Modeling the Angular Dependence of Emissivity of Randomly Rough Surfaces

Abstract

Directional emissivity (DE) describes how the emissivity of an isothermal surface changes with viewing angle across thermal infrared wavelengths. The Oxford Space Environment Goniometer (OSEG) is a novel instrument that has been specifically designed to measure the DE of regolith materials derived from planetary surfaces. The DE of Nextel high‐emissivity black paint was previously measured by the OSEG and showed that the measured emissivity decreases with increasing emission angle, from an emissivity of 0.97 ± 0.01 at 0° emission angle to an emissivity of 0.89 ± 0.01 at 71° emission angle. The Nextel target measured was isothermal (<0.1 K surface temperature variation), and the observed change in emissivity was due to Fresnel‐related effects and was not due to nonisothermal effects. Here we apply several increasingly complex modeling techniques to model the measured DE of Nextel black paint. The modeling techniques used here include the Hapke DE model, the Fresnel equations, a multiple slope Fresnel model, and a Monte Carlo ray tracing model. It was found that only the Monte Carlo ray tracing model could accurately fit the OSEG measured Nextel data. We show that this is because the Monte Carlo ray tracing model is the only model that fully accounts for the surface roughness of the Nextel surface by including multiple scattering effects.

Comment on "Collision and radiative processes in emission of atmospheric carbon dioxide"

“…The analysis of Smirnov, as well as ours, has considered the simple case of radiative transfer in a perpendicular direction to Earth's surface, assuming a homogeneous column of air, and the isotropy of Blackbody radiation from Earth. This last assumption is confirmed by other authors [18,19], however, the former simplifications induce a few errors: For example if we assume a perpendicular direction for radiative transfer, we are underestimating the length for the column of air for the rays more tangential to the Earth's surface (as seen at sunset when only radiation from the red part of the sun's spectrum is transmitted). One may then carry out a more exact ray-tracing calculation using [20]:…”

Spectral Characterization of Bennu Analogs Using PASCALE: A New Experimental Set‐Up for Simulating the Near‐Surface Conditions of Airless Bodies

“…SLEC's lamp has a 30° incidence angle while PASCALE's lamp has a 55° incidence angle. Recent work by Warren et al (2019) has shown that the emissivity of a randomly rough surface has an angular dependence, which suggests that the observed SAE spectral differences might be related to the different lamp geometries. Since the SLEC and PASCALE measurements are a first of their kind, further SAE measurements of the CV and CM meteorites are needed to better understand the observed contrast enhancements in the SLEC spectra.…”

Electric Transverse Emissivity of Sinusoidal Surfaces Determined by a Differential Method: Comparison with Approximation of Geometric Optics

“…For a fixed height h of the grating, by increasing the geometric period so as to make the emissivity tends β towards zero, the emissivity should tend towards that of the smooth flat surface in the direction 10 °. is is of the order of 0.23 as shown by the calculation using Fresnel formulas [34][35][36][37][38][39][40][41][42]. is appears clearly in Figure 1 where the angle β reaches 0.5 °for d/λ equal to 20.5 and h � 0.1λ On the other hand, for h equal to 1λ (Figure 1(b)) only the last four values of (32 °, 17.35 °, 8.88 °, and 5.57 °), translate this agreement is translated.…”