The emissivity is an important surface property parameter in many fields, including infrared temperature measurement. In this research, a symmetry theoretical model of directional spectral emissivity prediction is proposed based on Gaussian random rough surface theory. A numerical solution based on a matrix method is determined based on its symmetrical characteristics. Influences of the index of refraction n and the root mean square (RMS) roughness σ_rms on the directional spectrum emissivity ε are analyzed and discussed. The results indicate that surfaces with higher n and lower σ_rms tend to have a peak in high viewing angles. On the contrary, surfaces with lower n and higher σ_rms tend to have a peak in low viewing angles. Experimental verifications based on infrared (IR) temperature measurement of Inconel 718 sandblasted surfaces were carried out. This model would contribute to understand random rough surfaces and their emitting properties in fields including machining, process controlling, remote sensing, etc.

中文翻译：

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用矩阵法对随机粗糙表面的定向谱发射率及其模式进行理论建模和分析

发射率是许多领域的重要表面特性参数，包括红外测温。本研究基于高斯随机粗糙表面理论，提出了定向光谱发射率预测的对称性理论模型。基于矩阵法的数值解是根据其对称特性确定的。分析和讨论了折射率n和均方根 (RMS) 粗糙度σ _rms对定向光谱发射率ε的影响。结果表明，具有较高n和较低σ _{rms 的}表面往往在高视角下具有峰值。相反，具有较低 n 和较高σ _rms往往在低视角下出现峰值。对 Inconel 718 喷砂表面进行了基于红外 (IR) 温度测量的实验验证。该模型将有助于理解随机粗糙表面及其在加工、过程控制、遥感等领域的发射特性。