## 3 Simulation Results
### RDA Compensation Simulation  
Based on the above analysis, for the ISAL images affected by atmospheric turbulence, the RDA was simulated. Due to the limitations of the experimental conditions, an aircraft model was used. The transmission signal in the simulation was the LFM signal. The parameters of the target plane simulated to be in rotation is shown in Table 1, including both the translations and angular motion errors. The target model composed of point scatters with uniform reflectivity is shown in Figure 3.  
ISAL transmits N chirped pulse signals to the target, and M samples are taken in each chirped pulse. The ISAL imaging results without turbulence are shown in Figure 4, where the ISAL imaging time \(\tau_{T}\) is equal to 1.3 s. It can be seen that without turbulence, TMC and RMC overcame image blurring and defocusing caused by target motion, which can effectively improve the ISAL imaging quality. To investigate the influence of atmospheric turbulence on ISAL imaging, the aircraft model in the ISAL process with different atmospheric coherent times \(\tau_{c}\) is shown in Figure 5. The turbulence nearly had no influence on the ISAL process (see the top row) for \begin{table}
\begin{tabular}{c c} \hline \hline
**Radar and Target Parameter** & **Value** \\ \hline Laser wavelength (nm) & 1024 \\ Pulse repetition frequency (Hz) & 17,987 \\ Range sampling number & 64 \\ Pulse number & 512 \\ Distance of the target (m) & 1000 \\ Range resolution (m) & 0.2927 \\ Cross-range resolution (m) & 0.0556 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main parameters of the ladar and target. Figure 3: Simulated target model. (i.e., the turbulence was frozen under the whole ISAL process). However, atmospheric turbulence would significantly reduce the imaging quality of ISAL when \(\tau_{c}\leq\tau_{T}\). The reason for this phenomenon is that the turbulence remains in a frozen state throughout the entire ISAL process for \(\tau_{c}\ll\tau_{T}\), implying that the induced phase fluctuation is smaller, and thus the ISAL imaging quality is higher; otherwise, the result will be the opposite. Figure 4: Compensation results for ISAL imaging without atmospheric turbulence, where each column from left to right represents ISAL imaging without compensation and compensated by TMC or TMC + RMC. Figure 5: ISAL image with different values of atmospheric coherent time (**top** to **bottom**: \(\tau_{c}=100\) ms, 20 ms, and 1 ms; **left** to **right**: without, TMC, and TMC + PFA), where pulse duration time \(\tau_{p}=5.12\) ms and ISAL imaging time \(\tau_{T}=1.3\) s.  
Compared with Figure 4, Figure 5 shows that the TMC and RMC algorithms can effectively overcome the adverse effects induced by turbulence. The phase correction mechanism is the key problem. There are two possible correction mechanisms. The first one is that TMC can correct the phase fluctuations throughout the entire ISAL process. The second one is that it can only correct the phase fluctuations between different pulses. Next, we shall further explore the mechanisms of TMC. Phase fluctuations at different pulses and in the entire ISAL process can reduce the ISAL imaging quality without TMC, as illustrated in Figure 6. Moreover, the phase fluctuations between different pulses can be corrected effectively by using TMC and RMC. However, these cannot be corrected through the entire ISAL process. The reason for this phenomenon is that TMC includes range alignment and phase adjustment. Phase adjustment eliminates the phase drift between different pulses as the range profiles are aligned, which means that TMC can only correct the phase fluctuation between different pulses. From the TMC compensation principle, it can be seen that the relative difference between the atmospheric coherent time \(\tau_{c}\) and pulse duration time \(\tau_{p}\) determines the ISAL imaging quality in turbulent conditions. To verify the above anticipation, ISAL images were plotted with different pulse duration times \(\tau_{p}\) and ISAL imaging times \(\tau_{T}\) in atmospheric conditions.