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Angular and Spectral Bandwidth Considerations in BRDF Measurements of Interference and Diffraction-Based Coatings  
Angular and Spectral Bandwidth Considerations in BRDF Measurements of Interference and Diffraction-Based Coatings


the term goniochromatism or iridescence measures the phenomenon in which the color of a sample changes with the angle of illumination and observation.
The goniochromatism that occurs in coatings with special light effects such as metallized car paints, cosmetics or packaging products can be achieved by interference phenomena or by diffraction pigments embedded in the material, and its description is different for each case.
Interference pigments consist of two or more layers with a large difference in the refractive index, which favors multiple reflections and the appearance of interference from light waves. This interference, which results in additive color mixing, is only observed around specular directions with respect to the pigment surface (same angle for incoming and reflected light).
In coatings based on interference pigments, the color change is mainly important when varying the angle of incidence, maintaining a constant low aspecular angle (angle between the observation and specular directions), because it is in these when a greater proportion of the Effect pigments contribute to the reflected light in the viewing direction.
When diffractive effect pigments are used, the color change is due to diffraction rather than interference. In this case, the effect pigments contribute similarly to reflected light for all lighting and observation geometry.

Bidirectional reflectance distribution function

The bidirectional reflectance distribution function (BRDF) is a quantity that describes the variation in reflectance for any combination of irradiation and reflection directions, and enables reflectance to be calculated for any solid angle of irradiation and collection. This distribution function, which also includes spectral dependence, is key to describe the goniochromatism of iridescent surfaces, such as those with special effect coatings that are widely used in the automotive, cosmetic or packaging sectors, among others.

The bi-directional reflectance distribution function (BRDF) of iridescent (or goniochromatic) surfaces can vary markedly with color and angle and thus the finite spectral bandwidth and collection of solid angles inherent in any measuring instrument. enter a difference between the measured value and the correct value.
In the work, experimental data from highly goniochromatic samples have been used to analyze their impact on the measurement uncertainty. The results indicate that it is advisable to standardize the spectral and angular bandwidths, because the systematic error likely to appear is not negligible for typical measurement systems.
95% of the distribution of the BRDF measurement error is due to these finite bandwidths, and also 95% of the resulting calculated color differences, have been used as criteria to establish recommended values ​​of spectral bandwidths. and angular.
For a similar uncertainty value, the angular and spectral bandwidth requirements are more stringent for diffraction-based coatings than for interference-based ones.

The spectral BRDF of goniochromatic surfaces changes greatly for different combinations of illumination and observation directions, and this makes their colorimetric description complex.
Most of the research work on the appearance of goniochromatic surfaces has dealt with the appropriate methodology to describe their color by selecting suitable geometries, and using measurements to represent such surfaces. However, the metrological aspect of measuring spectral BRDF and color with real instruments, with finite sized apertures, has not yet been systematically studied as in this work.

Proper understanding of the uncertainty due to this cause is not only important for good measurement, but also for improving the design of multi-angle spectrophotometers or gonio spectrophotometers dedicated to monitoring the appearance of iridescent surfaces.
The objective of this work is to develop a methodology that relates the spectral bandwidth and the collection of solid angles used with the resulting measurement uncertainty, and to provide recommendations on the appropriate or upper limit values ​​of these variables. The conclusions of this study are being discussed in the technical committee “Recommendation on the geometrical parameters for the measurement of the bidirectional reflectance distribution function (BRDF)” of the CIE (International Commission on Illumination), dedicated to establishing recommendations to correctly measure BRDF .

Quality control of goniochromatic paints in the industry could benefit from these recommendations, as well as instrument designers who must pay attention to the balance between spectral and angular bandwidths when optimizing the signal-to-noise ratio of their instruments.

Link to article

This is a work from the Optical Institute (CSIC)
Investigación financiada por el Ministerio de Ciencia e Innovación y la Agencia Estatal de Investigación
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