Data-driven algorithm to classify the degree of isotropy in the bidirectional reflectance distribution function

Anne W Werkley,Todd V Small,Michael A Marciniak,Samuel D Butler

doi:10.1117/1.oe.60.9.094108

Abstract

The bidirectional reflectance distribution function (BRDF) is used to describe reflectances of materials by calculating the ratio of the reflected radiance to the incident irradiance. While it was found that the isotropic models maintained symmetry about ϕs = π, such symmetry was not maintained about the θs = θi axis, except for close to the specular peak. This led to the development of a data-driven metric for how isotropic a BRDF measurement is. Research efforts centered around developing an algorithm that could determine material anisotropy without having to fit to models. This algorithm was tested using high fidelity data (containing off-axis BRDFs), which was collected via a modified Complete Angle Scatter Instrument (CASI®) with a CCD array detector. The algorithm accurately characterized the degree of isotropy for four out of five materials and worked for cases where the BRDF is higher than 100 sr − 1. This algorithm is intended to improve BRDF characterization, and the applications of light curve analysis, scene generation, and remote sensing.

Highlights

The bidirectional reflectance distribution function (BRDF) is a description of the ratio of the reflected radiance to the incident irradiance,[1] f ðω^ ; ω^ ; λÞ 1⁄4 dLdEðω^ðω^; ω^; λ;ÞλÞ ; EQ-TARGET;temp:intralink-;e001;116;327 r i s ri s ii (1)where fr is the BRDF, ω^ i is the incident vector with respect to the material’s surface normal, ω^ s is the “scattered” vector, Lr is the reflected radiance, Ei is the incident irradiance, and λ is the respective wavelength
We show that the BRDF is crucial to describe the reflected radiance in applications such as scene generation and remote sensing
X and y center of each contour, the full width half maximum (FWHM) of the data against Δα, and the eccentricity of each contour centered about the peak BRDF value

Summary

Introduction

The bidirectional reflectance distribution function (BRDF) is a description of the ratio of the reflected radiance to the incident irradiance,[1] f ðω^ ; ω^ ; λÞ 1⁄4 dLdEðω^ðω^; ω^; λ;ÞλÞ ; EQ-TARGET;temp:intralink-;e001;116;327 r i s ri s ii (1)where fr is the BRDF, ω^ i is the incident vector with respect to the material’s surface normal, ω^ s is the “scattered” vector, Lr is the reflected radiance, Ei is the incident irradiance, and λ is the respective wavelength. The bidirectional reflectance distribution function (BRDF) is a description of the ratio of the reflected radiance to the incident irradiance,[1] f ðω^ ; ω^ ; λÞ 1⁄4 dLdEðω^ðω^; ω^; λ;ÞλÞ ; EQ-TARGET;temp:intralink-;e001;116;327 r i s ri s ii (1). Where Ls is the scattered radiance, Li is the incident radiance, Le is the emitted radiance, and Ωþ represents the incident hemisphere We show that the BRDF is crucial to describe the reflected radiance in applications such as scene generation and remote sensing. BRDF is commonly represented using either physical optics models or microfacet models. The microfacet models use a geometric optics approximation to reduce computational complexity, making modeling BRDF more feasible for most applications, including light curve analysis[3]

Methods

Results

Conclusion