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A Numerical Method for Color Uncertainty



Yoshihiro Ohno


A method for calculating uncertainties of color quantities has been developed using a numerical approach based on the ISO Guide to the Expression of Uncertainty in Measurement. The uncertainties of any color quantities such as chromaticity coordinates, correlated color temperature, and color rendering indices, arising from uncertainties in spectral values of the source or the uncertainties in the wavelength scale, can be calculated with this numerical method with no need of deriving partial derivatives analytically. The partial derivatives - thus the sensitivity coefficients - of a color quantity in terms of each spectral value are obtained by simply calculating the color quantity with a small change of each input spectral value. The uncertainty of the color quantity is then obtained as a combined uncertainty for all spectral values. Since this method uses the color calculation program itself to obtain the partial derivatives, there is no need for analytical process, and the uncertainties can be calculated for any color quantities no matter how complicated the equations and the process may be.
Proceedings Title
Proceedings of CIE Expert Symposium 2001 on Uncertainty Evaluation
Conference Dates
January 1, 2001
Conference Location
Vienna, AU
Conference Title
CIE Expert Symposium


chromaticity coordinates, color temperature, colorimetry, measurement, photometry, spectroradiometer, spectroradiometry, uncertainty


Ohno, Y. (2001), A Numerical Method for Color Uncertainty, Proceedings of CIE Expert Symposium 2001 on Uncertainty Evaluation, Vienna, AU (Accessed February 25, 2024)
Created January 1, 2001, Updated June 2, 2021