## 1 Introduction  
Active optical imaging has a wide range of applications, such as remote sensing [1], airborne surveillance [2], target recognition [3], augmented reality [4], navigation [5], landing [6], and so on. Among the proposed methods for imaging measurement, LiDAR exhibits exceptional potential for long-range and real-time applications. These capabilities surpass alternative techniques such as stereo-vision [7] and structured-light [8], which are typically constrained to shorter ranges. Regarding the full-scale range [9], LiDAR [10] systems can be categorized into short range (up to a few meters, e.g., in augmented reality for gaming), medium range (up to a few tens of meters, e.g., in industrial automation), and long range (hundreds of meters or kilometers, e.g., automotive and satellite vision). Achieving long ranges requires pulsed-LiDAR techniques combined with high-power lasers, detectors with high sensitivity, and timing electronics with sufficient full-scale range. However, implementing and applying this technology for outdoor applications face challenges due to various interfering factors, such as strong solar background illumination and increment weather conditions such as rain and fog. To overcome these challenges, denoising technologies, including temporal filtering [11], spatial filtering [12], spectral filtering [13], polarization filtering [14], etc., have been developed. Depending on the requirements of different application scenarios, one or multiple technologies are selected. When reconstructing two- or three-dimensional (2D and 3D) scenes using LiDAR, scanning is crucial [15; 16]. This can be achieved by utilizing optomechanical elements [17] (such as rotating mirrors and prisms), electromechanical moving parts (such as electric motors with mechanical stages), or compact micro electro-mechanical system (MEMS) mirrors [18] and solid-state optical phase arrays (OPAs) [19]. The selection of the scanning scheme necessitates careful consideration of multiple parameters, including laser energy, repetition frequency, eye-safety thresholds, detector architecture, measurement speed, and system complexity. For instance, MEMS and OPAs offer a more compact and lightweight alternative to electromechanical scanning while also enabling faster scanning through the utilization of resonant mirrors. It is important to note that each technology has its own limitations; therefore, there is no universally preferred option for all applications. In this work, focusing on long-range imaging LiDAR systems (exceeding ten kilometers with high-power lasers), the scanning mechanism adopts optomechanical elements. Array-based imaging utilizing single photon avalanche diodes (SPADs) presents a relatively accessible technology, as evidenced by numerous research reports. For instance, [PERSON] et al. showcased laser ranging up to 32 m utilizing a 1 GHz sine-wave InGaAs/InP SPAD [20]. Other studies demonstrated sub-centimeter resolution ranging at a stand-off distance of 330 m using superconducting niobium nitride nanowire single-photon detectors [21], and centimeter resolution depth imaging with low signature objects at distances up to 1 km employing an InGaAs/InP SPAD [22]. A study employing a 32 \(\times\) 32 InGaAs/InP Geiger-mode array demonstrated three-dimensional imaging over ranges extending to 9 km [23; 24]. Moreover, [PERSON] et al. provided an experimental demonstration of long-range 3D imaging surpassing 200 km [25]. Nonetheless, achieving high-resolution imaging at kilometer-scale distances introduces formidable challenges, primarily the dearth of signal photons and the significant solar background illumination. Traditional long range LiDAR imaging systems that rely on SPAD array detectors for single photon operations are not only costly but also largely experimental. This dependence frequently precipitates a precipitous decrease in the signal-to-background ratio (SBR) as the imaging distance increases, thereby constraining the effectiveness of image reconstruction [26].