A Fast Algorithm for the Computation of Color Hardcopy Color Gamuts

抄録

We earlier developed a fast algorithm for computing the color gamuts of dye sets used in subtractive color mixtures in which Lambert-Beer's Law holds. This fast algorithm is based on the concept of dye amount space. In adapting this algorithm to reflection prints, we had to deal with the fact that the relationship between reflection density and dye amount is nonlinear. This problem was solved by using a function to convert reflection density to transmission density, which is linear in relation to dye amount. Because Beer's Law holds, multiplication of a given dye amount, expressed in an arbitrary unit, by the spectral transmission densities for that arbitrary unit, yields the spectral transmission densities corresponding to the given dye amount. After the densities of all three dyes are calculated, the total transmission density is converted to reflection density. In applying the algorithm to hardcopy systems, we faced the additional problem that, unfortunately, Beer's Law does not apply to the dyes in some of these systems (e.g. some thermal dye transfer systems), even in the domain of transmission density. In these cases, the spectral transmission density distributions do not rise proportionally with dye amount, but, instead, distort with the increase of dye. However, by establishing and interpolating these distributions, the same algorithm which we applied to conventional photographic materials also proved accurate with hardcopy systems. This accuracy was confirmed by comparing color gamuts computed through the algorithm with observed values.