# Performance Analysis of Ocean Surface Topography
## 3 OST Altimetry Results and Analysis of InIRA
### Interferometric Data Processing  
The interferometric data need to be coregistered, flat-earth phase removed and calibrated to finally obtain the absolute ocean surface height [10]. Though the parameter calibration of InIRA has not yet proceeded, we can still utilize the relative phase change to estimate the altimetric precision after the flat-earth phase removal.  
Figure 7a is the slant-range image, under the modulation of antenna pattern, ocean surface intensity decreases rapidly in the far range, which indicates the decrease of SNR as well. Figure 7b is the coregistered phase of two SAR complex images, and fringes among the ocean area is the classic flat-earth phase. The flat-earth phase exists and changes regularly in the slant-range direction even if the topography does not change at all [10]. Among the mountainous area, the fringes seem to be distorted, which is caused by the elevation change of the mountains. Due to the decrease of SNR, phases in the far range are much noisier.  
Phases in the black box in Figure 7b contains both the flat-earth phase and relative phase, which corresponds to the OST change. To acquire the relative phase, the flat-earth phase should be removed first. The flat-earth phase can be expressed by:  
\[\varphi(B,\alpha,n)=\frac{2\pi B\sin(\theta-\alpha)}{\lambda}=\varphi_{ fringe}+2\pi n \tag{13}\]  
where the baseline length \(B\), baseline tilt angle \(\alpha\) and wavelength number \(n\) need to be calibrated. \(\varphi_{ fringe}\) is the wrapped flat-earth phase, which changes regularly along the slant-range direction, as shown in the black box in Figure 7b.  
Since the relative phase change is very small according to the altimetric sensitivity simulation in Section 2.1, hence phases in the black box are mostly composed by the wrapped flat-earth phase \(\varphi_{ fringe}\), which contains precise information of the parameters that need to be calibrated.  
Therefore, we utilize the flat-earth phase to calibrate the system parameters. Phases in the black box in Figure 7b are selected to acquire the flat-earth phase curve along the slant-range direction, then the flat-earth phase curve is fitted to the nominal Equation (13). By changing different combination of parameters \((B,\alpha,n)\) and seeking the minimum RMSE between flat-earth phase curve and the nominal equation. The parameters are calibrated in this way, as given in (14), and the nominal flat-earth phase is calculated and eliminated throughout the entire image. Besides, most of the systematic errors, such as differential phase drift [22], are also eliminated during this process.  
\[(B,\overset{\wedge}{\alpha},n)=\text{argmin}[\varphi_{ fringe}-\varphi(B,\alpha,n)] \tag{14}\]  
Figure 6: SAR intensity image of the South China Sea, acquired by InIRA in September 2016. The image is geocoded, the modulation of antenna pattern along the range direction is corrected. The azimuth and range directions are indicated by arrows.  
The relative phases which correspond to the topography are shown in Figure 7c. The phases vary notably among the mountainous area due to the large terrain variation. However, among the ocean area, the phases hardly change and tend to be near 0 rad. In the far range, where the internal waves exists, the phase deviates from 0 rad and looks much noisier; this phenomenon will be analyzed in Section 3.2.  
Figure 7d is the coherence between two SAR complex images, and most of the ocean surface area is above 0.95. However, the coherence drops in the far range because of the decrease of SNR, especially in the internal wave area. Coherence of the mountainous area is between 0.3 and 0.7, and this relatively low coherence is mainly caused by volumetric decorrelation of the Ku-band signal, since mountains in Vietnam are covered by lush vegetation.  
Figure 7: _Cont._