J. Eur. Opt. Society-Rapid Publ. 22, 6( 2026) 47
hydrodynamic processes, serving as an effective tool for observing ocean surface waves [ 33, 34 ] and internal waves [ 35, 36 ].
Underwater target detection is now emerging as a new direction for lidar applications, which has importance influences on human activities, such as navigation planning and port construction [ 2, 23 ]. In the field of underwater target detection, current research mainly focuses on two directions: underwater imaging and rapid detection of underwater targets. Since the first application of single-photon avalanche diode( SPAD) arrays to underwater imaging is represented, single-photon imaging technology has steadily advanced [ 37 ]. Subsequently, the first fully submerged underwater lidar transceiver system based on single-photon detection technologies has been demonstrated, achieving images of stationary targets at ranges up to 7.5 attenuation lengths [ 38 ]. More recently, a compact, all-fiber underwater imaging lidar has been presented that achieved imaging distances exceeding 10 times the optical attenuation length, further highlighting the progress in underwater imaging lidar research [ 39 ]. However, the application of lidar for rapidly detecting underwater targets from above water surface remains limited. Only some mapping lidar systems possess the capability for rapid target detection, and there is no dedicated lidar system specifically designed for this purpose. The underwater obstruction detection capabilities of the Scanning Hydrographic Operational Airborne Lidar Survey( SHOALS) were discussed by adopting the enhanced object detection algorithm [ 12, 13, 40 ]. A lightweight UAV-borne lidar Mapper4000 U was developed for shallow water mapping, which had the ability to recognize the existence of a 1-m cube and the rough shape of a 2-m cube at a depth of 12 m by point cloud fitting [ 41 ].
There is also a great deal of algorithms to generate lidar signals, such as the lidar equation, analytical model and Monte Carlo simulation technique. The lidar equation is able to describe depth-dependent lidar signals quickly but has limitations in dealing with multiple scattering [ 42, 43 ]. The analytical model is highly difficult to solve due to its complexity. Only approximate solutions can be achieved through some idealized assumption [ 44 ]. The standard Monte Carlo method is based on a huge number of random calculations of photons’ movements in the water, and photons can be accepted only when they finally arrive at the receiver aperture. The condition is too strict to reconstruct the lidar profiles, consuming a large amount of computing power and time [ 45 ]. The semi-analytic Monte Carlo radiative transfer model for oceanographic lidar systems( SALMON) is based on the method of stochastic and analytic techniques, which estimates the contribution of each scattered photon by the function from a particle scattering position to the detector [ 46 ]. With the advantages in computational efficiency and accuracy, the SALMON model has been the foundation of the MC simulator for oceanic lidar. After decades of development, the semi-analytical MC model has been applied in seabed mapping, retrievals of bio-optical properties and polarized signal analysis and so on [ 47 – 52 ]. However, current research in ocean mapping or target detection is primarily focused on the seabed modeling and has some overly idealized assumptions, which assumes that the seabed fills the entire lidar field of view and simplifies the photon – seabed interactions, without accounting for three-dimensional interactions or the blocking effect on the beam transmission [ 53, 54 ]. Besides, the majority of these studies assume a homogeneous water body and neglect environmental noises, making it difficult to capture the complexity of realistic detection scenarios. On the other hand, the simulators for oceanic lidar profiling have made some advancements in accuracy. While these simulators mainly focus on the slope variations of lidar returns that are closely related to signal retrieval, photon propagation only needs to account for the effects of absorption and scattering by the water, which makes them incapable of detecting three-dimensional target.
As it stands, lidar systems that are applicable to or specifically designed for underwater target detection have yet to be widely developed. A dedicated Monte Carlo simulator for three-dimensional underwater target detection has yet to be established. Three-dimensional simulations are crucial for capturing spatial heterogeneity, beam divergence, and realistic scanning geometries. Therefore, it is highly necessary to develop a simulator that not only emphasizes accuracy but also generates three-dimensional target detection as well as a lidar system designed base on the simulator’ s guidance.
Our research group has already conducted extensive prior work in this area. A standard MC model to detect infinite planar target [ 55 ] and a semi-analytical MC model to detect a two-dimensional flat plane with limited size [ 56 ] have been proposed. In this paper, we present a refined semi-analytical Monte Carlo model for underwater threedimensional target detection( MCT), especially including the interaction process between the beam and the target, the blocking effect on the beam transmission and the reception of the target reflection signals. The MCT model can simulate the scanning signals for underwater threedimensional targets through surface waves in stratified water columns, and incorporate realistic environmental noise to better approximate field conditions. We develop a miniaturized, linear scanning oceanic lidar system( SOL) deployable on commercial UAV platforms. The MCT model is validated by comparisons with the lidar equation results and field measurements from SOL. Furthermore, using MCT, we evaluate SOL’ s detection capabilities in Jerlov II and Jerlov 3C waters, define an extended detection range metric, and examine its relationship with vertical penetration and horizontal scanning resolution, offering an integrated framework for system performance assessment and design optimization in realistic marine environments.
In the rest of this paper, we present the MCT model in Section 2. We present the SOL system in Section 3. The MCT model is validated in Section 4. The target detection capabilities of SOL in different waters are evaluated in Section 5. The conclusion is made up in Section 6.
2 Monte Carlo model of underwater target detection
For a complete and detailed introduction to the MCT model, a cylinder target is chosen as a representative