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    This study introduces a precise 3D geometrical attenuation factor formulation for Gaussian random rough surfaces. This improves bidirectional reflectance distribution function (BRDF) models, especially near grazing angles.

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    Area of Science:

    • Optics and Photonics
    • Surface Science
    • Computer Graphics

    Background:

    • Accurate bidirectional reflectance distribution function (BRDF) models are crucial for realistic rendering and optical simulations.
    • Existing geometrical attenuation factor calculations often oversimplify surface topography, neglecting key micro-scale effects.
    • This leads to inaccuracies, particularly under grazing illumination conditions.

    Purpose of the Study:

    • To develop a more precise three-dimensional (3D) geometrical attenuation factor formulation.
    • To address limitations in conventional BRDF models by incorporating micro-surface correlations and self-shadowing.
    • To enhance the accuracy of BRDF models, especially for non-ideal viewing and lighting geometries.

    Main Methods:

    • Development of a novel 3D geometrical attenuation factor formulation based on 3D Gaussian random rough surfaces.
    • Numerical analysis to evaluate the proposed formulation.
    • Comparison with conventional methods to highlight improvements in precision.

    Main Results:

    • The proposed 3D formulation accurately accounts for the correlation between height and slope on rough surfaces.
    • It effectively models self-shadowing and self-masking effects on micro-surfaces.
    • Numerical results demonstrate significantly improved precision compared to traditional methods, particularly near grazing angles.

    Conclusions:

    • The novel 3D geometrical attenuation factor formulation provides a more accurate representation of surface interactions.
    • This advancement enables the construction of more complete and realistic BRDF models.
    • The findings are particularly valuable for applications requiring high fidelity rendering and optical analysis under challenging illumination conditions.