In industrial practice, it is often required that weighting tables were prepared in advance and tristimulus values can then be directly computed using summation of the products of the weights and measured reflectance values. The CIE has never provided precise procedure to calculate the weighting tables, and various discrepant methods have been used. Hence it is possible to obtain significantly different tristimulus values from the same set of spectral data.
In order to overcome this problem, the American Society for Testing and Materials (ASTM Intl.) has published two sets of weighting tables known as Table 5 and Table 6 respectively. Each set includes 36 weighting tables covering 9 illuminants and two standard colorimetric observers at two wavelength intervals (10-nm and 20-nm). The weighting tables of Table 5 must be used with the reflectance corrected using the Stearns and Stearns (SS) method, and weighting tables of Table 6 must be used with the measured reflectance values without the SS correction. In practice, the illuminant used may be different from the CIE standard illuminants and users have to prepare their own weighting tables corresponding to the illuminant actually used. ASTM Intl. E2022-99 provided a standard calculation method to generate weighting tables of Table 5 for a non-standard illuminant. No standard procedure is given to calculate weighting tables of Table 6 since it consisted of Venable and Stearns correction weights, and the Venable optimum weight is computed by an iterative procedure.
In this article, we will report some recent progress in generating weighting tables; compare the performances among the weighting tables such as ASTM Intl. Tables of Table 5 and Table 6, Optimum weighting tables, Least Square weighting tables, and Direct selection tables; quantify the possible colorimetric errors for each of the tables; and finally recommend for standardization of a method for generating weighting tables.