Introduction to material measurements : from theory to rendering
by Chloé Therreau
OceanTM is a realistic renderer that, based on 3D and material data, provides predictive render. OceanTM can deal with a large panel of tabulated material data, either theoretical or measured.
In case of surface characterization, Bidirectional Reflectance Distribution function (BRDF) describes, in one point, how light is diffused or reflected by the surface, for each angle and for each wavelength.
As shown in figure 1, BRDF can be described by different contributions : a diffuse, glossy and specular component. Diffuse surface scatters light in all direction. Glossy surface scatters light in preferred directions. Perfect specular surface, such as mirror for example, scatters incident light in a single outgoing direction. Real materials usually have BRDF which are a combination of those three categories.
Car paints have the specificity to have complex appearance, in particular, due to the use of flakes inside those paints. Flakes’ properties will introduce a complex glossy component to the appearance. In order to propose predictive appearance image, laboratory measurements of car paint can be done and implemented into OceanTM.
Figure 1 - BRDF principle description
BRDF MEASUREMENTS AND IMPLEMENTATION INTO OCEAN™
In this example, a green car paint sample is studied. A photography of the sample is presented in figure 2, with artificial (a) and natural (b) light. The sample has a light uniform green color with visible fine flakes and clear vernish.
Figure 2 - Sample photography with artificial (a) and natural (b) light (move your mouse over the image to see a zoom version)
BRDF measurements are often made using a gonio-spectrophotometer. A spectrophotometer allows for the measurement of the reflection properties of a material as a function of wavelength. The term “gonio”, from the ancient Greek “gonia” meaning “angle”, indicated that this measurement can be done for different angles, allowing the measurement of the different BRDF components. As shown in figure 3, the sample is exposed to a light in a given direction and the reflection properties of the surface is measured by the spectrophotometer in several out-going direction. Usually, the two zenithal angles (the one between the sample and the light direction, θin, and the one between the sample and the detector, θout, see figure 3) are varying.
Figure 3 - Gonio spectrophotometer measurements principle.
An example of measurements, made on the green car paint with a commercial gonio-spectrophotometer is shown in the animation in figure 4. The measurement of the reflection (r [∅]) is shown for each wavelength (shown in the colorbar), as a function of , for each . The diffuse part of the BRDF is clearly visible and already shows that the sample is green (green is the most reflected color, with the largest r). The glossy part is also visible around the existing angle, and is approximately 20° wide. Because of measurement limitation when using a gonio-spectrophotometer, the specular contribution is determined with a spectrophotometer that include an integrating sphere. Finally, the properties of flakes is measured with a specific, non-commercial, device and will not be discussed here.
Figure 4 - BRDF measurements. The right plot is part of the animation on the left side and allow for the description of the measurement.
INTEGRATION IN OCEAN™
We have measured our sample with three different devices and we now need to implement these into OceanTM. OceanTM is able to directly read and import BRDF data thanks to the BSDF converter toolbox, shown in figure 5 (BSDF is equivalent to BRDF but including both reflection and transmission of the considering material). This toolbox allows for splitting the BSDF into diffuse, glossy and specular components, using an advanced algorithm. The angular specular/glossy and glossy/diffuse angular limits may be adjusted, highlighted by the green square in figure 5. When this option is used, the created BSDF is of Additive BSDF type, shown in figure 6, with child BSDFs corresponding to each component (i.e. specular, glossy and diffuse). The specular component was measured thanks to the integrating sphere measurement, while the flakes properties measurements can be add as a contribution to the glossy component of the BRDF. The "Sparkily" BRDF includes sparkles properties, while gonio-spectrophotometer measurements are saved into the Rusinkiewicz tables (used for the glossy and diffuse components).
Figure 5 - Screen capture of the BSDF Converter tool in OceanTM. The green square highlights the option that allows to split the imported BRDF. The red square highlights the parameters that defined the sampling resolution of the imported BRDF.
Figure 6 - Screen capture of the Additive BRDF created by the BSDF converter tools.
The “H Steps / D steps” parameters seen in figure 5 (red square) define the sampling resolution of the imported BSDF, as described in the Rusinkiewicz coordinates system. It is crucial here to not propose a too small or too large sampling resolution when importing BSDF. Indeed, as shown in figure 7, an over sampling (too small H and D steps) will result into an unphysical black lines, while an under sampling (too large H and D steps) will result into an unphysical black blurs. The upper part of figure 7 shows the BRDF measurement made with the gonio-spectrophotometer in the Rusinkiewicz coordinates system. The color bar indicated the intensity of the measured reflection.
Figure 7 - Simulation of the car paint as a function of the sampling resolution chosen when importing the BRDF
RESULTS OF THE SIMULATION
Results of the simulation of the sample are shown in figures 8. An in-situ simulation is proposed and shown in the left. The light green color and sparkles are visibles, in particular in the right image where a zoom of the sample is provided. The light green color and sparkles sizes are closed to reallity. A quantitative study of the sample was made and shaw a good agreement between simulation and physical sample. This study is not shown here as it is not the goal of this article.
Figure 8 - Left: Simulation result using the green car paint. Right : Zoom allowing to see the small sparkles.
Figure 9 - In situ simulation made using the measured car paint
In this article, the study of a car paint is proposed. This material has the particularity to have a complex light reflectance behavior, described by its BRDF. Measurements, in particular using a gonio-spectrophotometer, are used and imported into OceanTM, showing a good agreement, in term of image and colorimetry, between real sample and renders.
 Integrating sphere is an optical device with diffusely reflecting inner surface. Input light is then spread over the entire surface of the sphere. By measuring the quantity of light reflected or transmitted by a sample into the sphere, accurate and non-angular dependent reflectance or transmittance measurement can be provided.
 Rusinkiewicz coordinates system was proposed by Szymon Rusinkiewicz in 1998 and which allows for a more efficient BSDF storage. See https://www.cs.princeton.edu/~smr/papers/brdf_change_of_variables/brdf_change_of_variables.pdf