CIE Method for Calculating Tristimulus Values

Abstract

Between 1981 and 1983, a working Group of USTC‐1.3 of the CIE prepared new recommendations giving for the first time detailed instructions for the calculation of CIE tristimulus values, for inclusion in Publication CIE No. 15.2, a revision of the CIE document on colorimetry first published in 1971. The new recommendations state that the standard method of performing the integration forming the basic definition of tristimulus values shall be by summation at a wavelength interval of 1 nm over the wavelength ranCe 360–830 nm, but that for most colorimetric purposes the approximation of summation at a 5‐nm interval over the range 380–780 nm should suffice. Recognizing that measured data fulfilling these requirements are not usually available, recommendations were also made concerning abridgement, interpolation, extrapolation, truncation, and the calculation of weighting factors. Although tables of weighting factors were not included in the recommendations to the CIE, they have since been calculated in cooperation with the Working Group and published by the ASTM. This article describes the recommendations, now accepted by the CIE and providing clear and complete guidelines for the uniform calculation of CIE tristimulus values.

Antioxidant activity and phenolic profiles of Sauvignon Blanc wines made by various maceration techniques

“…The browning of juice and wines was measured with a Thermo Helios gamma spectrophotometer (Thermo Fisher Scientific) at 420 nm. Wine tristimulus colour was obtained by full spectrum scanning from 280 nm to 780 nm at 5-nm increments, followed by integration (Billmeyer and Fairman 1987).…”

Accurate representation of interference colours (Michel–Lévy chart): from rendering to image colour correction

“…The first step in these calculations is finding the XYZ value of the colour. For objects transmitting light, XYZ is found using the below equation (Billmeyer & Fairman, ; CIE, 1971): where k is a normalising constant defined as where λ is the wavelength of light, S the spectral power distribution of the light source, τ the transmittance of the illuminated object and are colour‐matching functions of a standard observer, specified by the CIE 1931 standard colorimetric system (Smith & Guild, ). The spectral power distribution, S , reflects the colour temperature of the light source, and was obtained using the MATLAB script PlancLociCalc.m, written by G. J. Hakim at the University of Washington (http://www.atmos.washington.edu/~hakim/301/planck.m).…”

“…For objects transmitting light, XYZ is found using the below equation (Billmeyer & Fairman, 1987;CIE, 1971):…”

Testing the accuracy of methods for the computation of CIE tristimulus values using weighting tables

“…Some notes to the ASTM E308‐85 publication may be useful: This set of weighting tables was developed by the Working Group VIII of US TC‐1.3 Colorimetry led by Billmeyer and Fairman between 1981 and 1983 for inclusion in the revision of CIE Publication 15. However, the weighting tables were not included in final version of this revision of CIE Publication 15 but they were published by ASTM in 1985 as ASTM E308 Standard Practice for Computing the Colors of Objects by Using the CIE System . ASTM E308‐85 weighting tables must be used with reflectance values corrected using the Stearns and Stearns 3‐term bandpass error correction formulae.…”

“…The use of 1‐nm summation was first recommended by the Working Group VIII of the US CIE TC‐1.3 Colorimetry Committee in 1983, and it was officially recommended by CIE in 1986 . The SPDs, , for CIE Standard Illuminants D65 and A are available at 1 nm intervals .…”