Quantifying the validity conditions of the Beckmann-Kirchhoff scattering model
Quantifying the validity conditions of the Beckmann-Kirchhoff scattering model
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DOI：
10.1117/12.2639003
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
Helia Hooshmand;Mingyu Liu;R. Leach;S. Piano
中科院分区：
文献类型：
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作者：
Helia Hooshmand;Mingyu Liu;R. Leach;S. Piano
近似方法和严格方法被广泛用于模拟表面的光散射。边界元方法(BEM)是一种考虑极化和多次散射效应的严格模型。边界元适用于模拟具有复杂几何形状的曲面的散射光，这些曲面包含悬挑和折入特征。Beckmann-Kirchhoff(BK)散射模型是一种近似模型，可以用来预测慢变表面的散射行为。虽然近似BK模型不能应用于产生多次散射效应的复杂表面几何形状，但由于其快速和简单的实现，已被用于模拟散射场。虽然许多近似模型仅限于高度变化相对较小的表面特征(通常不到入射光波长的一半)，但BK模型可以预测高度变化较大的表面的光散射，只要表面是具有小曲率的“局部平坦的”。到目前为止，已经尝试确定BK模型的有效性条件。基本的有效性条件是，任何表面不规则性的曲率半径都应该明显大于光的波长。然而，要获得BK模型最准确的结果，量化有效性条件是至关重要的。这项工作的目的是根据不同的表面规格，如坡度和曲率，量化BK模型的有效性条件。为此，用边界元模型和BK模型模拟了不同正弦分布的散射场，并比较了它们的差异。结果表明，BK模型在存在大倾角和大曲率时失效，并对这些条件进行了量化。
Approximate and rigorous methods are widely used to model light scattering from a surface. The boundary element method (BEM) is a rigorous model that accounts for polarisation and multiple scattering effects. BEM is suitable to model the scattered light from surfaces with complex geometries containing overhangs and re-entrant features. The Beckmann- Kirchhoff (BK) scattering model, which is an approximate model, can be used to predict the scattering behaviour of slowlyvarying surfaces. Although the approximate BK model cannot be applied to complex surface geometries that give rise to multiple scattering effects, it has been used to model the scattered field due to its fast and simple implementation. While many of the approximate models are restricted to surface features with relatively small height variations (typically less than half the wavelength of the incident light), the BK model can predict light scattering from surfaces with large height variations, as long as the surfaces are “locally flat” with small curvatures. Thus far, attempts have been made to determine the validity conditions for the BK model. The primary validity condition is that the radius of curvature of any surface irregularity should be significantly greater than the wavelength of the light. However, to have the most accurate results for the BK model, quantifying the validity conditions is critical. This work aims to quantify the validity conditions of the BK model according to different surface specifications, e.g., slope angles and curvatures. For this purpose, the scattered fields from various sinusoidal profiles are simulated using the BEM and the BK models and their differences are compared. The result shows that the BK model fails when there are high slope angles and large curvatures, and these conditions are quantified.