Samuel D. Butler

Comparison of microfacet BRDF model to modified Beckmann-Kirchhoff BRDF model for rough and smooth surfaces.

A popular class of BRDF models is the microfacet models, where geometric optics is assumed. In contrast, more complex physical optics models may more accurately predict the BRDF, but the calculation is more resource intensive. These seemingly disparate approaches are compared in detail for the rough and smooth surface approximations of the modified Beckmann-Kirchhoff BRDF model, assuming Gaussian surface statistics. An approximation relating standard Fresnel reflection with the semi-rough surface polarization term, Q, is presented for unpolarized light. For rough surfaces, the angular dependence of direction cosine space is shown to be identical to the angular dependence in the microfacet distribution function. For polished surfaces, the same comparison shows a breakdown in the microfacet models. Similarities and differences between microfacet BRDF models and the modified Beckmann-Kirchhoff model are identified. The rationale for the original Beckmann-Kirchhoff F(bk)(2) geometric term relative to both microfacet models and generalized Harvey-Shack model is presented. A modification to the geometric F(bk)(2) term in original Beckmann-Kirchhoff BRDF theory is proposed.

Comparison of microfacet BRDF model elements to diffraction BRDF model elements

A popular class of BRDF models is the microfacet model, where geometric optics is assumed, but where physical optics effects such as accurate wavelength scaling, important to Hyperspectral Imagery, are lost. More complex physical optics models may more accurately predict the BRDF, but the calculation is time-consuming. These seemingly disparate approaches are compared in detail. The linear systems direction cosine space is compared to microfacet coordinates, and the microfacet models Fresnel reflection in microfacet coordinates is compared to diffraction theory’s Fresnel-like term. Similarities and differences between these terms are highlighted to merge these two approaches to the BRDF.

Robust categorization of microfacet BRDF models to enable flexible application-specific BRDF adaptation

Since the development of the Torrance-Sparrow bidirectional re ectance distribution function (BRDF) model in 1967, several BRDF models have been created. Previous attempts to categorize BRDF models have relied upon somewhat vague descriptors, such as empirical, semi-empirical, and experimental. Our approach is to instead categorize BRDF models based on functional form: microfacet normal distribution, geometric attenua- tion, directional-volumetric and Fresnel terms, and cross section conversion factor. Several popular microfacet models are compared to a standardized notation for a microfacet BRDF model. A library of microfacet model components is developed, allowing for creation of unique microfacet models driven by experimentally measured BRDFs.

Experimental analysis of bidirectional reflectance distribution function cross section conversion term in direction cosine space

Of the many classes of bidirectional reflectance distribution function (BRDF) models, two popular classes of models are the microfacet model and the linear systems diffraction model. The microfacet model has the benefit of speed and simplicity, as it uses geometric optics approximations, while linear systems theory uses a diffraction approach to compute the BRDF, at the expense of greater computational complexity. In this Letter, nongrazing BRDF measurements of rough and polished surface-reflecting materials at multiple incident angles are scaled by the microfacet cross section conversion term, but in the linear systems direction cosine space, resulting in great alignment of BRDF data at various incident angles in this space. This results in a predictive BRDF model for surface-reflecting materials at nongrazing angles, while avoiding some of the computational complexities in the linear systems diffraction model.

Grazing angle experimental analysis of modification to microfacet BRDF model for improved accuracy

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.

Wave optics simulation of statistically rough surface scatter

The bidirectional reflectance distribution function (BRDF) describes optical scatter from surfaces by relating the incident irradiance to the exiting radiance over the entire hemisphere. Laboratory verification of BRDF models and experimentally populated BRDF databases are hampered by sparsity of monochromatic sources and ability to statistically control the surface features. Numerical methods are able to control surface features, have wavelength agility, and via Fourier methods of wave propagation, may be used to fill the knowledge gap. Monte-Carlo techniques, adapted from turbulence simulations, generate Gaussian distributed and correlated surfaces with an area of 1 cm2 , RMS surface height of 2.5 μm, and correlation length of 100 μm. The surface is centered inside a Kirchhoff absorbing boundary with an area of 16 cm2 to prevent wrap around aliasing in the far field. These surfaces are uniformly illuminated at normal incidence with a unit amplitude plane-wave varying in wavelength from 3 μm to 5 μm. The resultant scatter is propagated to a detector in the far field utilizing multi-step Fresnel Convolution and observed at angles from −2 μrad to 2 μrad. The far field scatter is compared to both a physical wave optics BRDF model (Modified Beckmann Kirchhoff) and two microfacet BRDF Models (Priest, and Cook-Torrance). Modified Beckmann Kirchhoff, which accounts for diffraction, is consistent with simulated scatter for multiple wavelengths for RMS surface heights greater than λ/2. The microfacet models, which assume geometric optics, are less consistent across wavelengths. Both model types over predict far field scatter width for RMS surface heights less than λ/2.

Experimentally validated modification to Cook-Torrance BRDF model for improved accuracy.

The BRDF describes optical scatter off realistic surfaces. The microfacet BRDF model assumes geometric optics but is computationally simple compared to wave optics models. In this work, MERL BRDF data is fitted to the original Cook-Torrance microfacet model, and a modified Cook-Torrance model using the polarization factor in place of the mathematically problematic cross section conversion and geometric attenuation terms. The results provide experimental evidence that this modified Cook-Torrance model leads to improved fits, particularly for large incident and scattered angles. These results are expected to lead to more accurate BRDF modeling for remote sensing.

Experimental measurement and analysis of wavelength-dependent properties of the BRDF

The microfacet BRDF model is preferred to describe reflectance in many applications due to its closed-form approximation to the BRDF which is relatively easy to use; however, it almost entirely excludes wavelength-dependent scaling of the reflectance distribution. To rectify this, the BRDF was measured at multiple incident angles and for multiple materials at several wavelengths between 3.39 μm and 10.6 μm. Results quantify the dramatic change in the specular BRDF of a variety of materials even after accounting for overall reflectance, and suggests it is necessary to modify the wavelength dependence in the microfacet model.

Analysis of wave optics BRDF model elements for a moderately rough surface

The bidirectional reflectance distribution function (BRDF) describes realistic scattering of light off materials. Microfacet BRDF’s often only describe one type of material and neglect wavelength effects. Wave-optics BRDF expressions, however, can describe wavelength effects at the expense of being more computationally cumbersome. Previous work relating wave-optics BRDF coordinates to micro-facet coordinates led to a complicated, but versatile, BRDF. In this work, the infinite summation found in the previous derivation is investigated, leading toward a closed-form BRDF model that describes wavelength-dependent effects for materials with various surface parameters, and which will be usable in remote sensing applications.

A novel image-based BRDF measurement system and its application to human skin

Human skin detection is an important first step in search and rescue (SAR) scenarios. Previous research performed human skin detection through an application specific camera system that ex- ploits the spectral properties of human skin at two visible and two near-infrared (NIR) wavelengths. The current theory assumes human skin is diffuse; however, it is observed that human skin exhibits specular and diffuse reflectance properties. This paper presents a novel image-based bidirectional reflectance distribution function (BRDF) measurement system, and applies it to the collection of human skin BRDF. The system uses a grid projecting laser and a novel signal processing chain to extract the surface normal from each grid location. Human skin BRDF measurements are shown for a variety of melanin content and hair coverage at the four spectral channels needed for human skin detection. The NIR results represent a novel contribution to the existing body of human skin BRDF measurements.