Sci Rep. 2025 Jul 2;15(1):23664. doi: 10.1038/s41598-025-07694-z.
ABSTRACT
This study introduces new approach which combines the geometrical theory of diffraction (GTD) and the ray tracing (RT) method to analyze the produced scattering pattern due to a striking plane wave on a rough surface with random attributes regarding electromagnetic and statistical properties. The Fresnel equation-based model is utilized to determine the distribution of scattered power for both reflection from the region above the surface and transmission into the region beneath the surface. The polarization (direction of electric field) of the incident optical wave is also considered. The proposed algorithm addresses multi-bounce of striking ray, making it an advanced higher-order GTD-RT approach. The precision of the findings is validated by comparing them with scattering pattern data from empirical observations produced by a Radiant beam striking paper sheets with different roughness properties and different probabilistic characteristics. This study’s numerical results explore how the scattering pattern is influenced by surface degree of granularity, incidence angle, and light refraction coefficient of the rough surface. Additionally, first and second order scattering are calculated and compared. The second-order GTD-RT method provides slightly improved accuracy over the first-order method, especially for highly rough surfaces, but the enhancement remains marginal. Given its low average error (< 2.5%) and significantly lower computational cost, the first-order GTD-RT method offers a more practical and efficient solution for optical scattering analysis in rough surface scenarios. To validate the accuracy and reliability of the proposed model, a subset of the numerical results obtained in this study has been systematically compared with previously published findings derived using alternative analytical approaches, specifically the Geometrical Optics (GO) method and the second-order Kirchhoff approximation. These comparisons serve to highlight the consistency of the presented approach with established theoretical models and underscore its capability to accurately characterize the scattering behavior from rough surfaces under similar conditions.
PMID:40604003 | DOI:10.1038/s41598-025-07694-z
