# Perspectives on the Structural Health Monitoring of Bridges by Synthetic Aperture Radar
## 3 Analyses of Structural Integrity of Bridges from SAR
### Study Case 1
We conclude this case study observing that the Doppler sub-apertures are equal to half the available azimuth band, so the azimuth spatial resolution decreases by a factor 1/2 and we show  
Figure 5: Optical representation of dilatation joints: (**a**) Joint number 1, (**b**) Joint number 2, (**c**) Joint number 3. Figure 6: Temporal trend of vibrations. Figure 7: Vibration trend spectrum (DFT of Figure 6). (**a**) Spectrum in the linear scale, (**b**) Particular 1 of the spectrum trend (**a**), (**c**) Vibration spectrum in the logarithm scale. the effect in discriminating targets selecting a full and a half band in the following. In Figure 8 the optical image of the Ponte dell'Industria is depicted. Points A and B were taken as a test to measure the Rayleigh distance, and therefore the resolution as the Doppler band used during azimuth focusing varies. These points consist of the iron scaffolding that acts as a railing at the bridge, therefore very visible to the SAR. The distance measured \"in-situ\" is about 7 m. The CSK product used for processing is a stripmap that guarantees a spatial resolution of 3 m, so points A and B must be displayed separately. In Figure 9a,b the SLC SAR images of the \"Ponte dell'Industria\" observed with full and half Doppler band is depicted, and in Figure 10a,b the reflectivity profiles extrapolated along the red line depicted in Figure 9a,b are depicted. The reflectivity profiles are extrapolated following the red box-profile depicted in Figures 8 and 9a,b. Figure 10a is the full Doppler band image and Figure 10b in the one observed processing only half Doppler band. In Figure 10a is imaged in the linear scale, and the blue function is the imaging function estimated processing the entire Doppler bandwidth and the brown function is the one estimated using only half Doppler band. In Figure 10b is imaged in the log scale, and the blue function is the imaging function estimated processing the entire Doppler bandwidth and the brown function is the one estimated using only half Doppler band. The energy peaks of the iron railing, taken as a test, are correctly separated in distance, in the case of full band, the \"sinc\" is narrower and has a minimum local separation equal to about \(-7.8\) dB, while in the case of half band, the separation is weaker, but always feels, localized at about \(-2.8\) dB. However, the bridge, even if processing half-band Doppler is clearly displayed, and the railings are separated the same in a bit lower energy depth. As a result of this first analysis, it is possible to state that the proposed methodology is able to extract the position and energy intensity of points along motorway bridges, that could be possible candidates for cracks, even when different acquisition geometries are used. It is also worth to highlight that the proposed technique has evident band limitations that do not allow for the measurement of very low frequencies, also below Hz, due to the reduced time exposure of the target radiation footprint. In high frequencies, on the other hand, the sensitivity cut is limited by the sampling theorem and limited to half of the maximum Doppler band used to synthesize azimuth resolution. Figure 8: Optical image.