# Laser Phase Noise Compensation Method Based on Dual Reference Channels in Inverse Synthetic Aldar
## 4 Results and Analysis
### Range-Doppler Imaging of Stationary Targets  
To calibrate the performance of the experimental system, we applied this method to conduct range-Doppler imaging of stationary targets. We used silver reflective bright strips as cooperative targets, as illustrated in Figure 12(a1). This choice enhances target reflectivity and facilitates system detection. The background (red) of the bright strip consists of diffusely reflective sponge material, which effectively mitigates the interference caused by reflections from metal mechanical components. We positioned the target approximately 5.5 m from the transceiver system to ensure the light spot fully covered the target.  
In the experiment, we implemented delay optical fibers with lengths of 650 m, 1.46 km, and 2.11 km, respectively, which were installed between the EDFA and the transmitting collimating lens to simulate the transmission path of long-distance targets. Considering the refractive index of the fiber is 1.466, the optical path and corresponding coherence length for each fiber are 952.9 m (34\(\times\) coherence length), 2.14 km (76\(\times\) coherence length), and 3.09 km (110\(\times\) coherence length).  
Figure 12: Range-Doppler imaging results of a stationary single-point target: (**a1**) target layout; (**a2**) a narrow linewidth laser signal with 650 m fiber optic transmission; (**b1**) 650 m fiber optic transmission without compensating for phase noise; (**c1**) 1460 m fiber optic transmission without compensating for phase noise; (**d1**) 2110 m fiber optic transmission without compensating for phase noise; (**b2–d2**) DRC fine compensation results for (**b1–d1**), respectively.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Index** & **DRC** & **PLE** \\ \hline Peak power (dB) & 108.02 & 106.97 \\ Range resolution (cm) & 3.48 & 3.50 \\ Range PSLR (dB) & \(-\)10.80 & \(-\)11.19 \\ Range ISLR (dB) & \(-\)8.87 & \(-\)8.94 \\ Doppler resolution (kHz) & 0.29 & 0.29 \\ Azimuth PSLR (dB) & \(-\)30.42 & \(-\)31.04 \\ Azimuth ISLR (dB) & \(-\)28.03 & \(-\)26.89 \\ Running time (s) & 12.938 & 123.341 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of profile indices and method runtime.  
Figure 12(b1) displays the range-Doppler image obtained using 650 m of optical fiber to extend the signal transmission distance equivalently. The defocus in the range direction is significant, resulting in a resolution of only 5.10 cm. Consequently, this approach is not suitable for detecting long-distance targets without compensation.  
The image shown in Figure 12(b2) illustrates the result after compensating for laser phase noise using the DRC method, achieving a range resolution close to the theoretical value of 3.32 cm. Notably, this method retains its compensation effectiveness even when the fiber length extends to 1.46 km (Figure 12(c2)) and 2.11 km (Figure 12(d2)).  
Additionally, we observed that as the round-trip distance increases, the order of cascading required for the CGP method will also rise. The accumulation of phase estimation errors will increase the sidelobe in the range direction. The image appears slightly defocused.  
We also established a control group and utilized a 100 Hz narrow linewidth laser (NKT Company, Koheras ADJUSTIK E15) to conduct ISAL imaging at a fiber length of 2.11 km. The low-phase noise characteristic of narrow linewidth lasers eliminates the need for laser phase noise compensation. The results in Figure 12(a2-d2) indicate that after applying the DRC method to compensate for the phase noise of the 3.41 MHz linewidth laser, the range-Doppler imaging achieved is comparable to that obtained with the narrow linewidth laser even when the round-trip distance exceeds one hundred times the coherence length.