# Laser Phase Noise Compensation Method Based on Dual Reference Channels in Inverse Synthetic Aldar
## 1 Introduction
[24] developed a laser noise model incorporating multi-sinusoidal frequency modulation and proposed a compensation method based on digital delay. Using a transmitting reference channel compensation and LO reference channel correction, they eliminated high-order phase errors, enabling range-Doppler imaging at 5.4 km. However, this approach requires a precise noise model and is computationally intensive. Furthermore, the experiments were performed with a 1 kHz linewidth laser, keeping phase noise low and coherence intact without compensation, so the method robustness remains unclear for longer distances or moving targets. [PERSON] et al. [25; 26] applied a concatenated generated phase (CGP) method, which is commonly employed in coherent optical frequency domain reflectometry (C-OFDR) [30], to enhance the SNR in the frequency-modulated continuous wave (FMCW) lidar under atmospheric interference conditions. However, the characteristics of the FMCW system determine that the phase extracted in the auxiliary interferometer (reference channel) is discontinuous. The resulting error will accumulate as the cascade order increases. Thismethod, designed for FMCW systems, may not be suitable for other coherent lidar systems using matched filtering techniques such as phase-encoded lidar [31]. [PERSON] et al. [27] introduced a digital coherent detection technique that compensates laser phase noise using a multi-channel delay self-homodyne approach combined with a generalized inverse algorithm. This method achieves coherent detection over distances exceeding 1000 times the laser coherence length. However, environmental sensitivity and the need for high sampling rates constrain its practical use. While these studies demonstrate noise compensation in spectrum and pulse compression results, they do not report ISAL imaging results. We conducted studies focused on coherent lidar phase noise compensation to address these challenges. Our work includes a direct intermediate frequency sampling structure with a digital dechirp pulse compression method to maintain phase continuity and facilitate effective compensation [32]. Based on this structure, [PERSON] et al. previously introduced a calibration-free carrier phase-noise cancellation algorithm using an auxiliary interferometer and adaptive filters [28]. Range-Doppler imaging experiments were performed on stationary and rotating extended targets, demonstrating the algorithm's robustness. In this method, a DAS (delay and sum) filter executes the CGP process, which is followed by a PAD (proportion and delay) filter to correct residual errors. However, the PAD filter, a linear estimate of residual error, has limitations in accuracy, and both filters require iterative searches, resulting in substantial computational demands. In this paper, we propose a dual reference channel (DRC) laser phase-noise compensation method to enhance compensation speed and maintain accuracy. This approach uses two reference channels with different delay lengths to extract the laser carrier phase noise: the long delay channel for coarse compensation and the short delay channel for fine adjustment. Using a 3.41 MHz linewidth, 1550 nm laser, we simulated target channel transmission distances with polarization-maintaining delay fibers of 650 m, 1460 m, and 2110 m. Experiments on stationary and rotating targets validate the DRC method's effectiveness, achieving distances over 110 times the laser's coherence length and increasing compensation speed tenfold. The structure of this paper is as follows. Section 2 details the phase noise model and DRC compensation principles. Section 3 describes the experimental setup and equipment parameters. Section 4 presents ISAL imaging results on stationary and rotating targets, which is followed by an analysis of the findings. Finally, Section 5 discusses limitations and future research directions.