## 2 Monitoring Method of Bridge Dynamic Deformation  
### Digital Close-Range Photogrammetry Technology  
Differential interferometry is utilized to process radar data collected in the monitoring process by selecting an appropriate reference time base and differential interferometry. A deformation time series of bridge monitoring points can be obtained by calculating the deformation values of corresponding points at different time scales; subsequently, other parameters of bridge dynamic characteristics can be obtained. The main data processing and analysis procedures are as follows:  
(1) Reference time base selection  
The beginning of radar data acquisition is selected as the reference time base for data processing. Assume that the bridge deformation value at this moment is 0, and based on the radar data at other times, the calculated deformation value is relative to the reference time base. (2) Windowing treatment  
Radar echo data collected by the IBIS-S system are a sample in the frequency domain, which should be focused. In other words, a Discrete Fourier inversion is adopted to convert the frequency domain data into spatial domain data; thus, the deformation information of each resolution unit in the range direction of the radar monitoring region can be extracted. Herein, before focusing on the distance direction of radar monitoring data, a hanning window function is utilized; thus, the radar data signal is windowed to eliminate the side lobe effect. (3) Differential interferometry treatment  
First, the ground-based radar image contains amplitude and phase information, which is reflected by the geometric distance between the radar and the target. Therefore, an interferometric technique can be utilized to retrieve the displacement change between the radar and target according to the phase change of radar images obtained at different times. If it is assumed that two scene radar images (t\({}_{1}>\) t\({}_{0}\)) are obtained at different times, namely t\({}_{0}\) and t\({}_{1}\), and that the phase value of the same pixel is the same as that of the radar image at the aforementioned times, the following formula applies:  
\[\phi_{0}=\frac{4\pi S_{0}}{\lambda}+\phi_{\text{divert},0}+\phi_{\text{air},0}+ \phi_{strepitus,0} \tag{1}\]  
\[\phi_{1}=\frac{4\pi S_{1}}{\lambda}+\phi_{\text{divert},1}+\phi_{\text{air},1}+ \phi_{strepitus,1} \tag{2}\]  
where \(\lambda\) denotes the wavelength of the radar transmission signal; \(S_{0}\) and \(S_{1}\) denote the geometric distance between the radar and the target at two times, namely t\({}_{0}\) and t\({}_{1}\); \(\phi_{\text{divert}}\) denotes a phase change occasioned by the interaction of the microwave and monitored object; \(\phi_{\text{air}}\) denotes the phase occasioned by atmospheric interference between the radar and monitored object; and \(\phi_{strepitus}\) denotes a random noise phase. After interference processing, the interferometric phase \(\Delta\phi_{10}\) of the radar image at t\({}_{0}\) and t\({}_{1}\) can be obtained as follows:  
\[\Delta\phi_{10}=\phi_{1}-\phi_{0}=\frac{4\pi(S_{1}-S_{0})}{\lambda}+(\phi_{ divert,1}-\phi_{divert,0})+(\phi_{air,1}-\phi_{air,0})+\phi_{strepitus} \tag{3}\]  
Assuming that the phase-shift component \(\phi_{\text{divert}}\) is constant in the radar images obtained at times t\({}_{0}\) and t\({}_{1}\), Formula (3) can be simplified as follows:  
\[\Delta\phi_{10}=\phi_{1}-\phi_{0}=\frac{4\pi d_{Lo}}{\lambda}+(\phi_{air,1}- \phi_{air,0})+\phi_{strepitus} \tag{4}\]  
In Formula (4), d\({}_{Lo}=R_{1}-R_{0}\) denotes the displacement change between t\({}_{0}\) and t\({}_{1}\) when the target object appears upward in the radar line of sight.