KEYWORDS: Error analysis, Data modeling, Mid-IR, Polarization, Long wavelength infrared, Near infrared, Statistical modeling, Solids, Signal attenuation, Bidirectional reflectance transmission function
The bidirectional reflectance distribution function (BRDF) describes optical scattering off realistic surfaces. The microfacet BRDF, while computationally simple, lacks accuracy especially for grazing angles. An approximation, which replaces mathematically problematic elements of the microfacet model with the polarization factor from wave optics, has proved useful in accurately modeling the grazing region. We now expand upon this analysis by additionally varying the microfacet distribution function—a fundamental part of microfacet BRDF models. We find that after choosing the best microfacet distribution, 12 of the 18 materials studied show a significant improvement in the BRDF fit at grazing angles using the proposed approximation. Additionally, there was one case for which the approximation produced a model statistically tied for best within the experimental uncertainty of the data. The remaining five materials have significant sources of error outside the grazing region and will be further studied in future work.
The bidirectional reflectance distribution function (BRDF) describes material reflectance by relating incident irradiance to scattered radiance. One popular class of BRDF models is the microfacet model, which assumes geometric optics but is more readily applicable to remote sensing. One drawback of this geometric optics model is the need for a cross section conversion term, which diverges at grazing angles. This problem is only partially addressed by adding a geometric attenuation term to conserve energy, while still neglecting wave optics effects. Based on previous work comparing microfacet and wave optics models, Butler proposed to replace the geometric attenuation and cross-section conversion terms with a theoretical approximation, the closed-form polarization factor, Q. Analysis presented both at Optics and Photonics by Butler in 2017 and SPIE Defense and Commercial Sensing (DCS) by Ewing in 2018 show this modification to be effective for both high density (but low fidelity) data, and low density (but high fidelity) data, particularly at grazing angles, but that analysis only examined unpolarized data. In this work, the theoretical modification is analyzed using high fidelity, low density, in-plane polarimetric oblique and grazing angle BRDF data. These polarimetric data are fit to the novel version of the microfacet model for each polarization separately, using the polarization factor Q, and the error in the fits are compared to the unpolarized fits that were presented at SPIE DCS. These results suggest incorporating the polarization factor to improve the quality of fit consistently for materials, including substantial improvement at grazing angles.
The BRDF describes optical scatter off realistic surfaces. The microfacet BRDF model assumes geometric optics but is computationally simple compared to wave optics models. Previously, densely-sampled MERL BRDF data for several materials was analyzed using a novel variation of a microfacet BRDF that used a polarization factor in place of the cross section conversion and geometric attenuation terms, demonstrating improved accuracy. This paper extends that analysis to examine high-fidelity grazing angle BRDF data measured in-plane with the novel BRDF modification. Results indicate that for many materials the novel BRDF modification is more accurate than the Traditional Cook-Torrance BRDF at near grazing angles. We show as much as an order of magnitude improvement in the fit error using this novel BRDF modification. These results are expected to lead to more accurate BRDF modeling for remote sensing, computer graphics, and scene generation.
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