in SAR Intererometry". IEEE Transaction on Geoscience and Remote Sensing, Vol. 3 o. 4, July 994. [.]. Adam, "Das erste Cross-Intererogramm aus Aunahmen der Radarsensoren EVISAT/ASAR und ERS-", online at: [3.] First Cross Intererogram using EVISAT ASAR and ERS- SAR Radar Data, available on-line at: