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

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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.

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Abbreviations

f r :

Bidirectional reflectance distribution function (BRDF)

p :

Gaussian distribution function

R :

(Directional-hemispherical) reflectance of rough surfaces

R 0 :

(Directional-hemispherical) reflectance of smooth surfaces

w :

Root-mean-square slope, \( w = \sqrt 2 \upsigma /\uptau \)

θi :

Zenith angle of incidence

λ:

Wavelength in vacuum

ξ:

Height of surface roughness

σ:

Root-mean-square roughness

τ:

Autocorrelation length

ψ:

Local incidence angle

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Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Korea government (MSIT) (Nos. 2016R1A2B4012875 and 2018M1A3A3A02065823).

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  1. School of Mechanical Engineering, Kookmin University, Seoul, 02707, Republic of Korea

    H. J. Lee

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Lee, H.J. Simple Regression Model for Estimating Reflectance Reduction due to Random Surface Roughness. Int J Thermophys 40, 55 (2019). https://doi.org/10.1007/s10765-019-2523-3

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