Simple Regression Model for Estimating Reflectance Reduction due to Random Surface Roughness

Abstract

Radiative properties of rough surfaces differ from those of smooth surfaces due to their tendency to scatter electromagnetic waves. Accurate evaluation of property change of rough surfaces requires theoretical background and numerical techniques for solving the scattering of electromagnetic waves, which is challenging and time-consuming. Therefore, this study proposes a simple regression model for estimating the reflectance reduction due to random surface roughness. Because reflectance reduction is significant when multiple reflections occur due to large surface roughness, a Monte Carlo ray-tracing (MCRT) method based on geometric optics approximation was used to evaluate reflectance reduction. Then, a regression analysis based on the numerical results of the MCRT method was implemented. A regression equation was derived as a function of the smooth-surface reflectance and a roughness slope parameter. For silicon and aluminum surfaces, the results of the proposed regression model agreed with those obtained using the MCRT method under 4.4 % error limit. Hopefully, the proposed model can be used to easily bridge between radiative properties of rough surfaces and statistics of surface roughness without relying on laborious numerical techniques for light scattering problems.