Making sense of measurement geometries for multi‐angle spectrophotometers

Abstract

We have developed new parameters that help to interpret multi‐angle reflection data. By expressing measurement geometries in terms of so‐called flake‐based parameters, a physical explanation is given for several well‐known colorimetric characteristics of effect coatings. The new concepts are based on expressing angles with respect to the normal vector of flakes, instead of the conventional usage of the coating normal as a reference. We discuss and give physical explanations for the usefulness and limitations of previously defined concepts such as aspecular angle, cis‐ versus trans‐geometries, interference lines and aspecular lines. For example, it is known that the trans‐15° geometry has added value next to the cis+15° geometry when samples are analyzed that contain colored effect pigments with large color travel, such as Colorstream, Chromaflair, or chromatic Xirallic pigments. Our results demonstrate and explain why there is much less added value in the case of samples that contain less striking chromatic effect pigments, such as metallic or mica‐based effect pigments, or “white” Xirallic pigments. Further, interference lines are shown to be suitable for characterizing effect pigments because they selectively sample the reflectance values of flakes as a function of the angle of incidence with respect to the flake normal. In another example, the similarity between an off‐plane measurement geometry and several in‐plane geometries is investigated. The results are clearly explained when referring to the corresponding values of the flake‐based parameters. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2012

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

“…Following the approach suggested by Kirchner and Cramer [19], the flake-related reflection phenomenon is modeled as shown in Fig. 2.…”

“…The light is reflected at the flake's surface at an angle θ 0 s with respect to the sample's normal, transmitted again through the binder, and refracted at the interface an angle θ s , which is the measurement's viewing angle. For a calculation of the flake parameters, the reader may refer to the literature [19].…”

“…Second, θ flake is quite linked to the aspecular angle (θ asp , angular difference between the specular angle and the viewing angle). If θ flake is zero, the viewing is done in specular conditions; if θ flake is negative, the viewing lies on what is known in the literature as transgeometry (negative aspecular angle); and if θ flake is positive, the viewing lies on what is known as cisgeometry (positive aspecular angle) [19]. The relation between θ flake and θ asp for 648 measurement geometries (with θ i and θ s ranging from 0°to 85°at steps of 5°, for ϕ s 0°and 180°) is shown in Fig.…”

“…The relation between θ flake and θ asp for 648 measurement geometries (with θ i and θ s ranging from 0°to 85°at steps of 5°, for ϕ s 0°and 180°) is shown in Fig. 3 (the binder's refractive index is assumed to be 1.5, which is correct for most effect-coatings [19]). A particular value of θ asp corresponds approximately to a value of θ flake within a 3.5°range.…”

“…The procedure that was followed to reduce the number of measurement geometries is based on the physical interpretation recently used by Kirchner and Cramer [19]. They proposed a new perspective to better understand the spectral reflectance for different geometries: Instead of using the conventional experimental parameters (irradiation and viewing angles), they opted to include flake-related ones, such as flake orientation and incident angle on the flake.…”