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J. Eur. Opt. Society-Rapid Publ. 22, 6( 2026)
the volume scattering coefficient calculated by( 6) at the scattering angle of p. K lidar is the lidar attenuation coefficient which is calculated by [ 43 ]
K lidar ðz w Þ ¼ K d ðz w
Þþ ½ c total ðz w Þ�K d ðz w ÞŠ exp ½ �0:85c total ðz w ÞDz ð w ÞŠ; ð20Þ
Fig. 6.( a) Chlorophyll concentration profile of SPG water,( b) comparison between MC simulation signal and lidar equation signal.
focal plane. After aperture-stop limitation, the echoes pass through a collimating lens and a narrowband filter to enhance beam collimation and spectral selectivity, suppressing interference from other wavelengths. The conditioned echoes are then separated by a polarizing beam splitter, refocused by focusing lenses, and detected by PMTs, enabling high-sensitivity detection of the return signals.
In the scanning subsystem, a paraxial structure is chosen with the emission subsystem and the receiver subsystem separated at both ends to implement mechanical synchronous scanning. Besides, a reflective photoelectric incremental encoder is equipped to obtain angle information during scanning. It continuously outputs high-resolution TTL pulse signals in A, B, and Z phases. One full rotation corresponds to 163480 pulse signals, yielding a minimum angular resolution of 7.9 arcseconds, which meets the angular accuracy requirements of the UAV-borne lidar system.
4
Model validation
We first simulated water signals and compared them with lidar equation results for model theoretical validation, then simulated the underwater target signals and compared them with the measured profiles to verify the function of the photon’ s interaction with target in the model.
4.1 Comparison with lidar equation
The oceanic lidar equation has been broadly applied to validate various lidar signal simulators [ 47, 49 ]. The depthdependent lidar return signal of the lidar equation is [ 42, 43 ]
N s ðz w Þ ¼ E hm A ð Þ OT 2 2 a T 2 s c vDt p g oe
n w H þ z w
g qe b p ðz w Þexp �2
Z zw
0
� K lidar z 0 0 dz; ð19Þ
where z w = z � H is water depth in this study, Ns is the received signal, E is the laser energy for one pulse, O is the overlap factor, Dt p is the pulse width, T a is the transmission of atmosphere, v is the frequency of the laser, b p( z) is where c total( z w) is the extinction coefficient, D w( z w) isthe lidar spot diameter at different water depth, K d( z w) isthe diffuse attenuation coefficient.
Because of the limitation of lidar equation in dealing with multiple scattering, the water environment has to be as clean as possible to reduce multiple scattering. Referring to Morel’ s research, we choose the simulation seawater from the South Pacific anticyclonic gyre( SPG) which is oligotrophic and the“ clearest” [ 57 ]. Figure 6a shows the chlorophyll concentration profile of SPG water, and the calculated inherent optical properties based on the chlorophyll concentration [ 43, 57 – 62 ].
The relative error used here, which describes how closely the simulated signals match the lidar equation signal, is as follows j d ¼ X s � X R j
100 %; ð21Þ
X R
where X S is the simulated value, and X R is the result of lidar equation. We take the mean relative error at 100 m intervals for statistics. We set the number of photons to 10 7 and take the average results of five simulations for comparison. For simplicity, the MC simulation result and the lidar equation result are normalized based on their respective sea surface signals.
Figure 6b compares the normalized lidar return signals from the lidar equation and the MCT model. A strong agreement between the two results is shown over most depth ranges, indicating the MCT model can accurately reproduce the expected lidar signal attenuation behavior. Slight deviations appear at the deeper water layers, which can be attributed to the cumulative effects of multiple scattering. These effects are inherently captured by the MCT model but simplified in the analytical lidar equation. These deviations can be further characterized through quantitative analysis. The mean relative error is less than 5 % within a depth of 50 m and increases to approximately 19.4 % at a depth of 100 m. Overall, these results demonstrate that the proposed MCT model achieves high accuracy while providing a more comprehensive and physically realistic description of underwater lidar signal propagation.
4.2 Experiment validation
The measurement experiments of SOL were conducted in the Thousand-Island Lake, Zhejiang province, China. The mean depth of the Thousand-Island Lake is about 34 m, and the maximum depth is more than 100 m. We chose the area near the Gangkou Bridge between two groups of mountains as the experimental area( Fig. 7a). On this occasion, the wind disturbance can be drastically avoided, and the water surface is wide enough. The inherent optical properties of water were measured by Spectral Absorption and