## 3 Results and Analysis  
### Analysis of the Single-SAR Imaging Simulation Results  
Wind speeds of 10 m/s, 13 m/s, and 15 m/s were assigned Equation (1), and the 1D PM spectrum was simulated, as shown in Figure 1. It can be seen from the figure that although the spectrum in theory includes the constituent waves with frequencies from zero to infinity, a significant portion of the spectrum is concentrated in only a narrow frequency range. The wave height and the period range increase as the wind speed increases, and the position of the peak shifts in the direction of low frequency [33]. A wind direction angle of 45\({}^{\circ}\) and wind speeds of 10 m/s and 15 m/s at a height of 10 m were assigned to Equation (4), and the 2D PM wave spectra were simulated. The spectra are shown in the figures below. Wind direction angle is regarded as the direction of wave propagation, defined as the angle to the range direction. The range of the wavenumbers in the azimuth and range directions is determined by the size of the ocean surface and the sampling interval. The color bars on the right side of the figures represent the magnitude of the wavenumber spectrum and represent the energy of the wavenumber spectrum. It can be seen from Figure 2a,b that when the sampling pitch is constant, the wind speed is higher, and the energy of the wave spectrum is stronger and more concentrated. Figure 2a,c show that when the wind speed is constant, the sampling interval is larger and the wavenumber range is smaller. The sampling pitch is inversely proportional to the wavenumber range. According to Figure 1 and the gravity dispersion relation \(\alpha^{2}=kg\), it can be concluded that the higher the wind speed is, the smaller the wavenumber range corresponding to the PM spectrum. The 2D ocean surface was simulated by using the 2D PM wave spectrum as the spectral model, as shown in Figure 3a,b. These results are based on Equations (5) and (6). The ocean surface area size is 1024 m \(\times\) 1024 m, which can be adjusted according to the actual needs, but it is recommended to set the area size to the power of two to facilitate the subsequent FFT. Since the wave propagation direction is perpendicular to the wave stripe, the wave propagation direction in the figure is 45\({}^{\circ}\), which is in accordance with the initial input conditions of the simulation. Moreover, the height fluctuation of the sea surface increases with increasing wind speed, which is consistent with the variation characteristics of the real ocean surface. This result confirms the effectiveness of the Monte Carlo method. The ocean surface backscattering coefficient of wind speeds of 10 m/s and 15 m/s could be obtained by Equations (7)-(9), as shown in Figure 4. The stripe trend of the backscattering coefficient is basically consistent with the streak trend of the corresponding ocean surface. The trend can show the variation in ocean surface fluctuation by the brightness levels of the trough and the peak, which proves that it is feasible to calculate the ocean surface backscatter coefficient by the two-scale model. Figure 1: The one-dimensional (1D) Pierson Moskowitz (PM) spectra at different wind speeds. After calculating the backscattering coefficient, the ocean surface echo signals were calculated based on Equations (10) and (11), as shown in Figure 5. The figure does not show any information about the ocean surface. This condition exists because the original echo signals are obscure and must be processed by the imaging algorithm to obtain feature information of the imaging target from the SAR images. When a SAR images the ocean surface, the scanning band generated by the electromagnetic wave needs to sweep across the ocean surface; that is, the ocean surface needs to be located in the SAR imaging coordinate system. Since the simulated ocean area was approximately 1 km \(\times\) 1 km, for the SAR, the width was small enough to cause ground bending.