The uncertainty ellipse equation is developed for the general case of propagation of errors in tristimulus colorimetry, where spectral tristimulus values as well as spectral radiance factors are deemed uncertain. Two applications are presented as special cases. In the first, uncertainty in chromaticity coordinates for spectrum colors, uncertainties of spectral tristimulus values are based on the CIE standard observer system and the 2°- and 10°-field systems derived from Stiles’ data by Judd and Kelly. In the second, uncertainties in chromaticity coordinates of fluorescent light sources, uncertainties in spectral emittances are based on five sets of data for one source. It is important that an international standard-observer system be specified not only by mean tristimulus values of the spectrum but also by their variances; otherwise the significance of the departure of an individual experimental datum from that by the standard observer cannot be assessed.
ISADORE NIMEROFF, "Propagation of Errors in Tristimulus Colorimetry," J. Opt. Soc. Am. 47, 697-701 (1957)