Objective  The traditional LiDAR system operates at a single wavelength, which limits the acquisition of target attribute information. The spectral information captured by laser backscatter intensity is relatively insufficient, and the detection ability of ground object categories is also limited. Hyperspectral LiDAR, on the other hand, is an active remote sensing method that can obtain spectral and spatial information of targets simultaneously. In addition to 3D coordinates, hyperspectral LiDAR also records the backscatter intensity of each point, enabling the detection of the geometric and reflection characteristics of targets. However, the backscatter intensity of the laser is affected by multiple factors during scanning, making it unsuitable for directly reflecting the reflection characteristics of the target surface. One of the most crucial factors is the laser incidence angle. In practical applications, there are few complete Lambertian targets, and the reflection characteristics of the scanned objects are very complex. Moreover, the roughness of the scanned target deviates from the Lambertian model. Therefore, considering the roughness and micro-structure of the target surface, this study proposes a BRDF model for rough surfaces based on the backscatter intensity of hyperspectral LiDAR through the combination of bidirectional reflection distribution function (BRDF) and radar equation.

  Methods  This paper proposes a BRDF model based on the Oren-Nayar model for rough surfaces to address the effect of incident angle on the backscatter intensity data of hyperspectral LiDAR. The hyperspectral LiDAR system comprises key components such as a laser transmitting unit, a laser receiving unit, a scanning and control unit. By combining theory with experiments, eight typical rough targets were selected to analyze the relationship between backscatter intensity and incident angle of hyperspectral LiDAR and quantify the effect of surface roughness on intensity. The radiometric correction method for the incident angle effect was studied based on the constructed model.

  Results and Discussions   The incident angle of the laser has a significant effect on the backscatter intensity of the original record, and the intensity decreases with the increase of the incident angle. For the white paper sample, the curve of the backscatter intensity of 21 wavelengths with the incident angle shows a trend similar to the cosine function. However, the changing trend of other samples deviates from the Lambertian model to varying degrees. After radiometric correction based on the constructed model, the standard deviation of reflectance at different angles was no more than 0.06, and the average improvement rate of the standard deviation was 67.86% compared to before correction. The proposed model exhibited higher correction accuracy than the Lambertian model. The results show that the proposed method successfully eliminates the influence of the incident angle of hyperspectral LiDAR.

  Conclusions  In this study, we analyze the relationship between the backscatter intensity of hyperspectral LiDAR and the incident angle for rough surfaces. We construct a BRDF model that considers target roughness by combining the Oren-Nayar model with the radar equation. By quantitatively calculating the standard deviation of the slope of the rough surface, we establish an accurate radiometric correction model. This correction model enables us to effectively eliminate the impact of incident angles on reflectance. We selected eight typical rough samples for experiments and obtained experimental results at different incident angles. These results show that the backscatter intensity of the hyperspectral LiDAR does not completely follow the Lambertian model, especially for targets with large roughness. The larger the standard deviation of the slope is, the more the backscatter intensity deviates from the Lambertian model. The proposed correction model offers higher accuracy compared to the Lambertian model. The maximum improvement rate of the sample in the experiment is 80.95%, and the average improvement rate for all samples is 67.86%. Our study opens up new prospects for improving the accuracy of point cloud segmentation and classification based on the hyperspectral LiDAR. The quantitative calculation of roughness also provides new ideas for feature extraction of point clouds. This proposed method offers an effective solution for the radiometric correction of incident angle effects of hyperspectral LiDAR and provides a good physical basis for data analysis and application.