# Laser Phase Noise Compensation Method Based on Dual Reference Channels in Inverse Synthetic Aldar
## 1 Introduction  
In recent years, numerous low Earth orbit (LEO) satellites, such as Starlink, have been launched for applications in communication and Earth observation, generating a substantial increase in the demand for the precise high-resolution imaging of these small and remote targets [1, 2, 3, 4]. With increased international scrutiny over such satellite deployments, the global community prioritizes advanced imaging and monitoring technologies [5, 6]. Traditional optical imaging methods, once widely relied upon, now face limitations in achieving the resolution required for accurate satellite observation due to constraints imposed by the physical aperture size [7, 8]. To overcome these limitations, researchers have explored inverse synthetic aperture lidar (ISAL), which is a technique that provides high-resolution imaging by capturing the range-Doppler distribution of targets, effectively bypassing the diffraction limit [9]. ISAL advances synthetic aperture techniques from the microwave to the optical domain,leveraging the shorter wavelength of laser carriers to achieve superior theoretical resolution. In addition to enhanced resolution, ISAL offers reduced synthetic aperture time and improved image recognition capabilities, making it a promising technology for the evolving needs of satellite observation and monitoring [10]. To advance the practical application of the inverse synthetic aperture lidar (ISAL), numerous research teams have conducted kilometer-scale experiments, both in laboratory environments and outdoors, to evaluate system usability and algorithm effectiveness [11; 12; 13]. Our team has performed ISAL imaging at distances of 1 km [14], 7 km [15; 16], and 22.5 km, achieving successful imaging with cooperative targets. However, the ISAL imaging of remote targets requires further advancements in several key areas: target tracking, atmospheric turbulence mitigation [17; 18], weak signal detection [19; 20], motion error correction [16; 21], and, importantly, laser phase noise suppression [22; 23; 24; 25; 26; 27; 28]. Laser phase noise, in particular, fundamentally limits the range and performance of coherent lidar systems like ISAL. The laser coherence length, inversely related to its linewidth, constrains the effective operational range of coherent lidar. Therefore, imaging distant targets requires lasers with narrow linewidths, which are often in the kilohertz range. As distance increases, accumulated phase noise can significantly degrade resolution and the signal-to-noise ratio (SNR). Furthermore, remote target detection demands high laser power, which current laser technologies find challenging to deliver cost-effectively with a narrow linewidth. High-power lasers often suffer from amplified spontaneous emission (ASE) and nonlinear interference, which complicates their use in these applications [29]. Consequently, suppressing laser phase noise could help overcome coherence length limitations, extending the effective detection range of coherent lidar systems. This advancement may also reduce system costs by enabling more affordable high-power lasers with wider linewidths, eliminating the need for complex, environment-sensitive narrow-linewidth lasers. Existing phase noise compensation methods can be categorized into two primary approaches: analog and digital domain techniques. The analog domain method, proposed by Raytheon in 2013 [22] and achieving ISAL imaging in 2018 [23], involves using a delay fiber to transmit the local oscillator (LO) signal, which is coherently mixed with the echo signal. By minimizing the delay difference between the interferometer arms, this approach effectively suppresses phase noise. However, its application is limited to targets with known distances because of the fixed length of the delay fiber, making it unsuitable for long-distance, non-cooperative moving targets. Additionally, the use of ultra-long delay fibers substantially increases equipment size, complicating system miniaturization. Digital domain compensation approaches vary in technique. [PERSON] et al.