## 4 Simulation Analysis
### Multi-Component Vibration Error Compensation  
In this sub-section, the simulation results of multi-component vibration error compensation are provided to assess the performance of the proposed vibration error compensation method for THz-SAR imaging. Similarly, when the echo signal of multi-point targets is generated, the two components high-frequency vibration error is added. The Sol containing vibration error is extracted firstly according to the above steps. Similarly, the results obtained by the rough estimation method based on the STFT-based rough estimation method and the STFT-based rough estimation method with the optimal window width are also given here. Using the STFT, we can obtain the IF of the Sol, and the vibration frequency is obtained from the amplitude spectrum of the IF. On the basis of the estimated vibration frequency, the vibration amplitude and initial phase are obtained through the LS regression. Table 4 lists all the estimated parameters and MLF values. Figure 9 shows the true vibration error and the estimated vibration error. It can be seen from the Table 4 that the estimated values by the STFT with \(h=20\) have a large deviation from the true ones. Hence, we can see from the red line of Figure 9 that the estimated vibration displacement also deviates from the true ones, especially at extreme point of vibration. Accordingly, the MLF value is much smaller than the true MLF value, implying that the performance of the STFT-based rough estimation method is poor. Although the performance of the STFT with the optimal window width \(h_{op}=26\) is improved, the estimates still diverge from the true values due to  
Figure 8: Azimuth-dimensional amplitude profiles of center-point target. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **IRW (m)** & **PSLR (dB)** & **ISLR (dB)** \\ \hline theoretical values & \(0.050\) & \(-11.95\) & \(-13.73\) \\ \(h=20\) & \(0.064\) & \(-0.21\) & \(-5.38\) \\ \(h_{op}=26\) & \(0.053\) & \(-7.10\) & \(-8.57\) \\ \(h_{op}=26\) with RANASAC & \(0.051\) & \(-12.37\) & \(-11.48\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Imaging quality evaluation after vibration error compensation. the singular IF estimates. However, of value is that the estimated values of parameters by the proposed improved STFT-based method are consistent with the true ones, as shown in Table 4. It implies that the improved method greatly suppresses both the effects of window width and the singular values of IF estimation, which is also verified by the MLF value in Table 4 and the estimated vibration displacement in the green line of Figure 9.  
The vibration error is compensated for in the THz-SAR imaging process, and the performance of different estimation methods are then analyzed and compared. Figure 10a shows the focusing results of the RD algorithm. Due to vibration error, the SAR image are completely defocused. Figure 10b-d shows the imaging results after the vibration error is compensated for based on the above methods, respectively. Figure 11 also gives the phase difference between the true vibration phase and the estimated vibration phase. We can see from Figure 10a,b that the image quality after vibration error compensation is improved, but it is still affected by paired echoes. This is caused by the residual period-modulated phase error greater than \(\pi/4\), which is shown in the red line of Figure 11. Meanwhile, the green line of Figure 11 shows that the residual phase is no greater than \(\pi/4\), but is still periodically modulated. Therefore, the imaging quality of Figure 10c is further improved, but its side lobes are still relatively high. Fortunately, the residual phase error is smaller than \(\pi/4\) and no longer periodically modulated after vibration error compensation by the