# 3D Monitoring of Buildings Using TerraSAR-X InSAR, DInSAR and PolSAR Capacities
## 4 Measuring the Deformation Trough Differential Interferometry
### Analysis of the Estimated Deformation
#### 4.3.2 Comparison with In Situ Measurements  
The Societe d'Exploitation de la Tour Eiffel (SETE) has charged the company OSMOS to monitor routinely the deformations of the Eiffel Tower thanks to their optical strand system pictured in Figure 7a. This process is based on the principle of the modulation of light intensity by measuring analog attenuation along an optical fibre coil. The deformation are average on a measurement interval leading a very low variability of the measurement. For over 20 years, OSMOS has monitored the stability of the main structural elements of the Eiffel towers, through several local deformation measurements, performed at numerous locations on the structure.  
The SETE granted us access to 36 deformation measures for 8 optical strands installed at the first floor of the Eiffel Tower, at the specific times of SAR acquisitions. Two optical strands are installed horizontally on each side of the tower, one on the exterior part of the first floor and one on the interior part. The minimum and the maximum values for the optical strands are represented in Figure 7b. The observed variation are caused to anisotropic deformation leading to bigger deformation on some sides of the Eiffel Tower than the others. These differences are more likely to be due to deformation induced by the sunlight, since only one side of the structure is illuminated.  
In order to compare the same physical quantities, we have converted our measurements into linear deformation, assuming that the main deformation axis is vertical, and dividing the total deformation by the height of the turn portion on which deformation is estimated. Figure 7b represents the mean linear deformation measured by DInSAR, as well as the maximal and minimal linear deformation measured by the optical strands.  
Even if the chosen strands are not in the studied area, Figure 7b shows that the order of magnitude of the DInSAR deformations agree with the optical strands measurements. A quarter of the DInSAR deformation are between the minimal and the maximal optical strand measured deformations.  
The comparison of our global deformation with the local deformation obtained by the optical strand is not an individual validation of our measurement. However, the orders of magnitude are valid, although this comparison has been performed on the Eiffel Tower, which is the building showing the largest and the most chaotic deformation pattern. Moreover, we measured linear deformations by making a very coarse hypothesis on the deformation, assuming that it is linear, and oriented along a vertical axis. However, we know that is certainly not the case, and that it is difficult to extrapolate a point measure to a global homoegenous linear measure. Therefore, the relatively good agreement between the values of the DInSAR deformations and the optical-strand deformations validate the  
Figure 7: Comparison between linear deformation measured by DInSAR ant the linear deformation measured by the optical strands installed on the Eiffel Tower by OSMOS. (**a**) Optical strand on the Eiffel Tower ©OSMOS (**b**) \(\bullet\) Lineic DInSAR deformation estimated for the Eiffel Tower — Minimal and Maximal lineic deformation measured by optical strands.  
developed process chain. It also support our hypothesis that the unrealistic-InSAR height are due to deformations of the buildings between the acquisitions.  
Neglecting the impact of the atmosphere limits however the accuracy of the estimated DInSAR deformation since variation in the optical path length due to the atmosphere can wrongly be attributed to scatterers deformation [27]. The impact of the atmosphere is thus discussed in the next section.