Accuracy of Tristimulus Computations*

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

“…Note also that the DS method has historically been named the weighted‐ordinate method . An alternative method to the weighted‐ordinate method is the selected‐ordinate method.…”

“…As examples, the weights and selected ordinates for some of the CIE illuminants can be found in Hardy's book, and Table III(3.3.8) in Wyszecki and Stiles' book provides the weights and selected ordinates for CIE illuminant A and the CIE 1931 standard observer. De Kerf reported that the weighted‐ordinate method is more accurate with Δ λ = 5 nm in most practical cases, although Δ λ = 10 nm also provided accurate results in many practical cases, the exception being cases where the reflectance functions were highly irregular . Another similar method to the selected‐ordinate one is the Gaussian quadrature method .…”

“…22,24 Note also that the DS method has historically been named the weighted-ordinate method. 29,[32][33][34] An alternative method to the weighted-ordinate method is the selected-ordinate method. For the weighted ordinate method, there are (n 1 1) different weights in each of the X, Y, and Z directions.…”

Colorimetry

“…These reflectances apply to the specimens measured except for small wavelength-scale and photometric-scale corrections which have not been applied. [114] and De Kerf [27] have published studies of It will be seen that tristimulus colorimeters give adjustment to a color match are supplied. This form of identification leads naturally into a speci-j fication in which the luminance [20] of the un-\> known is given and the chromaticity is specified i by two variables in polar coordinates.…”

“…Errors introduced by using summation as in eq (2) instead of integration to evaluate tristimulus values X.Y,Z, have been treated by Nickerson [114] and by De Kerf [27] …”