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J. Eur. Opt. Society-Rapid Publ. 22, 6( 2026)
Fig. 1. Flow chart of MCT simulation model.
example. The cylindrical geometry captures essential features relevant to underwater lidar detection, including extended surfaces, well-defined edges, and stable occlusion characteristics under scanning illumination. As a representative intermediate case, the cylindrical geometry combines manageable geometric complexity with physically meaningful target characteristics relevant to practical detection scenarios. It is worth emphasizing that the proposed MCT model is formulated in a geometry-independent manner. Other target can be incorporated by modifying the geometric description.
The main parts are introduced below, and the flow chart of the model is shown in Figure 1. The whole simulation starts with the emission of photons and ends with their final death. During the propagation process, the photon can be scattered, reflected by the target, escaping from the boundary, or received by the detector. The surface of the target is seen as ideal Lambertian. The inherent optical properties( IOPs) model of water used in simulation is based on previous research [ 43, 57 – 62 ].
2.1 Launching
The Cartesian coordinates of the simulation model are shown in Figure 2a, the initial position of the lidar system is P st =[ x st, y st, 0 ], and the downward direction of the z-axis is positive. The intensity of the emitted beam follows a Gaussian distribution, and the initial position of the photon is sampled from the laser spot on the water surface( Fig. 2b). The intensity distribution on the water surface is [ 63 ]
Ið R G Þ ¼ I
0 pffiffiffiffiffi exp � R2 G
; ð1Þ
2p r 2r 2
where r is standard deviation of Gaussian distribution. The sampled spot radius R G is expressed as p R G ¼ r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
�2lnðn rnd Þ; ð2Þ
where n rnd is a random number uniformly distributed over( 0, 1). The initial azimuth angle on the Gaussian spot is sampled as follow