# Laser Phase Noise Compensation Method Based on Dual Reference Channels in Inverse Synthetic Aldar
## 4 Results and Analysis
### Fiber-Based Signal Transmission Experiment
#### 4.1.2 Range-Doppler Imaging  
After compensating the echo signal for laser phase noise, we segmented the data into a two-dimensional matrix and applied two-dimensional compression in both the range and azimuth directions. Figure 9 shows the resulting range-Doppler image. Figure 9a-d3 correspond to the sequence in Figure 7, illustrating the effects of various compensation strategies. Figure 8: Comparison of matched filtering results in peak power and SNR across various compensation strategies: (a) without compensation; (b) short delay coarse compensation only; (c1) coarse compensation with \(N_{1}=31\); (c2) fine compensation with dual reference channel (DRC) and \(N_{1}=31\); (c3) fine compensation with phase linear estimation (PLE) and \(N_{1}=31\); (d1) coarse compensation with \(N_{1}=30\); (d2) fine compensation with DRC and \(N_{1}=30\); (d3) fine compensation with PLE and \(N_{1}=30\). Figure 9a shows the uncompensated imaging results. When the round-trip distance significantly exceeds the laser coherence length, the image becomes severely defocused along the range direction. The theoretically ideal single-point image is stretched into strips, failing to meet imaging requirements. Figure 9b presents the results of phase compensation using only short optical fiber channels. Due to significant phase estimation errors accumulating over numerous cascade orders, the compensation capacity is limited. Figure 9c1 displays the result of coarse compensation with SRC when the cascade order is \(N_{1}=31\). Figure 9c2,c3 illustrate the enhanced imaging results achieved with fine compensation using DRC and PLE, respectively. Figure 9d1 shows compensation results for a cascade order of \(N_{1}=30\). When the cascade order estimation in coarse compensation is insufficient, the image remains defocused in the range direction, which affects subsequent target recognition. Figure 9d2,d3 illustrate the'remedial' results in such scenarios, which are achieved through DRC and PLE precision compensation methods, respectively. Both images achieve effective focusing. We analyzed the range and azimuth profiles at the image center to demonstrate the compensation effect, as illustrated in Figure 10. We assessed the profiles using a normalized linear coordinate system to compare the effects of various compensation methods. Since laser phase noise primarily impacts the distance dimension of the image, our analysis will focus on relevant indicators for this direction. Key parameters, including the impulse response width (IRW), peak side-lobe ratio (PSLR), and integrated side-lobe ratio (ISLR), are shown in Figure 11. The IRW is used to evaluate image resolution. When the cascade order estimation is accurate (\(N_{1}=31\)), the fine compensation method produces a well-focused range-Doppler image (Line (c2)). Compared to (\(N_{1}=31\)) coarse compensation (Line (c1)), the peak power and range resolution of the resulting image improve by 117 % and 4.6 %, respectively. Figure 9: Comparison of range-Doppler imaging results using various compensation strategies: (**a**) no compensation; (**b**) coarse compensation with only short delay; (**c1**) coarse compensation with \(N_{1}=31\); (**c2**) fine compensation with \(N_{1}=31\) using dual reference channel (DRC); (**c3**) fine compensation with \(N_{1}=31\) using phase linear estimation (PLE); (**d1**) coarse compensation with \(N_{1}=30\); (**d2**) fine compensation with \(N_{1}=30\) using DRC; (**d3**) fine compensation with \(N_{1}=30\) using PLE. Notably, the resolution achieved in both the range and azimuth directions is 3.48 cm and 0.29 kHz, respectively, which closely aligns with the theoretical values of \(\delta_{r}=0.886\frac{\xi}{2B}=3.32\) cm and \(\delta_{f}=0.886\frac{PRF}{N_{a}}=0.276\) kHz. This alignment demonstrates that the phase noise compensation method based on dual reference channels (DRCs) effectively enhances compensation accuracy and mitigates the accumulation of estimation errors.