SAR Interferometry (InSAR) and SAR Differential Interferometry (DInSAR) are two well-known techniques of Synthetic Aperture Radar (SAR) image processing. SAR Interferometry measures the phase difference between 2 images acquired from slightly different points of view to obtain the height of the scatterers. Interferometry is often multi-pass: the two images are acquired by the same sensor at different time. But it can be mono-pass if the two images are acquired at the same time,  such as TerraSAR-X and TanDEM-X conjoint acquisitions. SAR Differential Interferometry is always multi-pass: this technique permits to retrieve the movement of the scatterers between the date of acquisition from the phase difference between 2 images acquired from the same point of view.

In this article, we show that the height retrieval from multi-pass acquisition over target which shape changes can give tricky results. We carry out this study on a temporal serie of 10 SAR images acquired by TerraSAR-X in 2009 and we focus on the measure of the height of the Eiffel Tower since it is normally a target with a well-known height!

After unwrapping the phase on the Eiffel Tower, we compute its height throught interferometry. The measured height could exceed 1km! We credit this error to the mixture of the interferometric phase with the phase due to the displacement of the scatterers in time: DInSAR is needed.

To supress the interferometric component, we used the official height of the Eiffel Tower as a DEM.  We found dilatation up to 4cm. Depending on the baseline, this deformation could lead to the kilometric error on the interferometric height. If a deformation model was available, it would be possible to compute the deformation conjointly with the height. Studies on the deformation of buildings make often the assumption that the variation of height is linear and estimate only a deformation velocity. This is not possible for the Eiffel Tower because its deformation depends heavily on the weather (temperature, wind and the amount of sunshine per day). It is not regular in time. Complementary information on the deformation of structure and the weather at the time of acquisition are thus needed to validate to estimate conjointly the height of the first acquisition and the deformation.