Ana M. Rabal

Spectral and geometrical variation of the bidirectional reflectance distribution function of diffuse reflectance standards

A study on the variation of the spectral bidirectional reflectance distribution function (BRDF) of four diffuse reflectance standards (matte ceramic, BaSO(4), Spectralon, and white Russian opal glass) is accomplished through this work. Spectral BRDF measurements were carried out and, using principal components analysis, its spectral and geometrical variation respect to a reference geometry was assessed from the experimental data. Several descriptors were defined in order to compare the spectral BRDF variation of the four materials.

Spectral BRDF-based determination of proper measurement geometries to characterize color shift of special effect coatings

A reduced set of measurement geometries allows the spectral reflectance of special effect coatings to be predicted for any other geometry. A physical model based on flake-related parameters has been used to determine nonredundant measurement geometries for the complete description of the spectral bidirectional reflectance distribution function (BRDF). The analysis of experimental spectral BRDF was carried out by means of principal component analysis. From this analysis, a set of nine measurement geometries was proposed to characterize special effect coatings. It was shown that, for two different special effect coatings, these geometries provide a good prediction of their complete color shift.

Variables separation of the spectral BRDF for better understanding color variation in special effect pigment coatings

A type of representation of the spectral bidirectional reflectance distribution function (BRDF) is proposed that distinctly separates the spectral variable (wavelength) from the geometrical variables (spherical coordinates of the irradiation and viewing directions). Principal components analysis (PCA) is used in order to decompose the spectral BRDF in decorrelated spectral components, and the weight that they have at every geometrical configuration of irradiation/viewing is established. This method was applied to the spectral BRDF measurement of a special effect pigment sample, and four principal components with relevant variance were identified. These four components are enough to reproduce the great diversity of spectral reflectances observed at different geometrical configurations. Since this representation is able to separate spectral and geometrical variables, it facilitates the interpretation of the color variation of special effect pigments coatings versus the geometrical configuration of irradiation/viewing.

Color representation and interpretation of special effect coatings

A representation of the color gamut of special effect coatings is proposed and shown for six different samples, whose colors were calculated from spectral bidirectional reflectance distribution function (BRDF) measurements at different geometries. The most important characteristic of the proposed representation is that it allows a straightforward understanding of the color shift to be done both in terms of conventional irradiation and viewing angles and in terms of flake-based parameters. A different line was proposed to assess the color shift of special effect coatings on a*,b*-diagrams: the absorption line. Similar to interference and aspecular lines (constant aspecular and irradiation angles, respectively), an absorption line is the locus of calculated color coordinates from measurement geometries with a fixed bistatic angle. The advantages of using the absorption lines to characterize the contributions to the spectral BRDF of the scattering at the absorption pigments and the reflection at interference pigments for different geometries are shown.

Principal components analysis on the spectral bidirectional reflectance distribution function of ceramic colour standards

The Bidirectional Reflectance Distribution Function (BRDF) is essential to characterize an objects reflectance properties. This function depends both on the various illumination-observation geometries as well as on the wavelength. As a result, the comprehensive interpretation of the data becomes rather complex. In this work we assess the use of the multivariable analysis technique of Principal Components Analysis (PCA) applied to the experimental BRDF data of a ceramic colour standard. It will be shown that the result may be linked to the various reflection processes occurring on the surface, assuming that the incoming spectral distribution is affected by each one of these processes in a specific manner. Moreover, this procedure facilitates the task of interpolating a series of BRDF measurements obtained for a particular sample.

A single analytical model for sparkle and graininess patterns in texture of effect coatings.

Flakes in effect coatings, which are responsible for its color shift, are not perfectly horizontally oriented, producing a non uniform texture when observed from a distance of around one meter or less. If the coating is illuminated by a diffuse source, a granular appearance is observed, called graininess. But when the coating is illuminated by unidirectional light, some luminous spots on a dark background appear, effect that is known as sparkle. The characterization of these two textures is getting more important for automotive industry because of the high percentage of cars with effect coatings and because improvements in imaging technology allows this effect to be measured by, for instance, commercial instruments as BYK-mac. A single analytical model to understand and radiometrically characterize both sparkle and graininess in effect coatings is presented and studied in this work. It allows both patterns to be explained and, despite its simplicity, includes variables related to the optical system (Point Spread Function (PSF) and size of the entrance pupil), its distance to the coating, the diffusion grade of the illumination, the illumination and observation directions, and coating parameters.

Bidirectional reflectance distribution function of diffuse reflectance standards around the retro-reflection direction

The increase in the bidirectional reflectance distribution function around the retro-reflection direction was characterized for four common diffuse standard reflectance materials: Spectralon, matte white Russian opal glass, matte white ceramic standard and pressed barium sulphate (BaSO4) powder. The characterized increase or surge is high enough to be considered in low-uncertainty reflectance factor measurements, where the values are usually extrapolated around that direction due to instrumental limitations. In order to make the corrections for this surge, the coherent backscattering of light model and a much simpler exponential function were fitted to the measurements.