Uncertainty analysis of reflectance colorimetry

The specification of the color of an object is important, sometimes crucially, to its acceptability for an intended application. When quantitative measurements are used to determine the color of an object, an uncertainty is required to satisfy the requirements of traceability. Determining the uncertainty of a color measurement has been a topic of interest for many years, and has received additional impetus with the publication of the ISO Guide to the Expression of Uncertainty in Measurement, which describes methods for estimating uncertainties in a consistent manner. These methods are applied to the case of reflectance colorimetry, where many of the sources of uncertainty are caused by systematic effects and are therefore correlated. Analytical expressions are derived for the combined uncertainties in the quantitative expression of color due to both correlated and uncorrelated effects. The measurement equation is used to derive the uncertainties in reflectance factor from different sources, and to take correlations between signals at the same wavelength into account. The correlations between reflectance factors at different wavelengths are also included in the analysis. These concepts are illustrated by considering uncertainties from common sources for selected colored specimens.