# Laser Phase Noise Compensation Method Based on Dual Reference Channels in Inverse Synthetic Aldar
## 3 Systems and Materials  
Based on the principle proposed in Section 2, we conducted an indoor verification experiment to demonstrate the effectiveness of the dual-reference-channel laser phase-noise compensation method. Here, we employed an ISAL imaging system, which demands high coherence among lidar components. Figure 5 shows the schematic block diagram of the lidar system. In the experiment, we selected a broad-linewidth laser (Connet, CoSF-D-EY) with a nominal linewidth of 3 MHz, corresponding to a coherence length of approximately 30 m. This choice is justified, as broad-linewidth lasers more effectively illustrate the impact of laser phase noise on the system and the effectiveness of the compensation method. Moreover, the short coherence length simplifies the experimental setup, facilitating simulation and testing. We measured the laser linewidth using the delayed self-heterodyne method. Figure 6 shows the photocurrent power spectrum and the corresponding fit curve. The measured linewidth is 3.41 MHz, and the coherence length is \(l_{c}=c/(\pi\Delta v)\approx 28\) m.  
Figure 4: The flowchart of the laser phase noise compensation method based on dual reference channels in ISAL. Figure 3: Schematic diagram of different RPN compensation methods within the mismatch region. (**a**) Dual reference channel (DRC) method; (**b**) phase linear estimation (PLE) method. Table 1 lists the main parameters of the experimental system. A beam splitter (BS) divides the laser's optical output into two parts. One portion (90%) goes into the electro-optic modulator (EOM), which consists of dual parallel Mach-Zehnder modulators with I/Q modulation capability. The modulation signal is a high-pulse repetition frequency (PRF) linear frequency-modulated continuous wave (LFMCW) signal generated by an arbitrary waveform generator (AWG, KeySight Technologies, Chengdu, China). After modulation, the signal is amplified by an erbium-doped fiber amplifier (EDFA, Connet, Shanghai, China) and transmitted as the probe beam. TX and RX are collimators used to transmit and receive the beams. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Value** & **Unit** \\ \hline Laser wavelength & 1550 & nm \\ Laser linewidth & 3.41 & MHz \\ Transmission power & 200 & mW \\ Laser coherence length & 28 & m \\ Ref. channel 1 fiber length & 20 & m \\ Ref. channel 2 fiber length & 4 & m \\ Target channel fiber length & 650/1460/2110 & m \\ LFM signal bandwidth & 4 & GHz \\ Repetition frequency & 20 & kHz \\ AOFS frequency shift & 80 & MHz \\ ADC sampling rate & 16 & GS/s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental system parameters. Figure 5: Block diagram of laser phase noise cancellation lidar system based on dual reference channels. Figure 6: Photocurrent power spectrum and fitted curve for laser linewidth measurement. Most of the modulated signal (99%) reaches the target channel (Ch.1) for detection. Before the beam enters the collimating mirror for emission, it passes through a coil of polarization-maintaining delay fiber, effectively increasing the round-trip distance. This design enables controlled laboratory experiments, eliminating the complications associated with distant target locations. Additionally, most of the probe beam's transmission path is within the polarization-maintaining optical fiber, which reduces power fluctuations and attenuation over distance. Transmission through optical fibers also minimizes the effects of atmospheric turbulence and other environmental noise. A small portion (1%) of the modulated signal enters the monitoring channel (Ch.2), which monitors the signal quality and verifies the system's normality. The LO signal for Ch.1 and Ch.2 originates from an additional split portion (10%) of the laser output. To reduce the effects of intensity noise and power fluctuations from the light source, an electronically adjustable optical attenuator (EVOA, Thorlabs) is used, ensuring that phase noise remains the primary focus of the study.