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

Abstract

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.

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

“…In order to accomplish this multivariate task, we resorted to PCA, whose ability to extract this kind of data patterns had been demonstrated in previous works [20,21]. Using this technique in combination with the physical model, it is possible to estimate the color of a coating for any geometry from the measurements at a small number of proper geometries.…”

“…In the previous paper mentioned above [21], the measurement and representation of the BRDF of the special-effect pigment material Colorstream T20-02 WNT Arctic Fire was thoroughly discussed [25]. The spectral BRDF was sampled at 448 different measurement geometries, each one of them corresponding to a specific combination of θ i and θ s (which take values ranging from 0°to 70°at steps of 10°), ϕ i (which takes only the value 0°), and ϕ s (which takes values ranging from 0°to 180°, at steps of 30°).…”

“…In a previous paper [21], the authors showed that, using a procedure based on PCA, it was possible to express the spectral BRDF of a special-effect pigment coating as a sum of components, in such a way that spectral and geometrical variables are separated:…”

“…The analysis of experimental spectral BRDF data was made without prior colorimetric simplification: the variation across the different geometries of colorimetric values, such as lightness, hue, or chroma had not been not previously studied; only the variation of the corresponding set of BRDF spectra had been analyzed from a strictly optical and mathematical point of view. In order to accomplish this multivariate task, principal components analysis (PCA) was used, whose ability to extract patterns out of this kind of data had been already proven in previous works [20,21]. PCA distinctly separates the spectral variable (wavelength) from the geometrical variables (spherical coordinates of the irradiation and viewing directions) by decomposing the spectral BRDF in decorrelated spectral components.…”

Color representation and interpretation of special effect coatings

“…This estimation is accomplished by using a principal components analysis (PCA) procedure [24,25] to determine the spectral reflectance of a representative flake and the orientation distribution of the flakes [D (θ flake )] [23]. It corroborated that the flake-based perspective is highly important to understand the color shift of special effect coatings.…”